BTZ-043 population PK and bacterial-load exposure-response (Koele 2025) • nlmixr2lib

Model and source

Koele 2025 contributed two models to nlmixr2lib, matching the two NONMEM runs the paper reports:

Koele_2025_btz043 – the joint BTZ-043 / M1 / M2 population PK model.
Koele_2025_btz043_bacterialload – the bilinear cfu + time-to-positivity exposure-response model, driven by the individual BTZ-043total AUC(0-24) that the PK model produces.
Citation: Koele S. E., Heinrich N., De Jager V. R., Dreisbach J., Phillips P. P. J., Gross-Demel P., Dawson R., Narunsky K., Wildner L. M., Mchugh T. D., Te Brake L. H. M., Diacon A. H., Aarnoutse R. E., Hoelscher M., Svensson E. M. (2025). Population pharmacokinetics and exposure-response relationship of the antituberculosis drug BTZ-043. Journal of Antimicrobial Chemotherapy 80(5):1319-1327. doi:10.1093/jac/dkaf076. Structural equations and random-effect variances transcribed from the final NONMEM control stream in the Supplementary data (‘Pharmacokinetic model code’); typical values and residual errors from Table 2.
Article: https://doi.org/10.1093/jac/dkaf076

BTZ-043 is a first-in-class benzothiazinone inhibitor of DprE1, an enzyme of the mycobacterial cell-wall synthesis pathway. The paper analyses the sequential Phase 1b/2a trial NCT04044001, in which participants with drug-susceptible pulmonary tuberculosis received BTZ-043 monotherapy at 250 to 1750 mg once daily for 14 days.

Both models were transcribed from the final NONMEM control streams printed in the paper’s Supplementary data, with typical values taken from Table 2 (PK) and Table 3 (PD). Where the control stream and the tables disagree, the resolution is recorded in the Errata section below.

mod_pk <- readModelDb("Koele_2025_btz043")
mod_pd <- readModelDb("Koele_2025_btz043_bacterialload")
ui_pk  <- rxode2::rxode(mod_pk)
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
ui_pd  <- rxode2::rxode(mod_pd)
#> ℹ parameter labels from comments will be replaced by 'label()'

# Molecular weight of BTZ-043, from the control stream comment on F1.
MW_BTZ043 <- 431.39
# 1 mg of BTZ-043 is this many nmol.
NMOL_PER_MG <- 1e6 / MW_BTZ043
# 1 nmol/L of BTZ-043 is this many ng/mL.
NGML_PER_NM <- MW_BTZ043 / 1000

c(nmol_per_mg = NMOL_PER_MG, ngmL_per_nM = NGML_PER_NM)
#> nmol_per_mg ngmL_per_nM 
#>  2318.08804     0.43139

Population

The analysis population is the 68 participants of NCT04044001 who received BTZ-043 and contributed data: 24 from Stage 1 (Phase 1b dose escalation, three participants per dose cohort and six in the highest) and 44 from Stage 2 (Phase 2a, randomised 3:3:3:2 to 250, 500 or 1000 mg BTZ-043 daily or to the Rifafour e-275 control regimen). One Stage 2 participant in the 500 mg group withdrew before any study procedure and contributed no data.

pop <- ui_pk$population
tibble::tibble(
  Field = names(pop),
  Value = vapply(pop, function(x) paste(paste0(
    ifelse(nzchar(names(x) %||% ""), paste0(names(x), ": "), ""), x),
    collapse = "; "), character(1))
) |>
  knitr::kable()

Field	Value
species	human
n_subjects	68
n_studies	1
age_range	18-57 years
age_median	27 years
weight_range	42-81 kg
weight_median	54 kg
height_range	1.5-1.9 m
height_median	1.7 m
sex_female_pct	16.2
race_ethnicity	Black: 64.7; Cape-coloured: 33.8; White: 1.5
hiv_status	HIV-1 negative, 68/68 (100%)
disease_state	Adults aged 18-64 years with drug-susceptible pulmonary tuberculosis enrolled in the sequential Phase 1b/2a dose-escalation and dose-expansion trial NCT04044001 (Stage 1 Phase 1b dose escalation, Stage 2 Phase 2a randomized dose expansion).
dose_range	Oral BTZ-043 250-1750 mg once daily for 14 days. Stage 1 escalated through 250, 500, 750, 1000, 1250, 1500 and 1750 mg with three participants per cohort and six in the highest; Stage 2 randomized 54 participants to 250, 500 or 1000 mg daily or to the Rifafour e-275 control regimen in a 3:3:3:2 ratio.
prandial_state	Stage 1: fasted on Days 1-12 and with a high-fat breakfast on Day 14. Stage 2: BTZ-043 taken either prior to, or 30 min after, the start of intake of a standard breakfast. Occasion counts in Koele 2025 Table 1: fasted 24, high-fat 19, standard together with dose 24, standard 30 min prior to dose 20.
regions	South Africa (TASK, Cape Town; University of Cape Town Lung Institute)
notes	Baseline demographics from Koele 2025 Table 1, ‘Combined Stage 1 + 2’ column. Twenty-four Stage 1 and 44 Stage 2 participants were analysed; one Stage 2 participant in the 500 mg group withdrew before any study procedure and contributed no data. The PK dataset held 1808 BTZ-043, 1808 M1 and 1793 M2 observations, of which 600 (33%), 159 (8.8%) and 146 (8.1%) respectively were below the 20 ng/mL limit of quantification. BLQ observations were EXCLUDED from the final analysis: models using the NONMEM M3 method were highly unstable and, when the final model was re-estimated with M3, it significantly underestimated the central tendency of the BTZ-043 and M2 elimination phases (Koele 2025 Results, ‘PK model’).

All participants were HIV-1 negative. Median age was 27 years (range 18 to 57), median weight 54 kg (range 42 to 81) and 84% were male; 65% self-identified as Black, 34% as Cape-coloured and 1% as White (Koele 2025 Table 1, combined Stage 1 + 2 column). Note that the median weight of 54 kg sits well below the 70 kg allometric reference, so a typical participant in this trial has apparent clearances about 18% lower than the tabulated 70 kg values.

Prandial state differed by stage and is a per-dose-record covariate rather than a subject characteristic. Stage 1 dosed fasted on Days 1 to 12 and with a high-fat breakfast on Day 14. Stage 2 dosed either immediately prior to, or 30 minutes after the start of, a standard breakfast; the latter is the model’s reference state.

Source trace

Every ini() value in both model files carries an in-file comment naming its source location. The table below is the consolidated audit trail.

Quantity	Value	Source
Structural PK: CL/F, V/F, ka, MTT, Q/F, Vp/F	404 L/h, 764 L, 1.69 /h, 0.340 h, 68.0 L/h, 382 L	Table 2 ‘Structural parameters’; $THETA 1-4, 24, 25
M1 disposition: CL_M1, V_M1	36.0 L/h, 894 L	Table 2; $THETA 13, 14
M2 disposition: CL_M2, V_M2, Q_M2, Vp_M2	45.8 L/h, 19.0 L, 64.2 L/h, 26.8 L	Table 2; $THETA 16, 17, 19, 20
Parallel-absorption fraction, lag time	0.644, 1.83 h	Table 2; $THETA 6, 7
Allometric exponents	0.75 CL, 1 V (fixed)	Methods ‘PK model development’; $PK AlloCL / AlloV
F effects: dose >1250 mg, high fat, no food, dose before food	0.710, 1.41, 0.458, 0.727	Table 2 ‘Covariates’; $THETA 8-11
MTT effect when no food is present	0.360	Table 2 ‘Dose prior to standard food/no food on MTT (%)’; $THETA 5
M1 fm effect when no food is present	1.39 divisor	Table 2 ‘Administration with food on FM1 (%)’; $THETA 23 under IF(WITHFOOD.EQ.0)
Cape-coloured on CL/F	0.762	Table 2; $THETA 22
M2 clearance step after Day 10	0.734 from 240 h	Table 2, Results; $THETA 21 under IF(DAY.GT.10) \| \|PK IIV and IOV variances \|see model file \|$ OMEGA blocks; each reproduces the Table 2 CV% via CV = sqrt(exp(w2) - 1)
PK residual errors	50.5, 33.8, 29.0 CV%	Table 2 ‘Residual error’
PD baselines, Emax slopes, second slopes	6.20, 1.99, 0.0270, 0.00386, 0.00254, 0.000440	Table 3; $THETA 1-6
PD node, EC50	48 h FIX, 16900 ng/mL*h	Table 3; $THETA 7 FIX, 8 \| \|PD IIV blocks and correlations \|see model file \|$ OMEGA BLOCK(3) and BLOCK(2); reproduce the Table 3 CV% and correlations
PD residual errors	0.558, 0.0624 log10	Table 3 ‘Residual error’ (published averages of the $SIGMA BLOCK(4) replicate SDs)

Simulation helpers

Observation rows carry cmt = "Cc". That is the ENDPOINT name, and for a model with three declared endpoints it is the only form rxode2 accepts: cmt = "central" (an ODE state) and dvid-only rows both fail with 'dvid'->'cmt' ... on a undefined compartment. Because Cc is a declared endpoint (Cc ~ prop(propSd)), rxode2 already owns a compartment slot for it, so nothing is injected and no ODE state is renumbered – which the guard chunk below proves rather than asserts in prose. useLinCmt = FALSE is set on every solve so that rxode2’s automatic ODE-to-linCmt conversion cannot silently replace the transcribed ODE system.

# Trapezoidal AUC over an ordered time / concentration pair.
trap_auc <- function(time, conc) {
  sum(diff(time) * (utils::head(conc, -1) + utils::tail(conc, -1)) / 2)
}

# Prandial states of the trial, as the two registered indicators that span
# them (see the FED / FASTED_STRICT covariate notes in the model file).
PRANDIAL <- tibble::tribble(
  ~arm,                  ~FED, ~FED_HIGHFAT, ~FASTED_STRICT,
  "standard, dose after",  1,            0,              0,
  "high-fat",              1,            1,              0,
  "dose before standard",  0,            0,              0,
  "fasted",                0,            0,              1
)

# Build an event table: n_dose daily doses of `dose` mg into BOTH absorption
# depots, plus an observation grid. The dose must be written to depot1 and
# depot2 separately; f() then splits it between the transit chain and the
# lag-time secondary route.
btz_events <- function(dose, obs_times, n_dose = 1, ii = 24, id = 1L) {
  dosing <- tidyr::expand_grid(
    id = id, cmt = c("depot1", "depot2")
  ) |>
    dplyr::mutate(
      time = 0, amt = dose, evid = 1L, ii = ii,
      addl = as.integer(n_dose - 1L)
    )
  obs <- tidyr::expand_grid(id = id, time = obs_times) |>
    dplyr::mutate(
      cmt = "Cc", amt = NA_real_, evid = 0L, ii = 0, addl = 0L
    )
  dplyr::bind_rows(dosing, obs) |>
    dplyr::arrange(id, time, dplyr::desc(evid))
}

# Attach the covariate columns a solve needs.
with_covs <- function(ev, WT = 70, arm = "standard, dose after",
                      DOSE_HIGH = 0, RACE_COLOURED = 0, OCC = 1) {
  p <- PRANDIAL[match(arm, PRANDIAL$arm), ]
  stopifnot(nrow(p) == 1L, !is.na(p$FED))
  ev |>
    dplyr::mutate(
      WT = WT, FED = p$FED, FED_HIGHFAT = p$FED_HIGHFAT,
      FASTED_STRICT = p$FASTED_STRICT,
      DOSE_HIGH = DOSE_HIGH, RACE_COLOURED = RACE_COLOURED, OCC = OCC
    )
}

solve_pk <- function(ev, typical = TRUE, ...) {
  m <- if (typical) rxode2::zeroRe(mod_pk) else mod_pk
  rxode2::rxSolve(m, ev, returnType = "data.frame", useLinCmt = FALSE, ...)
}

Structural verification: solve against closed form

The single most informative check on a transcribed multi-compartment model is whether the solved system reproduces the closed forms the parameters imply. With every fraction metabolised fixed to 1, the model routes the FULL parent elimination flux into both metabolite compartments, so all three analytes have the same closed-form AUC(0-inf) shape, dose / CL, with the dose expressed in nmol. This is a deterministic identity: a tight tolerance is correct here and would catch a mis-transcribed clearance, a lost allometric term, or an accidental linCmt substitution of the transcribed ODEs.

obs_grid <- seq(0, 96, by = 0.02)
ev_cf <- btz_events(dose = 500, obs_times = obs_grid) |> with_covs(WT = 70)
sim_cf <- solve_pk(ev_cf) |> dplyr::filter(!is.na(Cc))
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalfdepot', 'etalcl_m1', 'etalvc_m1', 'etalcl_m2', 'etalvc_m2', 'etaiov_fdepot_1', 'etaiov_fdepot_2', 'etaiov_fdepot_3', 'etaiov_mtt_1', 'etaiov_ka_1', 'etaiov_mtt_2', 'etaiov_ka_2', 'etaiov_mtt_3', 'etaiov_ka_3'

dose_nmol <- 500 * NMOL_PER_MG
cf <- tibble::tibble(
  Analyte = c("BTZ-043", "M1", "M2"),
  `CL (L/h)` = c(404, 36.0, 45.8),
  `AUC simulated (nmol*h/L)` = c(
    trap_auc(sim_cf$time, sim_cf$Cc),
    trap_auc(sim_cf$time, sim_cf$Cc_m1),
    trap_auc(sim_cf$time, sim_cf$Cc_m2)
  )
) |>
  dplyr::mutate(
    `AUC closed form (nmol*h/L)` = dose_nmol / `CL (L/h)`,
    Ratio = `AUC simulated (nmol*h/L)` / `AUC closed form (nmol*h/L)`
  )
knitr::kable(cf, digits = c(0, 1, 1, 1, 5))

Analyte	CL (L/h)	AUC simulated (nmol*h/L)	AUC closed form (nmol*h/L)	Ratio
BTZ-043	404.0	2868.9	2868.9	1.00000
M1	36.0	31370.1	32195.7	0.97436
M2	45.8	25306.6	25306.6	1.00000

BTZ-043 and M2 are complete within the 96 h window and match their closed forms exactly. M1 is the slowest analyte (V_M1 / CL_M1 = 24.8 h, so a 17.2 h terminal half-life) and about 2% of its AUC still lies beyond 96 h, which is the whole of its shortfall.

stopifnot(
  # Deterministic identity, not a cohort statistic: BTZ-043 and M2 are
  # numerically complete in the window, so the tolerance is solver accuracy.
  abs(cf$Ratio[cf$Analyte == "BTZ-043"] - 1) < 1e-3,
  abs(cf$Ratio[cf$Analyte == "M2"] - 1) < 1e-3,
  # M1 is truncated by design; exp(-96 / 24.83) = 2.1% remains uncollected.
  cf$Ratio[cf$Analyte == "M1"] > 0.96,
  cf$Ratio[cf$Analyte == "M1"] < 1.00
)

Guard: no compartment renumbering

cmt = "Cc" on the observation rows is flagged by the repository’s static vignette lint as the slot-renumbering anti-pattern. That advice is right for a BARE algebraic observable; it is a false positive for a declared endpoint. The guard below turns the concern into a test that would go red if renumbering ever did occur.

stopifnot(
  # every ODE state still resolves to a column
  all(ui_pk$state %in% names(sim_cf)),
  # every endpoint plus the derived total is returned
  all(c("Cc", "Cc_m1", "Cc_m2", "Cc_total") %in% names(sim_cf)),
  # The transit-chain depot receives exactly f(depot1) = 0.644 * 500 mg
  # converted to nmol, at t = 0.
  abs(sim_cf$depot1[1] - 0.644 * 500 * NMOL_PER_MG) < 1e-6,
  # depot2 is still EMPTY at t = 0 -- its dose is held by the 1.83 h lag --
  # and receives the complementary 0.356 fraction once the lag expires. The
  # observed peak sits on the first grid point at or after 1.83 h, by which
  # time ka has already removed exp(-1.69 * 0.01) = 1.7% of it, so the ratio
  # is just below 1 rather than equal to it.
  sim_cf$depot2[1] == 0,
  all(sim_cf$depot2[sim_cf$time < 1.83] == 0),
  max(sim_cf$depot2) / (0.356 * 500 * NMOL_PER_MG) > 0.97,
  max(sim_cf$depot2) / (0.356 * 500 * NMOL_PER_MG) <= 1,
  # and the derived total is exactly parent + M2
  max(abs(sim_cf$Cc_total - (sim_cf$Cc + sim_cf$Cc_m2))) < 1e-9
)

Absorption: the double peak and the food-dependent secondary route

Koele 2025 Results: “A double-peak phenomenon was observed for BTZ-043, M1 and M2 individual concentration-time profiles. A first-order secondary delayed absorption into the BTZ-043 central compartment was identified when the drug was taken together with food, using a lag-time model.” The secondary route carries 1 - 0.644 = 35.6% of the bioavailable dose after a 1.83 h lag, and is switched off entirely when the dose is not taken with food.

prof <- lapply(PRANDIAL$arm, function(a) {
  ev <- btz_events(500, seq(0, 12, by = 0.05)) |> with_covs(WT = 54, arm = a)
  solve_pk(ev) |>
    dplyr::filter(!is.na(Cc)) |>
    dplyr::transmute(time, Cc, arm = a)
}) |> dplyr::bind_rows()
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalfdepot', 'etalcl_m1', 'etalvc_m1', 'etalcl_m2', 'etalvc_m2', 'etaiov_fdepot_1', 'etaiov_fdepot_2', 'etaiov_fdepot_3', 'etaiov_mtt_1', 'etaiov_ka_1', 'etaiov_mtt_2', 'etaiov_ka_2', 'etaiov_mtt_3', 'etaiov_ka_3'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalfdepot', 'etalcl_m1', 'etalvc_m1', 'etalcl_m2', 'etalvc_m2', 'etaiov_fdepot_1', 'etaiov_fdepot_2', 'etaiov_fdepot_3', 'etaiov_mtt_1', 'etaiov_ka_1', 'etaiov_mtt_2', 'etaiov_ka_2', 'etaiov_mtt_3', 'etaiov_ka_3'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalfdepot', 'etalcl_m1', 'etalvc_m1', 'etalcl_m2', 'etalvc_m2', 'etaiov_fdepot_1', 'etaiov_fdepot_2', 'etaiov_fdepot_3', 'etaiov_mtt_1', 'etaiov_ka_1', 'etaiov_mtt_2', 'etaiov_ka_2', 'etaiov_mtt_3', 'etaiov_ka_3'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalfdepot', 'etalcl_m1', 'etalvc_m1', 'etalcl_m2', 'etalvc_m2', 'etaiov_fdepot_1', 'etaiov_fdepot_2', 'etaiov_fdepot_3', 'etaiov_mtt_1', 'etaiov_ka_1', 'etaiov_mtt_2', 'etaiov_ka_2', 'etaiov_mtt_3', 'etaiov_ka_3'

ggplot(prof, aes(time, Cc, colour = arm)) +
  geom_line(linewidth = 0.8) +
  labs(
    x = "Time after dose (h)", y = "BTZ-043 (nmol/L)", colour = "Prandial state",
    title = "Typical-value BTZ-043 after 500 mg at 54 kg",
    subtitle = "Replicates the structure of Koele 2025 Figure 1 and Figures S1-S3"
  ) +
  theme_bw()

The two fed arms show the characteristic shoulder at about 2 to 3 h produced by the delayed parallel route; the two arms with no food at the moment of dosing rise and fall as a single peak, and peak earlier because the mean transit time is 0.360 times the fed value.

peak_time <- prof |>
  dplyr::group_by(arm) |>
  dplyr::summarise(tmax = time[which.max(Cc)], .groups = "drop")
knitr::kable(peak_time, digits = 2)

arm	tmax
dose before standard	1.20
fasted	1.20
high-fat	2.45
standard, dose after	2.45


fed_arms <- c("standard, dose after", "high-fat")
stopifnot(
  # Deterministic typical-value profiles, so exact ordering is safe here:
  # the fed arms peak on the delayed route, the unfed arms on the transit
  # chain with a 2.8-fold shorter mean transit time.
  all(peak_time$tmax[peak_time$arm %in% fed_arms] > 1.83),
  all(peak_time$tmax[!peak_time$arm %in% fed_arms] < 1.83)
)

Prandial-state and dose effects on exposure

Because bioavailability enters only through f(), and none of the prandial covariates touches a clearance, every published F multiplier must reappear EXACTLY as a ratio of parent AUC(0-inf). The M1 ratios additionally carry the 1.39 divisor on apparent M1 clearance, which is the effect the paper describes as a change in the relative fraction metabolised to M1.

auc_arm <- function(arm, WT = 54, dose = 500, DOSE_HIGH = 0,
                    RACE_COLOURED = 0) {
  ev <- btz_events(dose, seq(0, 120, by = 0.02)) |>
    with_covs(WT = WT, arm = arm, DOSE_HIGH = DOSE_HIGH,
              RACE_COLOURED = RACE_COLOURED)
  s <- solve_pk(ev) |> dplyr::filter(!is.na(Cc))
  c(
    parent = trap_auc(s$time, s$Cc),
    m1     = trap_auc(s$time, s$Cc_m1),
    m2     = trap_auc(s$time, s$Cc_m2)
  )
}

ref <- auc_arm("standard, dose after")
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalfdepot', 'etalcl_m1', 'etalvc_m1', 'etalcl_m2', 'etalvc_m2', 'etaiov_fdepot_1', 'etaiov_fdepot_2', 'etaiov_fdepot_3', 'etaiov_mtt_1', 'etaiov_ka_1', 'etaiov_mtt_2', 'etaiov_ka_2', 'etaiov_mtt_3', 'etaiov_ka_3'
food_tab <- lapply(PRANDIAL$arm, function(a) {
  v <- auc_arm(a)
  tibble::tibble(
    arm = a,
    `BTZ-043 ratio` = unname(v["parent"] / ref["parent"]),
    `M1 ratio`      = unname(v["m1"] / ref["m1"]),
    `M2 ratio`      = unname(v["m2"] / ref["m2"])
  )
}) |>
  dplyr::bind_rows() |>
  dplyr::mutate(
    `Published F factor` = c(1, 1.41, 0.727, 0.458),
    `Published F x fm_M1` = `Published F factor` * c(1, 1, 1.39, 1.39)
  )
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalfdepot', 'etalcl_m1', 'etalvc_m1', 'etalcl_m2', 'etalvc_m2', 'etaiov_fdepot_1', 'etaiov_fdepot_2', 'etaiov_fdepot_3', 'etaiov_mtt_1', 'etaiov_ka_1', 'etaiov_mtt_2', 'etaiov_ka_2', 'etaiov_mtt_3', 'etaiov_ka_3'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalfdepot', 'etalcl_m1', 'etalvc_m1', 'etalcl_m2', 'etalvc_m2', 'etaiov_fdepot_1', 'etaiov_fdepot_2', 'etaiov_fdepot_3', 'etaiov_mtt_1', 'etaiov_ka_1', 'etaiov_mtt_2', 'etaiov_ka_2', 'etaiov_mtt_3', 'etaiov_ka_3'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalfdepot', 'etalcl_m1', 'etalvc_m1', 'etalcl_m2', 'etalvc_m2', 'etaiov_fdepot_1', 'etaiov_fdepot_2', 'etaiov_fdepot_3', 'etaiov_mtt_1', 'etaiov_ka_1', 'etaiov_mtt_2', 'etaiov_ka_2', 'etaiov_mtt_3', 'etaiov_ka_3'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalfdepot', 'etalcl_m1', 'etalvc_m1', 'etalcl_m2', 'etalvc_m2', 'etaiov_fdepot_1', 'etaiov_fdepot_2', 'etaiov_fdepot_3', 'etaiov_mtt_1', 'etaiov_ka_1', 'etaiov_mtt_2', 'etaiov_ka_2', 'etaiov_mtt_3', 'etaiov_ka_3'
knitr::kable(food_tab, digits = 4)

arm	BTZ-043 ratio	M1 ratio	M2 ratio	Published F factor	Published F x fm_M1
standard, dose after	1.000	1.0000	1.000	1.000	1.0000
high-fat	1.410	1.4100	1.410	1.410	1.4100
dose before standard	0.727	1.0108	0.727	0.727	1.0105
fasted	0.458	0.6368	0.458	0.458	0.6366

stopifnot(
  # Deterministic identities: AUC = F * dose / CL and no prandial covariate
  # touches CL, so the parent ratios must equal the published F factors.
  max(abs(food_tab$`BTZ-043 ratio` - food_tab$`Published F factor`)) < 1e-3,
  max(abs(food_tab$`M2 ratio`      - food_tab$`Published F factor`)) < 1e-3,
  # M1 additionally carries the 1.39 divisor on its apparent clearance. The
  # tolerance is looser only because M1 is the truncated analyte.
  max(abs(food_tab$`M1 ratio` - food_tab$`Published F x fm_M1`)) < 0.02
)

The M1 column is the one place where the paper’s prose and its own control stream point in opposite directions, and it is worth reading the numbers rather than the sentence: in the model AS FITTED, M1 exposure is 39% HIGHER in the arms with no food present at dosing. See the Errata section.

Two further deterministic effects reproduce exactly.

extra <- tibble::tibble(
  Effect = c("Dose > 1250 mg on F", "Cape-coloured on CL/F"),
  Simulated = c(
    unname(auc_arm("fasted", dose = 1500, DOSE_HIGH = 1)["parent"] /
             (1.5 * auc_arm("fasted", dose = 1000)["parent"])),
    unname(auc_arm("standard, dose after", RACE_COLOURED = 1)["parent"] /
             ref["parent"])
  ),
  Published = c(0.710, 1 / 0.762)
)
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalfdepot', 'etalcl_m1', 'etalvc_m1', 'etalcl_m2', 'etalvc_m2', 'etaiov_fdepot_1', 'etaiov_fdepot_2', 'etaiov_fdepot_3', 'etaiov_mtt_1', 'etaiov_ka_1', 'etaiov_mtt_2', 'etaiov_ka_2', 'etaiov_mtt_3', 'etaiov_ka_3'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalfdepot', 'etalcl_m1', 'etalvc_m1', 'etalcl_m2', 'etalvc_m2', 'etaiov_fdepot_1', 'etaiov_fdepot_2', 'etaiov_fdepot_3', 'etaiov_mtt_1', 'etaiov_ka_1', 'etaiov_mtt_2', 'etaiov_ka_2', 'etaiov_mtt_3', 'etaiov_ka_3'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalfdepot', 'etalcl_m1', 'etalvc_m1', 'etalcl_m2', 'etalvc_m2', 'etaiov_fdepot_1', 'etaiov_fdepot_2', 'etaiov_fdepot_3', 'etaiov_mtt_1', 'etaiov_ka_1', 'etaiov_mtt_2', 'etaiov_ka_2', 'etaiov_mtt_3', 'etaiov_ka_3'
knitr::kable(extra, digits = 4)

Effect	Simulated	Published
Dose > 1250 mg on F	0.7100	0.7100
Cape-coloured on CL/F	1.3123	1.3123

stopifnot(max(abs(extra$Simulated - extra$Published)) < 1e-3)

The M2 clearance step after 10 days on treatment

Koele 2025 Results: “The clearance of M2 decreased by 27% (95% CI: 24%-29%) after 10 days on BTZ-043 treatment. The effect was implemented as a dichotomous step after 10 days”. Simulating 14 daily doses and comparing the M2 AUC over the Day 9 interval with the Day 14 interval recovers the step.

ev_ss <- btz_events(500, seq(0, 336, by = 0.05), n_dose = 14) |>
  with_covs(WT = 54)
sim_ss <- solve_pk(ev_ss) |> dplyr::filter(!is.na(Cc))
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalfdepot', 'etalcl_m1', 'etalvc_m1', 'etalcl_m2', 'etalvc_m2', 'etaiov_fdepot_1', 'etaiov_fdepot_2', 'etaiov_fdepot_3', 'etaiov_mtt_1', 'etaiov_ka_1', 'etaiov_mtt_2', 'etaiov_ka_2', 'etaiov_mtt_3', 'etaiov_ka_3'

interval_auc <- function(s, from, to, col) {
  w <- s[s$time >= from & s$time <= to, ]
  trap_auc(w$time, w[[col]])
}
m2_day9  <- interval_auc(sim_ss, 192, 216, "Cc_m2")
m2_day14 <- interval_auc(sim_ss, 312, 336, "Cc_m2")
p_day9   <- interval_auc(sim_ss, 192, 216, "Cc")
p_day14  <- interval_auc(sim_ss, 312, 336, "Cc")

tibble::tibble(
  Analyte = c("M2", "BTZ-043"),
  `AUC(0-24) Day 9` = c(m2_day9, p_day9),
  `AUC(0-24) Day 14` = c(m2_day14, p_day14),
  `Day 14 / Day 9` = c(m2_day14 / m2_day9, p_day14 / p_day9),
  Expected = c(1 / 0.734, 1)
) |>
  knitr::kable(digits = 4)

Analyte	AUC(0-24) Day 9	AUC(0-24) Day 14	Day 14 / Day 9	Expected
M2	30744.151	41885.768	1.3624	1.3624
BTZ-043	3485.463	3485.463	1.0000	1.0000


stopifnot(
  # Deterministic typical-value steady state. M2 exposure rises by the
  # reciprocal of the published 73.4% factor; the parent is untouched.
  abs(m2_day14 / m2_day9 - 1 / 0.734) < 0.01,
  abs(p_day14 / p_day9 - 1) < 1e-3
)

sim_ss |>
  dplyr::filter(time >= 168) |>
  ggplot(aes(time / 24, Cc_m2)) +
  geom_line(linewidth = 0.6, colour = "#2b6cb0") +
  geom_vline(xintercept = 10, linetype = 2) +
  labs(
    x = "Day on treatment", y = "M2 (nmol/L)",
    title = "Typical-value M2 across the Day 10 clearance step",
    subtitle = "500 mg daily, 54 kg, standard breakfast; dashed line = 240 h"
  ) +
  theme_bw()

Virtual cohort and PKNCA

Koele 2025 publishes no NCA table, so there is nothing to compare a non-compartmental analysis against externally. PKNCA is used here for the check that is available and is worth more anyway: an independent implementation of AUC and Cmax run over a simulated cohort, with the typical-value AUC(0-inf) compared against F * dose / CL.

rxode2::rxSetSeed(20250908)
n_per_arm <- 60L
arms <- c("standard, dose after", "high-fat", "fasted")

cohort_ev <- lapply(seq_along(arms), function(k) {
  ids <- seq_len(n_per_arm) + (k - 1L) * n_per_arm
  btz_events(500, sort(unique(c(
    0, seq(0.25, 12, by = 0.25), seq(13, 24, by = 1)
  ))), id = ids) |>
    with_covs(WT = 54, arm = arms[k]) |>
    dplyr::mutate(arm = arms[k])
}) |> dplyr::bind_rows()

sim_cohort <- rxode2::rxSolve(
  mod_pk, cohort_ev, returnType = "data.frame", useLinCmt = FALSE,
  keep = c("arm", "WT")
) |>
  dplyr::filter(!is.na(Cc))
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
if (is.null(sim_cohort$id)) sim_cohort$id <- 1L
nrow(sim_cohort)
#> [1] 10980

vpc_dat <- sim_cohort |>
  dplyr::filter(arm == "standard, dose after") |>
  dplyr::select(id, time, `BTZ-043` = Cc, M1 = Cc_m1, M2 = Cc_m2) |>
  tidyr::pivot_longer(c(`BTZ-043`, M1, M2),
                      names_to = "analyte", values_to = "conc") |>
  dplyr::group_by(analyte, time) |>
  dplyr::summarise(
    lo  = quantile(conc, 0.025),
    mid = quantile(conc, 0.5),
    hi  = quantile(conc, 0.975),
    .groups = "drop"
  )

ggplot(vpc_dat, aes(time, mid)) +
  geom_ribbon(aes(ymin = lo, ymax = hi), alpha = 0.25, fill = "#2b6cb0") +
  geom_line(linewidth = 0.8, colour = "#2b6cb0") +
  facet_wrap(~analyte, scales = "free_y") +
  labs(
    x = "Time after dose (h)", y = "Concentration (nmol/L)",
    title = "Simulated 2.5th / 50th / 97.5th percentiles, 60 subjects",
    subtitle = "Replicates the layout of Koele 2025 Figure 2 (500 mg, standard breakfast, 54 kg)"
  ) +
  theme_bw()

conc_dat <- sim_cohort |>
  dplyr::filter(!is.na(Cc)) |>
  dplyr::transmute(id = as.integer(id), time, conc = Cc, treatment = arm)
stopifnot(nrow(conc_dat) > 0, all(conc_dat$conc >= 0))

dose_dat <- conc_dat |>
  dplyr::distinct(id, treatment) |>
  dplyr::mutate(time = 0, dose = 500)

o_conc <- PKNCA::PKNCAconc(conc_dat, conc ~ time | treatment + id)
o_dose <- PKNCA::PKNCAdose(dose_dat, dose ~ time | treatment + id)
o_data <- PKNCA::PKNCAdata(
  o_conc, o_dose,
  intervals = data.frame(
    start = 0, end = 24,
    cmax = TRUE, tmax = TRUE, auclast = TRUE, half.life = TRUE
  )
)
res <- suppressWarnings(PKNCA::pk.nca(o_data))
nca <- as.data.frame(res)

nca_summary <- nca |>
  dplyr::filter(PPTESTCD %in% c("cmax", "tmax", "auclast", "half.life")) |>
  dplyr::group_by(treatment, PPTESTCD) |>
  dplyr::summarise(
    Median = median(PPORRES, na.rm = TRUE),
    `P5` = quantile(PPORRES, 0.05, na.rm = TRUE),
    `P95` = quantile(PPORRES, 0.95, na.rm = TRUE),
    .groups = "drop"
  ) |>
  dplyr::rename("Prandial state" = treatment, "NCA parameter" = PPTESTCD)
knitr::kable(nca_summary, digits = 2)

Prandial state	NCA parameter	Median	P5	P95
fasted	auclast	1521.44	811.42	2575.60
fasted	cmax	438.87	228.04	1031.99
fasted	half.life	4.33	4.04	4.99
fasted	tmax	1.25	0.50	2.75
high-fat	auclast	4427.54	2696.38	9016.42
high-fat	cmax	1032.81	457.69	2073.63
high-fat	half.life	4.33	3.81	4.89
high-fat	tmax	2.50	2.25	3.25
standard, dose after	auclast	3435.66	1925.15	7487.71
standard, dose after	cmax	800.20	360.39	1992.69
standard, dose after	half.life	4.40	3.96	5.13
standard, dose after	tmax	2.50	2.24	3.75

The cohort medians order as the model requires, with the high-fat arm above the standard-breakfast reference and the fasted arm below it.

med_auc <- nca_summary |>
  dplyr::filter(`NCA parameter` == "auclast") |>
  dplyr::select(`Prandial state`, Median) |>
  tibble::deframe()
stopifnot(all(arms %in% names(med_auc)))

ratio_hf <- unname(med_auc["high-fat"] / med_auc["standard, dose after"])
ratio_fa <- unname(med_auc["fasted"] / med_auc["standard, dose after"])
c(high_fat = ratio_hf, fasted = ratio_fa)
#>  high_fat    fasted 
#> 1.2887025 0.4428388

stopifnot(
  # These are COHORT medians, not the deterministic ratios checked earlier,
  # so the bounds admit the sampling noise of a 60-subject arm while still
  # going red on a mis-transcribed F factor (which would move them by tens
  # of percent). Published factors are 1.41 and 0.458.
  ratio_hf > 1.15, ratio_hf < 1.75,
  ratio_fa > 0.33, ratio_fa < 0.62
)

A separate deterministic check ties PKNCA’s own integration back to the closed form, on the typical-value profile over a window long enough for BTZ-043 to be numerically complete.

ev_tv <- btz_events(500, sort(unique(c(
  seq(0, 12, by = 0.05), seq(12.5, 72, by = 0.5)
)))) |> with_covs(WT = 70)
sim_tv <- solve_pk(ev_tv) |> dplyr::filter(!is.na(Cc))
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalfdepot', 'etalcl_m1', 'etalvc_m1', 'etalcl_m2', 'etalvc_m2', 'etaiov_fdepot_1', 'etaiov_fdepot_2', 'etaiov_fdepot_3', 'etaiov_mtt_1', 'etaiov_ka_1', 'etaiov_mtt_2', 'etaiov_ka_2', 'etaiov_mtt_3', 'etaiov_ka_3'

tv_conc <- data.frame(id = 1L, treatment = "typical",
                      time = sim_tv$time, conc = sim_tv$Cc)
tv_dose <- data.frame(id = 1L, treatment = "typical", time = 0, dose = 500)
tv_res <- suppressWarnings(PKNCA::pk.nca(PKNCA::PKNCAdata(
  PKNCA::PKNCAconc(tv_conc, conc ~ time | treatment + id),
  PKNCA::PKNCAdose(tv_dose, dose ~ time | treatment + id),
  intervals = data.frame(start = 0, end = Inf, aucinf.obs = TRUE, cmax = TRUE)
)))
tv_nca <- as.data.frame(tv_res)
aucinf <- tv_nca$PPORRES[tv_nca$PPTESTCD == "aucinf.obs"]
stopifnot(length(aucinf) == 1L, !is.na(aucinf))

tibble::tibble(
  Quantity = "BTZ-043 AUC(0-inf), 500 mg, 70 kg, standard breakfast",
  `PKNCA (nmol*h/L)` = aucinf,
  `Closed form dose/CL (nmol*h/L)` = dose_nmol / 404,
  Ratio = aucinf / (dose_nmol / 404)
) |>
  knitr::kable(digits = c(0, 1, 1, 4))

Quantity	PKNCA (nmol*h/L)	Closed form dose/CL (nmol*h/L)	Ratio
BTZ-043 AUC(0-inf), 500 mg, 70 kg, standard breakfast	2869	2868.9	1


stopifnot(
  # Deterministic: PKNCA log-linear extrapolation of a typical-value profile
  # against the model's own closed form. Tolerance is the trapezoidal error
  # of the 0.05 h / 0.5 h grid.
  abs(aucinf / (dose_nmol / 404) - 1) < 0.01
)

Exposure-response: linking the two models

The PD model is driven by AUC_BTZ043TOT, the individual BTZ-043total (BTZ-043 + M2) AUC over the 24 h dosing interval expressed in ng/mL*h. The PK model works in nmol/L, so the link between the two models is one multiplication by MW / 1000. The paper computed the metric on Day 12 (Stage 1) or Day 14 (Stage 2); Day 14 is used here, which is on the far side of the M2 clearance step.

btz_total_auc <- function(dose, WT = 54, arm = "standard, dose after",
                          DOSE_HIGH = 0) {
  ev <- btz_events(dose, seq(312, 336, by = 0.02), n_dose = 14) |>
    with_covs(WT = WT, arm = arm, DOSE_HIGH = DOSE_HIGH, OCC = 3)
  s <- solve_pk(ev) |> dplyr::filter(!is.na(Cc))
  trap_auc(s$time, s$Cc_total) * NGML_PER_NM
}

EC50 <- exp(ui_pd$theta[["lec50"]])
auc500 <- btz_total_auc(500)
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalfdepot', 'etalcl_m1', 'etalvc_m1', 'etalcl_m2', 'etalvc_m2', 'etaiov_fdepot_1', 'etaiov_fdepot_2', 'etaiov_fdepot_3', 'etaiov_mtt_1', 'etaiov_ka_1', 'etaiov_mtt_2', 'etaiov_ka_2', 'etaiov_mtt_3', 'etaiov_ka_3'
tibble::tibble(
  Quantity = c("Simulated BTZ-043total AUC(0-24), Day 14, 500 mg, standard breakfast, 54 kg",
               "Published EC50"),
  `ng/mL*h` = c(auc500, EC50)
) |>
  knitr::kable(digits = 0)

Quantity	ng/mL*h
Simulated BTZ-043total AUC(0-24), Day 14, 500 mg, standard breakfast, 54 kg	19573
Published EC50	16900

Koele 2025 Results state the estimated EC50 is “similar to the exposure obtained after a 500 mg BTZ-043 dose following a standard breakfast”, and the Discussion repeats it as support for the 500 mg arm of the DECISION trial. The reconstruction puts that exposure at 1.9573^{4} ng/mLh against a published EC50 of 1.69^{4} ng/mLh – the same quantity to within about 16%, which is what a qualitative “similar to” supports given that the paper’s metric is a post-hoc individual estimate averaged over a cohort whose weights and prandial states varied.

stopifnot(
  # A qualitative claim ("similar to"), reconstructed deterministically. The
  # gate is a factor of two either way: it goes red on a wrong molar-to-mass
  # conversion (a 431-fold error), a wrong analyte (parent alone is 13-fold
  # below the total), or a wrong dosing day, but does not pretend the paper
  # stated a number it did not.
  auc500 / EC50 > 0.5, auc500 / EC50 < 2
)

The published dose-response claims

The abstract’s headline finding is that “Participants in the highest dose group in Stage 2 (1000 mg) had a 2-fold faster decrease in mycobacterial load during the initial 2 days compared with participants in the lowest dose group (250 mg)”. The Discussion adds that “The bacterial load decreased 5-6-fold faster in the first 2 days on treatment compared with Days 2-14”. Both are consequences of the Emax first-phase slope and the exposure-independent second-phase slope, so both can be reconstructed deterministically from the two packaged models chained together.

stage2_doses <- c(250, 500, 1000)
auc_by_dose <- vapply(stage2_doses, btz_total_auc, numeric(1))
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalfdepot', 'etalcl_m1', 'etalvc_m1', 'etalcl_m2', 'etalvc_m2', 'etaiov_fdepot_1', 'etaiov_fdepot_2', 'etaiov_fdepot_3', 'etaiov_mtt_1', 'etaiov_ka_1', 'etaiov_mtt_2', 'etaiov_ka_2', 'etaiov_mtt_3', 'etaiov_ka_3'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalfdepot', 'etalcl_m1', 'etalvc_m1', 'etalcl_m2', 'etalvc_m2', 'etaiov_fdepot_1', 'etaiov_fdepot_2', 'etaiov_fdepot_3', 'etaiov_mtt_1', 'etaiov_ka_1', 'etaiov_mtt_2', 'etaiov_ka_2', 'etaiov_mtt_3', 'etaiov_ka_3'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_mtt_1, etaiov_ka_1, etaiov_mtt_2, etaiov_ka_2, etaiov_mtt_3, etaiov_ka_3
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalfdepot', 'etalcl_m1', 'etalvc_m1', 'etalcl_m2', 'etalvc_m2', 'etaiov_fdepot_1', 'etaiov_fdepot_2', 'etaiov_fdepot_3', 'etaiov_mtt_1', 'etaiov_ka_1', 'etaiov_mtt_2', 'etaiov_ka_2', 'etaiov_mtt_3', 'etaiov_ka_3'

emax_cfu   <- exp(ui_pd$theta[["lemax_cfu"]])
slope2_cfu <- exp(ui_pd$theta[["lslope2_cfu"]])
slope1_cfu <- emax_cfu * auc_by_dose / (EC50 + auc_by_dose)

dr <- tibble::tibble(
  `Dose (mg)` = stage2_doses,
  `BTZ-043total AUC(0-24) (ng/mL*h)` = auc_by_dose,
  `Slope 1 cfu (log10/h)` = slope1_cfu,
  `Slope 1 / slope 2` = slope1_cfu / slope2_cfu
)
knitr::kable(dr, digits = c(0, 0, 5, 2))

Dose (mg)	BTZ-043total AUC(0-24) (ng/mL*h)	Slope 1 cfu (log10/h)	Slope 1 / slope 2
250	9786	0.00990	3.90
500	19573	0.01449	5.70
1000	39145	0.01886	7.42


ratio_1000_250 <- slope1_cfu[stage2_doses == 1000] /
  slope1_cfu[stage2_doses == 250]
c(`slope1 1000mg / slope1 250mg` = ratio_1000_250)
#> slope1 1000mg / slope1 250mg 
#>                     1.904625

stopifnot(
  # "2-fold faster" (abstract and Discussion). Deterministic given the two
  # models, so the band is narrow; it goes red if the EC50, either Emax or
  # the molar-to-mass conversion is mis-transcribed.
  ratio_1000_250 > 1.7, ratio_1000_250 < 2.3,
  # "5-6-fold faster in the first 2 days" (Discussion). The paper's figure is
  # a cohort average over the three Stage 2 dose groups, so the check is that
  # the reconstructed per-dose range brackets it rather than that any single
  # dose hits it.
  min(dr$`Slope 1 / slope 2`) < 5, max(dr$`Slope 1 / slope 2`) > 6
)

Bacterial-load trajectories

The PD model has no ODE states and no dosing events: it is a bilinear regression on time since the start of treatment, with a shared node fixed at 48 h. Both endpoints are on the log10 scale, cfu falling and TTP rising.

pd_events <- function(auc, times, id = 1L) {
  tidyr::expand_grid(id = id, time = times) |>
    dplyr::mutate(evid = 0L, AUC_BTZ043TOT = auc)
}

pd_times <- sort(unique(c(seq(0, 336, by = 2), 48)))
pd_typ <- lapply(seq_along(stage2_doses), function(k) {
  s <- rxode2::rxSolve(
    rxode2::zeroRe(mod_pd), pd_events(auc_by_dose[k], pd_times),
    returnType = "data.frame"
  )
  dplyr::transmute(s, time, log_cfu, log_ttp,
                   dose = paste0(stage2_doses[k], " mg"))
}) |> dplyr::bind_rows()
#> ℹ parameter labels from comments will be replaced by 'label()'
#> ℹ omega/sigma items treated as zero: 'etale0_cfu', 'etale0_ttp', 'etalemax_ttp', 'etalslope2_cfu', 'etalslope2_ttp'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> ℹ omega/sigma items treated as zero: 'etale0_cfu', 'etale0_ttp', 'etalemax_ttp', 'etalslope2_cfu', 'etalslope2_ttp'
#> ℹ parameter labels from comments will be replaced by 'label()'
#> ℹ omega/sigma items treated as zero: 'etale0_cfu', 'etale0_ttp', 'etalemax_ttp', 'etalslope2_cfu', 'etalslope2_ttp'

pd_typ |>
  tidyr::pivot_longer(c(log_cfu, log_ttp), names_to = "endpoint",
                      values_to = "value") |>
  dplyr::mutate(endpoint = dplyr::recode(
    endpoint,
    log_cfu = "log10 cfu/mL", log_ttp = "log10 TTP (h)"
  )) |>
  ggplot(aes(time / 24, value, colour = dose)) +
  geom_line(linewidth = 0.8) +
  geom_vline(xintercept = 2, linetype = 2) +
  facet_wrap(~endpoint, scales = "free_y") +
  labs(
    x = "Day on treatment", y = NULL, colour = "BTZ-043 dose",
    title = "Typical-value bilinear bacterial-load decline",
    subtitle = "Dashed line = the node fixed at 48 h; Stage 2 dose groups"
  ) +
  theme_bw()

base_row <- pd_typ |> dplyr::filter(time == 0, dose == "500 mg")
node_row <- pd_typ |> dplyr::filter(time == 48, dose == "500 mg")
stopifnot(nrow(base_row) == 1L, nrow(node_row) == 1L)

# Baselines at t = 0 must be the published typical values exactly.
stopifnot(
  abs(base_row$log_cfu - 6.20) < 1e-8,
  abs(base_row$log_ttp - 1.99) < 1e-8
)

# The bilinear form must be continuous at the node: the value there equals
# baseline minus (or plus) slope1 * 48 with no second-phase contribution.
auc500_lo <- auc_by_dose[stage2_doses == 500]
s1_cfu <- emax_cfu * auc500_lo / (EC50 + auc500_lo)
s1_ttp <- exp(ui_pd$theta[["lemax_ttp"]]) * auc500_lo / (EC50 + auc500_lo)
stopifnot(
  abs(node_row$log_cfu - (6.20 - s1_cfu * 48)) < 1e-8,
  abs(node_row$log_ttp - (1.99 + s1_ttp * 48)) < 1e-8
)

# And the second phase must be shallower than the first for cfu.
late <- pd_typ |> dplyr::filter(dose == "500 mg", time %in% c(48, 336))
stopifnot(diff(range(late$log_cfu)) / (336 - 48) < s1_cfu)

rxode2::rxSetSeed(20250908)
n_pd <- 100L
pd_obs_times <- c(0, 48, 72, 96, 144, 192, 264, 336)

pd_cohort_ev <- pd_events(auc_by_dose[stage2_doses == 500],
                          pd_obs_times, id = seq_len(n_pd))
pd_cohort <- rxode2::rxSolve(mod_pd, pd_cohort_ev,
                             returnType = "data.frame")
#> ℹ parameter labels from comments will be replaced by 'label()'
if (is.null(pd_cohort$id)) pd_cohort$id <- 1L

pd_cohort |>
  dplyr::select(id, time, `log10 cfu/mL` = log_cfu,
                `log10 TTP (h)` = log_ttp) |>
  tidyr::pivot_longer(c(`log10 cfu/mL`, `log10 TTP (h)`),
                      names_to = "endpoint", values_to = "value") |>
  dplyr::group_by(endpoint, time) |>
  dplyr::summarise(
    lo = quantile(value, 0.025), mid = quantile(value, 0.5),
    hi = quantile(value, 0.975), .groups = "drop"
  ) |>
  ggplot(aes(time / 24, mid)) +
  geom_ribbon(aes(ymin = lo, ymax = hi), alpha = 0.25, fill = "#b7791f") +
  geom_line(linewidth = 0.8, colour = "#b7791f") +
  facet_wrap(~endpoint, scales = "free_y") +
  labs(
    x = "Day on treatment", y = NULL,
    title = "Simulated 2.5th / 50th / 97.5th percentiles, 100 subjects at 500 mg",
    subtitle = "Replicates the layout of Koele 2025 Figure 4 (without the censoring panels)"
  ) +
  theme_bw()

bl <- pd_cohort |> dplyr::filter(time == 0)
end <- pd_cohort |> dplyr::filter(time == 336)
stopifnot(nrow(bl) == n_pd, nrow(end) == n_pd)

# Cohort statistics, so these are magnitude and trend checks, not exact
# values. Published baseline CVs are 15.2% (cfu) and 5.14% (TTP); the bands
# below sit well outside a 100-subject sampling spread but still go red on a
# variance transcribed on the wrong scale (a variance-vs-SD confusion would
# move them several-fold).
cv <- function(x) sd(x) / mean(x)
c(cv_cfu = cv(bl$log_cfu), cv_ttp = cv(bl$log_ttp))
#>     cv_cfu     cv_ttp 
#> 0.15318889 0.05416901
stopifnot(
  cv(bl$log_cfu) > 0.08, cv(bl$log_cfu) < 0.25,
  cv(bl$log_ttp) > 0.02, cv(bl$log_ttp) < 0.10,
  # Trend over 14 days: cfu falls, TTP rises, in the cohort median.
  median(end$log_cfu) < median(bl$log_cfu),
  median(end$log_ttp) > median(bl$log_ttp)
)

Assumptions and deviations

Two dose records per administration. The parallel-absorption structure needs the dose written to depot1 and depot2 at each dosing time; f() then splits it. This mirrors the source dataset, whose DOSEX column flags the second dose record for the parallel route. A simulation that doses only depot1 silently drops 35.6% of the fed bioavailable dose.
Molar bookkeeping. Amounts are nmol and concentrations nmol/L, following the source analysis (“Concentration data were transformed to molar units to preserve mass balance”). The mg-to-nmol conversion sits inside f(), so units$dosing is "mg" while units$concentration is "nmol/L"; the convention checker emits an informational note about this by design.
Fractions metabolised fixed to 1. The full parent elimination flux feeds BOTH metabolite compartments, so metabolite mass balance is relative, not absolute, and every clearance and volume is an apparent value. This is the authors’ choice, not a transcription artefact; changing it would invalidate every published estimate.
The M2 clearance step is derived from time, not from a data column. The source dataset carries a DAY item and switches under IF(DAY.GT.10). With Day 1 spanning 0 to 24 h this is t >= 240 h, which is how the model derives it, so no extra column is needed. A simulation whose event table does not start at the beginning of treatment will place the step incorrectly.
Prandial state is encoded as two registered indicators, not one four-level factor. FED marks food already present at dosing and FASTED_STRICT marks a dose with no food on either side; FED_HIGHFAT refines the fed level. The fourth state – dose taken immediately before a standard breakfast – is the complement (1 - FED) * (1 - FASTED_STRICT), derived inside model(). This reproduces the control stream’s FOOD codes exactly.
Between-occasion variability is retained. Relative bioavailability carries IIV plus IOV; mean transit time and ka carry IOV ONLY, as a correlated pair. Simulations in this vignette set OCC = 1 throughout, i.e. a single occasion, which is what the covariate documentation recommends when the occasion structure of the source trial is not being reproduced.
Not encoded: censoring. The PD model’s M3 partial likelihood, its LLOQ of 1 cfu/mL and ULOQ of log10(25 * 24) for TTP, and the baseline probability of a negative culture (0.9% for cfu, 0% for TTP) have no idiomatic nlmixr2lib encoding and are omitted. The packaged model predicts the uncensored trajectory; the censoring panels of Koele 2025 Figure 4 are therefore not reproduced.
Not encoded: replicate-level and cross-endpoint residual correlation. The PD $SIGMA BLOCK(4) resolves four replicate-level SDs with a full correlation matrix (see Errata). The packaged model uses the published per-endpoint averages with independent residuals.
Not encoded: the BLQ handling of the PK dataset. The published PK model excluded the 600 (33%) BTZ-043, 159 (8.8%) M1 and 146 (8.1%) M2 observations below the 20 ng/mL limit of quantification, because the M3 re-estimation was unstable. Simulations from the packaged model produce concentrations throughout the elimination phase that the source analysis never fitted; the paper is explicit that the BTZ-043 late-elimination phase is the part the model describes least well.
No published NCA table. Koele 2025 reports no Cmax / Tmax / AUC / half-life summary, so the PKNCA section compares against the model’s own closed forms rather than against published non-compartmental values.
cmt = "Cc" on observation rows. Required, not optional: with three declared endpoints rxode2 rejects an ODE-state cmt and rejects dvid-only rows. The repository’s static vignette lint flags this form; the guard chunk above demonstrates that no compartment is renumbered.

Errata and source conflicts

Three places where the paper is internally inconsistent. In each case the resolution is recorded here and in the model file comments.

1. The mean-transit-time sentence is inverted relative to the paper’s own table and control stream. Koele 2025 Results says “The mean transit time decreased by 64% (95% CI: 53%-72%) when taken together with any kind of food.” The corresponding Table 2 row is labelled “Dose prior to standard food/no food on MTT (%) 36.0 (27.6-46.8)”, and the control stream applies the factor under IF(WITHFOOD.EQ.0)MTTeff = THETA(5). Table and code agree with each other and with the physiology (food delays gastric emptying, so MTT is LONGER with food); the prose sentence has the direction backwards. The model follows the table and the code: MTT is 0.340 h with food and 0.340 * 0.360 = 0.122 h without.

2. The M1 fraction-metabolised effect is applied to the no-food arm in the control stream, while the Table 2 row label and the prose attribute it to the fed arm. The control stream reads FM1FOOD = 1; IF(WITHFOOD.EQ.0)FM1FOOD = THETA(23), then CLM1 = TVCLM1/FM1FOOD and VM1 = TVVM1/FM1FOOD, so M1 exposure is 1.39-fold HIGHER when no food is present at dosing. Table 2 labels the row “Administration with food on FM1 (%) 141 [sic 139]” and the Results say the fraction metabolised to M1 “increased by 39% … when BTZ-043 was administered together with food”. The model follows the executable control stream, for three reasons: it is the artefact that produced the published numbers; the immediately preceding MTT effect uses the identical IF(WITHFOOD.EQ.0) gate and there the table label agrees with the code, so the labelling convention in that block of Table 2 is “the arm the theta applies to”; and the same paragraph of the Results contains the demonstrably inverted MTT sentence. A user who needs the opposite direction can flip it by changing the exponent on e_fed_fm_m1 in model() from (1 - FED) to FED; the absolute M1 concentrations move by a factor of 1.39 in the fed arms.

3. Table 3 prints an impossible variability for the first TTP slope. The row reads “Emax slope 1 TTP … 75.9 (35.4-67.1)”: the point estimate lies outside its own confidence interval, and 75.9 is exactly the value printed one row below for the second cfu slope. The control stream’s $OMEGA BLOCK(3) third diagonal is 0.217, which gives CV = sqrt(exp(0.217) - 1) = 49.2% – inside the printed 35.4 to 67.1 interval. The model uses 0.217 and treats 75.9 as a copy-paste error.

Two smaller discrepancies, resolved in favour of the published tables because the supplementary $THETA blocks are initial estimates:

The PK control stream’s residual-error initials (0.477, 0.329, 0.285) differ from the Table 2 finals (0.505, 0.338, 0.290). Every other PK $THETA and every $OMEGA in that control stream equals the published final estimate exactly, which is what makes the three residual entries identifiable as stale initials. Table 2 is used.
The PD control stream rounds two slopes (0.0039 and 0.0004) relative to the Table 3 finals (0.00386 and 0.000440). Table 3 is used.

Finally, the supplementary $PRED block omits EXP(ETA(3)) from BETA1BTZTTP, even though ETA(3) is declared in $OMEGA BLOCK(3) with a non-zero variance and two estimated correlations, Table 3 reports its variability, and the Results state that IIV was identified on the first TTP slope. The packaged model applies it; the omission is a transcription slip.

For completeness, the full PD residual covariance the packaged model simplifies:

Supplementary $SIGMA BLOCK(4) (variances on the diagonal)
	cfu rep 1	cfu rep 2	TTP rep 1	TTP rep 2
cfu rep 1	0.2990	0.2780	-0.0180	-0.0175
cfu rep 2	0.2780	0.3220	-0.0194	-0.0189
TTP rep 1	-0.0180	-0.0194	0.0043	0.0033
TTP rep 2	-0.0175	-0.0189	0.0033	0.0035

Endpoint	Mean replicate SD	Table 3 value
cfu	0.5571	0.5580
TTP	0.0624	0.0624

Session information

sessionInfo()
#> R version 4.6.1 (2026-06-24)
#> Platform: x86_64-pc-linux-gnu
#> Running under: Ubuntu 24.04.5 LTS
#> 
#> Matrix products: default
#> BLAS:   /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3 
#> LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so;  LAPACK version 3.12.0
#> 
#> locale:
#>  [1] LC_CTYPE=C.UTF-8       LC_NUMERIC=C           LC_TIME=C.UTF-8       
#>  [4] LC_COLLATE=C.UTF-8     LC_MONETARY=C.UTF-8    LC_MESSAGES=C.UTF-8   
#>  [7] LC_PAPER=C.UTF-8       LC_NAME=C              LC_ADDRESS=C          
#> [10] LC_TELEPHONE=C         LC_MEASUREMENT=C.UTF-8 LC_IDENTIFICATION=C   
#> 
#> time zone: UTC
#> tzcode source: system (glibc)
#> 
#> attached base packages:
#> [1] stats     graphics  grDevices utils     datasets  methods   base     
#> 
#> other attached packages:
#> [1] ggplot2_4.0.3         tibble_3.3.1          tidyr_1.3.2          
#> [4] dplyr_1.2.1           rxode2_5.1.6          PKNCA_0.12.1         
#> [7] nlmixr2lib_0.3.2.9000
#> 
#> loaded via a namespace (and not attached):
#>  [1] gtable_0.3.6        xfun_0.60           bslib_0.12.0       
#>  [4] lattice_0.22-9      vctrs_0.7.3         tools_4.6.1        
#>  [7] generics_0.1.4      parallel_4.6.1      symengine_0.2.13   
#> [10] pkgconfig_2.0.3     data.table_1.18.6.1 checkmate_2.3.4    
#> [13] RColorBrewer_1.1-3  S7_0.2.2            desc_1.4.3         
#> [16] RcppParallel_6.2.1  lifecycle_1.0.5     compiler_4.6.1     
#> [19] farver_2.1.2        textshaping_1.0.5   fontawesome_0.5.3  
#> [22] htmltools_0.5.9     sys_3.4.3           sass_0.4.10        
#> [25] yaml_2.3.12         pillar_1.11.1       pkgdown_2.2.1      
#> [28] crayon_1.5.3        jquerylib_0.1.4     whisker_0.4.1      
#> [31] openssl_2.4.2       cachem_1.1.0        nlme_3.1-169       
#> [34] tidyselect_1.2.1    digest_0.6.39       lotri_1.0.4        
#> [37] purrr_1.2.2         labeling_0.4.3      rxode2ll_2.0.17    
#> [40] fastmap_1.2.0       grid_4.6.1          cli_3.6.6          
#> [43] dparser_1.3.1-13    magrittr_2.0.5      withr_3.0.3        
#> [46] scales_1.4.0        backports_1.5.1     rmarkdown_2.32     
#> [49] otel_0.2.0          askpass_1.2.1       ragg_1.5.2         
#> [52] memoise_2.0.1       evaluate_1.0.5      knitr_1.52         
#> [55] rex_1.2.2           PreciseSums_0.7     rlang_1.3.0        
#> [58] downlit_0.4.5       Rcpp_1.1.2          glue_1.8.1         
#> [61] xml2_1.6.0          jsonlite_2.0.0      R6_2.6.1           
#> [64] systemfonts_1.3.2   fs_2.1.0