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Imipenem (Feng 2026)

Source: vignettes/articles/Feng_2026_imipenem_pbpk.Rmd
Feng_2026_imipenem_pbpk.Rmd

Model and source

  • Citation: Feng C, Xiao P, Qu Y, Fan K, Wang Y, Zhang X, Wang X, Pan J, Deng Y, Yu Y. Physiologically based pharmacokinetic modeling and dose adjustment of imipenem in pediatric patients with renal impairment. Front Cell Infect Microbiol. 2026;16:1798911. doi:10.3389/fcimb.2026.1798911. PMCID PMC13194417. Clearance, steady-state volume of distribution, half-life, GFR and unbound fraction for every simulated population are Supplementary Table S3; the clinical studies that supplied the observed data and the per-study demographics are Supplementary Tables S1 (adults) and S2 (children). Predicted and observed AUC0-t and Cmax are Table 2 (adults) and Table 3 (children). Pediatric AUC0-24h by WHO age band and renal-function stratum, the geometric mean ratios and the proposed doses are Table 4. The WHO age bands (preschool 3-6, school-age 6-12, adolescent 12-18 years) and the FDA renal-function classification (GFR >= 90, 60-89, 30-59, 15-29 mL/min/1.73 m^2) are Methods. The PK/PD target 70%fT>MIC, the >= 80% PTA acceptance criterion and the infusion-duration comparison are Methods ‘Pharmacodynamic evaluation of imipenem’; the resulting PTA curves are Figure 6.
  • Article: https://doi.org/10.3389/fcimb.2026.1798911
  • Supplement: https://www.frontiersin.org/articles/10.3389/fcimb.2026.1798911/full#supplementary-material

PBPK-derived reduced one-compartment intravenous model for imipenem across healthy adults, adults with renal impairment (RI), and children aged 3-18 years with normal renal function or mild / moderate / severe RI. The source paper built a whole-body PBPK model in GastroPlus 9.9, using the software’s age-related physiology module to generate organ weights, blood flows, cardiac output and in vivo renal clearance; that whole-body structure is a GastroPlus platform model whose ODEs, organ volumes, blood flows and tissue-to-plasma partition coefficients are NOT written out in the publication and are therefore not reproduced here. What IS fully reported, and is what this file encodes, is the reduced disposition model the authors carried out of the PBPK and into their dose-adjustment and Monte Carlo target-attainment analysis: Supplementary Table S3 tabulates total clearance, steady-state volume of distribution, half-life and unbound fraction for every simulated population, and those triples satisfy t(1/2) = ln2 * Vss / CL to within 0.5% on every row, i.e. the paper’s own summary of its PBPK is mono-exponential. Volume is weight-normalized and shared by every stratum (Vss / body weight is 0.155-0.173 L/kg across all Table S3 rows with a published weight, spanning 58.75-86.6 kg adults and, independently, an 8-year-old child). Clearance is stratum-specific: adult clearance is absolute and body-weight-independent (10.7-11.3 L/h over a 58.75-86.6 kg range, because it is driven by glomerular filtration), while pediatric clearance is weight-normalized because pediatric dosing is per kg. Intravenous infusion dosing; linear elimination; no absorption model. The PK/PD index is the percentage of the dosing interval during which the free concentration exceeds the MIC (%fT>MIC) with 70%fT>MIC as the target and a probability of target attainment of at least 80% as the acceptance criterion; %fT>MIC is computed from the simulated profile using the unbound fraction carried in the model rather than integrated as a model state, following the Yang_2024_meropenem_pbpk precedent. The paper ran a 200-subject population simulator and reports 90% confidence intervals graphically, but reports no interindividual variance magnitudes and no residual error model, so all etas are omitted and both residual error terms are encoded as fixed(0).

Feng 2026 built a whole-body physiologically based pharmacokinetic (PBPK) model of imipenem in GastroPlus 9.9, verified it against eight published clinical studies in healthy adults, adults with renal impairment (RI) and children, and then extrapolated it to children aged 3-18 years with RI in order to propose dose adjustments. The GastroPlus whole-body structure – its ODEs, organ volumes, blood flows and tissue-to-plasma partition coefficients – is not written out anywhere in the paper, so it is not reproduced here.

What the paper does publish, in Supplementary Table S3, is a complete reduced disposition card: total clearance, steady-state volume of distribution, half-life, glomerular filtration rate and unbound fraction for every population it simulated. That card is what this model file encodes, following the Yang_2024_meropenem_pbpk precedent for a platform-PBPK paper that carries a reduced model into its own dosing analysis.

Population

Eight clinical studies were pooled from the literature and digitised with GetData Graph Digitizer 2.26. Six are adult (Supplementary Table S1): Wang 2021 (China, n = 12, 34.2 years, 60.4 kg), Jaruratanasirikul 2005 (Thailand, n = 8, 28.3 years, 58.8 kg), Nilsson 1991 (Sweden, n = 8, 33 years, 74 kg), Norrby 1983 (Sweden, n = 8, 25 years, 75 kg), Drusano 1984 (USA, n = 6, 19-34 years) and Gibson 1985 (USA, n = 6 each in mild, moderate and severe RI, 47.7-60.8 years, 71.3-86.6 kg). Two are paediatric (Supplementary Table S2): Claesson 1992 (Sweden, children 3-12 years with peritonitis, n = 8 at 15 mg/kg and n = 2 at 25 mg/kg) and Bradley 2023 (USA, children 2-6 years with gram-negative infections, n = 6, 15.4 kg).

Every study administered imipenem together with cilastatin or another enzyme inhibitor, so the renal clearance the model carries is the cilastatin-inhibited value (Table 1 footnote). Renal function is classified per FDA guidance on glomerular filtration rate: normal >= 90, mild 60-89, moderate 30-59 and severe 15-29 mL/min/1.73 m^2. The paediatric age bands are the WHO ones the paper adopts: preschool 3-6, school-age 6-12 and adolescent 12-18 years, represented in the simulations by 3-, 8- and 16-year-old children.

There are no paediatric renal-impairment PK data anywhere in the source. The paper says so explicitly in its Limitations, and the paediatric RI arm is a pure extrapolation of the software’s built-in renal physiology.

#> List of 13
#>  $ species       : chr "human"
#>  $ n_subjects    : num 76
#>  $ n_studies     : num 8
#>  $ age_range     : chr "Adults 18-68 years (study means 25-60.8 years, Supplementary Table S1); children 2-12 years (Supplementary Tabl"| __truncated__
#>  $ weight_range  : chr "Adult study means 58.75-86.6 kg (individual range 51-116 kg, Supplementary Table S1); Bradley 2023 pediatric co"| __truncated__
#>  $ sex_female_pct: num NA
#>  $ race_ethnicity: chr NA
#>  $ disease_state : chr "Healthy adult volunteers; adults with mild, moderate or severe renal insufficiency (Gibson 1985); children with"| __truncated__
#>  $ dose_range    : chr "Adults 0.25-1.0 g as an intravenous bolus or a 0.15, 0.5 or 2.0 h infusion, single dose and q6h; children 15 an"| __truncated__
#>  $ regions       : chr "China, Thailand, Sweden, United States"
#>  $ renal_function: chr "Normal (GFR >= 90), mild (60-89), moderate (30-59) and severe (15-29) renal impairment per the FDA classificati"| __truncated__
#>  $ co_medication : chr "All included clinical studies administered imipenem with cilastatin or with another enzyme inhibitor, and all r"| __truncated__
#>  $ notes         : chr "Eight clinical studies pooled from the literature and digitized with GetData Graph Digitizer 2.26: six adult (W"| __truncated__

Source trace

Per-parameter origins are recorded as in-file comments beside each ini() entry in inst/modeldb/specificDrugs/Feng_2026_imipenem_pbpk.R; they are collected here for review.

Equation / parameter Value Source location
lvcPerKg 0.1636 L/kg Supplementary Table S3 Vss divided by the Supplementary Table S1 weights (seven rows, 0.1555-0.1730)
lcl_adult 11.176 L/h Supplementary Table S3, Wang 2021 q6h / Drusano 1984 rows; Discussion quotes “approximately 11.126 L/h”
e_renalimp_mild_cl_adult 0.95580 Supplementary Table S3, Gibson mild CL 10.682 / 11.176
e_renalimp_mod_cl_adult 0.57051 Supplementary Table S3, Gibson moderate CL 6.376 / 11.176
e_renalimp_sev_cl_adult 0.31192 Supplementary Table S3, Gibson severe CL 3.486 / 11.176
lclPerKg_preschool 0.47835 L/h/kg Table 4 preschool normal, 15 / 31.358
lclPerKg_schoolage 0.35032 L/h/kg Table 4 school-age normal, 15 / 42.818
lclPerKg_adolescent 0.17280 L/h/kg Table 4 adolescent normal, 15 / 86.804
e_renalimp_*_cl_preschool 0.96246 / 0.80554 / 0.49650 Table 4 preschool, 31.358 / (32.581, 38.928, 63.158)
e_renalimp_*_cl_schoolage 0.95723 / 0.79639 / 0.46826 Table 4 school-age, 42.818 / (44.731, 53.765, 91.441)
e_renalimp_*_cl_adolescent 0.94831 / 0.74580 / 0.42434 Table 4 adolescent, 86.804 / (91.535, 116.39, 204.56)
fup_adult 0.80000 Table 1 Fup 80%; Supplementary Table S3 healthy adult rows
fup_adult_mild / _mod / _sev 0.80588 / 0.82723 / 0.83352 Supplementary Table S3, Gibson rows
fup_ped 0.81217 Supplementary Table S3, Claesson 1992 row (Bradley 2023 row gives 0.81182)
addSd, propSd fixed(0) Not reported anywhere in the paper or its supplement
WHO age bands 3 / 6 / 12 / 18 years n/a Methods, “Prediction of imipenem exposures in pediatric patients with RI”
FDA renal classification n/a Methods, “Model for adult patients with RI”
d/dt(central) <- -kel * central n/a Reduction of the GastroPlus whole-body model; justified below
70%fT>MIC target, PTA >= 80% n/a Methods, “Pharmacodynamic evaluation of imipenem”

Why a one-compartment reduction is the right shape

Supplementary Table S3 reports CL, Vss and T1/2 for every simulated population – 15 rows, of which 13 carry distinct parameter triples (the two Jaruratanasirikul 0.5 g rows are identical to each other, as are the two Claesson rows, so the table below lists each triple once). If those three numbers describe a mono-exponential disposition then T1/2 = ln2 * Vss / CL must hold exactly. It does, on every row.

The same check settles a unit error. Supplementary Table S3 heads its volume column Vss(L/kg), and the Results text repeats it (“about 3.259 L/kg in children, compared with 11.663 L/kg in adults”). That cannot be right: 11.663 L/kg in a 74 kg adult is 863 L, which with the tabulated 11.126 L/h clearance gives a 54 h half-life for a drug the same row calls 0.723 h. The identity below closes only when Vss is read as absolute litres.

s3 <- tibble::tribble(
  ~study,                 ~renal,        ~CL,     ~Vss,   ~thalf,  ~WT,
  "Wang 2021 0.25 g",     "Normal",   10.972,  10.447,   0.660,  60.40,
  "Jaruratanasirikul 0.5 g", "Normal", 10.726,  9.135,   0.590,  58.75,
  "Jaruratanasirikul 1.0 g", "Normal", 10.726,  9.135,   0.590,  58.75,
  "Nilsson 1991 1.0 g",   "Normal",   11.126,  11.663,   0.723,  74.00,
  "Norrby 1983 0.5 g",    "Normal",   11.262,  12.371,   0.761,  75.00,
  "Norrby 1983 1.0 g",    "Normal",   11.262,  12.371,   0.761,  75.00,
  "Wang 2021 q6h",        "Normal",   11.176,  11.663,   0.723,  NA_real_,
  "Drusano 1984 q6h",     "Normal",   11.176,  11.663,   0.723,  NA_real_,
  "Gibson 1985",          "Mild RI",  10.682,  14.081,   0.913,  86.60,
  "Gibson 1985",          "Moderate RI", 6.376, 12.275,   1.334,  76.50,
  "Gibson 1985",          "Severe RI",   3.486, 12.194,   2.424,  71.30,
  "Claesson 1992",        "Normal",    7.886,   3.259,   0.286,  NA_real_,
  "Bradley 2023",         "Normal",    8.489,   4.221,   0.345,  NA_real_
) |>
  mutate(
    thalf_identity = log(2) * Vss / CL,
    pct_error      = 100 * (thalf_identity - thalf) / thalf,
    VssPerKg       = Vss / WT
  )

s3 |>
  select(study, renal, CL, Vss, thalf, thalf_identity, pct_error, VssPerKg) |>
  rename(
    "Study" = study, "Renal function" = renal,
    "CL (L/h)" = CL, "Vss (L)" = Vss,
    "T1/2 published (h)" = thalf, "ln2*Vss/CL (h)" = thalf_identity,
    "Error (%)" = pct_error, "Vss/WT (L/kg)" = VssPerKg
  ) |>
  knitr::kable(
    digits = c(0, 0, 3, 3, 3, 4, 3, 4),
    caption = paste(
      "Supplementary Table S3 of Feng 2026 is internally mono-exponential.",
      "The published half-life is recovered from ln2 * Vss / CL on every row,",
      "which is only dimensionally possible with Vss in absolute litres --",
      "falsifying the printed 'L/kg' unit. Vss / body weight is then a",
      "physiological 0.155-0.173 L/kg across 58.75-86.6 kg adults."
    )
  )
Supplementary Table S3 of Feng 2026 is internally mono-exponential. The published half-life is recovered from ln2 * Vss / CL on every row, which is only dimensionally possible with Vss in absolute litres – falsifying the printed ‘L/kg’ unit. Vss / body weight is then a physiological 0.155-0.173 L/kg across 58.75-86.6 kg adults.
Study Renal function CL (L/h) Vss (L) T1/2 published (h) ln2*Vss/CL (h) Error (%) Vss/WT (L/kg)
Wang 2021 0.25 g Normal 10.972 10.447 0.660 0.6600 -0.003 0.1730
Jaruratanasirikul 0.5 g Normal 10.726 9.135 0.590 0.5903 0.056 0.1555
Jaruratanasirikul 1.0 g Normal 10.726 9.135 0.590 0.5903 0.056 0.1555
Nilsson 1991 1.0 g Normal 11.126 11.663 0.723 0.7266 0.498 0.1576
Norrby 1983 0.5 g Normal 11.262 12.371 0.761 0.7614 0.053 0.1649
Norrby 1983 1.0 g Normal 11.262 12.371 0.761 0.7614 0.053 0.1649
Wang 2021 q6h Normal 11.176 11.663 0.723 0.7234 0.049 NA
Drusano 1984 q6h Normal 11.176 11.663 0.723 0.7234 0.049 NA
Gibson 1985 Mild RI 10.682 14.081 0.913 0.9137 0.077 0.1626
Gibson 1985 Moderate RI 6.376 12.275 1.334 1.3344 0.033 0.1605
Gibson 1985 Severe RI 3.486 12.194 2.424 2.4246 0.026 0.1710
Claesson 1992 Normal 7.886 3.259 0.286 0.2865 0.158 NA
Bradley 2023 Normal 8.489 4.221 0.345 0.3447 -0.100 NA 

# Deterministic arithmetic on published numbers, so a tight bound is correct
# here; this is not a cohort-derived quantity.
stopifnot(max(abs(s3$pct_error)) < 0.6)
stopifnot(all(s3$VssPerKg > 0.15 & s3$VssPerKg < 0.18, na.rm = TRUE))

The volume the model carries, 0.1636 L/kg, is the mean of the seven Vss / WT values above that have a published weight. It is confirmed independently below by an 8-year-old child.

Virtual cohort

The packaged model has no interindividual variability and no residual error – Feng 2026 publishes neither – so it is fully deterministic and one subject per scenario is sufficient. Every arm below is far under the 200-per-arm cap.

Two arms are simulated: the ten adult regimens of Table 2 (each at its own study’s body weight from Supplementary Table S1) and the paediatric regimens of Tables 3 and 4.

# One subject per published regimen. `tend` is set to at least a dozen
# half-lives so the terminal phase is fully characterised for NCA, without
# running so far that concentrations underflow and PKNCA's log-down
# trapezoid takes the log of a round-off negative.
make_subject <- function(id, label, arm, amt, dur, WT, AGE,
                         mild = 0, mod = 0, sev = 0, tend = 24) {
  # Round before de-duplicating: the two seq() grids generate the same nominal
  # time (e.g. 0.15) by different arithmetic, so without rounding `unique()`
  # leaves near-duplicate times that differ in the last bit.
  grid <- sort(unique(round(c(
    seq(0, min(4, tend), by = 0.005),
    seq(0, tend, by = 0.05)
  ), 6)))
  dplyr::bind_rows(
    tibble::tibble(id = id, time = 0, evid = 1L, amt = amt, dur = dur,
                   cmt = "central"),
    tibble::tibble(id = id, time = grid, evid = 0L, amt = NA_real_, dur = 0,
                   cmt = "central")
  ) |>
    dplyr::mutate(
      label = label, arm = arm, WT = WT, AGE = AGE,
      RENALIMP_MILD = mild, RENALIMP_MOD = mod, RENALIMP_SEV = sev
    )
}

# ---- Arm 1: adults, Table 2 (weights from Supplementary Table S1) ----------
adult_spec <- tibble::tribble(
  ~label,                        ~amt, ~dur,  ~WT,  ~mild, ~mod, ~sev, ~tend,
  "Wang 0.25 g / 0.5 h",          250, 0.50, 60.40,     0,    0,    0,     10,
  "Jarurat. 0.5 g / 0.5 h",       500, 0.50, 58.75,     0,    0,    0,     10,
  "Nilsson 1.0 g / 0.5 h",       1000, 0.50, 74.00,     0,    0,    0,     10,
  "Jarurat. 0.5 g / 2 h",         500, 2.00, 58.75,     0,    0,    0,     12,
  "Jarurat. 1.0 g / 2 h",        1000, 2.00, 58.75,     0,    0,    0,     12,
  "Norrby 0.5 g bolus",           500, 0.00, 75.00,     0,    0,    0,     10,
  "Norrby 1.0 g bolus",          1000, 0.00, 75.00,     0,    0,    0,     10,
  "Gibson mild 0.25 g",           250, 0.15, 86.60,     1,    0,    0,     12,
  "Gibson moderate 0.25 g",       250, 0.15, 76.50,     0,    1,    0,     18,
  "Gibson severe 0.25 g",         250, 0.15, 71.30,     0,    0,    1,     30
)
# ---- Arm 2: children, Tables 3 and 4 --------------------------------------
# A mg/kg dose makes both AUC and Cmax independent of body weight in this
# model (dose and clearance both scale with WT, and so does volume), so the
# representative weights below only have to be plausible -- they cancel.
# `tend` is set to roughly 13-20 half-lives in every row. Longer is NOT better:
# the paediatric half-lives are as short as 0.24 h, so a 24 h window would run
# the amount in the central compartment down past the solver's absolute
# tolerance, and PKNCA's log-down trapezoid then takes the log of a round-off
# negative (known-vignette-failure-patterns: log-down NaNs on negative
# round-off). Thirteen half-lives already leaves < 0.02% of the dose.
ped_spec <- tibble::tribble(
  ~label,                          ~AGE, ~WT, ~mgkg, ~dur, ~mild, ~mod, ~sev, ~tend,
  "Preschool 3 y, normal",            3,  14,    15, 0.50,     0,    0,    0,     5,
  "Preschool 3 y, mild RI",           3,  14,    15, 0.50,     1,    0,    0,     5,
  "Preschool 3 y, moderate RI",       3,  14,    15, 0.50,     0,    1,    0,     6,
  "Preschool 3 y, severe RI",         3,  14,    15, 0.50,     0,    0,    1,     8,
  "School-age 8 y, normal",           8,  25,    15, 0.50,     0,    0,    0,     6,
  "School-age 8 y, mild RI",          8,  25,    15, 0.50,     1,    0,    0,     6,
  "School-age 8 y, moderate RI",      8,  25,    15, 0.50,     0,    1,    0,     8,
  "School-age 8 y, severe RI",        8,  25,    15, 0.50,     0,    0,    1,    12,
  "Adolescent 16 y, normal",         16,  55,    15, 0.50,     0,    0,    0,    12,
  "Adolescent 16 y, mild RI",        16,  55,    15, 0.50,     1,    0,    0,    12,
  "Adolescent 16 y, moderate RI",    16,  55,    15, 0.50,     0,    1,    0,    16,
  "Adolescent 16 y, severe RI",      16,  55,    15, 0.50,     0,    0,    1,    26
)
build_arm <- function(spec, arm, id_offset, dose_fn, age_fn = NULL) {
  out <- vector("list", nrow(spec))
  for (i in seq_len(nrow(spec))) {
    r <- spec[i, ]
    out[[i]] <- make_subject(
      id    = id_offset + i,
      label = r$label,
      arm   = arm,
      amt   = dose_fn(r),
      dur   = r$dur,
      WT    = r$WT,
      AGE   = if (is.null(age_fn)) 35 else r$AGE,
      mild  = r$mild, mod = r$mod, sev = r$sev,
      tend  = r$tend
    )
  }
  dplyr::bind_rows(out)
}

events <- dplyr::bind_rows(
  build_arm(adult_spec, "Adult",     0L, function(r) r$amt),
  build_arm(ped_spec,   "Paediatric", 100L, function(r) r$mgkg * r$WT, age_fn = TRUE)
)

# Disjoint ids across arms (a duplicate id silently merges two subjects).
stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))
stopifnot(length(unique(events$id)) == nrow(adult_spec) + nrow(ped_spec))

Simulation 

mod <- readModelDb("Feng_2026_imipenem_pbpk")

# No etas are declared, so `omega = NA` / `zeroRe()` would error
# (known-vignette-failure-patterns.md pattern 9) and is unnecessary: the
# model is already deterministic.
sim <- rxode2::rxSolve(
  mod, events = events,
  keep = c("label", "arm", "WT", "AGE",
           "RENALIMP_MILD", "RENALIMP_MOD", "RENALIMP_SEV")
) |>
  as.data.frame() |>
  # `keep` can return character columns as factors; downstream joins are on
  # `label` against character literals, which would error on a factor.
  dplyr::mutate(label = as.character(label), arm = as.character(arm))
#> Warning: multi-subject simulation without without 'omega'

stopifnot(nrow(sim) > 0, !anyNA(sim$Cc))
# Free concentration must be the unbound fraction of total wherever there is
# drug. The ratio is tested only where Cc > 0 -- at t = 0 on an infusion row
# both are exactly 0 and a strict ratio bound is undefined, not violated.
pos <- sim$Cc > 0
stopifnot(any(pos))
fup_ratio <- sim$Cfree[pos] / sim$Cc[pos]
# Every fup the model can resolve lies in [0.800, 0.834] (Supplementary Table
# S3), so this pins the covariate wiring, not just the sign.
stopifnot(all(fup_ratio >= 0.7999), all(fup_ratio <= 0.8340))

The individual parameters the model resolves for each stratum are worth showing directly, because they are the whole content of the reduction.

sim |>
  group_by(arm, label) |>
  summarise(CL = first(cl), Vc = first(vc), fup = first(fup), .groups = "drop") |>
  mutate(`T1/2 (h)` = log(2) * Vc / CL) |>
  rename("Arm" = arm, "Regimen" = label, "CL (L/h)" = CL, "Vc (L)" = Vc,
         "Unbound fraction" = fup) |>
  knitr::kable(digits = 4, caption = "Model-resolved disposition per simulated regimen.")
Model-resolved disposition per simulated regimen.
Arm Regimen CL (L/h) Vc (L) Unbound fraction T1/2 (h)
Adult Gibson mild 0.25 g 10.6820 14.1678 0.8059 0.9193
Adult Gibson moderate 0.25 g 6.3760 12.5154 0.8272 1.3606
Adult Gibson severe 0.25 g 3.4860 11.6647 0.8335 2.3194
Adult Jarurat. 0.5 g / 0.5 h 11.1760 9.6115 0.8000 0.5961
Adult Jarurat. 0.5 g / 2 h 11.1760 9.6115 0.8000 0.5961
Adult Jarurat. 1.0 g / 2 h 11.1760 9.6115 0.8000 0.5961
Adult Nilsson 1.0 g / 0.5 h 11.1760 12.1064 0.8000 0.7509
Adult Norrby 0.5 g bolus 11.1760 12.2700 0.8000 0.7610
Adult Norrby 1.0 g bolus 11.1760 12.2700 0.8000 0.7610
Adult Wang 0.25 g / 0.5 h 11.1760 9.8814 0.8000 0.6129
Paediatric Adolescent 16 y, mild RI 9.0127 8.9980 0.8122 0.6920
Paediatric Adolescent 16 y, moderate RI 7.0881 8.9980 0.8122 0.8799
Paediatric Adolescent 16 y, normal 9.5040 8.9980 0.8122 0.6562
Paediatric Adolescent 16 y, severe RI 4.0329 8.9980 0.8122 1.5465
Paediatric Preschool 3 y, mild RI 6.4455 2.2904 0.8122 0.2463
Paediatric Preschool 3 y, moderate RI 5.3946 2.2904 0.8122 0.2943
Paediatric Preschool 3 y, normal 6.6969 2.2904 0.8122 0.2371
Paediatric Preschool 3 y, severe RI 3.3250 2.2904 0.8122 0.4775
Paediatric School-age 8 y, mild RI 8.3834 4.0900 0.8122 0.3382
Paediatric School-age 8 y, moderate RI 6.9748 4.0900 0.8122 0.4065
Paediatric School-age 8 y, normal 8.7580 4.0900 0.8122 0.3237
Paediatric School-age 8 y, severe RI 4.1010 4.0900 0.8122 0.6913

Replicate Figure 5

Figure 5 of Feng 2026 shows the predicted plasma concentration-time profile of imipenem in a representative school-age child after 15 mg/kg, panel A as a 0.5 h infusion and panel B as a 3 h infusion.

fig5_spec <- tidyr::crossing(
  tibble::tibble(renal = c("Normal", "Mild RI", "Moderate RI", "Severe RI"),
                 mild  = c(0, 1, 0, 0), mod = c(0, 0, 1, 0), sev = c(0, 0, 0, 1)),
  tibble::tibble(infusion = c("A: 0.5 h infusion", "B: 3 h infusion"),
                 dur = c(0.5, 3.0))
)

fig5_events <- dplyr::bind_rows(lapply(seq_len(nrow(fig5_spec)), function(i) {
  r <- fig5_spec[i, ]
  make_subject(id = 500L + i, label = r$renal, arm = r$infusion,
               amt = 15 * 25, dur = r$dur, WT = 25, AGE = 8,
               mild = r$mild, mod = r$mod, sev = r$sev, tend = 6)
}))

fig5 <- rxode2::rxSolve(mod, events = fig5_events,
                        keep = c("label", "arm")) |>
  as.data.frame() |>
  dplyr::mutate(label = as.character(label), arm = as.character(arm))
#> Warning: multi-subject simulation without without 'omega'

ggplot(fig5, aes(time, Cc, colour = label)) +
  geom_line(linewidth = 0.7) +
  facet_wrap(~arm) +
  scale_y_log10() +
  labs(x = "Time (h)", y = "Imipenem plasma concentration (mg/L)",
       colour = "Renal function",
       title = "Figure 5 -- school-age child (8 years), 15 mg/kg",
       caption = "Replicates Figure 5 of Feng 2026.")
#> Warning in scale_y_log10(): log-10 transformation introduced infinite values.

PKNCA validation 

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

# Guarantee a time = 0 row per subject. Imipenem is given intravenously with
# no prior exposure, so the pre-dose concentration is 0.
sim_nca <- dplyr::bind_rows(
  sim_nca,
  sim_nca |> dplyr::distinct(id, label, arm) |> dplyr::mutate(time = 0, Cc = 0)
) |>
  dplyr::distinct(id, time, .keep_all = TRUE) |>
  dplyr::arrange(id, time)

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

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

dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | label + id, doseu = "mg")

intervals <- data.frame(
  start = 0, end = Inf,
  cmax = TRUE, tmax = TRUE, aucinf.obs = TRUE, half.life = TRUE
)

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

Comparison against the paper’s own PBPK predictions

The reduction’s job is to reproduce what the whole-body GastroPlus model predicted, so the paper’s predicted AUC and Cmax are the reference. Adult values are Table 2 and paediatric values are Tables 3 and 4. The paper reports AUC0-t (truncated at each study’s last sampling time) whereas the simulation reports AUC0-inf, so the simulated AUC should sit at or slightly above the published one.

published <- tibble::tribble(
  ~label,                          ~cmax,  ~aucinf.obs,
  "Wang 0.25 g / 0.5 h",           19.21,        22.59,
  "Jarurat. 0.5 g / 0.5 h",        43.62,        50.91,
  "Nilsson 1.0 g / 0.5 h",         71.15,        88.47,
  "Jarurat. 0.5 g / 2 h",          20.56,        46.20,
  "Jarurat. 1.0 g / 2 h",          41.12,        92.39,
  "Norrby 0.5 g bolus",           165.99,        43.86,
  "Norrby 1.0 g bolus",           331.99,        87.72,
  "Gibson mild 0.25 g",            23.03,        23.13,
  "Gibson moderate 0.25 g",        25.67,        37.69,
  "Gibson severe 0.25 g",          25.87,        66.65,
  "Preschool 3 y, normal",            NA,       31.358,
  "Preschool 3 y, mild RI",           NA,       32.581,
  "Preschool 3 y, moderate RI",       NA,       38.928,
  "Preschool 3 y, severe RI",         NA,       63.158,
  "School-age 8 y, normal",        56.42,       42.818,
  "School-age 8 y, mild RI",       57.37,       44.731,
  "School-age 8 y, moderate RI",   61.14,       53.765,
  "School-age 8 y, severe RI",     71.58,       91.441,
  "Adolescent 16 y, normal",          NA,       86.804,
  "Adolescent 16 y, mild RI",         NA,       91.535,
  "Adolescent 16 y, moderate RI",     NA,      116.390,
  "Adolescent 16 y, severe RI",       NA,      204.560
)

cmp <- nlmixr2lib::ncaComparisonTable(
  simulated     = nca_res,
  reference     = published,
  by            = "label",
  units         = c(cmax = "mg/L", aucinf.obs = "mg*h/L"),
  tolerance_pct = 20
)

knitr::kable(
  cmp,
  caption = paste(
    "Reduced model vs the whole-body GastroPlus predictions of Feng 2026.",
    "* marks a difference above 20%. Every starred cell is a Cmax, and every",
    "one of them is a regimen whose input is faster than the distribution the",
    "reduction cannot see: the two instantaneous boluses and the two shortest",
    "(0.15 h) infusions. No AUC is starred, and no Cmax on any regimen the",
    "paper actually recommends is starred. Discussed below."
  )
)
Reduced model vs the whole-body GastroPlus predictions of Feng 2026. * marks a difference above 20%. Every starred cell is a Cmax, and every one of them is a regimen whose input is faster than the distribution the reduction cannot see: the two instantaneous boluses and the two shortest (0.15 h) infusions. No AUC is starred, and no Cmax on any regimen the paper actually recommends is starred. Discussed below.
NCA parameter label Reference Simulated % diff
Cmax (mg/L) Wang 0.25 g / 0.5 h 19.2 19.3 +0.6%
Cmax (mg/L) Jarurat. 0.5 g / 0.5 h 43.6 39.4 -9.6%
Cmax (mg/L) Nilsson 1.0 g / 0.5 h 71.2 66.2 -7.0%
Cmax (mg/L) Jarurat. 0.5 g / 2 h 20.6 20.2 -1.8%
Cmax (mg/L) Jarurat. 1.0 g / 2 h 41.1 40.4 -1.8%
Cmax (mg/L) Norrby 0.5 g bolus 166 40.7 -75.5%*
Cmax (mg/L) Norrby 1.0 g bolus 332 81.5 -75.5%*
Cmax (mg/L) Gibson mild 0.25 g 23 16.7 -27.6%*
Cmax (mg/L) Gibson moderate 0.25 g 25.7 19.2 -25.1%*
Cmax (mg/L) Gibson severe 0.25 g 25.9 21 -19.0%
Cmax (mg/L) Preschool 3 y, normal — 48.2 —
Cmax (mg/L) Preschool 3 y, mild RI — 49.2 —
Cmax (mg/L) Preschool 3 y, moderate RI — 53.9 —
Cmax (mg/L) Preschool 3 y, severe RI — 65.2 —
Cmax (mg/L) School-age 8 y, normal 56.4 56.3 -0.2%
Cmax (mg/L) School-age 8 y, mild RI 57.4 57.4 -0.0%
Cmax (mg/L) School-age 8 y, moderate RI 61.1 61.7 +0.9%
Cmax (mg/L) School-age 8 y, severe RI 71.6 72.1 +0.7%
Cmax (mg/L) Adolescent 16 y, normal — 71.2 —
Cmax (mg/L) Adolescent 16 y, mild RI — 72.1 —
Cmax (mg/L) Adolescent 16 y, moderate RI — 75.8 —
Cmax (mg/L) Adolescent 16 y, severe RI — 82.1 —
AUC0-∞ (obs) (mg*h/L) Wang 0.25 g / 0.5 h 22.6 22.4 -1.0%
AUC0-∞ (obs) (mg*h/L) Jarurat. 0.5 g / 0.5 h 50.9 44.7 -12.1%
AUC0-∞ (obs) (mg*h/L) Nilsson 1.0 g / 0.5 h 88.5 89.5 +1.1%
AUC0-∞ (obs) (mg*h/L) Jarurat. 0.5 g / 2 h 46.2 44.7 -3.2%
AUC0-∞ (obs) (mg*h/L) Jarurat. 1.0 g / 2 h 92.4 89.5 -3.2%
AUC0-∞ (obs) (mg*h/L) Norrby 0.5 g bolus 43.9 44.7 +2.0%
AUC0-∞ (obs) (mg*h/L) Norrby 1.0 g bolus 87.7 89.5 +2.0%
AUC0-∞ (obs) (mg*h/L) Gibson mild 0.25 g 23.1 23.4 +1.2%
AUC0-∞ (obs) (mg*h/L) Gibson moderate 0.25 g 37.7 39.2 +4.0%
AUC0-∞ (obs) (mg*h/L) Gibson severe 0.25 g 66.6 71.7 +7.6%
AUC0-∞ (obs) (mg*h/L) Preschool 3 y, normal 31.4 31.4 -0.0%
AUC0-∞ (obs) (mg*h/L) Preschool 3 y, mild RI 32.6 32.6 -0.0%
AUC0-∞ (obs) (mg*h/L) Preschool 3 y, moderate RI 38.9 38.9 -0.0%
AUC0-∞ (obs) (mg*h/L) Preschool 3 y, severe RI 63.2 63.2 -0.0%
AUC0-∞ (obs) (mg*h/L) School-age 8 y, normal 42.8 42.8 -0.0%
AUC0-∞ (obs) (mg*h/L) School-age 8 y, mild RI 44.7 44.7 -0.0%
AUC0-∞ (obs) (mg*h/L) School-age 8 y, moderate RI 53.8 53.8 -0.0%
AUC0-∞ (obs) (mg*h/L) School-age 8 y, severe RI 91.4 91.4 -0.0%
AUC0-∞ (obs) (mg*h/L) Adolescent 16 y, normal 86.8 86.8 +0.0%
AUC0-∞ (obs) (mg*h/L) Adolescent 16 y, mild RI 91.5 91.5 +0.0%
AUC0-∞ (obs) (mg*h/L) Adolescent 16 y, moderate RI 116 116 +0.0%
AUC0-∞ (obs) (mg*h/L) Adolescent 16 y, severe RI 205 205 +0.0%

The comparison is quantified below so it can be asserted rather than eyeballed. Every quantity here is deterministic – the model has no random effects – so tight bounds are appropriate and will catch a regression.

sim_wide <- as.data.frame(nca_res) |>
  dplyr::select(label, PPTESTCD, PPORRES) |>
  tidyr::pivot_wider(names_from = PPTESTCD, values_from = PPORRES)

score <- published |>
  dplyr::left_join(sim_wide, by = "label", suffix = c("_pub", "_sim")) |>
  dplyr::mutate(
    infusion    = !grepl("bolus", label),
    auc_ratio   = aucinf.obs_sim / aucinf.obs_pub,
    cmax_ratio  = cmax_sim / cmax_pub
  )

# The join must have matched every published row (a silent zero-row lookup
# would make every assertion below vacuously true).
stopifnot(nrow(score) == nrow(published), !anyNA(score$auc_ratio))

score |>
  dplyr::select(label, aucinf.obs_pub, aucinf.obs_sim, auc_ratio,
                cmax_pub, cmax_sim, cmax_ratio) |>
  dplyr::rename(
    "Regimen" = label,
    "AUC published" = aucinf.obs_pub, "AUC simulated" = aucinf.obs_sim,
    "AUC ratio" = auc_ratio,
    "Cmax published" = cmax_pub, "Cmax simulated" = cmax_sim,
    "Cmax ratio" = cmax_ratio
  ) |>
  knitr::kable(digits = 3,
               caption = "Reduced model / published PBPK prediction, per regimen.")
Reduced model / published PBPK prediction, per regimen.
Regimen AUC published AUC simulated AUC ratio Cmax published Cmax simulated Cmax ratio
Wang 0.25 g / 0.5 h 22.590 22.369 0.990 19.21 19.324 1.006
Jarurat. 0.5 g / 0.5 h 50.910 44.739 0.879 43.62 39.449 0.904
Nilsson 1.0 g / 0.5 h 88.470 89.477 1.011 71.15 66.161 0.930
Jarurat. 0.5 g / 2 h 46.200 44.739 0.968 20.56 20.183 0.982
Jarurat. 1.0 g / 2 h 92.390 89.477 0.968 41.12 40.366 0.982
Norrby 0.5 g bolus 43.860 44.739 1.020 165.99 40.750 0.245
Norrby 1.0 g bolus 87.720 89.477 1.020 331.99 81.500 0.245
Gibson mild 0.25 g 23.130 23.404 1.012 23.03 16.684 0.724
Gibson moderate 0.25 g 37.690 39.209 1.040 25.67 19.231 0.749
Gibson severe 0.25 g 66.650 71.715 1.076 25.87 20.959 0.810
Preschool 3 y, normal 31.358 31.357 1.000 NA 48.179 NA
Preschool 3 y, mild RI 32.581 32.581 1.000 NA 49.206 NA
Preschool 3 y, moderate RI 38.928 38.927 1.000 NA 53.876 NA
Preschool 3 y, severe RI 63.158 63.157 1.000 NA 65.190 NA
School-age 8 y, normal 42.818 42.818 1.000 56.42 56.282 0.998
School-age 8 y, mild RI 44.731 44.731 1.000 57.37 57.359 1.000
School-age 8 y, moderate RI 53.765 53.765 1.000 61.14 61.692 1.009
School-age 8 y, severe RI 91.441 91.440 1.000 71.58 72.108 1.007
Adolescent 16 y, normal 86.804 86.805 1.000 NA 71.230 NA
Adolescent 16 y, mild RI 91.535 91.537 1.000 NA 72.125 NA
Adolescent 16 y, moderate RI 116.390 116.392 1.000 NA 75.785 NA
Adolescent 16 y, severe RI 204.560 204.566 1.000 NA 82.140 NA 

is_ped <- grepl("^(Preschool|School-age|Adolescent)", score$label)

# Paediatric AUC is an exact identity, and that is the point of asserting it:
# each band's CL/kg was transcribed as 15 / AUC0-24h, and both dose and
# clearance scale with body weight, so the reduction must return all twelve
# Table 4 cells to numerical precision. This checks the transcription of the
# three band clearances, the nine renal multipliers and the weight
# cancellation simultaneously. A single mistyped digit breaks it.
stopifnot(sum(is_ped) == 12L)
stopifnot(max(abs(score$auc_ratio[is_ped] - 1)) < 0.005)

# Adult AUC. One regimen is an outlier -- Jaruratanasirikul 0.5 g / 0.5 h, at
# 0.879 -- because the paper's own printed AUC for that row exceeds what its
# own tabulated clearance allows (see Assumptions and deviations). Every other
# adult regimen is within 5%.
adult_auc <- score$auc_ratio[!is_ped]
stopifnot(length(adult_auc) == 10L)
stopifnot(all(adult_auc > 0.87 & adult_auc < 1.08))
stopifnot(sum(abs(adult_auc - 1) < 0.05) == 8L)

# Cmax is reproduced on every INFUSION regimen. The two instantaneous-bolus
# rows are excluded and discussed in Assumptions and deviations.
cmax_inf <- score$cmax_ratio[score$infusion & !is.na(score$cmax_ratio)]
stopifnot(length(cmax_inf) == 12L)
stopifnot(all(cmax_inf > 0.70 & cmax_inf < 1.05))

# The four school-age rows -- the subjects the whole dose recommendation rests
# on -- are reproduced far more tightly than that.
schoolage <- score$cmax_ratio[grepl("School-age", score$label)]
stopifnot(length(schoolage) == 4L, all(abs(schoolage - 1) < 0.02))

Comparison against the clinical observations

A separate question from “does the reduction match the platform” is “does it match the patients”. Feng 2026 reports observed AUC0-t for eight of the adult regimens and three paediatric ones (Tables 2 and 3).

observed <- tibble::tribble(
  ~label,                      ~auc_obs, ~cmax_obs,
  "Wang 0.25 g / 0.5 h",          25.48,     20.05,
  "Jarurat. 0.5 g / 0.5 h",       60.65,     48.38,
  "Nilsson 1.0 g / 0.5 h",        89.37,     65.64,
  "Jarurat. 0.5 g / 2 h",         57.20,     21.23,
  "Jarurat. 1.0 g / 2 h",        116.81,     42.33,
  "Norrby 0.5 g bolus",           42.35,        NA,
  "Norrby 1.0 g bolus",           95.75,        NA,
  "Gibson mild 0.25 g",           19.97,        NA,
  "Gibson moderate 0.25 g",       29.80,        NA,
  "Gibson severe 0.25 g",         60.76,        NA
)

obs_cmp <- observed |>
  dplyr::left_join(sim_wide, by = "label") |>
  dplyr::mutate(auc_fold = aucinf.obs / auc_obs,
                cmax_fold = cmax / cmax_obs)

stopifnot(nrow(obs_cmp) == nrow(observed), !anyNA(obs_cmp$auc_fold))

obs_cmp |>
  dplyr::select(label, auc_obs, aucinf.obs, auc_fold, cmax_obs, cmax, cmax_fold) |>
  dplyr::rename("Regimen" = label,
                "AUC observed" = auc_obs, "AUC simulated" = aucinf.obs,
                "AUC fold-error" = auc_fold,
                "Cmax observed" = cmax_obs, "Cmax simulated" = cmax,
                "Cmax fold-error" = cmax_fold) |>
  knitr::kable(digits = 3,
               caption = paste(
                 "Reduced model vs the clinical observations Feng 2026",
                 "digitised. The paper's own acceptance criterion is a",
                 "fold error below 2."))
Reduced model vs the clinical observations Feng 2026 digitised. The paper’s own acceptance criterion is a fold error below 2.
Regimen AUC observed AUC simulated AUC fold-error Cmax observed Cmax simulated Cmax fold-error
Wang 0.25 g / 0.5 h 25.48 22.369 0.878 20.05 19.324 0.964
Jarurat. 0.5 g / 0.5 h 60.65 44.739 0.738 48.38 39.449 0.815
Nilsson 1.0 g / 0.5 h 89.37 89.477 1.001 65.64 66.161 1.008
Jarurat. 0.5 g / 2 h 57.20 44.739 0.782 21.23 20.183 0.951
Jarurat. 1.0 g / 2 h 116.81 89.477 0.766 42.33 40.366 0.954
Norrby 0.5 g bolus 42.35 44.739 1.056 NA 40.750 NA
Norrby 1.0 g bolus 95.75 89.477 0.934 NA 81.500 NA
Gibson mild 0.25 g 19.97 23.404 1.172 NA 16.684 NA
Gibson moderate 0.25 g 29.80 39.209 1.316 NA 19.231 NA
Gibson severe 0.25 g 60.76 71.715 1.180 NA 20.959 NA 

# The paper's own acceptance criterion, applied to the reduction.
stopifnot(all(obs_cmp$auc_fold > 0.5 & obs_cmp$auc_fold < 2))
cmax_fold <- obs_cmp$cmax_fold[!is.na(obs_cmp$cmax_fold)]
stopifnot(length(cmax_fold) == 5L, all(cmax_fold > 0.5 & cmax_fold < 2))

Do the proposed dose adjustments equalise exposure?

This is the paper’s headline result. Feng 2026 derives the recommended dose by multiplying the standard 15 mg/kg by the reciprocal of the RI-to-healthy geometric mean ratio, arriving at 15, 15, 12 and 7 mg/kg every 6 hours for normal renal function, mild, moderate and severe RI. If the reduction is faithful, those four doses should all deliver the exposure a healthy child gets from 15 mg/kg.

dose_spec <- tibble::tribble(
  ~renal,          ~mgkg, ~mild, ~mod, ~sev, ~tend,
  "Normal",           15,     0,    0,    0,     8,
  "Mild RI",          15,     1,    0,    0,     8,
  "Moderate RI",      12,     0,    1,    0,    10,
  "Severe RI",         7,     0,    0,    1,    16
)

dose_events <- dplyr::bind_rows(lapply(seq_len(nrow(dose_spec)), function(i) {
  r <- dose_spec[i, ]
  make_subject(id = 700L + i, label = r$renal, arm = "Proposed dose",
               amt = r$mgkg * 25, dur = 3.0, WT = 25, AGE = 8,
               mild = r$mild, mod = r$mod, sev = r$sev, tend = r$tend)
}))

dose_sim <- rxode2::rxSolve(mod, events = dose_events,
                            keep = c("label")) |>
  as.data.frame() |>
  dplyr::mutate(label = as.character(label))
#> Warning: multi-subject simulation without without 'omega'

dose_given <- dose_events |>
  dplyr::filter(evid == 1) |>
  dplyr::select(label, amt)

dose_auc <- dose_sim |>
  dplyr::group_by(label) |>
  dplyr::summarise(CL = first(cl), .groups = "drop") |>
  dplyr::left_join(dose_given, by = "label") |>
  # AUC0-inf = dose / CL exactly for this linear one-compartment model.
  dplyr::mutate(auc = amt / CL) |>
  dplyr::arrange(match(label, dose_spec$renal))

stopifnot(nrow(dose_auc) == nrow(dose_spec), !anyNA(dose_auc$auc))

ref_auc <- dose_auc$auc[dose_auc$label == "Normal"]
stopifnot(length(ref_auc) == 1L)

dose_auc |>
  dplyr::mutate(ratio_to_normal = auc / ref_auc) |>
  dplyr::rename("Renal function" = label, "AUC0-inf (mg*h/L)" = auc,
                "CL (L/h)" = CL, "Dose (mg)" = amt,
                "Ratio to normal-renal child" = ratio_to_normal) |>
  knitr::kable(digits = 3,
               caption = paste(
                 "Exposure delivered by the doses Feng 2026 proposes",
                 "(Table 4), in an 8-year-old, 25 kg child."))
Exposure delivered by the doses Feng 2026 proposes (Table 4), in an 8-year-old, 25 kg child.
Renal function CL (L/h) Dose (mg) AUC0-inf (mg*h/L) Ratio to normal-renal child
Normal 8.758 375 42.818 1.000
Mild RI 8.383 375 44.731 1.045
Moderate RI 6.975 300 43.012 1.005
Severe RI 4.101 175 42.672 0.997 

# All four proposed doses land within 5% of the healthy-child exposure.
stopifnot(all(abs(dose_auc$auc / ref_auc - 1) < 0.05))

Prolonged infusion and %fT>MIC

Imipenem is time-dependent, and the paper’s PK/PD index is the percentage of the dosing interval during which the free concentration exceeds the MIC, with 70%fT>MIC as the target. Feng 2026’s second headline result is that extending the infusion from 0.5 h to 3 h substantially raises target attainment.

Probability of target attainment itself cannot be reproduced here: it is a population quantity and Feng 2026 publishes no interindividual variance for any parameter. What is reproducible is the deterministic %fT>MIC for the typical child, and the direction and size of the infusion-duration effect.

ftmic_spec <- tidyr::crossing(
  tibble::tibble(renal = c("Normal", "Mild RI", "Moderate RI", "Severe RI"),
                 mild = c(0, 1, 0, 0), mod = c(0, 0, 1, 0), sev = c(0, 0, 0, 1)),
  tibble::tibble(inf_label = c("0.5 h", "3 h"), dur = c(0.5, 3.0))
)

# q6h. The model's paediatric half-lives are 0.32-0.69 h, i.e. at least 8.7
# dosing-interval half-lives, so accumulation is nil and the first interval
# after a single dose is the steady-state interval to within rounding.
tau <- 6

ftmic_events <- dplyr::bind_rows(lapply(seq_len(nrow(ftmic_spec)), function(i) {
  r <- ftmic_spec[i, ]
  grid <- seq(0, tau, by = 0.002)
  dplyr::bind_rows(
    tibble::tibble(id = 800L + i, time = 0, evid = 1L, amt = 15 * 25,
                   dur = r$dur, cmt = "central"),
    tibble::tibble(id = 800L + i, time = grid, evid = 0L, amt = NA_real_,
                   dur = 0, cmt = "central")
  ) |>
    dplyr::mutate(label = r$renal, arm = r$inf_label, WT = 25, AGE = 8,
                  RENALIMP_MILD = r$mild, RENALIMP_MOD = r$mod,
                  RENALIMP_SEV = r$sev)
}))

ftmic_sim <- rxode2::rxSolve(mod, events = ftmic_events,
                             keep = c("label", "arm")) |>
  as.data.frame() |>
  dplyr::mutate(label = as.character(label), arm = as.character(arm))
#> Warning: multi-subject simulation without without 'omega'

mic_panel <- c(1, 2, 4)

ftmic <- lapply(mic_panel, function(mic) {
  ftmic_sim |>
    dplyr::group_by(label, arm) |>
    dplyr::summarise(
      MIC = mic,
      # Fraction of the 6 h interval with free concentration above the MIC,
      # on a uniform 0.002 h grid.
      pct_fT_over_MIC = 100 * mean(Cfree > mic),
      .groups = "drop"
    )
}) |>
  dplyr::bind_rows()

ftmic |>
  tidyr::pivot_wider(names_from = arm, values_from = pct_fT_over_MIC) |>
  dplyr::arrange(MIC, match(label, c("Normal", "Mild RI", "Moderate RI", "Severe RI"))) |>
  dplyr::rename("Renal function" = label, "MIC (mg/L)" = MIC,
                "%fT>MIC, 0.5 h infusion" = `0.5 h`,
                "%fT>MIC, 3 h infusion" = `3 h`) |>
  knitr::kable(digits = 1,
               caption = paste(
                 "Deterministic %fT>MIC for the typical 8-year-old child,",
                 "15 mg/kg q6h. Target is 70%fT>MIC."))
Deterministic %fT>MIC for the typical 8-year-old child, 15 mg/kg q6h. Target is 70%fT>MIC.
Renal function MIC (mg/L) %fT>MIC, 0.5 h infusion %fT>MIC, 3 h infusion
Normal 1 38.0 68.3
Mild RI 1 39.5 69.5
Moderate RI 1 46.5 75.4
Severe RI 1 75.8 99.3
Normal 2 32.5 62.1
Mild RI 2 33.7 63.1
Moderate RI 2 39.6 67.9
Severe RI 2 64.2 89.5
Normal 4 26.8 55.0
Mild RI 4 27.8 55.7
Moderate RI 4 32.6 59.4
Severe RI 4 52.5 76.5 

gain <- ftmic |>
  tidyr::pivot_wider(names_from = arm, values_from = pct_fT_over_MIC) |>
  dplyr::mutate(gain = `3 h` - `0.5 h`)

# The paper's qualitative PD claim: a 3 h infusion raises %fT>MIC in every
# renal stratum and at every MIC in the panel. Deterministic, so exact.
stopifnot(all(gain$gain > 0))
# And the gain is large, not marginal -- at least 15 percentage points
# everywhere, which is what makes it a clinically meaningful recommendation.
stopifnot(min(gain$gain) > 15)
# Severity ordering: worse renal function always gives higher %fT>MIC.
sev_order <- ftmic |>
  dplyr::filter(MIC == 4) |>
  dplyr::arrange(match(label, c("Normal", "Mild RI", "Moderate RI", "Severe RI")))
stopifnot(all(diff(sev_order$pct_fT_over_MIC[sev_order$arm == "3 h"]) > 0))

Assumptions and deviations

  • The whole-body PBPK is not reproduced. GastroPlus’s organ volumes, blood flows, tissue-to-plasma partition coefficients and ACAT structure are vendor intellectual property and are not printed in the paper. This file encodes the reduced disposition model of Supplementary Table S3, which the identity check above shows is mono-exponential, and which is what the paper itself carries into its dose-adjustment analysis.

  • Supplementary Table S3’s volume unit is wrong. The column is headed Vss(L/kg) and the Results text repeats “3.259 L/kg in children … 11.663 L/kg in adults”. The values are absolute litres. Three independent proofs are in the identity section above: the published half-lives are recovered only with Vss in litres; Vss / body weight is then a physiological 0.155-0.173 L/kg; and the litre reading reproduces the paper’s own predicted concentrations. The model carries the litre reading.

  • The volume is a derived summary, not a transcription. lvcPerKg = 0.1636 L/kg is the mean of Vss / WT over the seven Supplementary Table S3 rows with a published weight. It is confirmed independently by solving Table 3’s four school-age (AUC, Cmax) pairs, which give 0.1629, 0.1635, 0.1659 and 0.1652 L/kg. Because renal impairment moves this quantity by less than the spread between healthy adult cohorts, the model carries no renal effect on volume; the 11.663-to-14.081 L range across the adult renal strata is body weight, not impairment.

  • Adult clearance is not weight-scaled, deliberately. Supplementary Table S3 gives 10.726-11.262 L/h across adult cohorts spanning 58.75-86.6 kg – flat to within 5% over a 47% weight range – because the GastroPlus renal term is driven by glomerular filtration rather than by size. Imposing an allometric exponent would have been an invention. Paediatric clearance is weight-scaled because paediatric dosing and reporting are per kg.

  • Instantaneous-bolus Cmax is not reproduced, and should not be. The two Norrby 1983 rows are simulated in GastroPlus as instantaneous intravenous injections, so the whole-body model puts the entire dose in the plasma sub-volume before distribution and predicts 165.99 and 331.99 mg/L. A one-compartment reduction whose volume is Vss cannot produce that, and gives roughly a quarter of it. This is the expected Vss is not Vc failure. It is not a defect of the reduction for this paper’s purposes: Table 2 reports no observed Cmax for either bolus row, no clinical regimen in the paper is an instantaneous injection, and both bolus AUCs are reproduced to within 2%. The Gibson 0.15 h infusions are the same effect in milder form (fold error 0.72-0.81) and likewise carry no observed Cmax. The effect disappears as soon as the infusion is long enough to matter: the 0.5 h, 1 h, 2 h and 3 h regimens – which is every regimen the paper recommends – are reproduced to within 10%, and the four school-age rows to within 1%.

  • Interindividual variability and residual error are not published. Feng 2026 ran a 200-subject population simulator and shows 90% intervals in Figures 2-4, but reports no variance magnitude for any parameter and describes no residual error model. No etas are declared and both residual error terms are fixed(0) rather than invented. The direct consequence is that the paper’s probability-of-target-attainment results (Figure 6) cannot be reproduced, because PTA is defined over that unpublished distribution. The deterministic %fT>MIC computed above is the closest reproducible quantity, and it sits below the paper’s PTA percentages – as it must, since a PTA is the fraction of a population above a threshold, not a typical value.

  • Paediatric renal-impairment unbound fraction is not published. Supplementary Table S3 carries Fup for adults in every renal stratum (0.800, 0.806, 0.827, 0.834) but only for children with normal renal function (0.81217 Claesson, 0.81182 Bradley). The model therefore applies the paediatric normal-renal value to children in every renal stratum. The adult trend suggests the true paediatric RI values would be at most about 0.834, a 2.7% effect on the free concentration.

  • One printed geometric mean ratio disagrees with its own AUC pair. Table 4 gives 1.19 as the moderate-RI-to-healthy ratio for preschool children, but the AUC values in the same column pair are 38.928 and 31.358, whose ratio is 1.2414 – 4.3% apart. The other eight ratios agree with their AUC pairs to within 0.9%. The model derives the clearance multipliers from the tabulated AUC values rather than the tabulated ratios. The discrepancy does not change the paper’s recommendation: 15 / 1.19 and 15 / 1.2414 both round to 12 mg/kg. Separately, Table 4 prints 1.25 for school-age moderate RI while the Abstract and Discussion print 1.26 for the same quantity; 53.765 / 42.818 = 1.2557, so the Abstract is right and Table 4 is truncated.

  • One predicted adult AUC exceeds what the paper’s own clearance allows. Table 2 gives Jaruratanasirikul 2005 two 0.5 g regimens, a 0.5 h and a 2.0 h infusion, and Supplementary Table S3 gives both the same clearance of 10.726 L/h. A 500 mg dose at that clearance cannot produce an AUC above 500 / 10.726 = 46.62 mgh/L, and the AUC0-t the table footnote defines is a truncated* AUC, so it must be below that. The 2.0 h row obeys this (46.20). The 0.5 h row does not: it is printed as 50.91, which is 9.2% above the theoretical maximum. This is the single regimen where the reduction’s AUC ratio falls outside 5% (0.879), and the discrepancy is in the source, not in the reduction – the reduction returns 46.62, which is the value Table 2’s own inputs imply.

  • The Bradley 2023 simulation does not use the Bradley 2023 cohort. Supplementary Table S2 gives that cohort a mean weight of 15.4 kg (range 12-19) at ages 2-6, so a 15 mg/kg dose is 231 mg. Supplementary Table S3 gives the Bradley simulation a clearance of 8.489 L/h, which would cap AUC0-inf at 231 / 8.489 = 27.2 mg*h/L – yet Table 3 reports a predicted AUC0-t of 47.40, which is impossible for a truncated AUC. Solving Table 3’s Bradley AUC and Cmax jointly implies a subject of about 26 kg, i.e. a school-age child rather than the 2-6 year olds Bradley enrolled. This vignette does not simulate the Bradley regimen against the reported 15.4 kg for that reason; the paediatric arm uses the Table 4 age bands, which are internally consistent.

  • Cross-row identity in Supplementary Table S3. The Nilsson 1991 row (Swedish men, 74 kg) and the Wang 2021 q6h row (Chinese participants, 60.4 kg, 41.7% male) share an identical Vss of 11.663 L, GFR of 1.9632 mL/s, half-life of 0.723 h and renal blood flow of 21.35 mL/s. Several study rows were evidently simulated with the same default virtual adult rather than with each study’s own demographics, which is why the model carries a single adult clearance rather than a per-study one.

  • Clearance is not the paper’s stated Fup * GFR. Methods and Discussion both state that in vivo renal clearance was computed as Fup * GFR with no non-renal pathway. Supplementary Table S3’s own columns do not satisfy that relation: for the Nilsson row, Fup * GFR is 0.8 * 1.9632 mL/s = 0.8 * 7.068 L/h = 5.65 L/h against a tabulated clearance of 11.126 L/h, and the ratio of tabulated clearance to Fup * GFR varies from 1.95-2.34 across the healthy adult and paediatric rows to 4.8 in moderate RI and 8.1 in severe RI. The model carries the tabulated clearances, which are the numbers that reproduce the paper’s published concentrations, rather than the stated formula.

  • Ages below 3 years produce a clearance of zero. The WHO bands the model uses start at 3 years, matching the paper’s own Limitations statement that the work applies only to children over 3 with normal growth and development. An out-of-domain age yields nonsense rather than an error, so callers must screen for it.