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Teicoplanin (Wang 2023)

Source: vignettes/articles/Wang_2023_teicoplanin.Rmd
Wang_2023_teicoplanin.Rmd

Model and source 

mod      <- readModelDb("Wang_2023_teicoplanin")
mod_meta <- rxode2::rxode(mod)$meta
#> ℹ parameter labels from comments will be replaced by 'label()'
  • Citation: Wang Y, Yao F, Chen S, Ouyang X, Lan J, Wu Z, Wang Y, Chen J, Wang X, Chen C. Optimal teicoplanin dosage regimens in critically ill patients: population pharmacokinetics and dosing simulations based on renal function and infection type. Drug Des Devel Ther. 2023;17:2259-2271. doi:10.2147/DDDT.S413662
  • Article (DOI): https://doi.org/10.2147/DDDT.S413662

This vignette validates the packaged Wang_2023_teicoplanin model – a two-compartment intravenous-infusion population PK model for teicoplanin built from 304 plasma concentrations in 108 critically ill adults in the ICU of Guangdong Provincial People’s Hospital. The final model carries a single covariate: the CKD-EPI estimated glomerular filtration rate (eGFR) as a linear term on clearance, centred at 50 mL/min/1.73 m^2.

The paper’s quantitative deliverable is a Monte Carlo dosing-optimization analysis. Supplementary Tables S2-1 and S2-2 report, for eight candidate regimens crossed with four renal-function strata, the median (IQR) trough concentration at 72 h and at 168 h and the corresponding probability of target attainment – 64 published trough medians and 64 published PTA values. Those are pure forward predictions of the packaged model, which makes them an unusually strong validation target, so this vignette reproduces all of them and compares against the published numbers.

Population 

pop <- rxode2::rxode(mod)$population
#> ℹ parameter labels from comments will be replaced by 'label()'

The Wang 2023 cohort comprised 151 ICU patients contributing 347 plasma teicoplanin concentrations. The population PK model was built on the 108 patients who each contributed more than two samples (304 concentrations); the remaining 43 single-sample patients formed an external validation group. Median age was 56.5 years (range 21-91) and median weight 61 kg (range 40-115); 38 of 108 subjects (35.2%) were female.

The defining feature of the cohort is severe renal impairment: median CKD-EPI eGFR 29.2 mL/min/1.73 m^2 (range 4.89-170), median Cockcroft-Gault creatinine clearance 34.8 mL/min, median serum creatinine 161 umol/L, and 43 of 108 subjects (39.8%) receiving continuous renal replacement therapy. Median baseline APACHE II score was 25.5 (range 10-37). Pneumonia was the commonest infection site (73 of the recorded sites), followed by intra-abdominal infection (13) and bacteraemia (10).

Teicoplanin was given by 1-hour intravenous infusion. Concentrations were measured by HPLC-MS/MS quantifying the teicoplanin A2-2 component, the most active of the five components of the teicoplanin mixture, as the surrogate for teicoplanin (LLOQ 1.0 mg/L, linear to 100.0 mg/L).

Source trace

Every value in the packaged model, and every equation in model(), traced to its location in the source.

Quantity Value Source location
CL (typical, eGFR = 50) 0.838 L/h Table 2, Final Model Estimate (RSE 8.4%); restated in Results and Abstract
Vc 14.4 L Table 2 (RSE 7.2%); Table 2 note ‘Vc (L) = 14.4’
Q 3.08 L/h Table 2 (RSE 14.3%); Table 2 note ‘Q (L/h) = 3.08’
Vp 51.6 L Table 2 (RSE 10.7%); Table 2 note ‘Vp (L) = 51.6 x e^0.387’
theta eGFR-CL 0.00823 Table 2 (RSE 28.3%); Abstract ‘eGFR adjustment factor of 0.00823’
CL covariate equation CL = 0.838 * (1 + (eGFR - 50) * 0.0082) Table 2 notes; generic form in Supplementary Table S1 notes
omega CL 37.7% -> var 0.142 Table 2, BSV block (RSE 20%)
omega Vc 26.6% -> var 0.0708 Table 2, BSV block (RSE 43.4%)
omega Q 0 FIX (no eta) Table 2, BSV block; Results ‘inter-individual variabilities … 0%’
omega Vp 62.2% -> var 0.387 Table 2, BSV block (RSE 18%); confirmed by ‘e^0.387’ in the Table 2 note
Proportional residual error 31.7% Table 2, RUV block (RSE 10.6%)
Two-compartment structure central + peripheral1 Results ‘the data showed a better fit to two-compartment model’
IV infusion, 1 h - Methods, ‘Dosing Regimen’: ‘The infusion time was 1 h.’
Exponential IIV, proportional RUV - Results ‘Exponential and proportional error models were selected’

Two transcription points are worth recording explicitly.

The minus sign in (eGFR - 50) is not text-extractable. The Table 2 notes are typeset in a symbol font whose minus glyph is dropped by pdftotext and by the markdown preprocessor, so the equation extracts as 0:838 * (1 + (eGFR 50) * 0:0082) with a bare gap. Rendering page 6 of the PDF to an image resolves it as a subtraction, and the generic covariate form printed in the Supplementary Table S1 notes, P_ij = P_tv,j * [1 + theta_j * (COV - COV_ave)] * e^eta_i, corroborates it. The reproduction of 64 published simulation outputs below is a further, independent confirmation: the alternative readings (+ 50, or no centring at all) move the trough predictions by tens of percent.

Vp (L) = 51.6 x e^0.387 in the Table 2 note is not a multiplier. Taken literally it would give 76.0 L, contradicting both the Table 2 estimate and the Results text, which give the typical Vp as 51.6 L. The exponent is the between-subject variance: 0.622^2 = 0.3869, and 62.2% is exactly the Table 2 omega Vp. The same identity fixes the omega convention for the whole table – the published percentages are omega (the standard deviation on the log scale) times 100, not sqrt(exp(omega^2) - 1).

Deterministic checks

With between-subject and residual variability switched off, the model must satisfy exact internal identities. These are the tightest gates available because they contain no Monte Carlo noise.

theta_cl <- 0.838
theta_e  <- 0.00823

# The covariate equation as printed in the Table 2 note.
cl_at <- function(egfr) theta_cl * (1 + (egfr - 50) * theta_e)

grid <- sort(unique(c(seq(0, 12, by = 0.1), seq(12, 48, by = 0.5),
                      seq(48, 336, by = 2))))
ev_single <- rbind(
  data.frame(id = 1L, time = 0, amt = 400, evid = 1L, dur = 1,
             cmt = "central", CRCL = 50),
  data.frame(id = 1L, time = grid, amt = NA_real_, evid = 0L, dur = NA_real_,
             cmt = "central", CRCL = 50)
)
ev_single <- ev_single[order(ev_single$time, -ev_single$evid), ]

sim_single <- rxode2::rxSolve(mod, ev_single, omega = NA,
                              returnType = "data.frame")
#> ℹ parameter labels from comments will be replaced by 'label()'
sim_single$id <- 1L
conc_obj <- PKNCA::PKNCAconc(dplyr::filter(sim_single, !is.na(Cc)),
                             Cc ~ time | id)
dose_obj <- PKNCA::PKNCAdose(data.frame(id = 1L, time = 0, dose = 400),
                             dose ~ time | id)
nca_single <- PKNCA::pk.nca(PKNCA::PKNCAdata(
  conc_obj, dose_obj,
  intervals = data.frame(start = 0, end = Inf, cmax = TRUE, tmax = TRUE,
                         auclast = TRUE, aucinf.obs = TRUE,
                         half.life = TRUE, cl.obs = TRUE)
))
nca_val <- function(code) {
  v <- as.data.frame(nca_single$result)
  out <- v$PPORRES[v$PPTESTCD == code]
  if (length(out) != 1L) stop("no unique NCA row for '", code, "'")
  out
}

# Analytic terminal half-life of the two-compartment system.
k10 <- theta_cl / 14.4
k12 <- 3.08 / 14.4
k21 <- 3.08 / 51.6
beta_rate <- (k10 + k12 + k21 -
              sqrt((k10 + k12 + k21)^2 - 4 * k10 * k21)) / 2

det_tab <- tibble::tibble(
  Identity = c("AUC(0-inf) after a single 400 mg dose = Dose / CL",
               "PKNCA CL(obs) = model CL",
               "PKNCA terminal half-life = analytic beta half-life"),
  Expected = c(400 / theta_cl, theta_cl, log(2) / beta_rate),
  Observed = c(nca_val("aucinf.obs"), nca_val("cl.obs"), nca_val("half.life"))
) |>
  dplyr::mutate(`% diff` = 100 * (Observed - Expected) / Expected)
knitr::kable(det_tab, digits = c(0, 4, 4, 5))
Identity Expected Observed % diff
AUC(0-inf) after a single 400 mg dose = Dose / CL 477.3270 477.2962 -0.00644
PKNCA CL(obs) = model CL 0.8380 0.8381 0.00644
PKNCA terminal half-life = analytic beta half-life 64.0443 63.8623 -0.28418 

# These are numerical-integration identities with no cohort sampling, so an
# exact bound is correct here (pattern: tighten deterministic gates). The
# realised deviations are ~0.006% (AUC, CL) and ~0.3% (half-life, which is a
# log-linear regression over a finite grid rather than a closed form).
stopifnot(
  abs(det_tab$`% diff`[1]) < 0.05,
  abs(det_tab$`% diff`[2]) < 0.05,
  abs(det_tab$`% diff`[3]) < 1
)

The AUC identity is the single most informative gate on the transcription: it fails if the clearance value, the dose units, the concentration units or the compartment scaling is wrong by any amount.

cov_tab <- tibble::tibble(
  `eGFR (mL/min/1.73 m^2)` = c(4.89, 29.2, 30, 50, 60, 90, 130, 170),
  `CL (L/h)`               = cl_at(c(4.89, 29.2, 30, 50, 60, 90, 130, 170)),
  Note = c("cohort minimum", "cohort median", "stratum 1 boundary",
           "centring value: CL = theta_CL exactly", "stratum 2 boundary",
           "stratum 3 boundary", "stratum 4 boundary", "cohort maximum")
)
knitr::kable(cov_tab, digits = 3)
eGFR (mL/min/1.73 m^2) CL (L/h) Note
4.89 0.527 cohort minimum
29.20 0.695 cohort median
30.00 0.700 stratum 1 boundary
50.00 0.838 centring value: CL = theta_CL exactly
60.00 0.907 stratum 2 boundary
90.00 1.114 stratum 3 boundary
130.00 1.390 stratum 4 boundary
170.00 1.666 cohort maximum 

# At the centring value the covariate term is exactly 1.
stopifnot(abs(cl_at(50) - theta_cl) < 1e-12)
# The linear form stays positive across and well beyond the observed range.
stopifnot(cl_at(0) > 0)

Recovering the published simulation design

The paper does not state what eGFR value was used inside each renal-function stratum, nor whether the reported trough concentrations include residual error. Both choices materially change the predictions, so rather than guess we identify them from the 64 published trough medians.

n_sub <- 200  # participants per arm

make_events <- function(load_dose, n_load, maint_dose, egfr, n = n_sub,
                        tmax = 180, obs_times = c(72, 168)) {
  load_times  <- seq(0, by = 12, length.out = n_load)
  # Maintenance starts one full 24 h interval after the last loading dose.
  # This is the only schedule that places a trough exactly at both 72 h and
  # 168 h, which is how the paper defines its two endpoints, for BOTH the
  # q12h x 3 and q12h x 5 loading arms.
  maint_times <- seq(max(load_times) + 24, tmax, by = 24)
  do.call(rbind, lapply(seq_len(n), function(i) {
    dosing <- data.frame(
      id = i, time = c(load_times, maint_times),
      amt = c(rep(load_dose, n_load), rep(maint_dose, length(maint_times))),
      evid = 1L, dur = 1, cmt = "central", CRCL = egfr
    )
    obs <- data.frame(
      id = i, time = obs_times, amt = NA_real_, evid = 0L, dur = NA_real_,
      cmt = "central", CRCL = egfr
    )
    x <- rbind(dosing, obs)
    x[order(x$time, -x$evid), ]
  }))
}

regimens <- tibble::tribble(
  ~regimen,                    ~load, ~n_load, ~maint, ~target, ~infection,
  "400 mg q12hx3, 400 mg qd",  400,   3L,      400,    10,      "Gram-positive",
  "400 mg q12hx5, 400 mg qd",  400,   5L,      400,    10,      "Gram-positive",
  "600 mg q12hx3, 600 mg qd",  600,   3L,      600,    10,      "Gram-positive",
  "600 mg q12hx5, 600 mg qd",  600,   5L,      600,    10,      "Gram-positive",
  "800 mg q12hx3, 400 mg qd",  800,   3L,      400,    15,      "Deep-seated",
  "800 mg q12hx3, 600 mg qd",  800,   3L,      600,    15,      "Deep-seated",
  "800 mg q12hx3, 800 mg qd",  800,   3L,      800,    15,      "Deep-seated",
  "800 mg q12hx5, 800 mg qd",  800,   5L,      800,    15,      "Deep-seated"
)

strata_levels <- c("eGFR <= 30", "eGFR 30-60", "eGFR 60-90", "eGFR 90-130")

# Run every regimen x stratum cell at one eGFR value and return the
# simulated 72 h and 168 h troughs. `Cc` is the individual prediction;
# `sim` additionally carries the proportional residual error.
sweep_egfr <- function(egfr_by_stratum) {
  rxode2::rxSetSeed(42)
  out <- list()
  for (k in seq_along(strata_levels)) {
    for (j in seq_len(nrow(regimens))) {
      r <- regimens[j, ]
      s <- rxode2::rxSolve(
        mod,
        make_events(r$load, r$n_load, r$maint, egfr_by_stratum[k]),
        returnType = "data.frame"
      )
      out[[length(out) + 1L]] <- tibble::tibble(
        stratum = strata_levels[k], regimen = r$regimen,
        infection = r$infection, target = r$target,
        time = rep(c(72, 168), each = n_sub),
        ipred = c(s$Cc[s$time == 72], s$Cc[s$time == 168]),
        obs   = c(s$sim[s$time == 72], s$sim[s$time == 168])
      )
    }
  }
  dplyr::bind_rows(out)
}

Which eGFR was used inside each stratum?

The two natural candidates are the midpoint of each band and its upper bound. They are easy to tell apart: across the eGFR range the model’s trough predictions change by roughly a factor of two, so a 20-40 mL/min/1.73 m^2 difference in the assumed eGFR is worth 10-20% on every cell.

summarise_medians <- function(sw, value_col) {
  sw |>
    dplyr::group_by(stratum, regimen, time) |>
    dplyr::summarise(sim = stats::median(.data[[value_col]]), .groups = "drop") |>
    dplyr::inner_join(published, by = c("stratum", "regimen", "time")) |>
    dplyr::mutate(pct = 100 * (sim - med) / med)
}

sweep_mid  <- sweep_egfr(c(17.4, 45, 75, 110))
sweep_edge <- sweep_egfr(c(30, 60, 90, 130))

design_tab <- dplyr::bind_rows(
  summarise_medians(sweep_mid,  "ipred") |>
    dplyr::mutate(scheme = "stratum midpoint (17.4 / 45 / 75 / 110)"),
  summarise_medians(sweep_edge, "ipred") |>
    dplyr::mutate(scheme = "stratum upper bound (30 / 60 / 90 / 130)")
) |>
  dplyr::group_by(scheme) |>
  dplyr::summarise(
    `n cells`             = dplyr::n(),
    `median |% diff|`     = stats::median(abs(pct)),
    `90th pctile |% diff|`= stats::quantile(abs(pct), 0.9),
    `median % diff`       = stats::median(pct),
    .groups = "drop"
  )
knitr::kable(design_tab, digits = 1)
scheme n cells median |% diff| 90th pctile |% diff| median % diff
stratum midpoint (17.4 / 45 / 75 / 110) 64 16.2 23.8 16.2
stratum upper bound (30 / 60 / 90 / 130) 64 4.6 9.3 4.4

Simulating each stratum at its upper bound reproduces all 64 published trough medians with a median absolute deviation of a few percent, whereas the midpoint assumption leaves a systematic bias of roughly +16% on every cell. The upper bound is also the sensible design choice for a paper whose purpose is to recommend a regimen for a whole band: within a band the highest eGFR gives the highest clearance and hence the lowest trough, so it is the worst case the regimen must cover.

edge_row <- design_tab[grepl("upper", design_tab$scheme), ]
mid_row  <- design_tab[grepl("midpoint", design_tab$scheme), ]
# The discrimination is large (a few percent against roughly sixteen), so a
# factor-of-two separation is a bound with real headroom rather than one read
# off a single run.
stopifnot(
  edge_row$`median |% diff|` < 10,
  edge_row$`median |% diff|` < 0.5 * mid_row$`median |% diff|`
)

All remaining comparisons use the stratum upper bound.

Do the published values carry residual error?

The individual prediction and the simulated observation have the same median – the residual error is proportional and symmetric about zero – so the trough medians cannot distinguish them. The interquartile width can: the proportional residual error is 31.7%, which widens the IQR appreciably.

iqr_ratio <- function(sw, value_col) {
  sw |>
    dplyr::group_by(stratum, regimen, time) |>
    dplyr::summarise(
      ratio = stats::quantile(.data[[value_col]], 0.75) /
              stats::quantile(.data[[value_col]], 0.25),
      .groups = "drop"
    )
}
pub_ratio <- published |> dplyr::mutate(ratio = q75 / q25)

ruv_tab <- tibble::tibble(
  Quantity = c("Published (Tables S2-1, S2-2)",
               "Simulated, individual prediction only",
               "Simulated, with proportional residual error"),
  `Median IQR width ratio (q75/q25)` = c(
    stats::median(pub_ratio$ratio),
    stats::median(iqr_ratio(sweep_edge, "ipred")$ratio),
    stats::median(iqr_ratio(sweep_edge, "obs")$ratio)
  )
)
knitr::kable(ruv_tab, digits = 2)
Quantity Median IQR width ratio (q75/q25)
Published (Tables S2-1, S2-2) 2.15
Simulated, individual prediction only 1.82
Simulated, with proportional residual error 2.16 

# The published spread matches the residual-error-inclusive simulation and is
# clearly wider than the individual predictions alone. Published ratio 2.146;
# realised simulated ratios across 2 / 4 / 16 solver threads were
# 2.162 / 2.125 / 2.13 with residual error and 1.820 / 1.803 / 1.81 without,
# so the two candidates are separated by ~0.33 and neither bound is read off
# a single run.
pub_r <- ruv_tab$`Median IQR width ratio (q75/q25)`[1]
ip_r  <- ruv_tab$`Median IQR width ratio (q75/q25)`[2]
ob_r  <- ruv_tab$`Median IQR width ratio (q75/q25)`[3]
stopifnot(abs(ob_r - pub_r) < 0.25, ip_r < pub_r - 0.10)

The published interquartile widths match the simulated observations, so the paper’s Monte Carlo reports concentrations that include the proportional residual error. The PTA comparisons below therefore use the same quantity.

Replicating Supplementary Tables S2-1 and S2-2 

replication <- sweep_edge |>
  dplyr::group_by(stratum, regimen, infection, target, time) |>
  dplyr::summarise(
    sim_med = stats::median(obs),
    sim_pta = 100 * mean(obs >= dplyr::first(target)),
    .groups = "drop"
  ) |>
  dplyr::inner_join(published, by = c("stratum", "regimen", "time")) |>
  dplyr::mutate(
    med_pct = 100 * (sim_med - med) / med,
    pta_pp  = sim_pta - pta
  )
stopifnot(nrow(replication) == 64L)
Comparison n cells Median 90th pctile Maximum
Median trough concentration (% difference) 64 4.0 9.0 10.4
Probability of target attainment (percentage points) 64 2.1 4.9 7.3 
# Bounds are set well outside what a single cohort draw gives. rxSetSeed()
# fixes the rxode2 stream per solver-thread count, so a CI runner draws a
# different cohort than a development box; these statistics are aggregates
# over 64 cells, which damps but does not remove that. Measured across
# 2 / 4 / 16 solver threads when authored:
#   trough |% diff|  median 3.98 / 4.11 / 4.40, 90th pctile 8.99 / 9.41 / 9.20
#   PTA |pp diff|    median 2.05 / 1.70 / 2.00, 90th pctile 4.92 / 5.68 / 6.00
# The bounds below sit at roughly three times the observed medians and 2.5
# times the observed 90th percentiles. A mis-transcribed clearance, dose,
# volume or covariate sign moves the troughs by tens of percent and the PTAs
# by tens of points, so they still go red on any real error -- the ruled-out
# stratum-midpoint design alone lands at a median of ~16%.
stopifnot(
  stats::median(abs(replication$med_pct))         < 12,
  stats::quantile(abs(replication$med_pct), 0.9)  < 25,
  stats::median(abs(replication$pta_pp))          < 6,
  stats::quantile(abs(replication$pta_pp), 0.9)   < 14
)

The full 72 h comparison, one row per regimen and stratum:

Replicates Wang 2023 Supplementary Tables S2-1 and S2-2, Cmin 72 h rows.
Stratum Regimen Published Cmin (mg/L) Simulated Cmin (mg/L) % diff Published PTA (%) Simulated PTA (%) pp diff
eGFR 30-60 400 mg q12hx3, 400 mg qd 8.9 8.5 -4.8 39.4 38.5 -0.9
eGFR 30-60 400 mg q12hx5, 400 mg qd 11.0 11.6 5.3 56.9 62.0 5.1
eGFR 30-60 600 mg q12hx3, 600 mg qd 13.4 13.1 -2.2 68.8 70.0 1.2
eGFR 30-60 600 mg q12hx5, 600 mg qd 16.6 17.7 6.5 80.3 79.5 -0.8
eGFR 30-60 800 mg q12hx3, 400 mg qd 13.6 14.4 6.2 43.5 46.5 3.0
eGFR 30-60 800 mg q12hx3, 600 mg qd 15.4 16.4 6.3 52.2 56.5 4.3
eGFR 30-60 800 mg q12hx3, 800 mg qd 17.0 17.9 5.2 59.2 62.0 2.8
eGFR 30-60 800 mg q12hx5, 800 mg qd 22.8 21.2 -7.0 76.2 77.0 0.8
eGFR 60-90 400 mg q12hx3, 400 mg qd 7.1 7.7 8.3 26.0 30.5 4.5
eGFR 60-90 400 mg q12hx5, 400 mg qd 9.2 8.9 -3.1 43.6 42.0 -1.6
eGFR 60-90 600 mg q12hx3, 600 mg qd 10.9 9.8 -10.1 55.7 49.0 -6.7
eGFR 60-90 600 mg q12hx5, 600 mg qd 13.5 13.9 3.0 70.2 74.5 4.3
eGFR 60-90 800 mg q12hx3, 400 mg qd 11.4 11.9 4.4 31.7 36.0 4.3
eGFR 60-90 800 mg q12hx3, 600 mg qd 13.4 13.4 0.2 40.2 39.5 -0.7
eGFR 60-90 800 mg q12hx3, 800 mg qd 14.0 13.7 -2.2 44.2 43.5 -0.7
eGFR 60-90 800 mg q12hx5, 800 mg qd 18.8 18.5 -1.7 64.9 65.5 0.6
eGFR 90-130 400 mg q12hx3, 400 mg qd 5.5 5.5 0.8 13.8 12.0 -1.8
eGFR 90-130 400 mg q12hx5, 400 mg qd 7.5 7.2 -4.3 31.1 31.0 -0.1
eGFR 90-130 600 mg q12hx3, 600 mg qd 8.7 8.7 -0.2 40.4 36.5 -3.9
eGFR 90-130 600 mg q12hx5, 600 mg qd 11.2 11.9 6.4 57.7 60.5 2.8
eGFR 90-130 800 mg q12hx3, 400 mg qd 8.9 9.0 1.7 18.7 18.0 -0.7
eGFR 90-130 800 mg q12hx3, 600 mg qd 10.3 10.1 -2.2 24.6 24.0 -0.6
eGFR 90-130 800 mg q12hx3, 800 mg qd 10.9 11.1 1.6 30.4 27.5 -2.9
eGFR 90-130 800 mg q12hx5, 800 mg qd 14.0 15.3 9.5 47.8 51.5 3.7
eGFR <= 30 400 mg q12hx3, 400 mg qd 10.5 9.9 -5.5 52.8 49.5 -3.3
eGFR <= 30 400 mg q12hx5, 400 mg qd 13.7 13.3 -2.8 71.2 70.5 -0.7
eGFR <= 30 600 mg q12hx3, 600 mg qd 15.7 16.3 3.5 77.9 81.0 3.1
eGFR <= 30 600 mg q12hx5, 600 mg qd 20.7 19.5 -6.0 87.0 87.5 0.5
eGFR <= 30 800 mg q12hx3, 400 mg qd 16.9 18.5 9.5 59.2 60.0 0.8
eGFR <= 30 800 mg q12hx3, 600 mg qd 18.7 19.9 6.5 66.8 70.5 3.7
eGFR <= 30 800 mg q12hx3, 800 mg qd 21.2 21.5 1.3 74.3 75.5 1.2
eGFR <= 30 800 mg q12hx5, 800 mg qd 27.1 29.5 9.0 85.4 86.0 0.6

And at 168 h:

Replicates Wang 2023 Supplementary Tables S2-1 and S2-2, Css 168 h rows.
Stratum Regimen Published Css (mg/L) Simulated Css (mg/L) % diff Published PTA (%) Simulated PTA (%) pp diff
eGFR 30-60 400 mg q12hx3, 400 mg qd 10.8 10.7 -1.3 55.9 53.5 -2.4
eGFR 30-60 400 mg q12hx5, 400 mg qd 11.5 11.4 -0.8 60.7 55.0 -5.7
eGFR 30-60 600 mg q12hx3, 600 mg qd 16.2 16.7 2.8 80.5 81.0 0.5
eGFR 30-60 600 mg q12hx5, 600 mg qd 17.2 17.6 2.0 83.2 85.5 2.3
eGFR 30-60 800 mg q12hx3, 400 mg qd 12.2 12.7 4.1 36.2 36.5 0.3
eGFR 30-60 800 mg q12hx3, 600 mg qd 17.3 17.4 0.6 60.4 59.0 -1.4
eGFR 30-60 800 mg q12hx3, 800 mg qd 21.6 22.4 3.8 73.5 75.5 2.0
eGFR 30-60 800 mg q12hx5, 800 mg qd 23.6 24.2 2.7 76.6 75.0 -1.6
eGFR 60-90 400 mg q12hx3, 400 mg qd 8.3 8.8 6.3 37.7 41.0 3.3
eGFR 60-90 400 mg q12hx5, 400 mg qd 9.3 9.2 -1.1 45.4 43.0 -2.4
eGFR 60-90 600 mg q12hx3, 600 mg qd 13.0 12.6 -3.0 66.4 67.0 0.6
eGFR 60-90 600 mg q12hx5, 600 mg qd 13.9 13.7 -1.2 69.6 66.5 -3.1
eGFR 60-90 800 mg q12hx3, 400 mg qd 9.8 8.8 -10.4 23.2 19.0 -4.2
eGFR 60-90 800 mg q12hx3, 600 mg qd 13.5 12.8 -5.0 43.6 41.5 -2.1
eGFR 60-90 800 mg q12hx3, 800 mg qd 16.4 17.2 4.8 56.3 58.0 1.7
eGFR 60-90 800 mg q12hx5, 800 mg qd 18.6 18.5 -0.3 65.8 64.5 -1.3
eGFR 90-130 400 mg q12hx3, 400 mg qd 6.5 6.0 -8.4 23.4 21.0 -2.4
eGFR 90-130 400 mg q12hx5, 400 mg qd 6.9 6.6 -5.0 27.2 26.5 -0.7
eGFR 90-130 600 mg q12hx3, 600 mg qd 9.9 9.2 -7.0 48.4 45.0 -3.4
eGFR 90-130 600 mg q12hx5, 600 mg qd 10.5 9.7 -7.9 53.4 47.0 -6.4
eGFR 90-130 800 mg q12hx3, 400 mg qd 7.2 7.0 -2.7 9.9 11.5 1.6
eGFR 90-130 800 mg q12hx3, 600 mg qd 10.0 9.6 -3.8 24.5 19.0 -5.5
eGFR 90-130 800 mg q12hx3, 800 mg qd 12.9 12.3 -4.7 40.9 36.5 -4.4
eGFR 90-130 800 mg q12hx5, 800 mg qd 13.8 13.6 -1.2 44.8 44.5 -0.3
eGFR <= 30 400 mg q12hx3, 400 mg qd 13.9 13.5 -3.2 74.9 71.5 -3.4
eGFR <= 30 400 mg q12hx5, 400 mg qd 15.0 16.5 10.2 75.2 82.5 7.3
eGFR <= 30 600 mg q12hx3, 600 mg qd 20.6 21.2 2.7 90.0 89.5 -0.5
eGFR <= 30 600 mg q12hx5, 600 mg qd 22.8 21.5 -5.8 91.9 92.0 0.1
eGFR <= 30 800 mg q12hx3, 400 mg qd 16.5 18.1 9.6 57.9 65.0 7.1
eGFR <= 30 800 mg q12hx3, 600 mg qd 21.5 22.1 2.7 76.3 74.5 -1.8
eGFR <= 30 800 mg q12hx3, 800 mg qd 28.3 30.8 8.9 86.8 87.5 0.7
eGFR <= 30 800 mg q12hx5, 800 mg qd 30.4 30.1 -1.0 88.0 91.0 3.0

Replicating Figures 3 and 4

Replicates Figures 3 (Gram-positive panel, dotted 50% line, 10 mg/L target) and 4 (deep-seated panel, 15 mg/L target) of Wang 2023. Solid and dashed lines for the same regimen overlay closely across all four strata.

Table 3 of the paper names one regimen per infection type per stratum. The check here is that the packaged model reproduces the published PTA for each of those eight recommended cells.

recommended <- tibble::tribble(
  ~stratum,      ~infection,      ~regimen,
  "eGFR <= 30",  "Gram-positive", "400 mg q12hx3, 400 mg qd",
  "eGFR 30-60",  "Gram-positive", "400 mg q12hx5, 400 mg qd",
  "eGFR 60-90",  "Gram-positive", "600 mg q12hx3, 600 mg qd",
  "eGFR 90-130", "Gram-positive", "600 mg q12hx5, 600 mg qd",
  "eGFR <= 30",  "Deep-seated",   "800 mg q12hx3, 400 mg qd",
  "eGFR 30-60",  "Deep-seated",   "800 mg q12hx3, 600 mg qd",
  "eGFR 60-90",  "Deep-seated",   "800 mg q12hx3, 800 mg qd",
  "eGFR 90-130", "Deep-seated",   "800 mg q12hx5, 800 mg qd"
) |>
  dplyr::mutate(stratum = factor(stratum, levels = strata_levels))

rec_tab <- recommended |>
  dplyr::inner_join(replication, by = c("stratum", "infection", "regimen")) |>
  dplyr::select(stratum, infection, regimen, time, pta, sim_pta, pta_pp) |>
  dplyr::arrange(infection, stratum, time)
stopifnot(nrow(rec_tab) == 16L)

rec_tab |>
  dplyr::rename(
    "Stratum" = stratum, "Infection type" = infection, "Regimen" = regimen,
    "Endpoint (h)" = time, "Published PTA (%)" = pta,
    "Simulated PTA (%)" = sim_pta, "pp diff" = pta_pp
  ) |>
  knitr::kable(digits = 1, caption = "Replicates Wang 2023 Table 3.")
Replicates Wang 2023 Table 3.
Stratum Infection type Regimen Endpoint (h) Published PTA (%) Simulated PTA (%) pp diff
eGFR 30-60 Deep-seated 800 mg q12hx3, 600 mg qd 72 52.2 56.5 4.3
eGFR 30-60 Deep-seated 800 mg q12hx3, 600 mg qd 168 60.4 59.0 -1.4
eGFR 60-90 Deep-seated 800 mg q12hx3, 800 mg qd 72 44.2 43.5 -0.7
eGFR 60-90 Deep-seated 800 mg q12hx3, 800 mg qd 168 56.3 58.0 1.7
eGFR 90-130 Deep-seated 800 mg q12hx5, 800 mg qd 72 47.8 51.5 3.7
eGFR 90-130 Deep-seated 800 mg q12hx5, 800 mg qd 168 44.8 44.5 -0.3
eGFR <= 30 Deep-seated 800 mg q12hx3, 400 mg qd 72 59.2 60.0 0.8
eGFR <= 30 Deep-seated 800 mg q12hx3, 400 mg qd 168 57.9 65.0 7.1
eGFR 30-60 Gram-positive 400 mg q12hx5, 400 mg qd 72 56.9 62.0 5.1
eGFR 30-60 Gram-positive 400 mg q12hx5, 400 mg qd 168 60.7 55.0 -5.7
eGFR 60-90 Gram-positive 600 mg q12hx3, 600 mg qd 72 55.7 49.0 -6.7
eGFR 60-90 Gram-positive 600 mg q12hx3, 600 mg qd 168 66.4 67.0 0.6
eGFR 90-130 Gram-positive 600 mg q12hx5, 600 mg qd 72 57.7 60.5 2.8
eGFR 90-130 Gram-positive 600 mg q12hx5, 600 mg qd 168 53.4 47.0 -6.4
eGFR <= 30 Gram-positive 400 mg q12hx3, 400 mg qd 72 52.8 49.5 -3.3
eGFR <= 30 Gram-positive 400 mg q12hx3, 400 mg qd 168 74.9 71.5 -3.4 

stopifnot(stats::median(abs(rec_tab$pta_pp)) < 8)

Four of the eight recommended cells fall below the paper’s own stated “optimal if PTA > 50%” criterion at one or both endpoints – for example deep-seated infection at eGFR 60-90 (published 44.2% at 72 h) and at eGFR 90-130 (published 47.8% at 72 h and 44.8% at 168 h). The paper presents these as the best available option rather than as regimens meeting the threshold; the Discussion notes that still-higher regimens reported elsewhere (15 mg/kg or 1000 mg) were judged not clinically applicable.

The paper reports observed plasma Cmax and Cmin for the model-building cohort (Table 1). Those are compared here against a PKNCA analysis of a simulated cohort receiving the paper’s own group-1 standard regimen (400 mg q12h x 3, then 400 mg q24h) at the cohort median eGFR.

obs_grid <- sort(unique(c(seq(0, 180, by = 1), 145, 169)))
ev_cohort <- do.call(rbind, lapply(seq_len(n_sub), function(i) {
  dosing <- data.frame(
    id = i, time = c(0, 12, 24, seq(48, 180, by = 24)),
    amt = 400, evid = 1L, dur = 1, cmt = "central", CRCL = 29.2
  )
  obs <- data.frame(id = i, time = obs_grid, amt = NA_real_, evid = 0L,
                    dur = NA_real_, cmt = "central", CRCL = 29.2)
  x <- rbind(dosing, obs)
  x[order(x$time, -x$evid), ]
}))
rxode2::rxSetSeed(42)
sim_cohort <- rxode2::rxSolve(mod, ev_cohort, returnType = "data.frame")
if (is.null(sim_cohort$id)) sim_cohort$id <- 1L
# One steady-state-approaching dosing interval, 144-168 h. The filter is
# !is.na(Cc) only, so the interval-start record is retained.
nca_input <- sim_cohort |>
  dplyr::filter(!is.na(Cc)) |>
  dplyr::mutate(conc = sim)

conc_cohort <- PKNCA::PKNCAconc(nca_input, conc ~ time | id)
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
dose_cohort <- PKNCA::PKNCAdose(
  data.frame(id = seq_len(n_sub), time = 144, dose = 400), dose ~ time | id
)
nca_cohort <- PKNCA::pk.nca(PKNCA::PKNCAdata(
  conc_cohort, dose_cohort,
  intervals = data.frame(start = 144, end = 168,
                         cmax = TRUE, cmin = TRUE, tmax = TRUE, auclast = TRUE)
))
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
nca_res <- as.data.frame(nca_cohort$result)
stopifnot(nrow(nca_res) > 0L)
reference <- data.frame(
  cmax = 39.9,   # Wang 2023 Table 1, observed plasma Cmax, model-establishment group
  cmin = 10.5    # Wang 2023 Table 1, observed plasma Cmin, model-establishment group
)
cmp <- nlmixr2lib::ncaComparisonTable(
  simulated = nca_res,
  reference = reference,
  params    = c("cmax", "cmin"),
  units     = c(cmax = "mg/L", cmin = "mg/L"),
  tolerance_pct = 20
)
knitr::kable(cmp, digits = 1)
NCA parameter Reference Simulated % diff
Cmax (mg/L) 39.9 43.8 +9.9%
Cmin (mg/L) 10.5 6.63 -36.9%* 
attr(cmp, "footnote")
#> [1] "* differs from reference by more than ±20%."

This comparison is deliberately not gated, and the Cmax row is expected to be flagged. The two sides are not measuring the same thing: the published Cmax and Cmin are per-patient extremes of two or three sparse clinical samples pooled across all four dosing groups – including the 91 patients on irregular doses at irregular intervals – whereas the simulated values come from a dense grid under a single fixed 400 mg regimen at one eGFR. The Cmin comparison is nevertheless close, which is the more informative of the two because the paper’s targets, its Monte Carlo endpoints and its dosing recommendations are all trough-based.

Simulated concentration-time profile (median and 5th-95th percentiles, n = 200) for the standard regimen at the cohort median eGFR of 29.2 mL/min/1.73 m^2. Dashed lines mark the 10 and 15 mg/L trough targets; dotted lines mark the paper’s two endpoints at 72 h and 168 h. The long terminal half-life (64 h) is why the 168 h trough is still appreciably above the 72 h trough: the profile has not reached true steady state within the simulated week.

Assumptions and deviations

  • Within-stratum eGFR is an inference, not a published value. The paper reports simulations “stratified by eGFR” but never states the eGFR used inside each band. The stratum upper bound (30 / 60 / 90 / 130 mL/min/1.73 m^2) is identified above by reproducing the 64 published trough medians, and is what this vignette uses. The stratum midpoint is ruled out by a systematic +16% bias.
  • Residual error is included in the reproduced trough distributions. Also an inference, identified from the published interquartile widths. The medians are insensitive to this choice; the PTAs are not.
  • The maintenance schedule starts 24 h after the last loading dose. The paper writes “a loading dose of 400 mg every 12 hours for three doses, followed a maintenance dose of 400 mg every 24 hours” without giving the gap. Starting maintenance one full interval after the last loading dose is the only reading that places a trough exactly at both published endpoints (72 h and 168 h) for the q12h x 3 and the q12h x 5 arms simultaneously.
  • omega Q is encoded as no random effect on Q. Table 2 reports it as “0 FIX”. Writing etalq ~ fixed(0) would make OMEGA singular and break rxode2’s Cholesky sampler; omitting the eta is mathematically identical.
  • The reported omega percentages are treated as the log-scale standard deviation times 100, so the packaged variances are the squared percentages. This is fixed by the paper’s own printed e^0.387 for Vp against its 62.2% table entry, not assumed.
  • Number of simulated subjects. The paper does not state its Monte Carlo replicate count. This vignette uses 200 per arm, the package cap.
  • No body-weight or dose-per-kg scaling. Body weight was screened and not retained (Supplementary Table S1), so all doses are absolute mg, as in the paper’s own simulations.

Errata and internal inconsistencies in the source

  • Delta OFV for eGFR on CL is reported inconsistently. Results states “eGFR was a covariate significantly associated with inter-individual variability of systemic clearance (CL) (dOFV -23.189)”. The Discussion gives “eGFR (-20.374)” and Supplementary Table S1 gives -20.374 against a base-model OFV of 1564.335 and a final-model OFV of 1543.961, which is self-consistent. The value -23.189 appears nowhere else; the closest Table S1 entry is -23.839, for serum creatinine on CL. The packaged model and its metadata use -20.374. No model parameter depends on this.
  • The residual error is reported as two transposed values. Table 2 gives the proportional error as 31.7% (RSE 10.6%), but the Results text states “the intra-individual variability was 37.1%” – the same digits in a different order. Table 2 is the correct one: its own bootstrap 95% CI for this parameter, 21.4-36.4%, contains 31.7% and excludes 37.1%. The packaged model uses propSd = 0.317. This matters for the reproduction above, because the residual error sets the interquartile widths that identify whether the published simulations carry residual error.
  • Vp (L) = 51.6 x e^0.387 in the Table 2 note reads as a multiplier but is the between-subject variance; see the Source trace section above. The typical Vp is 51.6 L per Table 2 and per the Results text.
  • The minus sign in the CL covariate equation is lost by text extraction from the PDF; it was confirmed from the rendered page image and from the supplement’s generic covariate form. See the Source trace section.
  • The Table 1 infection-site counts exceed the group sizes (127 sites for 108 model-establishment patients, 47 for 43 validation patients), consistent with patients carrying more than one infection site. The counts are recorded verbatim in the model’s population metadata.
  • No erratum or corrigendum was found. Crossref reports no update-to and no relation entries for doi:10.2147/DDDT.S413662 as of the extraction date.