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Ampicillin (Tremoulet 2014)

Source: vignettes/articles/Tremoulet_2014_ampicillin.Rmd
Tremoulet_2014_ampicillin.Rmd

Model and source 

mod_meta <- nlmixr2est::nlmixr(readModelDb("Tremoulet_2014_ampicillin"))$meta
#> ℹ parameter labels from comments will be replaced by 'label()'
  • Citation: Tremoulet A, Le J, Poindexter B, Sullivan JE, Laughon M, Delmore P, Salgado A, Chong SI, Melloni C, Gao J, Benjamin DK Jr, Capparelli EV, Cohen-Wolkowiez M; Administrative Core Committee of the Best Pharmaceuticals for Children Act-Pediatric Trials Network. Characterization of the population pharmacokinetics of ampicillin in neonates using an opportunistic study design. Antimicrob Agents Chemother. 2014;58(6):3013-3020. doi:10.1128/AAC.02374-13
  • Description: One-compartment IV population PK model for ampicillin in preterm and term neonates (Tremoulet 2014; opportunistic POPS / PTN study). Clearance is allometrically scaled linearly to body weight and modulated by a serum-creatinine power factor (0.6/SCR)^0.428 and a postmenstrual-age power factor (PMA/37)^1.34. Central volume scales linearly with body weight (0.399 L/kg). Inter-individual variability is supported on CL only; residual variability is proportional.
  • Article (DOI): https://doi.org/10.1128/AAC.02374-13

This vignette validates the packaged Tremoulet_2014_ampicillin model – a one-compartment IV population PK model for ampicillin in 73 preterm and term neonates from the Pediatric Trials Network POPS opportunistic study (NICHD-2011-POP01) – against the source publication’s reported per-group typical CL and half-life (Table 5) and the per-group steady-state target attainment for time-above-MIC (Table 6 and Table 7).

Population

The Tremoulet 2014 cohort comprises 73 neonates from nine US NICU sites who received ampicillin per standard of care. The protocol stratified subjects on gestational age (<= 34 vs > 34 weeks) and postnatal age (<= 7 vs 8-28 days), yielding four groups; demographics are in Table 1 of the source paper.

  • Overall: median (range) GA 36 (24-41) weeks, PNA 5 (0-25) days, 52 % male. Race 77 % White, 16 % Black, 4 % Other, 1 % not reported. Ethnicity 18 % Hispanic / Latino, 77 % non-Hispanic, 6 % not reported.
  • 142 plasma samples were retained (median 2.1 per subject; 17 of 73 subjects contributed > 2). Median observed concentration 123 ug/mL (range 0.85-464). Bioanalysis was HPLC-MS/MS with LLOQ 0.05 ug/mL and validated range 0.05-50 ug/mL.
  • Doses were prescribed per standard of care, median 200 mg/kg/day (range 100-350) split 11 % q6h / 34 % q8h / 55 % q12h overall. One subject was excluded for receiving an intramuscular dose; all retained data are IV.

Body weight was not tabulated in Table 1; the simulations below use gestational-age-appropriate typical weights informed by Table 1’s per-group GA medians.

The same information is available programmatically via the model’s population metadata:

str(mod_meta$population)
#> List of 17
#>  $ species                : chr "human"
#>  $ n_subjects             : int 73
#>  $ n_studies              : int 1
#>  $ age_range              : chr "Postnatal age 0-25 days (median 5); gestational age 24-41 weeks (median 36)"
#>  $ age_median             : chr "PNA 5 days; GA 36 weeks"
#>  $ weight_range           : chr "Body weight not tabulated in Tremoulet 2014 Table 1; cohort spans extremely premature (GA 24 weeks) to term (GA"| __truncated__
#>  $ weight_median          : chr "Not tabulated"
#>  $ sex_female_pct         : num 47.9
#>  $ race_ethnicity         : chr "Race: 77% White, 16% Black, 4% Other, 1% not reported. Ethnicity: 18% Hispanic/Latino, 77% non-Hispanic, 6% not"| __truncated__
#>  $ disease_state          : chr "Hospitalised neonates receiving ampicillin per standard of care in the neonatal intensive care unit; indication"| __truncated__
#>  $ dose_range             : chr "Median 200 mg/kg/day (range 100-350); intervals 6, 8, or 12 h. Routes IV (one excluded subject received intramu"| __truncated__
#>  $ gestational_age_range  : chr "24-41 weeks (median 36)"
#>  $ postnatal_age_range    : chr "0-25 days (median 5)"
#>  $ postmenstrual_age_range: chr "Derived (PMA = GA + PNA/7); range spans approximately 24-45 weeks given the GA + PNA ranges above"
#>  $ samples_plasma         : chr "142 plasma samples from 73 neonates (median 2.1 per subject; 17 (23%) of subjects contributed more than 2 samples)"
#>  $ regions                : chr "United States (9 NICU centres; Pediatric Trials Network sites under POPS protocol NICHD-2011-POP01)"
#>  $ notes                  : chr "Demographics from Tremoulet 2014 Table 1. Original enrolment was 75 neonates; 2 excluded (one with a single bel"| __truncated__

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Tremoulet_2014_ampicillin.R. The table below collects them in one place; values come from Tremoulet 2014 Table 4 (Final pharmacokinetic model parameters).

Parameter / equation Value Source location
lcl = log(theta_CL) log(0.078) Table 4 row “CL”, point estimate = 0.078 L/h/kg
lvc = log(theta_V) log(0.399) Table 4 row “V”, point estimate = 0.399 L/kg
e_creat_cl (exponent on (0.6/SCR)) 0.428 Table 4 row “CL, SCR”, point estimate = 0.428
e_page_cl (exponent on (PMA/37)) 1.34 Table 4 row “CL, PMA”, point estimate = 1.34
etalcl (variance on log-CL) 0.05068 Table 4 row “CL IIV”, reported CV % = 22.8; omega^2 = log(1+0.228^2)
propSd (proportional residual SD) 0.339 Table 4 row “Residual variability”, reported CV % = 33.9
cl = exp(lcl + etalcl) * WT * ... n/a Results: “CL = theta(2) * WTKG * (0.6/SCR)^theta(3) * (PMA/37)^theta(4)”
vc = exp(lvc) * WT n/a Results: “V = theta(1) * WTKG”
d/dt(central) = -kel * central n/a Methods: “1-compartment model (ADVAN1 TRANS2)”
Cc ~ prop(propSd) n/a Methods: proportional and additive explored; final retains proportional only

Virtual cohort

Original POPS plasma observations are not publicly available. The vignette uses four virtual cohorts matching the protocol-defined groups (Table 1). Within each group, GA and PNA are sampled uniformly within the group’s GA band and PNA band, weight is sampled from a normal centred on the gestational-age-typical neonatal weight, and serum creatinine is sampled from a normal centred on a postmenstrual-age-appropriate typical value.

PMA at the time of sampling is computed as GA + PNA / 7 (weeks) per the paper’s covariate definition.

set.seed(2014L)

# Helper: build a single-group cohort and return an rxode2-ready event
# table with id_offset so cohorts can be bind_rows()-ed safely.
make_cohort <- function(n, ga_lo, ga_hi, pna_lo, pna_hi,
                        wt_mean, wt_sd, scr_mean, scr_sd, dose_mg_per_kg,
                        tau_h, label, id_offset = 0L) {
  subj <- tibble::tibble(
    id        = id_offset + seq_len(n),
    GA        = runif(n, ga_lo, ga_hi),                  # weeks at birth
    PNA_days  = runif(n, pna_lo, pna_hi),                # days since birth
    WT        = pmax(0.5, rnorm(n, wt_mean, wt_sd)),     # kg
    CREAT     = pmax(0.2, rnorm(n, scr_mean, scr_sd)),   # mg/dL
    cohort    = label,
    tau       = tau_h,
    amt_mg    = dose_mg_per_kg * WT
  ) |>
    dplyr::mutate(PAGE = GA + PNA_days / 7)              # weeks PMA

  # 7 multiples of tau dosing window for steady-state assessment.
  dose_times <- seq(0, 6 * tau_h, by = tau_h)
  obs_times  <- sort(unique(c(seq(0, 7 * tau_h, by = 0.25), dose_times)))

  events <- subj |>
    dplyr::rowwise() |>
    dplyr::do({
      .subj <- .
      doses <- tibble::tibble(
        id = .subj$id, time = dose_times, amt = .subj$amt_mg,
        evid = 1L, cmt = "central"
      )
      obs <- tibble::tibble(
        id = .subj$id, time = obs_times, amt = NA_real_,
        evid = 0L, cmt = "central"
      )
      dplyr::bind_rows(doses, obs) |>
        dplyr::arrange(time) |>
        dplyr::mutate(
          WT     = .subj$WT,
          PAGE   = .subj$PAGE,
          CREAT  = .subj$CREAT,
          cohort = .subj$cohort
        )
    }) |>
    dplyr::ungroup()

  list(subj = subj, events = events)
}

# Per-group typical values are informed by Table 1 (GA / PNA medians) plus
# externally-typical neonatal body weight and SCR centiles -- see the
# "Assumptions and deviations" section.
groups <- list(
  list(label = "Group 1 (GA<=34, PNA<=7)",
       ga_lo = 24, ga_hi = 34, pna_lo = 0, pna_hi = 7,
       wt_mean = 1.7,  wt_sd = 0.45,
       scr_mean = 0.9, scr_sd = 0.20,
       dose_mg_per_kg = 100, tau_h = 12),
  list(label = "Group 2 (GA<=34, PNA 8-28)",
       ga_lo = 24, ga_hi = 34, pna_lo = 8, pna_hi = 28,
       wt_mean = 1.4,  wt_sd = 0.35,
       scr_mean = 0.6, scr_sd = 0.15,
       dose_mg_per_kg = 100, tau_h = 12),
  list(label = "Group 3 (GA>34, PNA<=7)",
       ga_lo = 34, ga_hi = 41, pna_lo = 0, pna_hi = 7,
       wt_mean = 3.1,  wt_sd = 0.45,
       scr_mean = 0.8, scr_sd = 0.20,
       dose_mg_per_kg = 75, tau_h = 8),
  list(label = "Group 4 (GA>34, PNA 8-28)",
       ga_lo = 34, ga_hi = 41, pna_lo = 8, pna_hi = 28,
       wt_mean = 3.4,  wt_sd = 0.50,
       scr_mean = 0.45, scr_sd = 0.15,
       dose_mg_per_kg = 100, tau_h = 8)
)

n_per_group <- 100L
built <- vector("list", length(groups))
id_offset <- 0L
for (i in seq_along(groups)) {
  g <- groups[[i]]
  built[[i]] <- make_cohort(
    n              = n_per_group,
    ga_lo          = g$ga_lo,   ga_hi = g$ga_hi,
    pna_lo         = g$pna_lo,  pna_hi = g$pna_hi,
    wt_mean        = g$wt_mean, wt_sd  = g$wt_sd,
    scr_mean       = g$scr_mean, scr_sd = g$scr_sd,
    dose_mg_per_kg = g$dose_mg_per_kg,
    tau_h          = g$tau_h,
    label          = g$label,
    id_offset      = id_offset
  )
  id_offset <- id_offset + n_per_group
}

subj_all   <- dplyr::bind_rows(lapply(built, `[[`, "subj"))
events_all <- dplyr::bind_rows(lapply(built, `[[`, "events"))

stopifnot(!anyDuplicated(unique(events_all[, c("id", "time", "evid")])))

Simulation 

mod <- readModelDb("Tremoulet_2014_ampicillin")

# Typical-value simulation (ETA = 0) to compare against Table 5 medians.
mod_typical <- rxode2::zeroRe(mod)
#> ℹ parameter labels from comments will be replaced by 'label()'
sim_typical <- rxode2::rxSolve(
  mod_typical,
  events = events_all,
  keep   = c("cohort", "WT", "PAGE", "CREAT")
) |> as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalcl'
#> Warning: multi-subject simulation without without 'omega'

# Stochastic simulation (with IIV and residual error) for T>MIC checks.
sim_iiv <- rxode2::rxSolve(
  mod,
  events = events_all,
  keep   = c("cohort", "WT", "PAGE", "CREAT")
) |> as.data.frame()
#> ℹ parameter labels from comments will be replaced by 'label()'

Replicate published table 5 (typical CL/kg, V/kg, half-life by group)

Tremoulet 2014 Table 5 reports the median individual empirical-Bayes post-hoc estimates per group. The packaged model is a structural-only re-implementation; the typical-value simulation below should reproduce the group medians for V/kg (always 0.40 by definition) and approximate the CL/kg and half-life ordering across groups. Per-group typical CL/kg is computed by averaging the individual typical CLs across the cohort.

per_subj <- sim_typical |>
  dplyr::distinct(id, cohort, WT, PAGE, CREAT) |>
  dplyr::mutate(
    cl_per_kg = 0.078 * (0.6 / CREAT)^0.428 * (PAGE / 37)^1.34,
    v_per_kg  = 0.399,
    half_life = log(2) * v_per_kg / cl_per_kg
  )

published_t5 <- tibble::tibble(
  cohort       = c("Group 1 (GA<=34, PNA<=7)",
                   "Group 2 (GA<=34, PNA 8-28)",
                   "Group 3 (GA>34, PNA<=7)",
                   "Group 4 (GA>34, PNA 8-28)"),
  cl_pub       = c(0.055, 0.070, 0.086, 0.110),
  v_pub        = c(0.40,  0.40,  0.40,  0.40),
  thalf_pub_h  = c(5.0,   4.0,   3.2,   2.4)
)

simulated_t5 <- per_subj |>
  dplyr::group_by(cohort) |>
  dplyr::summarise(
    cl_sim       = median(cl_per_kg),
    v_sim        = median(v_per_kg),
    thalf_sim_h  = median(half_life),
    .groups      = "drop"
  )

dplyr::left_join(published_t5, simulated_t5, by = "cohort") |>
  dplyr::transmute(
    cohort,
    `CL (L/h/kg) -- Pub`  = sprintf("%.3f", cl_pub),
    `CL (L/h/kg) -- Sim`  = sprintf("%.3f", cl_sim),
    `V  (L/kg)   -- Pub`  = sprintf("%.2f", v_pub),
    `V  (L/kg)   -- Sim`  = sprintf("%.2f", v_sim),
    `t1/2 (h)    -- Pub`  = sprintf("%.1f", thalf_pub_h),
    `t1/2 (h)    -- Sim`  = sprintf("%.1f", thalf_sim_h)
  ) |>
  knitr::kable(caption = "Tremoulet 2014 Table 5: published medians vs simulated typical-value medians.")
Tremoulet 2014 Table 5: published medians vs simulated typical-value medians.
cohort CL (L/h/kg) – Pub CL (L/h/kg) – Sim V (L/kg) – Pub V (L/kg) – Sim t1/2 (h) – Pub t1/2 (h) – Sim
Group 1 (GA<=34, PNA<=7) 0.055 0.049 0.40 0.40 5.0 5.7
Group 2 (GA<=34, PNA 8-28) 0.070 0.065 0.40 0.40 4.0 4.2
Group 3 (GA>34, PNA<=7) 0.086 0.072 0.40 0.40 3.2 3.8
Group 4 (GA>34, PNA 8-28) 0.110 0.102 0.40 0.40 2.4 2.7

Replicate published figure 1 (CL and half-life vs PMA)

Figure 1 of Tremoulet 2014 plots the per-subject post-hoc CL and half-life against postmenstrual age. The corresponding typical-value relationships from the packaged model are plotted below; they capture the published monotone increase in CL with PMA and the corresponding monotone decrease in half-life.

fig1 <- per_subj |>
  tidyr::pivot_longer(c(cl_per_kg, half_life),
                      names_to = "metric", values_to = "value") |>
  dplyr::mutate(metric = dplyr::recode(metric,
    cl_per_kg = "CL (L/h/kg)",
    half_life = "Half-life (h)"
  ))

ggplot(fig1, aes(PAGE, value, colour = cohort)) +
  geom_point(alpha = 0.7) +
  facet_wrap(~ metric, scales = "free_y") +
  labs(x = "Postmenstrual age (weeks)", y = NULL,
       colour = "Cohort",
       title = "Figure 1 -- typical CL and half-life vs PMA",
       caption = "Replicates Figure 1 of Tremoulet 2014.") +
  theme(legend.position = "bottom")

PKNCA validation – steady-state interval

The paper’s Monte Carlo simulations focus on steady-state target attainment (% subjects with trough >= 8 ug/mL, i.e. 100 % time-above-MIC at MIC = 8 ug/mL). The PKNCA recipe below computes the steady-state Cmax, Cmin, Cavg, and AUC0-tau on the final dosing interval, stratified by cohort.

# PKNCA needs concentration and dose frames in long form, with units.
sim_nca <- sim_iiv |>
  dplyr::filter(!is.na(Cc), Cc > 0) |>
  dplyr::select(id, time, Cc, cohort)

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

conc_obj <- PKNCA::PKNCAconc(
  data = sim_nca,
  formula = Cc ~ time | cohort + id,
  concu = "ug/mL", timeu = "h"
)
dose_obj <- PKNCA::PKNCAdose(
  data = dose_df,
  formula = amt ~ time | cohort + id,
  doseu = "mg"
)

# Steady-state interval: from the final dose to the final dose + tau.
ss_intervals <- subj_all |>
  dplyr::group_by(cohort) |>
  dplyr::summarise(tau = unique(tau), .groups = "drop") |>
  dplyr::mutate(
    start    = 6 * tau,        # final dose time
    end      = 7 * tau,        # final dose + tau
    cmax     = TRUE,
    cmin     = TRUE,
    cav      = TRUE,
    auclast  = TRUE
  ) |>
  dplyr::select(-tau)

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

nca_tbl <- as.data.frame(nca_res$result)

# Per-cohort medians of the simulated NCA parameters.
nca_summary <- nca_tbl |>
  dplyr::filter(PPTESTCD %in% c("cmax", "cmin", "cav", "auclast")) |>
  dplyr::group_by(cohort, PPTESTCD) |>
  dplyr::summarise(median = median(PPORRES, na.rm = TRUE), .groups = "drop") |>
  tidyr::pivot_wider(names_from = PPTESTCD, values_from = median) |>
  dplyr::select(cohort, cmax, cmin, cav, auclast)

knitr::kable(
  nca_summary,
  digits  = 1,
  caption = paste(
    "Simulated steady-state NCA per cohort (medians; concentrations in",
    "ug/mL, AUC in ug*h/mL). cmin and ctau are trough metrics."
  )
)
Simulated steady-state NCA per cohort (medians; concentrations in ug/mL, AUC in ug*h/mL). cmin and ctau are trough metrics.
cohort cmax cmin cav auclast
Group 1 (GA<=34, PNA<=7) 326.6 75.9 171.8 2061.9
Group 2 (GA<=34, PNA 8-28) 292.1 41.5 128.4 1541.0
Group 3 (GA>34, PNA<=7) 247.4 59.5 131.8 1054.7
Group 4 (GA>34, PNA 8-28) 288.5 37.9 123.5 987.8

Comparison against published target attainment (Table 6)

Tremoulet 2014 Table 6 reports the percentage of simulated subjects achieving 100 % time-above-MIC at MIC = 8 ug/mL under the “typical POPS doses” regimens (the same regimens encoded in the cohorts above). The table below reports the simulated trough (ctau) >= 8 ug/mL percentage – the same surrogate metric – and the published target attainment.

tmic_sim <- nca_tbl |>
  dplyr::filter(PPTESTCD == "cmin") |>
  dplyr::group_by(cohort) |>
  dplyr::summarise(
    pct_ctau_ge_8 = mean(PPORRES >= 8, na.rm = TRUE) * 100,
    n             = sum(!is.na(PPORRES)),
    .groups       = "drop"
  )

published_tmic <- tibble::tibble(
  cohort                    = c("Group 1 (GA<=34, PNA<=7)",
                                "Group 2 (GA<=34, PNA 8-28)",
                                "Group 3 (GA>34, PNA<=7)",
                                "Group 4 (GA>34, PNA 8-28)"),
  pct_100Tabove8_pub_typicalPOPS = c(99.2, 97.1, 98.1, 98.3)
)

dplyr::left_join(published_tmic, tmic_sim, by = "cohort") |>
  dplyr::mutate(
    `100% T>8 ug/mL -- Tremoulet 2014 Table 6 (% subjects)` =
        sprintf("%.1f%%", pct_100Tabove8_pub_typicalPOPS),
    `Steady-state Cmin >=8 ug/mL -- Simulated (% subjects)` =
        sprintf("%.1f%%", pct_ctau_ge_8)
  ) |>
  dplyr::select(cohort,
                `100% T>8 ug/mL -- Tremoulet 2014 Table 6 (% subjects)`,
                `Steady-state Cmin >=8 ug/mL -- Simulated (% subjects)`) |>
  knitr::kable(
    caption = paste(
      "Tremoulet 2014 Table 6 (Typical POPS doses, MIC = 8 ug/mL,",
      "100% T>MIC) vs simulated steady-state interval-Cmin attainment.",
      "The metrics are not numerically identical (Cmin is the lowest",
      "concentration in the final dosing interval; 100% T>MIC requires",
      "the whole interval to remain above MIC) but for a monotonically",
      "decreasing 1-compartment IV profile within tau, Cmin >= MIC is",
      "equivalent to 100% T>MIC. The published 97-99% attainment is",
      "reproduced qualitatively."
    )
  )
Tremoulet 2014 Table 6 (Typical POPS doses, MIC = 8 ug/mL, 100% T>MIC) vs simulated steady-state interval-Cmin attainment. The metrics are not numerically identical (Cmin is the lowest concentration in the final dosing interval; 100% T>MIC requires the whole interval to remain above MIC) but for a monotonically decreasing 1-compartment IV profile within tau, Cmin >= MIC is equivalent to 100% T>MIC. The published 97-99% attainment is reproduced qualitatively.
cohort 100% T>8 ug/mL – Tremoulet 2014 Table 6 (% subjects) Steady-state Cmin >=8 ug/mL – Simulated (% subjects)
Group 1 (GA<=34, PNA<=7) 99.2% 100.0%
Group 2 (GA<=34, PNA 8-28) 97.1% 97.0%
Group 3 (GA>34, PNA<=7) 98.1% 100.0%
Group 4 (GA>34, PNA 8-28) 98.3% 96.0%

Assumptions and deviations

  • Body weight per cohort. Tremoulet 2014 Table 1 does not tabulate body weight. The virtual cohorts use gestational-age-appropriate typical neonatal weights drawn from clinical experience (Group 1 ~1.7 kg, Group 2 ~1.4 kg [more premature], Group 3 ~3.1 kg, Group 4 ~3.4 kg). The exact weight choice does not affect per-kg CL or V (the model is per-kg) but does affect absolute dose and concentration amplitudes.
  • Serum creatinine per cohort. The paper says (Methods) “current weight (kg) (WTKG) and SCR used for each cohort were from a prior trial in premature infants” without listing values per group. The virtual cohorts use postmenstrual-age-appropriate typical SCRs (Group 1 ~0.9, Group 2 ~0.6, Group 3 ~0.8, Group 4 ~0.45 mg/dL) drawn from neonatal clinical reference ranges. The SCR factor enters CL as (0.6 / CREAT)^0.428; smaller CREAT (more mature renal function) increases CL.
  • Race / ethnicity distribution. Race is not a model covariate. Demographics from Table 1 are reproduced narratively but not in the virtual cohort.
  • PNA and GA distributions. PNA and GA within each group are sampled uniformly within the group’s stated bands (<= 7 vs 8-28 days for PNA; <= 34 vs > 34 weeks for GA). The paper’s actual cohort medians per group are tighter (Table 1) but were not used so each cohort spans the full eligibility band as the simulation extrapolation target.
  • Steady-state trough vs T-above-MIC. Tremoulet 2014 Table 6 reports the percentage of subjects with 100 % time-above-MIC at MIC = 8 ug/mL, which requires the concentration trace to remain >= 8 ug/mL across the entire dosing interval. The validation table above reports the percentage with the single end-of-interval trough (Ctau) >= 8 ug/mL – the same surrogate the paper’s optimal-dosing derivation in Table 7 also targets (“achieving steady-state trough concentrations >= 8 ug/mL in >= 90 % of subjects”). The two metrics agree under monotone-decreasing concentration profiles within a tau, which holds for this 1-compartment IV bolus model.
  • Final-model residual error. Tremoulet 2014 Methods says “Proportional and additive residual error models were explored.” Only one residual sigma (33.9 % CV) is reported in Table 4, consistent with retention of the proportional form. The model file encodes that proportional residual (propSd = 0.339).
  • Single ETA on CL only. The paper notes (Discussion) that “our final PK model supported a single ETA only for CL (not V).” The packaged model preserves this (etalcl only; no etalvc).