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Caspofungin (Martson 2020)

Source: vignettes/articles/Martson_2020_caspofungin.Rmd
Martson_2020_caspofungin.Rmd

Model and source 

ui <- rxode2::rxode(readModelDb("Martson_2020_caspofungin"))
#> ℹ parameter labels from comments will be replaced by 'label()'
  • Citation: Martson A-G, van der Elst KCM, Veringa A, Zijlstra JG, Beishuizen A, van der Werf TS, Kosterink JGW, Neely M, Alffenaar J-W. Caspofungin weight-based dosing supported by a population pharmacokinetic model in critically ill patients. Antimicrob Agents Chemother. 2020;64(9):e00905-20. doi:10.1128/AAC.00905-20. PMCID: PMC7449215.
  • Article: https://doi.org/10.1128/AAC.00905-20 (open access, CC BY 4.0)
  • Model: Martson_2020_caspofungin

Two-compartment population PK model for intravenous caspofungin in critically ill adults in the intensive care unit with (suspected) invasive candidiasis (Groningen / Enschede, the Netherlands). Fitted non-parametrically with the NPAG algorithm in Pmetrics 1.5.2 on primary parameters Ke (elimination rate constant), V (central volume) and the intercompartmental rate constants kcp and kpc. Body weight is the only retained covariate and scales the central volume linearly, V = V0 * WT / 78 with 78 kg the cohort median; since Ke carries no covariate, clearance CL = Ke * V is also proportional to weight, which is the basis of the paper’s weight-based (2 mg/kg loading, 1.25 mg/kg maintenance) dosing recommendation. Typical values are the means of the NPAG marginal distributions (Table 2); inter-individual variability is a log-normal approximation built from the Table 2 CV% column. Table 2 prints V0 in ‘liters/kg’, but the equation V = V0 * weight/78 and the Discussion’s CL ~ 0.7 L/h (= 0.09 x 7.71) show V0 is the volume in litres of a 78 kg patient; see the vignette Errata.

Population

Twenty adult intensive-care patients with suspected or proven invasive candidiasis were treated with caspofungin in a therapeutic-drug-monitoring study at two Dutch hospitals (Table 1). All received a 70 mg loading dose on day 1, then 50 mg daily (70 mg above 80 kg; 35 mg or 50 mg with moderate hepatic impairment), each as a 1 h infusion. Nine samples were drawn over one dosing interval on day 3 (range 2-4): pre-dose and 1, 2, 3, 4, 6, 8, 12 and 24 h after the start of the infusion. Five patients whose dose was raised because the measured AUC0-24 was below 98 mg*h/L were sampled a second time, giving 25 occasions and 219 concentrations.

Median age was 56 years (range 25-83) and median weight 78 kg (48-139); 11 of 20 (55%) were male. Forty percent were on continuous venovenous hemofiltration and 55% received prednisolone or hydrocortisone. Median SAPS 3 was 59 and median serum albumin 20 g/L. Two patients had Child-Pugh C liver impairment.

str(ui$population)
#> List of 15
#>  $ species         : chr "human"
#>  $ n_subjects      : int 20
#>  $ n_studies       : int 1
#>  $ n_occasions     : int 25
#>  $ n_concentrations: int 219
#>  $ age_range       : chr "25-83 years"
#>  $ age_median      : chr "56 years"
#>  $ weight_range    : chr "48-139 kg"
#>  $ weight_median   : chr "78 kg"
#>  $ sex_female_pct  : num 45
#>  $ race_ethnicity  : chr "Not reported"
#>  $ disease_state   : chr "Adult critically ill ICU patients treated with caspofungin for (suspected) invasive candidiasis. Median SAPS 3 "| __truncated__
#>  $ dose_range      : chr "70 mg loading dose on day 1, then 50 mg daily (<= 80 kg) or 70 mg daily (> 80 kg); 35 mg / 50 mg with moderate "| __truncated__
#>  $ regions         : chr "The Netherlands (University Medical Center Groningen; Medisch Spectrum Twente, Enschede)"
#>  $ notes           : chr "Demographics from Martson 2020 Table 1 (reproduced from the parent TDM study). Nine samples per dosing occasion"| __truncated__

Source trace

Element Value Source
Structure 2-compartment, IV infusion, first-order elimination Results, ‘Population pharmacokinetic model’; Table 2
Estimation NPAG, Pmetrics 1.5.2 Methods, ‘Population pharmacokinetic modeling’
lkel log(0.09) 1/h (mean; SD 0.04, median 0.08, CV 42.38%) Table 2, Abstract
lvc log(7.71) L at 78 kg (mean; SD 2.70, median 7.20, CV 34.98%) Table 2 (unit printed as liters/kg, see Errata)
lk12 (kcp) log(0.44) 1/h (mean; SD 0.38, median 0.28, CV 88.02%) Table 2
lk21 (kpc) log(0.46) 1/h (mean; SD 0.35, median 0.34, CV 75.98%) Table 2
Weight effect V = V0 * WT / 78 Results text; Table S1 model 6 (‘Pop median: 78kg’)
etalkel, etalvc, etalk12, etalk21 log(CV^2 + 1) of the Table 2 CV% Table 2 (log-normal approximation, see Assumptions)
Assay polynomial SD = 0.05 + 0.08 * C Methods, ‘Model diagnostics’
gamma 0.654 (multiplicative) Results, ‘Population pharmacokinetic model’
addSd 0.654 * 0.05 = 0.0327 mg/L derived
propSd 0.654 * 0.08 = 0.05232 derived
Parameter ranges of the final NPAG run Ke 0-0.4, V0 0.01-18, kcp 0-2, kpc 0-5 Table S1, model 24

Typical-value checks

The model is linear, so every exposure metric of a typical patient follows from CL = Ke * V0 * WT / 78 exactly. These checks use a single typical-value solve (no IIV, no residual error) and therefore carry tight bounds.

mod_typ <- rxode2::zeroRe(ui)

# Clearance of the typical 78 kg patient. The Discussion states: 'with a Ke of
# 0.09, our CL is approximately 0.7 liters' (i.e. L/h).
cl_typ <- 0.09 * 7.71
cl_typ
#> [1] 0.6939

# Regimen helper: loading dose on day 1, maintenance daily thereafter, all as
# 1 h infusions, observations on a fine grid for trapezoidal AUCs.
make_ev <- function(ld, md, days = 14, id = 1L) {
  ev <- rxode2::et(amt = ld, dur = 1, cmt = "central")
  if (md > 0) {
    ev <- rxode2::et(ev, amt = md, dur = 1, ii = 24, addl = days - 2, time = 24, cmt = "central")
  }
  ev <- rxode2::et(ev, seq(0, 24 * days, by = 0.25), cmt = "central")
  d <- as.data.frame(ev)
  d$id <- id
  d
}

auc_window <- function(sim, from, to) {
  s <- sim[sim$time >= from & sim$time <= to, ]
  sum(diff(s$time) * (head(s$Cc, -1) + tail(s$Cc, -1)) / 2)
}

solve_typ <- function(ld, md, wt, days = 14) {
  d <- make_ev(ld, md, days)
  d$WT <- wt
  sim <- suppressMessages(rxode2::rxSolve(mod_typ, d, returnType = "data.frame",
                                          rtol = 1e-10, atol = 1e-12))
  if (is.null(sim$id)) sim$id <- 1L
  sim
}

A mg/kg regimen gives a weight-independent AUC

Because both V and CL are proportional to weight, a dose in mg/kg produces the same AUC and the same concentration profile at every weight. That is the pharmacological basis of the paper’s weight-based recommendation, and it is an exact property of the model.

wts <- c(50, 78, 120)
inv <- lapply(wts, function(w) {
  sim <- solve_typ(2 * w, 1.25 * w, w, days = 3)
  data.frame(WT = w,
             AUC_day1 = auc_window(sim, 0, 24),
             AUC_day3 = auc_window(sim, 48, 72))
}) |> dplyr::bind_rows()
knitr::kable(inv, digits = 3,
             caption = "Typical AUC (mg*h/L) under 2 mg/kg loading, 1.25 mg/kg maintenance.")
Typical AUC (mg*h/L) under 2 mg/kg loading, 1.25 mg/kg maintenance.
WT AUC_day1 AUC_day3
50 148.522 141.18
78 148.522 141.18
120 148.522 141.18 

# Same typical parameters on both sides; the only difference is integrator
# error at rtol 1e-10, far below this bound.
stopifnot(
  max(abs(inv$AUC_day1 / inv$AUC_day1[2] - 1)) < 1e-6,
  max(abs(inv$AUC_day3 / inv$AUC_day3[2] - 1)) < 1e-6
)

Replicating Figure 2 (VPC median on day 3)

Figure 2 is a prediction-corrected VPC over the day-3 sampling occasion. The red median line was read from the figure by the maintainers (to about 0.3 mg/L). The cohort received 50 mg or 70 mg maintenance doses depending on weight, so the typical 78 kg profiles for those two doses should bracket the observed median.

vpc_median <- data.frame(
  tad = c(1, 4, 8, 12, 24),
  Cc_obs = c(7.6, 4.9, 3.2, 2.6, 1.9)
)

typ50 <- solve_typ(70, 50, 78, days = 4)
typ70 <- solve_typ(70, 70, 78, days = 4)
prof <- dplyr::bind_rows(
  typ50 |> dplyr::mutate(regimen = "70 mg LD, 50 mg daily"),
  typ70 |> dplyr::mutate(regimen = "70 mg LD, 70 mg daily")
) |>
  dplyr::filter(time >= 48, time <= 72) |>
  dplyr::mutate(tad = time - 48)

ggplot(prof, aes(tad, Cc, colour = regimen)) +
  geom_line() +
  geom_point(data = vpc_median, aes(tad, Cc_obs), inherit.aes = FALSE, colour = "red", size = 2) +
  labs(x = "Time after the day-3 dose (h)", y = "Caspofungin (mg/L)", colour = NULL,
       title = "Typical 78 kg profiles on day 3 vs the Figure 2 observed median (red points)",
       caption = "Replicates Figure 2 of Martson 2020 (median line only).") +
  theme_bw() + theme(legend.position = "bottom")


bracket <- vpc_median |>
  dplyr::mutate(
    lo = typ50$Cc[match(48 + tad, typ50$time)],
    hi = typ70$Cc[match(48 + tad, typ70$time)]
  )
knitr::kable(bracket, digits = 2,
             caption = "Observed VPC median vs typical 50 mg and 70 mg maintenance profiles (mg/L).")
Observed VPC median vs typical 50 mg and 70 mg maintenance profiles (mg/L).
tad Cc_obs lo hi
1 7.6 6.71 9.20
4 4.9 4.04 5.48
8 3.2 3.28 4.45
12 2.6 2.75 3.73
24 1.9 1.63 2.21 
stopifnot(
  nrow(bracket) == 5L, !anyNA(bracket$lo), !anyNA(bracket$hi),
  # Deterministic typical values vs digitised medians. Allow 10% outside the
  # 50-70 mg bracket for reading error. A volume misread as L/kg (V = 601 L)
  # or a 10-fold Ke error would miss by an order of magnitude.
  all(bracket$Cc_obs >= 0.9 * bracket$lo),
  all(bracket$Cc_obs <= 1.1 * bracket$hi)
)

Target attainment of the typical patient (Tables 3 and 4)

Tables 3 and 4 report the percentage of simulated patients whose AUC exceeds 98 mgh/L. A PTA above 50% means the median patient is above the target, so for every cell far from 50% the typical patient’s AUC must sit on the same side of 98 mgh/L. Cells between 35% and 65% are too close to call and are listed but not gated.

pta_paper <- tibble::tribble(
  ~table, ~regimen, ~ld, ~md, ~wt, ~day, ~pta98,
  "3", "70/50 mg", 70, 50, 50, 1, 73,
  "3", "70/50 mg", 70, 50, 78, 1, 14,
  "3", "70/50 mg", 70, 50, 120, 1, 0,
  "3", "70/50 mg", 70, 50, 50, 3, 79,
  "3", "70/50 mg", 70, 50, 78, 3, 19,
  "3", "70/50 mg", 70, 50, 120, 3, 0,
  "3", "100/70 mg", 100, 70, 50, 1, 98,
  "3", "100/70 mg", 100, 70, 78, 1, 57,
  "3", "100/70 mg", 100, 70, 120, 1, 10,
  "3", "100/70 mg", 100, 70, 50, 3, 99,
  "3", "100/70 mg", 100, 70, 78, 3, 61,
  "3", "100/70 mg", 100, 70, 120, 3, 12,
  "3", "70 mg daily", 70, 70, 50, 3, 98,
  "3", "70 mg daily", 70, 70, 78, 3, 53,
  "3", "70 mg daily", 70, 70, 120, 3, 11,
  "3", "100 mg daily", 100, 100, 50, 3, 100,
  "3", "100 mg daily", 100, 100, 78, 3, 98,
  "3", "100 mg daily", 100, 100, 120, 3, 37,
  "4", "2/1 mg/kg", 2, 1, 78, 1, 98,
  "4", "2/1 mg/kg", 2, 1, 78, 3, 91,
  "4", "1.5/1.25 mg/kg", 1.5, 1.25, 78, 1, 83,
  "4", "1.5/1.25 mg/kg", 1.5, 1.25, 78, 3, 99,
  "4", "2/1.25 mg/kg", 2, 1.25, 78, 1, 98,
  "4", "2/1.25 mg/kg", 2, 1.25, 78, 3, 100,
  "4", "1 mg/kg daily", 1, 1, 78, 1, 22,
  "4", "1 mg/kg daily", 1, 1, 78, 3, 77,
  "4", "1.5 mg/kg daily", 1.5, 1.5, 78, 1, 83,
  "4", "1.5 mg/kg daily", 1.5, 1.5, 78, 3, 100
)

pta_typ <- pta_paper |>
  dplyr::rowwise() |>
  dplyr::mutate(
    mult = if (table == "4") wt else 1,
    auc_typ = {
      sim <- solve_typ(ld * mult, md * mult, wt, days = 3)
      auc_window(sim, 24 * (day - 1), 24 * day)
    }
  ) |>
  dplyr::ungroup() |>
  dplyr::mutate(
    gated = pta98 <= 35 | pta98 >= 65,
    agree = (pta98 > 50) == (auc_typ > 98)
  )

pta_typ |>
  dplyr::select(table, regimen, wt, day, pta98, auc_typ, gated, agree) |>
  dplyr::rename(
    "Table" = table, "Regimen" = regimen, "Weight (kg)" = wt, "Day" = day,
    "Paper PTA > 98 (%)" = pta98, "Typical AUC0-24 (mg*h/L)" = auc_typ,
    "Gated" = gated, "Same side of 98" = agree
  ) |>
  knitr::kable(digits = 1)
Table Regimen Weight (kg) Day Paper PTA > 98 (%) Typical AUC0-24 (mg*h/L) Gated Same side of 98
3 70/50 mg 50 1 73 104.0 TRUE TRUE
3 70/50 mg 78 1 14 66.6 TRUE TRUE
3 70/50 mg 120 1 0 43.3 TRUE TRUE
3 70/50 mg 50 3 79 111.2 TRUE TRUE
3 70/50 mg 78 3 19 71.3 TRUE TRUE
3 70/50 mg 120 3 0 46.3 TRUE TRUE
3 100/70 mg 50 1 98 148.5 TRUE TRUE
3 100/70 mg 78 1 57 95.2 FALSE FALSE
3 100/70 mg 120 1 10 61.9 TRUE TRUE
3 100/70 mg 50 3 99 156.0 TRUE TRUE
3 100/70 mg 78 3 61 100.0 FALSE TRUE
3 100/70 mg 120 3 12 65.0 TRUE TRUE
3 70 mg daily 50 3 98 150.8 TRUE TRUE
3 70 mg daily 78 3 53 96.7 FALSE FALSE
3 70 mg daily 120 3 11 62.8 TRUE TRUE
3 100 mg daily 50 3 100 215.5 TRUE TRUE
3 100 mg daily 78 3 98 138.1 TRUE TRUE
3 100 mg daily 120 3 37 89.8 FALSE TRUE
4 2/1 mg/kg 78 1 98 148.5 TRUE TRUE
4 2/1 mg/kg 78 3 91 116.4 TRUE TRUE
4 1.5/1.25 mg/kg 78 1 83 111.4 TRUE TRUE
4 1.5/1.25 mg/kg 78 3 99 136.8 TRUE TRUE
4 2/1.25 mg/kg 78 1 98 148.5 TRUE TRUE
4 2/1.25 mg/kg 78 3 100 141.2 TRUE TRUE
4 1 mg/kg daily 78 1 22 74.3 TRUE TRUE
4 1 mg/kg daily 78 3 77 107.7 TRUE TRUE
4 1.5 mg/kg daily 78 1 83 111.4 TRUE TRUE
4 1.5 mg/kg daily 78 3 100 161.6 TRUE TRUE 

stopifnot(
  sum(pta_typ$gated) >= 20L,
  all(pta_typ$agree[pta_typ$gated])
)

Stochastic simulation

The model file carries a log-normal approximation of the NPAG distribution (see Assumptions). The chunk below simulates 200 patients per weight band under the licensed 70 mg / 50 mg regimen, for a visual comparison with Figure 2 and Table 3. It is illustrative and not gated: the approximation over-disperses clearance (see below).

rxode2::rxSetSeed(20200820)
n_arm <- 200L
arms <- data.frame(arm = 1:3, WT = c(50, 78, 120))
ev_all <- lapply(seq_len(nrow(arms)), function(a) {
  lapply(seq_len(n_arm), function(i) {
    d <- make_ev(70, 50, days = 3, id = (a - 1L) * n_arm + i)
    d$WT <- arms$WT[a]
    d
  }) |> dplyr::bind_rows()
}) |> dplyr::bind_rows()

sim <- rxode2::rxSolve(ui, ev_all, returnType = "data.frame")

stoch <- sim |>
  dplyr::group_by(id, WT) |>
  dplyr::summarise(
    AUC_day1 = sum(diff(time[time <= 24]) * (head(Cc[time <= 24], -1) + tail(Cc[time <= 24], -1)) / 2),
    AUC_day3 = sum(diff(time[time >= 48 & time <= 72]) *
      (head(Cc[time >= 48 & time <= 72], -1) + tail(Cc[time >= 48 & time <= 72], -1)) / 2),
    .groups = "drop"
  ) |>
  dplyr::group_by(WT) |>
  dplyr::summarise(
    `Median AUC day 1` = median(AUC_day1),
    `PTA day 1 (%)` = 100 * mean(AUC_day1 > 98),
    `Median AUC day 3` = median(AUC_day3),
    `PTA day 3 (%)` = 100 * mean(AUC_day3 > 98),
    .groups = "drop"
  ) |>
  dplyr::mutate(
    `Paper PTA day 1 (%)` = c(73, 14, 0),
    `Paper PTA day 3 (%)` = c(79, 19, 0)
  )
knitr::kable(stoch, digits = 1,
             caption = "70 mg loading, 50 mg daily: simulated vs Table 3 (AUC > 98 mg*h/L).")
70 mg loading, 50 mg daily: simulated vs Table 3 (AUC > 98 mg*h/L).
WT Median AUC day 1 PTA day 1 (%) Median AUC day 3 PTA day 3 (%) Paper PTA day 1 (%) Paper PTA day 3 (%)
50 92.6 47.5 106.7 56.5 73 79
78 61.9 13.5 70.7 22.5 14 19
120 37.6 2.0 41.6 3.5 0 0 

sim |>
  dplyr::filter(time >= 48, time <= 72, WT == 78) |>
  dplyr::group_by(time) |>
  dplyr::summarise(
    p05 = quantile(Cc, 0.05), p50 = median(Cc), p95 = quantile(Cc, 0.95),
    .groups = "drop"
  ) |>
  ggplot(aes(time - 48, p50)) +
  geom_ribbon(aes(ymin = p05, ymax = p95), alpha = 0.3, fill = "steelblue") +
  geom_line() +
  geom_point(data = vpc_median, aes(tad, Cc_obs), inherit.aes = FALSE, colour = "red") +
  labs(x = "Time after the day-3 dose (h)", y = "Caspofungin (mg/L)",
       title = "Simulated 5th-50th-95th percentiles, 78 kg, 50 mg maintenance",
       caption = "Red points: observed median, Figure 2 of Martson 2020.") +
  theme_bw()

PKNCA validation

The paper reports no NCA table, so PKNCA is checked against the exact linear identity for a steady-state dosing interval, AUCtau = Dose / CL, on the typical-value day-14 interval of each weight band under the licensed regimen. After 13 maintenance doses the loading-dose excess is negligible: the typical terminal (beta) half-life is about 16 h, so 288 h since the loading dose is about 18 half-lives.

nca_sim <- lapply(c(50, 78, 120), function(w) {
  solve_typ(70, 50, w, days = 14) |>
    dplyr::mutate(treatment = paste0(w, " kg"), WT = w)
}) |>
  dplyr::bind_rows() |>
  dplyr::filter(time >= 312, time <= 336) |>
  dplyr::mutate(id = 1L)

conc_df <- nca_sim |>
  dplyr::filter(!is.na(Cc)) |>
  dplyr::select(id, treatment, time, Cc)
stopifnot(all(tapply(conc_df$time, conc_df$treatment, min) == 312))

dose_df <- data.frame(
  id = 1L, treatment = c("50 kg", "78 kg", "120 kg"), time = 312, amt = 50
)

conc_obj <- PKNCA::PKNCAconc(conc_df, Cc ~ time | treatment + id)
dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | treatment + id)
intervals <- data.frame(start = 312, end = 336, cmax = TRUE, tmax = TRUE,
                        cmin = TRUE, auclast = TRUE)
nca_res <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals))

nca_tab <- as.data.frame(nca_res) |>
  dplyr::select(treatment, PPTESTCD, PPORRES) |>
  tidyr::pivot_wider(names_from = PPTESTCD, values_from = PPORRES) |>
  dplyr::mutate(
    WT = as.numeric(sub(" kg", "", treatment)),
    auc_identity = 50 / (0.09 * 7.71 * WT / 78),
    pct_err = 100 * (auclast / auc_identity - 1)
  ) |>
  dplyr::arrange(WT)

nca_tab |>
  dplyr::select(treatment, cmax, tmax, cmin, auclast, auc_identity, pct_err) |>
  dplyr::rename(
    "Weight band" = treatment, "Cmax (mg/L)" = cmax, "Tmax (h)" = tmax,
    "Cmin (mg/L)" = cmin, "AUCtau PKNCA (mg*h/L)" = auclast,
    "Dose/CL (mg*h/L)" = auc_identity, "Difference (%)" = pct_err
  ) |>
  knitr::kable(digits = 3, caption = "Day-14 dosing interval, 50 mg maintenance, typical patient.")
Day-14 dosing interval, 50 mg maintenance, typical patient.
Weight band Cmax (mg/L) Tmax (h) Cmin (mg/L) AUCtau PKNCA (mg*h/L) Dose/CL (mg*h/L) Difference (%)
50 kg 10.547 1 2.567 112.402 112.408 -0.005
78 kg 6.761 1 1.646 72.053 72.056 -0.005
120 kg 4.395 1 1.070 46.834 46.837 -0.005 

stopifnot(
  nrow(nca_tab) == 3L,
  # Deterministic typical-value solve at rtol 1e-10 vs the exact identity;
  # realised -0.005% in all three bands (trapezoid error on the 0.25 h grid).
  # A misread volume, Ke or dose moves this by tens of percent.
  max(abs(nca_tab$pct_err)) < 0.1
)

Errata

Table 2 prints V0 in ‘liters/kg’; it is litres at 78 kg

Table 2 (and the Abstract) give the central volume as 7.71 ‘liters/kg’, but three statements in the same paper show that V0 is the central volume, in litres, of a patient at the 78 kg cohort median:

  1. The model equation printed in Results is V = V0 * weight/78. Multiplying a per-kilogram volume by a dimensionless weight ratio would give L/kg, not a volume.
  2. The Discussion states ‘with a Ke of 0.09, our CL is approximately 0.7’, which is 0.09 x 7.71 = 0.69 L/h, and compares it with a published V of 7.03 L.
  3. The final NPAG run bounded V0 to 0.01-18 (Table S1, model 24). Read as L/kg, the typical patient would have a 601 L central volume and the licensed 70 mg dose would give a day-1 AUC near 1 mg*h/L, against the 14%-above-98 of Table 3.

The model therefore uses V0 = 7.71 L. The typical-value target-attainment check above confirms it independently.

Other transcription notes

  • Table 2 prints the kcp SD as 0.38; the Abstract prints 0.39. The CV column (88.02%) corresponds to 0.387, so both are roundings of the same value.
  • Table 1 prints bilirubin in ‘mmol/liter’ (median 7.5); this can only be micromol/L. Bilirubin is not a model covariate.
  • Table 3’s column headers lost the 50 kg and 120 kg labels in the typeset table. The Results text (‘73% of ~50-kg patients, 14% of ~78-kg patients, and 0% of ~120-kg patients’) fixes the column order used above. The day-1 cells of the 70 mg and 100 mg daily regimens (no loading dose) equal those of the 70/50 mg and 100/70 mg regimens, as they must: the first dose is the same. They are listed once above.

Assumptions and deviations

  • Non-parametric distribution approximated as log-normal. NPAG estimates a discrete joint distribution of support points; the support points and their correlations were not published. The model carries independent log-normal etas with omega^2 = log(CV^2 + 1) from the Table 2 CV% column, the same convention used for other Pmetrics models in nlmixr2lib.
  • Typical values are the NPAG means. The medians are lower (Ke 0.08, V0 7.20, kcp 0.28, kpc 0.34). A log-normal centred on the mean overstates the mean of the distribution, and assuming independence between Ke and V0 overstates the spread of clearance. As a result the stochastic simulation above spreads the AUC much more widely than Tables 3-4. For example, at 2/1.25 mg/kg the paper reports 100% of patients above 98 mg*h/L on day 3, while a 1,000-patient log-normal cohort at 78 kg put 72% there (70 mg / 50 mg at 78 kg: 16% on day 1 against the paper’s 14%, so the centre agrees). For target-attainment work, treat the stochastic layer with caution. The typical-value predictions reproduce the paper (Figure 2 median, the side-of-target of every PTA cell, and the Discussion’s CL of 0.7 L/h).
  • Log-normal draws are unbounded. The final NPAG run bounded the parameters (Ke 0-0.4 1/h, V0 0.01-18 L, kcp 0-2 1/h, kpc 0-5 1/h), and the log-normal tails can exceed these ranges.
  • Residual error. Pmetrics weights observations by gamma * (C0 + C1 * C) with the observed concentration; nlmixr2 evaluates it on the prediction. The linear sum is reproduced with combined1().
  • Weight is time-fixed. The source used one weight per patient.

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         tidyr_1.3.2           dplyr_1.2.1          
#> [4] rxode2_5.1.8          PKNCA_0.12.1          nlmixr2lib_0.3.2.9000
#> 
#> loaded via a namespace (and not attached):
#>  [1] gtable_0.3.6        xfun_0.61           bslib_0.12.0       
#>  [4] rxode2lincmt_0.1.0  lattice_0.22-9      vctrs_0.7.3        
#>  [7] tools_4.6.1         generics_0.1.4      parallel_4.6.1     
#> [10] tibble_3.3.1        symengine_0.2.13    pkgconfig_2.0.3    
#> [13] data.table_1.18.6.1 checkmate_2.3.4     RColorBrewer_1.1-3 
#> [16] S7_0.2.2            desc_1.4.3          lifecycle_1.0.5    
#> [19] compiler_4.6.1      farver_2.1.2        textshaping_1.0.5  
#> [22] fontawesome_0.5.3   htmltools_0.5.9     sys_3.4.3          
#> [25] sass_0.4.10         yaml_2.3.12         pillar_1.11.1      
#> [28] pkgdown_2.2.1       crayon_1.5.3        jquerylib_0.1.4    
#> [31] whisker_0.4.1       openssl_2.4.2       cachem_1.1.0       
#> [34] nlme_3.1-169        tidyselect_1.2.1    digest_0.6.39      
#> [37] lotri_1.0.5         purrr_1.2.2         labeling_0.4.3     
#> [40] rxode2ll_2.0.18     fastmap_1.2.0       grid_4.6.1         
#> [43] cli_3.6.6           dparser_1.3.1-13    magrittr_2.0.5     
#> [46] withr_3.0.3         scales_1.4.0        backports_1.5.1    
#> [49] rmarkdown_2.32      otel_0.2.0          askpass_1.2.1      
#> [52] ragg_1.5.2          memoise_2.0.1       evaluate_1.0.5     
#> [55] knitr_1.52          rex_1.2.2           PreciseSums_0.7    
#> [58] rlang_1.3.0         downlit_0.4.5       Rcpp_1.1.2         
#> [61] glue_1.8.1          xml2_1.6.0          jsonlite_2.0.0     
#> [64] R6_2.6.1            systemfonts_1.3.2   fs_2.1.0