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Plazomicin (Trang 2019)

Source: vignettes/articles/Trang_2019_plazomicin.Rmd
Trang_2019_plazomicin.Rmd

Model and source

  • Citation: Trang M, Seroogy JD, Van Wart SA, Bhavnani SM, Kim A, Gibbons JA, Ambrose PG, Rubino CM. 2019. Population pharmacokinetic analyses for plazomicin using pooled data from phase 1, 2, and 3 clinical studies. Antimicrob Agents Chemother 63:e02329-18. doi:10.1128/AAC.02329-18.
  • Description: Three-compartment population PK model for intravenous plazomicin in healthy adults and adults with complicated urinary tract infection, acute pyelonephritis, bloodstream infection or hospital-/ventilator-acquired bacterial pneumonia, with a sigmoidal Hill relationship between renal clearance and creatinine clearance and an additive continuous-renal-replacement-therapy clearance arm
  • Article: https://doi.org/10.1128/AAC.02329-18
  • Supplement (Fig. S1, Tables S1-S2): https://doi.org/10.1128/AAC.02329-18

Plazomicin is an aminoglycoside developed to overcome aminoglycoside-modifying enzymes in multidrug-resistant Enterobacteriaceae. It is given as a 30-min intravenous infusion on a milligram-per-kilogram basis, with dose adjustment for renal function and for a body weight at or above 125% of ideal body weight.

The structural model is three compartments with zero-order intravenous input and first-order elimination. Its defining feature is that total clearance is the sum of a constant non-renal arm and a saturable renal arm, the latter a sigmoidal Hill function of creatinine clearance carried as a time-varying covariate:

CL=(CLnonrenal+CLR,maxCLCRγCLCR,50γ+CLCRγ)(BW75)0.529(1+0.130AP−0.189BSI)+SC⋅(UFR+DFR) \mathrm{CL} = \left(\mathrm{CL_{nonrenal}} + \mathrm{CL_{R,max}}\, \frac{\mathrm{CL_{CR}}^{\gamma}}{\mathrm{CL_{CR,50}}^{\gamma} + \mathrm{CL_{CR}}^{\gamma}}\right) \left(\frac{\mathrm{BW}}{75}\right)^{0.529} \left(1 + 0.130\,\mathrm{AP} - 0.189\,\mathrm{BSI}\right) \;+\; \mathrm{SC}\cdot(\mathrm{UFR} + \mathrm{DFR})

The Discussion notes that glomerular filtration would ordinarily predict a linear relationship, and that the observed saturation at high creatinine clearance most likely reflects creatinine clearance becoming a poorer surrogate for glomerular filtration rate at the upper end of its range rather than saturation of the elimination process itself.

Population

The analysis pooled 564 subjects and 4,990 plasma plazomicin concentrations from seven studies: four phase 1 studies in healthy adults and in adults with varying degrees of renal function (001, 003, 004, 006; n = 143), one phase 2 study in complicated urinary tract infection (cUTI) and acute pyelonephritis (AP) (002; n = 92), and two phase 3 studies (007 in carbapenem-resistant Enterobacteriaceae infections and 009 in cUTI/AP; n = 329).

Baseline characteristics are Table 1 of Trang 2019: median age 39 years (18-90), median body weight 75.0 kg (40.5-165), median height 170 cm (142-194), median body surface area 1.86 m^2 (1.29-2.58), median creatinine clearance 90.2 mL/min/1.73 m^2 (7.37-226), 52.8% female, 78.5% White. Infection types were cUTI (37.8%), AP (29.1%), bloodstream infection (5.14%) and hospital-acquired or ventilator-associated bacterial pneumonia (2.66%), with 25.4% healthy subjects. Renal function ranged from normal (42.0%) to severe impairment (2.30%); nine subjects in study 007 received continuous renal replacement therapy (CRRT) during treatment, and 24 subjects (4.26%) received vasopressors.

Per-study retention is supplemental Table S1: 573 subjects and 5,142 samples at the start, reduced to 564 and 4,990 after excluding 106 outliers and 46 below-limit-of-quantification samples.

The same information is available programmatically via readModelDb("Trang_2019_plazomicin")()$population.

Source trace

Every ini() entry in inst/modeldb/specificDrugs/Trang_2019_plazomicin.R carries an in-file comment naming its source location. They are collected here for review. All final estimates come from Table 2 (“Final population PK model parameter estimates”), column “Final estimate”.

Equation / parameter Value Source location
Three-compartment structure, zero-order IV input, first-order elimination n/a Results “(i) Development of the structural population PK model”; Abstract; Discussion
lcl_nonren (non-renal CL) 0.491 L/h Table 2, “Nonrenal CL (liters/h)”
lcl_renal_max (asymptotic renal CL) 4.80 L/h Table 2, “CLR maximum (liters/h)”
lcrcl50 45.3 mL/min/1.73 m^2 Table 2, “Baseline CLCR50 (ml/min/1.73 m2)”
lhill 2.49 Table 2, “Hill coefficient”
Sigmoidal Hill form of CL_R vs CL_CR n/a Results “(iv) Final population PK model”, paragraph 2
e_wt_cl 0.529 Table 2, “CL-weight power”
e_ap_cl 0.130 Table 2, “Proportional increase for AP patients”
e_bsi_cl -0.189 Table 2, “Proportional increase for BSI patients”
lvc 9.10 L Table 2, Vc “Coefficient”
e_bsa_vc 1.23 Table 2, “Vc-BSA power”
e_cutiap_vc 1.05 Table 2, Vc “Proportional increase for cUTI and AP patients”
e_bsihabp_vc 1.55 Table 2, Vc “Proportional increase for BSI and HABP/VABP patients”
lq (the paper’s CLd1) 8.05 L/h Table 2, CLd1 “Coefficient”
e_cutiap_q -0.831 Table 2, CLd1 “Proportional increase for cUTI and AP patients”
lvp (the paper’s Vp1) 8.71 L Table 2, Vp1 “Coefficient”
e_bsa_vp 1.17 Table 2, “Vp1-BSA power”
e_age_vp 0.00954 /year Table 2, “Vp1-age slope”
e_cutiap_vp -0.437 Table 2, Vp1 “Proportional increase for cUTI and AP patients”
lq2 (the paper’s CLd2) 0.199 L/h Table 2, CLd2 “Coefficient”
e_ht_q2 3.38 Table 2, “CLd2-height power”
e_cutiap_q2 -0.299 Table 2, CLd2 “Proportional increase for cUTI and AP patients”
e_bsihabp_q2 2.86 Table 2, CLd2 “Proportional increase for BSI and HABP/VABP patients”
lvp2 (the paper’s Vp2) 6.98 L Table 2, Vp2 “Coefficient”
e_wt_vp2 1.62 Table 2, “Vp2-weight power”
e_inotrope_vp2 3.90 Table 2, Vp2 “Proportional increase for vasopressor use”
sc_crrt 0.734 Table 2, CLCRRT “Sieving coefficient”; re-estimated in final refinement from the base-model 0.926 (Results “(iii) Final covariate model refinement”)
CRRT CL = SC x (UFR + DFR), additive on residual CL, only while CRRT operative n/a Materials and Methods “(i) Development of the structural population PK model”; Results “(iv) Final population PK model”
etalcl, etalvc, etalvp block 0.103 / 0.211 / 0.0678 with covariances 0.0931, 0.0734, 0.0649 Table 2, omega-squared rows and the three “Covariance between …” rows
etalq, etalq2, etalvp2 0.0661 / 0.0350 / 0.170 Table 2, omega-squared rows
etaiov_cl_1 .. _4 0.00129 Table 2, “IOV on CL”; four occasions per Results “(ii) Covariate analysis”
addSd sqrt(0.0000414) = 0.006434 mg/L Table 2, residual variability “Additive component”
propSdPhase1 / 2 / 3 sqrt(0.0297 / 0.168 / 0.0846) Table 2, “CCV component for phase 1/2/3 studies”
Cockcroft-Gault CL_CR, BSA-normalised by Du Bois n/a Materials and Methods “Subject characteristics”
Typical CL = 4.57 L/h, CL_R = 4.08 L/h at BW 75 kg, BSA 1.73 m^2, CL_CR 90 n/a Results “(iv) Final population PK model”, paragraph 2 (used as the validation target below)
Per-study secondary PK parameters (Table 3) see NCA table Table 3

Virtual cohort

The original observed data are not publicly available. Two virtual cohorts are built whose covariate distributions approximate the published per-phase demographics of Table 1.

Covariates are drawn with R’s own RNG, so the cohort is byte-identical on any machine. Every assertion below is evaluated on a typical-value solve (rxode2::zeroRe()), which is fully deterministic; the between-subject solve is used only for the visual predictive-check figure, which carries no assertion. This sidesteps the fact that rxode2 partitions its simulation RNG per solver thread, so a stochastic cohort differs between a 2-core CI runner and a many-threaded workstation.

set.seed(20190401)

# Du Bois and Du Bois, as used by the paper (Materials and Methods,
# "Subject characteristics"): BSA = BW^0.425 * height^0.725 * 0.007184.
du_bois_bsa <- function(wt_kg, ht_cm) {
  wt_kg^0.425 * ht_cm^0.725 * 0.007184
}

# Draw a log-normal variate with the requested median, truncated to the
# published observed range so no virtual subject falls outside it.
rlnorm_bounded <- function(n, median, cv, lower, upper) {
  sdlog <- sqrt(log(cv^2 + 1))
  x <- stats::rlnorm(n, meanlog = log(median), sdlog = sdlog)
  pmin(pmax(x, lower), upper)
}

n_per_arm <- 150L

# Occasions, per Results "(ii) Covariate analysis": days 1-2, 3-6, 6-9, >9.
# The published day-6 boundary belongs to two occasions as printed; the
# upper-exclusive reading below is the only mutually-exclusive one.
occasion_of <- function(t) {
  cut(t,
    breaks = c(-Inf, 48, 144, 216, Inf),
    labels = FALSE, right = FALSE
  )
}

make_cohort <- function(n, label,
                        wt_median, wt_range, ht_median, ht_range,
                        age_median, age_range, crcl_median, crcl_range,
                        dose_mg_per_kg, n_doses, tau,
                        obs_times,
                        dis_cuti = 0, dis_ap = 0, dis_bsi = 0,
                        dis_habp = 0, dis_vabp = 0,
                        inotrope = 0, phase2 = 0, phase3 = 0,
                        id_offset = 0L) {
  # Weight and height are drawn independently, so an extreme-low pair can put
  # the derived Du Bois BSA fractionally outside the published pooled range
  # (1.29-2.58 m^2, Table 1). Draw a surplus pool and keep the first `n`
  # candidates whose BSA lands inside it, so every virtual subject sits inside
  # the covariate box the model was fitted over.
  pool <- 20L * n
  cand <- tibble(
    WT = rlnorm_bounded(pool, wt_median, 0.22, wt_range[1], wt_range[2]),
    HT = rlnorm_bounded(pool, ht_median, 0.07, ht_range[1], ht_range[2]),
    AGE = rlnorm_bounded(pool, age_median, 0.40, age_range[1], age_range[2]),
    CRCL = rlnorm_bounded(pool, crcl_median, 0.45, crcl_range[1], crcl_range[2])
  ) |>
    mutate(BSA = du_bois_bsa(WT, HT)) |>
    filter(BSA >= 1.29, BSA <= 2.58)
  stopifnot(nrow(cand) >= n)

  subj <- cand |>
    slice_head(n = n) |>
    mutate(
      id = id_offset + seq_len(n),
      DIS_CUTI = dis_cuti, DIS_AP = dis_ap, DIS_BACTEREMIA = dis_bsi,
      DIS_HABP = dis_habp, DIS_VABP = dis_vabp,
      CONMED_INOTROPE = inotrope,
      RRT_CRRT_EFFLUENT_FLOW = 0, RRT_CRRT_ACTIVE = 0,
      STUDY_PHASE2 = phase2, STUDY_PHASE3 = phase3,
      treatment = label,
      dose_mg = dose_mg_per_kg * WT
    )

  doses <- subj |>
    tidyr::crossing(dose_number = seq_len(n_doses)) |>
    mutate(
      time = (dose_number - 1) * tau,
      amt = dose_mg,
      # 30-min infusion (every study used a 30-min IV infusion).
      rate = dose_mg / 0.5,
      evid = 1L,
      cmt = "central"
    ) |>
    select(-dose_number)

  obs <- subj |>
    tidyr::crossing(time = obs_times) |>
    mutate(
      amt = NA_real_, rate = NA_real_, evid = 0L,
      # The ODE state, never the algebraic observable `Cc`.
      cmt = "central"
    )

  bind_rows(doses, obs) |>
    mutate(OCC = occasion_of(time)) |>
    arrange(id, time, desc(evid)) |>
    select(-dose_mg)
}

# Sampling grids. Log-spaced early points keep the trapezoidal AUC accurate
# through the 30-min infusion and the steep alpha phase.
grid_single <- sort(unique(c(
  0, exp(seq(log(0.05), log(120), length.out = 90))
)))
grid_multi <- sort(unique(c(
  0, exp(seq(log(0.05), log(96), length.out = 60)),
  96 + exp(seq(log(0.05), log(24), length.out = 45)), 96, 120
)))

events <- bind_rows(
  # Study 006: healthy adults, single 15 mg/kg 30-min infusion (phase 1).
  make_cohort(
    n_per_arm, "Healthy, 15 mg/kg single dose (study 006)",
    wt_median = 74.6, wt_range = c(53.5, 116),
    ht_median = 172, ht_range = c(146, 191),
    age_median = 29, age_range = c(18, 75),
    crcl_median = 93.4, crcl_range = c(7.37, 159),
    dose_mg_per_kg = 15, n_doses = 1L, tau = 24,
    obs_times = grid_single,
    id_offset = 0L
  ),
  # Study 002: cUTI / AP patients, 15 mg/kg q24h (phase 2).
  make_cohort(
    n_per_arm, "cUTI/AP, 15 mg/kg q24h (study 002)",
    wt_median = 66.0, wt_range = c(42, 100),
    ht_median = 160, ht_range = c(142, 183),
    age_median = 39.9, age_range = c(18.3, 77.4),
    crcl_median = 81.3, crcl_range = c(21.8, 212),
    dose_mg_per_kg = 15, n_doses = 5L, tau = 24,
    obs_times = grid_multi,
    dis_cuti = 1, phase2 = 1,
    id_offset = 1000L
  )
)

stopifnot(
  !anyDuplicated(events[events$evid == 0, c("id", "time")]),
  all(events$OCC %in% 1:4),
  # Every virtual subject sits inside the published covariate ranges.
  all(events$WT >= 40.5 & events$WT <= 165),
  all(events$HT >= 142 & events$HT <= 194),
  all(events$AGE >= 18 & events$AGE <= 90),
  all(events$CRCL >= 7.37 & events$CRCL <= 226),
  all(events$BSA >= 1.29 & events$BSA <= 2.58)
)

Simulation 

mod <- readModelDb("Trang_2019_plazomicin")

# Typical-value solve: deterministic, and the basis for every assertion.
sim <- rxode2::rxSolve(
  rxode2::zeroRe(mod),
  events = events,
  keep = c("treatment", "WT", "HT", "AGE", "CRCL", "BSA")
)
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> Warning: multi-subject simulation without without 'omega'
if (is.null(sim$id)) sim$id <- 1L

# Between-subject solve, used only for the visual predictive check.
sim_iiv <- rxode2::rxSolve(mod, events = events, keep = c("treatment"))
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line

Structural checks against the paper’s own printed values

These are exact-identity checks on the parts of the model that the paper states numerically. Unlike an NCA comparison against a cohort geometric mean, they do not depend on how closely the virtual cohort matches the real one, so they are asserted with tight absolute tolerances. Any transcription error in the clearance arm moves them by far more than the tolerance allows.

# A single reference subject at exactly the covariate values named in
# Results "(iv) Final population PK model": "the population mean total CL and
# CLR would be 4.57 liters/h ... and 4.08 liters/h ... in a typical cUTI or
# HABP/VABP patient with a BW of 75 kg, a body surface area (BSA) of 1.73 m2,
# and a CLCR of 90 ml/min."
probe <- function(crcl, wt = 75, bsa = 1.73, ht = 170, age = 39,
                  cuti = 1, ap = 0, bsi = 0, habp = 0, vabp = 0,
                  inotrope = 0, effluent = 0, crrt = 0,
                  phase2 = 0, phase3 = 0) {
  ev <- tibble(
    id = 1L, time = c(0, 1), amt = c(1000, NA_real_),
    rate = c(2000, NA_real_), evid = c(1L, 0L), cmt = "central",
    WT = wt, BSA = bsa, HT = ht, AGE = age, CRCL = crcl,
    DIS_CUTI = cuti, DIS_AP = ap, DIS_BACTEREMIA = bsi,
    DIS_HABP = habp, DIS_VABP = vabp, CONMED_INOTROPE = inotrope,
    RRT_CRRT_EFFLUENT_FLOW = effluent, RRT_CRRT_ACTIVE = crrt,
    STUDY_PHASE2 = phase2, STUDY_PHASE3 = phase3, OCC = 1
  )
  out <- as.data.frame(rxode2::rxSolve(rxode2::zeroRe(mod), events = ev))
  out[nrow(out), ]
}

ref <- probe(crcl = 90)
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'

# 1. Typical total clearance and renal clearance. The paper prints 4.57 and
#    4.08 L/h; its parameters are printed to three significant figures, so the
#    reproduction is compared on an ABSOLUTE tolerance rather than a relative
#    one (0.05 L/h is ~1%, while a mis-transcribed Hill parameter moves CL by
#    0.5 L/h or more).
cl_typ <- ref$cl
clr_typ <- ref$cl_renal
c(CL = cl_typ, CL_R = clr_typ)
#>       CL     CL_R 
#> 4.555435 4.064435

# 2. The Hill function is half-maximal exactly at CLCR50 = 45.3, by
#    definition. This pins CLCR50 into the right position in the equation.
half_max <- probe(crcl = 45.3)$cl_renal
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'

# 3. The renal arm saturates at CLR maximum = 4.80 L/h.
sat <- probe(crcl = 1e6)$cl_renal
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'

# 4. CRRT adds sieving coefficient x effluent flow, exactly and additively.
#    Table 2 gives the observed UFR + DFR as 1.14-1.8 L/h.
crrt_delta <- probe(crcl = 90, effluent = 1800, crrt = 1)$cl - cl_typ
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'

# 5. Infection-type shifts are exact multiplicative factors on the reference
#    (healthy) values.
vc_healthy <- probe(crcl = 90, cuti = 0)$vc
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
vc_cuti <- ref$vc
vc_bsi <- probe(crcl = 90, cuti = 0, bsi = 1)$vc
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
cl_ap <- probe(crcl = 90, cuti = 0, ap = 1)$cl
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
cl_bsi_only <- probe(crcl = 90, cuti = 0, bsi = 1)$cl
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'

# 6. The residual-error stratum selector picks the right phase.
sd_p1 <- probe(crcl = 90)$propSdSel
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
sd_p2 <- probe(crcl = 90, phase2 = 1)$propSdSel
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
sd_p3 <- probe(crcl = 90, phase3 = 1)$propSdSel
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'

stopifnot(
  # Paper's printed typical values (Results, paragraph 2).
  abs(cl_typ - 4.57) < 0.05,
  abs(clr_typ - 4.08) < 0.05,
  # Hill half-maximum and asymptote.
  abs(half_max - 4.80 / 2) < 1e-6,
  abs(sat - 4.80) < 1e-3,
  # CRRT arm: 0.734 * 1.8 L/h.
  abs(crrt_delta - 0.734 * 1.8) < 1e-8,
  # Vc: +105% for cUTI/AP, +155% for BSI/HABP/VABP.
  abs(vc_cuti / vc_healthy - 2.05) < 1e-8,
  abs(vc_bsi / vc_healthy - 2.55) < 1e-8,
  # CL: +13.0% for AP, -18.9% for BSI, and unchanged for cUTI (the CL:cUTI
  # shift was dropped during final refinement).
  abs(cl_ap / cl_typ - 1.130) < 1e-8,
  abs(cl_bsi_only / cl_typ - 0.811) < 1e-8,
  abs(probe(crcl = 90, cuti = 0)$cl - cl_typ) < 1e-10,
  # Residual-error strata are the square roots of the tabulated sigma^2.
  abs(sd_p1 - sqrt(0.0297)) < 1e-9,
  abs(sd_p2 - sqrt(0.168)) < 1e-9,
  abs(sd_p3 - sqrt(0.0846)) < 1e-9
)
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'

A negative control confirms these checks are not vacuous: moving creatinine clearance off 90 mL/min/1.73 m^2 must move total clearance, and the saturating shape means the move is sub-proportional.

cl_grid <- vapply(c(15, 30, 45.3, 60, 90, 120, 180), \(x) probe(crcl = x)$cl, numeric(1))
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
stopifnot(
  # Strictly increasing in CLCR.
  all(diff(cl_grid) > 0),
  # A doubling of CLCR from 90 to 180 raises CL by well under a factor of two
  # (saturation), yet by a clearly non-zero amount.
  cl_grid[7] / cl_grid[5] < 1.25,
  cl_grid[7] / cl_grid[5] > 1.05,
  # Anuric patient off CRRT retains only the non-renal arm plus a negligible
  # renal contribution.
  probe(crcl = 0.001)$cl < 0.55
)
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'

Replicate published figures 

# Replicates the CL-versus-CLCR panel of Figure 2 of Trang 2019, which shows
# total clearance rising sigmoidally with creatinine clearance and flattening
# at the top of the range.
crcl_seq <- seq(5, 226, length.out = 80)
tibble(
  CRCL = crcl_seq,
  cl = vapply(crcl_seq, \(x) probe(crcl = x)$cl, numeric(1))
) |>
  ggplot(aes(CRCL, cl)) +
  geom_line(linewidth = 1) +
  geom_hline(yintercept = 0.491 + 4.80, linetype = "dotted") +
  geom_vline(xintercept = 45.3, linetype = "dashed") +
  annotate("point", x = 90, y = 4.57, size = 3, shape = 21, fill = "white") +
  labs(
    x = expression(CL[CR] ~ (mL/min/1.73 ~ m^2)),
    y = "Total CL (L/h)",
    title = "Figure 2 - total clearance versus creatinine clearance",
    caption = paste(
      "Replicates the CL panel of Figure 2 of Trang 2019 for a typical",
      "75 kg cUTI patient. Dashed line: CLCR50 = 45.3. Dotted line:",
      "non-renal CL + CLR maximum = 5.29 L/h. Open point: the paper's",
      "printed typical CL of 4.57 L/h at CLCR = 90."
    )
  )
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'

# Replicates Figure 1 of Trang 2019: prediction-corrected visual predictive
# check over the first 48 h after a dose, stratified by infection type. Here
# the between-subject solve supplies the 5th / 50th / 95th percentile band.
sim_iiv |>
  filter(dplyr::between(time, 1e-9, 48)) |>
  group_by(treatment, time) |>
  summarise(
    Q05 = quantile(Cc, 0.05, na.rm = TRUE),
    Q50 = quantile(Cc, 0.50, na.rm = TRUE),
    Q95 = quantile(Cc, 0.95, na.rm = TRUE),
    .groups = "drop"
  ) |>
  ggplot(aes(time, Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.25) +
  geom_line(linewidth = 0.8) +
  facet_wrap(~treatment) +
  scale_y_log10() +
  labs(
    x = "Time (h)", y = "Plazomicin plasma concentration (mg/L)",
    title = "Figure 1 - simulated concentration-time profiles, first 48 h",
    caption = paste(
      "Replicates Figure 1 of Trang 2019. Band: 5th-95th percentile of the",
      "simulated cohort; line: median."
    )
  )

PKNCA validation

NCA is run on the deterministic typical-value solve. The single-dose healthy arm is summarised over 0-Inf; the multiple-dose cUTI/AP arm is summarised over the fifth dosing interval (96-120 h), by which point the profile is at steady state.

sim_nca <- sim |>
  dplyr::filter(!is.na(Cc)) |>
  dplyr::select(id, time, Cc, treatment)

# Guarantee a time-zero anchor per (treatment, id); plazomicin is given
# intravenously with no prior dose, so the pre-dose concentration is 0.
sim_nca <- dplyr::bind_rows(
  sim_nca,
  sim_nca |> dplyr::distinct(id, treatment) |>
    dplyr::mutate(time = 0, Cc = 0)
) |>
  dplyr::distinct(id, treatment, time, .keep_all = TRUE) |>
  dplyr::arrange(id, treatment, time)

conc_obj <- PKNCA::PKNCAconc(
  sim_nca, Cc ~ time | treatment + id,
  concu = "mg/L", timeu = "h"
)

dose_df <- events |>
  dplyr::filter(evid == 1) |>
  dplyr::select(id, time, amt, treatment)

dose_obj <- PKNCA::PKNCAdose(
  dose_df, amt ~ time | treatment + id,
  doseu = "mg", route = "intravascular", duration = 0.5
)

arms <- sort(unique(events$treatment))
single_arm <- arms[grepl("single dose", arms)]
multi_arm <- arms[grepl("q24h", arms)]

intervals <- data.frame(
  treatment = c(single_arm, multi_arm),
  start = c(0, 96),
  end = c(Inf, 120),
  cmax = TRUE,
  tmax = TRUE,
  cmin = c(FALSE, TRUE),
  auclast = c(FALSE, TRUE),
  aucinf.obs = c(TRUE, FALSE),
  half.life = c(TRUE, FALSE),
  stringsAsFactors = FALSE
)

nca_res <- PKNCA::pk.nca(
  PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals)
)

Comparison against published NCA

Table 3 of Trang 2019 reports geometric-mean secondary PK parameters by study. Study 006 (54 healthy subjects at 15 mg/kg) and study 002 (71 cUTI/AP patients) are the two arms reproduced here.

Two features of Table 3 shape the comparison. First, its AUC0-24 and CL columns satisfy AUC = Dose / CL to three significant figures for the healthy arm (1,116 mg / 4.50 L/h = 248 mgh/L), so the tabulated AUC0-24 is the dose-normalised total exposure rather than a truncated 0-24 h area; it is compared against AUCinf for the single-dose arm and against the steady-state AUC0-tau for the multiple-dose arm. Second, Table 3’s values are geometric means of individual post hoc* estimates over the real cohort, whereas the simulation here is a typical-value solve over an approximated covariate distribution, so agreement at the few-percent level is neither expected nor required; what the comparison tests is that no parameter, unit or dose has been mis-transcribed, which would move these quantities by tens of percent.

published <- tibble::tribble(
  ~treatment,   ~cmax, ~cmin,  ~aucinf.obs, ~auclast, ~half.life,
  single_arm,    84.6, NA_real_,      248,  NA_real_,       25.8,
  multi_arm,     54.5,    0.494, NA_real_,       233,   NA_real_
)

cmp <- nlmixr2lib::ncaComparisonTable(
  simulated = nca_res,
  reference = published,
  by = "treatment",
  units = c(
    cmax = "mg/L", cmin = "mg/L", aucinf.obs = "mg*h/L",
    auclast = "mg*h/L", tmax = "h", half.life = "h"
  ),
  tolerance_pct = 25
)

knitr::kable(
  cmp,
  caption = paste(
    "Simulated versus published NCA (Trang 2019 Table 3, studies 006 and",
    "002). * differs from the reference by more than 25%."
  )
)
Simulated versus published NCA (Trang 2019 Table 3, studies 006 and 002). * differs from the reference by more than 25%.
NCA parameter treatment Reference Simulated % diff
Cmax (mg/L) Healthy, 15 mg/kg single dose (study 006) 84.6 82.6 -2.4%
Cmax (mg/L) cUTI/AP, 15 mg/kg q24h (study 002) 54.5 51 -6.4%
Cmin (mg/L) cUTI/AP, 15 mg/kg q24h (study 002) 0.494 1.01 +105.4%*
AUC0-∞ (obs) (mg*h/L) Healthy, 15 mg/kg single dose (study 006) 248 248 -0.1%
AUClast (mg*h/L) cUTI/AP, 15 mg/kg q24h (study 002) 233 251 +7.6%
t½ (h) Healthy, 15 mg/kg single dose (study 006) 25.8 25.2 -2.5% 
# ncaComparisonTable() returns CHARACTER columns for display, so the numeric
# comparison is recomputed from the PKNCA result rather than parsed back out.
nca_wide <- as.data.frame(nca_res) |>
  dplyr::filter(PPTESTCD %in% c("cmax", "cmin", "aucinf.obs", "auclast", "half.life")) |>
  dplyr::group_by(treatment, PPTESTCD) |>
  dplyr::summarise(value = exp(mean(log(PPORRES))), .groups = "drop")

got <- function(arm, code) {
  v <- nca_wide$value[nca_wide$treatment == arm & nca_wide$PPTESTCD == code]
  stopifnot(length(v) == 1L, is.finite(v))
  v
}
pct <- function(arm, code, ref) 100 * (got(arm, code) - ref) / ref

diffs <- c(
  cmax_healthy = pct(single_arm, "cmax", 84.6),
  auc_healthy = pct(single_arm, "aucinf.obs", 248),
  thalf_healthy = pct(single_arm, "half.life", 25.8),
  cmax_cutiap = pct(multi_arm, "cmax", 54.5),
  auc_cutiap = pct(multi_arm, "auclast", 233),
  cmin_cutiap = pct(multi_arm, "cmin", 0.494)
)
round(diffs, 1)
#>  cmax_healthy   auc_healthy thalf_healthy   cmax_cutiap    auc_cutiap 
#>          -2.0           5.2          -5.6          -5.3          11.5 
#>   cmin_cutiap 
#>         139.8

stopifnot(
  # Peak concentration, total exposure and terminal half-life are the
  # quantities a mis-transcribed clearance, volume, dose or unit would move by
  # tens of percent. All four land within about 12%.
  abs(diffs[["cmax_healthy"]]) < 15,
  abs(diffs[["auc_healthy"]]) < 15,
  abs(diffs[["thalf_healthy"]]) < 15,
  abs(diffs[["cmax_cutiap"]]) < 20,
  abs(diffs[["auc_cutiap"]]) < 25,
  # Cmin is the one quantity that does NOT reproduce; see the narrative and
  # the decomposition chunk below. The bound is a sanity limit (a factor of
  # three) that would still catch a gross structural error, not a claim of
  # agreement.
  abs(diffs[["cmin_cutiap"]]) < 200
)

The trough of the cUTI/AP arm is the one starred row: the simulation predicts about 1.2 mg/L against the 0.494 mg/L of Table 3, roughly a factor of two high. It is not tuned away. Three differences between the simulated arm and study 002 account for part of the gap, and each is measured rather than asserted:

trough_at <- function(ev) {
  s <- rxode2::rxSolve(rxode2::zeroRe(mod), events = ev, keep = "treatment")
  if (is.null(s$id)) s$id <- 1L
  s |>
    dplyr::group_by(id) |>
    dplyr::summarise(c120 = Cc[which.min(abs(time - 120))], .groups = "drop") |>
    dplyr::summarise(g = exp(mean(log(c120)))) |>
    dplyr::pull(g)
}

ev_multi <- events |> dplyr::filter(treatment == multi_arm)

trough_parts <- c(
  # As simulated: every subject cUTI, every dose 15 mg/kg.
  as_simulated = trough_at(ev_multi),
  # Study 002 gave "10 or 15 mg/kg" (Table 4); the low dose alone.
  dose_10_mg_kg = trough_at(
    ev_multi |> dplyr::mutate(amt = amt * 10 / 15, rate = rate * 10 / 15)
  ),
  # Study 002 was 56.5% AP, and AP raises CL by 13.0%, lowering the trough.
  all_ap = trough_at(
    ev_multi |> dplyr::mutate(DIS_CUTI = 0, DIS_AP = 1)
  ),
  # Both together.
  ap_and_10_mg_kg = trough_at(
    ev_multi |> dplyr::mutate(
      DIS_CUTI = 0, DIS_AP = 1, amt = amt * 10 / 15, rate = rate * 10 / 15
    )
  )
)
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> Warning: multi-subject simulation without without 'omega'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> Warning: multi-subject simulation without without 'omega'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> Warning: multi-subject simulation without without 'omega'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> Warning: multi-subject simulation without without 'omega'
round(trough_parts, 3)
#>    as_simulated   dose_10_mg_kg          all_ap ap_and_10_mg_kg 
#>           1.202           0.801           0.833           0.555

stopifnot(
  # Each adjustment moves the trough toward the published 0.494 mg/L, and
  # together they close a substantial part of the gap -- but not all of it.
  trough_parts[["dose_10_mg_kg"]] < trough_parts[["as_simulated"]],
  trough_parts[["all_ap"]] < trough_parts[["as_simulated"]],
  trough_parts[["ap_and_10_mg_kg"]] < trough_parts[["dose_10_mg_kg"]],
  # The residual gap is real: even the most favourable combination stays
  # above the published trough.
  trough_parts[["ap_and_10_mg_kg"]] > 0.494
)

An inferred centring value is not the explanation. Re-solving the arm with every height set to the 170 cm reference (so the CLd2 height factor is exactly 1) moves the trough the wrong way and by only a few percent, so the steep 3.38 height power is not what drives the discrepancy:

trough_ht_ref <- trough_at(ev_multi |> dplyr::mutate(HT = 170))
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> Warning: multi-subject simulation without without 'omega'
c(at_cohort_heights = trough_at(ev_multi), at_reference_height = trough_ht_ref)
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> Warning: multi-subject simulation without without 'omega'
#>   at_cohort_heights at_reference_height 
#>            1.201515            1.251615

stopifnot(abs(trough_ht_ref / trough_at(ev_multi) - 1) < 0.15)
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_cl_1, etaiov_cl_2, etaiov_cl_3, etaiov_cl_4
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalq', 'etalq2', 'etalvp2', 'etaiov_cl_1', 'etaiov_cl_2', 'etaiov_cl_3', 'etaiov_cl_4'
#> Warning: multi-subject simulation without without 'omega'

What remains is a genuine over-prediction of the 24-h trough in the phase 2 cUTI/AP arm. It is confined to that quantity: peak concentration, total exposure, terminal half-life and steady-state volume all reproduce within about 12% in both arms. The trough sits furthest out in the terminal phase, which is governed by CLd2 (0.199 L/h) and Vp2 (6.98 L) – the model’s smallest and least precisely estimated disposition parameters, whose cUTI/AP and vasopressor shifts carry %SEE of 46.0 and 36.0 respectively. Table 3’s own trough values span more than fourfold across the four studies (0.372, 0.494, 0.880, 2.10) with coefficients of variation of 46-104%, so the trough is the least stable statistic the paper reports. Trough-based conclusions from this model should be treated as indicative rather than quantitative; exposure-based ones (the paper’s own AUC/MIC efficacy target) reproduce well.

Mass balance: clearance recovers the administered dose

For an intravenous drug with no bioavailability term, CL x AUCinf must equal the dose exactly. On the typical-value solve the individual clearance is constant within a subject, so this identity is exact up to the trapezoidal and extrapolation error of the NCA, and it independently confirms that the dose units, the infusion rate and the clearance equation are mutually consistent.

recovery <- as.data.frame(nca_res) |>
  dplyr::filter(treatment == single_arm, PPTESTCD == "aucinf.obs") |>
  dplyr::select(id, aucinf = PPORRES) |>
  dplyr::inner_join(
    sim |>
      dplyr::filter(treatment == single_arm) |>
      dplyr::distinct(id, cl),
    by = "id"
  ) |>
  dplyr::inner_join(
    events |>
      dplyr::filter(evid == 1, treatment == single_arm) |>
      dplyr::select(id, amt),
    by = "id"
  ) |>
  dplyr::mutate(pct_diff = 100 * (cl * aucinf - amt) / amt)

stopifnot(
  nrow(recovery) == n_per_arm,
  abs(median(recovery$pct_diff)) < 1,
  stats::quantile(abs(recovery$pct_diff), 0.9) < 2
)
summary(recovery$pct_diff)
#>      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
#> -0.106119  0.005713  0.008307  0.007498  0.011038  0.016495

Volume of distribution at steady state

Table 3 reports Vss = Vc + Vp1 + Vp2 per study (Materials and Methods, “Calculation of secondary PK parameters”). The model’s own volumes are compared directly against those values.

vss_tab <- sim |>
  dplyr::distinct(id, treatment, vc, vp, vp2) |>
  dplyr::mutate(vss = vc + vp + vp2) |>
  dplyr::group_by(treatment) |>
  dplyr::summarise(vss_sim = exp(mean(log(vss))), .groups = "drop") |>
  dplyr::mutate(
    vss_published = ifelse(treatment == single_arm, 25.0, 27.9),
    pct_diff = 100 * (vss_sim - vss_published) / vss_published
  )

knitr::kable(
  vss_tab |>
    dplyr::rename(
      "Arm" = treatment,
      "Vss simulated (L)" = vss_sim,
      "Vss published (L)" = vss_published,
      "Difference (%)" = pct_diff
    ),
  digits = 2,
  caption = "Simulated versus published steady-state volume (Trang 2019 Table 3)."
)
Simulated versus published steady-state volume (Trang 2019 Table 3).
Arm Vss simulated (L) Vss published (L) Difference (%)
Healthy, 15 mg/kg single dose (study 006) 25.94 25.0 3.76
cUTI/AP, 15 mg/kg q24h (study 002) 28.97 27.9 3.85 

stopifnot(all(abs(vss_tab$pct_diff) < 25))

Assumptions and deviations

  • Covariate reference values are inferred, not printed. The paper reports power and slope coefficients but never the values they are normalised to. Per the standing convention for an undefined centring value, each was taken from the Table 1 pooled medians, with two of them independently corroborated by the paper’s own text:
    • Body weight, 75 kg. This is the Table 1 pooled median and the value in the Results typical-patient sentence, and it is confirmed arithmetically: the printed typical CL of 4.57 L/h is reproduced by the Hill term alone (0.491 + 4.80 x 90^2.49 / (45.3^2.49 + 90^2.49) = 4.56 L/h), i.e. with the weight factor equal to 1.
    • Body surface area, 1.73 m^2, named in the same sentence.
    • Height, 170 cm, and age, 39 years: Table 1 pooled medians, with no independent corroboration available. The height exponent of 3.38 is steep, so CLd2 is sensitive to this choice; CLd2 is the smallest of the model’s clearances (0.199 L/h) and governs only the slow terminal phase.
  • The age effect on Vp1 is linear, not a power. Table 2 labels the coefficient a “Vp1-age slope” while labelling every body-size coefficient a “power”, so the two forms are distinguished by the paper’s own naming. The linear term (1 + 0.00954 x (AGE - 39)) stays positive over the whole observed 18-90 year range (0.80 to 1.49).
  • “Proportional increase” is encoded as (1 + theta). Several of these coefficients are negative (for example -0.831 on CLd1 for cUTI/AP), which is only consistent with a proportional-change reading; an exponential form would not be described as a proportional increase. All coefficients exceed -1, so every factor stays positive.
  • Table 2 and the Results prose disagree on one covariance pair. Table 2 estimates covariances between CL-Vc, CL-Vp1 and Vc-Vp1; the Results “(ii) Covariate analysis” text instead names eta_CL-eta_Vc, eta_CL-eta_CLd1 and eta_Vc-eta_CLd1. The table is the final parameter register and is followed here. Both readings give a positive-definite block; the table’s implied correlations are 0.632, 0.878 and 0.543.
  • The HABP/VABP stratum is a single pooled category. The paper never separates hospital-acquired from ventilator-associated pneumonia, so DIS_HABP and DIS_VABP always carry the same coefficient and are summed in model(). Set either one, or both, to select the stratum.
  • Occasion boundaries. The published occasions are “days 1 to 2, 3 to 6, 6 to 9, and >9” - day 6 is printed as belonging to two of them. The upper-exclusive reading ([0, 48), [48, 144), [144, 216), [216, Inf) hours) is the only one that makes the four mutually exclusive.
  • Inter-occasion variability shares one variance. Table 2 reports a single IOV on CL value, so occasions 2-4 repeat the occasion-1 variance as fixed(), the standard encoding of a NONMEM $OMEGA BLOCK(1) SAME. The magnitude is small (3.59% CV), consistent with the paper’s own remark that “CL is relatively stable across occasions”.
  • Residual error is stratified by study phase. STUDY_PHASE2 and STUDY_PHASE3 select the proportional component and touch nothing else. When simulating, choose the stratum matching the intended setting: phase 1 (both indicators 0) for a rich-sampling clinical-pharmacology study, phase 3 for a sparse-sampling trial.
  • CRRT is a per-period gate, not a subject flag. RRT_CRRT_ACTIVE should be 1 only while the circuit is running. RRT_CRRT_EFFLUENT_FLOW is the canonical column in mL/h and is divided by 1000 inside model(); Table 2 gives the observed sum of ultrafiltrate and dialysate flow rates as 1.14-1.8 L/h. Only 9 of 564 subjects received CRRT, and the sieving coefficient is correspondingly imprecise (%SEE 94.7; bootstrap 90% CI 0.405-0.999).
  • Virtual-cohort covariates are drawn independently. Body weight, height, age and creatinine clearance are sampled from independent bounded log-normals matched to the Table 1 per-phase medians and ranges, with body surface area then computed from weight and height by the Du Bois equation the paper used. In the real cohort creatinine clearance is a deterministic function of age, weight and sex through Cockcroft-Gault, so the simulated joint distribution is wider than the true one. Every assertion in this vignette is therefore made on the centre of the distribution or on an exact structural identity, never on a cohort extreme.
  • No parameter came from outside the paper. Every value traces to Table 2 of Trang 2019; the supplement (Tables S1-S2, Fig. S1) contains no parameter estimates, only the data-retention summary and the stepwise covariate-analysis objective-function table. No erratum or corrigendum was located for this article.
  • The cUTI/AP trough is over-predicted by about twofold. See the decomposition above. Part of the gap is that the simulated arm gives every subject 15 mg/kg while study 002 used “10 or 15 mg/kg” in an unpublished mix, and assigns every subject cUTI while the study was 56.5% acute pyelonephritis (which raises clearance by 13.0%). The remainder is a genuine limitation of the terminal phase as parameterised. Peak concentration, total exposure, terminal half-life and steady-state volume all reproduce within about 12%.
  • Not extracted: the dosing-adjustment nomogram. Table 4’s renal dose bands (15 mg/kg q24h above 60 mL/min down to 8 mg/kg q48h) and the adjusted-body- weight rule for a body weight at or above 125% of ideal body weight are trial dosing rules, not model components, and are applied on the data side rather than inside model().