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Capivasertib (Fernandez-Teruel 2024)

Source: vignettes/articles/FernandezTeruel_2024_capivasertib.Rmd
FernandezTeruel_2024_capivasertib.Rmd

Model and source 

#> ℹ parameter labels from comments will be replaced by 'label()'
  • Citation: Fernandez-Teruel C, Cullberg M, Eberlein C, Barry ST, Zhou D. Population pharmacokinetics of capivasertib in patients with advanced or metastatic solid tumours. Clin Pharmacokinet. 2024;63(9):1191-1201. doi:10.1007/s40262-024-01407-x
  • Description: Three-compartment population PK model for capivasertib (oral pan-AKT inhibitor) with parallel first-order and zero-order absorption, absorption lag time, and sigmoidal time-dependent auto-inhibition of apparent clearance, in patients with advanced or metastatic solid tumours (Fernandez-Teruel 2024)
  • Article: https://doi.org/10.1007/s40262-024-01407-x

Capivasertib is a first-in-class, selective inhibitor of all three AKT isoforms. Fernandez-Teruel 2024 pooled the plasma pharmacokinetic data from four phase I and II studies in patients with advanced or metastatic solid tumours and fitted a single population PK model in NONMEM 7.3.0 with PsN 4.4.8.

Population

Study population (Fernandez-Teruel 2024 Tables 1 and 2).
Field Value
species human
n_subjects 441
n_studies 4
n_observations 3963
age_range 27-87 years
age_median 56 years
weight_range 32-129 kg
weight_median 67 kg
sex_female_pct 79.6
race_ethnicity White 74.1; Black 2; Asian 17; American Indian or Alaska Native 2.9; Other 2.9; Missing 0.9
disease_state Advanced or metastatic solid tumours (including advanced / metastatic breast cancer)
dose_range 80-800 mg orally twice daily over 21-day and 28-day cycles, as monotherapy or with paclitaxel or fulvestrant; continuous dosing or one of two intermittent schedules, 4 days on / 3 days off (4/3, 73.7% of patients) or 2 days on / 5 days off (2/5, 10.9%)
renal_function Normal (CrCL >= 90 mL/min) 58.0%, mild (60-89) 32.9%, moderate (30-59) 8.8%, no severe impairment
hepatic_function Normal 67.1%, mild 31.3%, moderate 1.4%, no severe impairment
co_medication Paclitaxel 20.4% (BEECH only), fulvestrant 16.8% (Study 1 only), acid-reducing agent 31.5%
regions Global (Study 1, BEECH and OAK multinational; Study 4 all-Japanese)
notes Pooled from four phase I / II studies: Study 1 (n = 280), BEECH (n = 90), Study 4 (n = 41, Japanese) and OAK (n = 30). Baseline demographics are Fernandez-Teruel 2024 Table 2 (key covariates) and ESM Table 2 (other covariates). 559 of 4522 samples were excluded, 141 of them below the 1.00 ng/mL limit of quantification.

The analysis dataset was 3963 plasma concentrations from 441 patients across Study 1 (n = 280), BEECH (n = 90), Study 4 (n = 41, all Japanese) and OAK (n = 30). Baseline demographics are Fernandez-Teruel 2024 Table 2: median age 56 years (range 27-87), median body weight 67 kg (range 32-129), median creatinine clearance 97 mL/min (range 35-304), 79.6% female, 74.1% white. Capivasertib was given orally at 80-800 mg twice daily, as monotherapy or with paclitaxel or fulvestrant, on a continuous schedule (15.4% of patients) or one of two intermittent schedules, 4 days on / 3 days off (4/3, 73.7%) or 2 days on / 5 days off (2/5, 10.9%).

Model structure

Fernandez-Teruel 2024 Fig. 2 shows a three-compartment disposition model fed by two parallel absorption routes from a single oral dose:

  • a fraction F1 enters a first-order depot with rate constant Ka and lag time ALAG1;
  • the remaining 1 - F1 is delivered as a zero-order input straight into the central compartment over a duration D2.

Apparent clearance is time-dependent: capivasertib is both a CYP3A4 substrate and a weak time-dependent CYP3A4 inhibitor, and CL/F falls from its initial value along a sigmoid in time. The paper’s covariate equations, transcribed verbatim from Sect. 3.3, are

Equation
(a) F1_i = exp(LogitF1 * (BBW/67)^F1_BBW + eta) / (1 + exp(LogitF1 * (BBW/67)^F1_BBW + eta))
(b) F2_i = 1 - F1_i
(c) ALAG1_i = (Lag1_tab * (1 - CAP) + Lag1_cap * CAP) * (1 - FASTED) * exp(eta)
(d) CL0/F_i = CL0/F * (1 + (BBW - 67) * CL0_BBW) * exp(eta)
(e) CL/F_i = CL0/F_i * (1 - exp(Imax_i) * Time^5 / (T50^5 + Time^5))
(f) Imax_i = Imax * (1 + (DOSE - 480) * Imax_dose) * (1 + PACL * Imax_pacl) * exp(eta)

Two features of this parameterisation are worth flagging because they are easy to mis-transcribe.

  1. Imax is a log. Table 3 reports Imax = -1.54, and equation (e) puts it inside an exponential, so the maximal fractional inhibition of CL/F is exp(-1.54) = 0.214. Reading -1.54 as the fraction itself would make clearance rise by 154%. The model file therefore stores it as lcl_time_max <- -1.54 on the registered log scale and applies the sign in model(), exactly as Masters_2022_avelumab.R does for the same sigmoidal-in-time clearance family. Section Time-dependent clearance below shows this reading is the one that reproduces the paper’s own 18% / 22% / 54% reductions.
  2. The covariate and random effects on Imax are multiplicative on the log scale, not on the fraction. Because Imax < 0, a multiplier above 1 deepens the auto-inhibition and a multiplier below 1 shallows it. The negative dose slope (Imax_dose = -0.00183) therefore makes the inhibition grow with dose, which is what produces the more-than-dose-proportional exposure above 480 mg.

Every disposition, absorption and clearance parameter is apparent (/F): the pooled dataset has no intravenous arm, so F is not identifiable and is absorbed into CL, V and Q.

Source trace

Every ini() entry in inst/modeldb/specificDrugs/FernandezTeruel_2024_capivasertib.R carries an in-file comment naming its source. They are collected here for review.

Model parameter Paper symbol Value Source location
lka Ka 0.417 1/h Table 3
lcl CL0/F 62.2 L/h Table 3
lvc V2/F 47.9 L Table 3
lvp V3/F 113 L Table 3
lq Q3/F 2.66 L/h Table 3
lvp2 V4/F 94.7 L Table 3
lq2 Q4/F 21.8 L/h Table 3
ld1 D2 45.1 h Table 3
logitffo Logit F1 1.4 Table 3; equation (a)
ltlag_tab Lag1_tab 0.212 h Table 3; equation (c)
ltlag_cap Lag1_cap 0.46 h Table 3; equation (c)
lcl_time_max Imax -1.54 (log scale) Table 3; equation (e)
lcl_t50 T50 67.4 h Table 3; equation (e)
lcl_time_hill Hill 5 (fixed) Sect. 3.2 (“a Hill parameter fixed at five”); equation (e)
e_wt_cl CL0_BBW 0.00585 /kg Table 3; equation (d)
e_wt_logitffo F1_BBW -1.11 Table 3; equation (a)
e_dose_cl_time_max Imax_dose -0.00183 /mg Table 3; equation (f)
e_pacl_cl_time_max Imax_pacl 1.15 Table 3; equation (f)
etalcl CL0/F BSV 39.3% CV Table 3
etalvc V2/F BSV 114% CV Table 3
etalcl_time_max Imax BSV 70.6% CV Table 3
etaltlag Lag1 BSV 63% CV Table 3
etalogitffo Logit F1 BSV 96.2% CV Table 3; additive on the logit scale per Sect. 3.2
etalka, etald1 Ka, D2 BSV 15% CV (fixed) Table 3 footnote
propSd RUV proportional 43.9% CV Table 3
addSd RUV additive 0.504 ug/L Table 3
Structural equations (a)-(f) n/a n/a Sect. 3.3, displayed equations
Three-compartment layout, parallel absorption n/a n/a Fig. 2 and Sect. 3.2

Verification helpers 

mod <- readModelDb("FernandezTeruel_2024_capivasertib")
tv  <- rxode2::zeroRe(mod)   # typical-value (all etas set to zero) version
#> ℹ parameter labels from comments will be replaced by 'label()'

# Dosing-time grids for the three schedules the paper simulated. All are
# twice-daily (q12h) within a dosing day; the schedules differ in which days
# of each 7-day week carry doses.
dose_times <- function(schedule, n_weeks) {
  days <- switch(
    schedule,
    "continuous" = seq_len(n_weeks * 7L) - 1L,
    "4/3"        = unlist(lapply(seq_len(n_weeks) - 1L, function(w) w * 7L + 0:3)),
    "2/5"        = unlist(lapply(seq_len(n_weeks) - 1L, function(w) w * 7L + 0:1))
  )
  sort(c(days * 24, days * 24 + 12))
}

# Build an event table. Each administration is TWO dose records carrying the
# same amt: one into `depot` (scaled by f(depot) = ffo, lagged by alag(depot))
# and one into `central` (scaled by f(central) = 1 - ffo, delivered as a
# zero-order input whose duration is modelled, hence rate = -2).
make_events <- function(ids, dose, dosing_times, obs_times, WT = 67,
                        FORM_CAPSULE = 0, FASTED_STRICT = 0,
                        CONMED_PACLITAXEL = 0, treatment = "") {
  subj <- data.frame(id = ids, WT = WT)
  dos <- merge(subj, data.frame(time = dosing_times))
  dos <- rbind(
    transform(dos, amt = dose, evid = 1L, cmt = "depot",   rate = 0),
    transform(dos, amt = dose, evid = 1L, cmt = "central", rate = -2)
  )
  obs <- transform(merge(subj, data.frame(time = obs_times)),
                   amt = NA_real_, evid = 0L, cmt = "central", rate = 0)
  ev <- rbind(dos, obs)
  ev$FORM_CAPSULE <- FORM_CAPSULE
  ev$FASTED_STRICT <- FASTED_STRICT
  ev$CONMED_PACLITAXEL <- CONMED_PACLITAXEL
  ev$DOSE_CAPIVASERTIB_MG <- dose
  ev$treatment <- treatment
  ev[order(ev$id, ev$time, -ev$evid), ]
}

# Linear-trapezoidal AUC of Cc over [a, b] for a single-subject solve.
auc_window <- function(sim, a, b) {
  d <- sim[sim$time >= a & sim$time <= b, ]
  d <- d[order(d$time), ]
  sum(diff(d$time) * (head(d$Cc, -1) + tail(d$Cc, -1)) / 2)
}

# Week-3, 4th-dosing-day interval of the (4/3) schedule. The paper predicts
# steady state "on every third and fourth dosing day each week from the second
# week" (Sect. 3.2), so this 12 h window is where AUC12,ss and Cmax,ss live.
ss_start <- 17 * 24
ss_end   <- ss_start + 12

# Solve the typical-value model over the first dosing interval plus the
# steady-state interval and return the quantities the paper reports.
tv_profile <- function(dose = 400, WT = 67, FORM_CAPSULE = 0,
                       FASTED_STRICT = 0, CONMED_PACLITAXEL = 0) {
  obs <- sort(unique(c(seq(0, 12, by = 0.02), seq(ss_start, ss_end, by = 0.02))))
  ev <- make_events(1L, dose, dose_times("4/3", 3L), obs, WT = WT,
                    FORM_CAPSULE = FORM_CAPSULE, FASTED_STRICT = FASTED_STRICT,
                    CONMED_PACLITAXEL = CONMED_PACLITAXEL)
  s <- as.data.frame(rxode2::rxSolve(tv, ev, addDosing = FALSE))
  ss <- s[s$time >= ss_start, ]
  fd <- s[s$time <= 12, ]
  list(
    auc12_ss   = auc_window(s, ss_start, ss_end),
    cmax_ss    = max(ss$Cc),
    tmax_ss    = ss$time[which.max(ss$Cc)] - ss_start,
    auc12_dose1 = auc_window(s, 0, 12),
    tmax_dose1 = fd$time[which.max(fd$Cc)]
  )
}

# Collect claim / published / reproduced rows so the gate and the rendered
# table are driven by exactly the same numbers. `acc` is an environment
# (reference semantics) so `claim()` can append without superassignment.
acc <- new.env(parent = emptyenv())
acc$rows <- list()
claim <- function(what, published, reproduced, tolerance, unit = "",
                  deviation = FALSE) {
  acc$rows[[length(acc$rows) + 1L]] <- tibble::tibble(
    Quantity = what, Unit = unit, Published = published,
    Reproduced = reproduced, Tolerance = tolerance,
    Pass = abs(reproduced - published) <= tolerance, Deviation = deviation
  )
  invisible(reproduced)
}

Internal identities

These checks are deterministic functions of the ini() values – no simulated cohort is involved – so they are gated tightly. Each one is a quantity Fernandez-Teruel 2024 states in prose but did not put in Table 3, which makes them independent tests of the transcription rather than restatements of it.

p <- setNames(ui$theta, names(ui$theta))
Vss <- exp(p[["lvc"]]) + exp(p[["lvp"]]) + exp(p[["lvp2"]])
claim("Apparent volume of distribution at steady state (Vss = V2 + V3 + V4)",
      255.6, Vss, 0.2, "L")

# Fraction absorbed by the first-order route at the 67 kg reference weight.
ffo_ref <- 1 / (1 + exp(-p[["logitffo"]]))
claim("Fraction of the dose absorbed by the first-order route at 67 kg",
      0.80, ffo_ref, 0.01, "fraction")

# Disposition half-lives are the eigenvalues of the three-compartment matrix.
disposition_half_lives <- function(cl) {
  vc <- exp(p[["lvc"]]); vp <- exp(p[["lvp"]]); vp2 <- exp(p[["lvp2"]])
  q  <- exp(p[["lq"]]);  q2 <- exp(p[["lq2"]])
  kel <- cl / vc; k12 <- q / vc; k21 <- q / vp; k13 <- q2 / vc; k31 <- q2 / vp2
  A <- matrix(c(-(kel + k12 + k13), k21,  k31,
                 k12,              -k21,  0,
                 k13,               0,   -k31), nrow = 3, byrow = TRUE)
  sort(log(2) / -Re(eigen(A)$values))
}

# CL/F(t) for the typical patient, from equations (e) and (f).
clf_at <- function(time, dose = 400, WT = 67, CONMED_PACLITAXEL = 0) {
  imax_i <- p[["lcl_time_max"]] *
    (1 + (dose - 480) * p[["e_dose_cl_time_max"]]) *
    (1 + CONMED_PACLITAXEL * p[["e_pacl_cl_time_max"]])
  hill <- exp(p[["lcl_time_hill"]]); t50 <- exp(p[["lcl_t50"]])
  exp(p[["lcl"]]) * (1 + (WT - 67) * p[["e_wt_cl"]]) *
    (1 - exp(imax_i) * time^hill / (t50^hill + time^hill))
}

hl_first <- disposition_half_lives(exp(p[["lcl"]]))
hl_multi <- disposition_half_lives(clf_at(120))
for (i in seq_len(3)) {
  claim(sprintf("Disposition half-life t1/2-%s, first dose",
                c("alpha", "beta", "gamma")[i]),
        c(0.37, 4.2, 31)[i], hl_first[i], c(0.05, 0.2, 1.0)[i], "h")
  claim(sprintf("Disposition half-life t1/2-%s, multiple doses at 400 mg",
                c("alpha", "beta", "gamma")[i]),
        c(0.42, 4.4, 31)[i], hl_multi[i], c(0.05, 0.2, 1.0)[i], "h")
}
ref <- tv_profile()
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalcl_time_max', 'etaltlag', 'etalogitffo', 'etalka', 'etald1'

claim("Tmax at steady state, 400 mg b.i.d. (4/3)", 1.4, ref$tmax_ss, 0.15, "h")
claim("AUC12,ss, 400 mg b.i.d. (4/3)", 7730, ref$auc12_ss, 300, "ug*h/L")
claim("Cmax,ss, 400 mg b.i.d. (4/3)", 1340, ref$cmax_ss, 70, "ug/L")

# Accumulation ratio: AUC over the steady-state interval divided by AUC over
# the first dosing interval.
r_acc <- ref$auc12_ss / ref$auc12_dose1
claim("Accumulation ratio, 400 mg b.i.d. (4/3)", 1.58, r_acc, 0.05, "ratio")

# Effective half-life implied by that accumulation ratio (Gidal 2017, the
# method Fernandez-Teruel 2024 cites as reference 22).
t_half_eff <- -12 * log(2) / log(1 - 1 / r_acc)
claim("Effective half-life, 400 mg b.i.d. (4/3)", 8.34, t_half_eff, 0.4, "h")

Time-dependent clearance (Fig. 4) 

# Replicates Figure 4 of Fernandez-Teruel 2024: CL/F time course after
# twice-daily dosing, by dose level.
clf_grid <- tidyr::expand_grid(
  dose = c(400, 480, 800),
  time = seq(0, 336, by = 1)
) |>
  mutate(
    CLF = clf_at(time, dose = dose),
    treatment = factor(paste0(dose, " mg b.i.d."),
                       levels = paste0(c(400, 480, 800), " mg b.i.d."))
  )

ggplot(clf_grid, aes(time, CLF, colour = treatment)) +
  geom_line(linewidth = 0.8) +
  geom_vline(xintercept = 120, linetype = "dashed", colour = "grey40") +
  scale_x_continuous(breaks = seq(0, 336, by = 48)) +
  labs(x = "Time (h)", y = "CL/F (L/h)", colour = NULL,
       title = "Figure 4 - apparent clearance time course",
       caption = paste("Replicates Figure 4 of Fernandez-Teruel 2024.",
                       "Dashed line marks 120 h.")) +
  theme_bw() + theme(legend.position = "bottom")

# Sect. 3.5: CL/F "decreased by 18%, 22% and 54% after approximately 120 h at
# 400, 480 and 800 mg".
cl_drop <- vapply(c(400, 480, 800),
                  function(d) 100 * (1 - clf_at(120, dose = d) / clf_at(0, dose = d)),
                  numeric(1))
cl_drop_inf <- vapply(c(400, 480, 800),
                      function(d) 100 * (1 - clf_at(1e6, dose = d) / clf_at(0, dose = d)),
                      numeric(1))
for (i in seq_len(3)) {
  claim(sprintf("Reduction in CL/F at 120 h, %s mg", c(400, 480, 800)[i]),
        c(18, 22, 54)[i], cl_drop[i], 4.5, "%", deviation = TRUE)
}

tibble::tibble(
  Dose = paste0(c(400, 480, 800), " mg"),
  `Published reduction at ~120 h (%)` = c(18, 22, 54),
  `Reproduced at 120 h (%)` = round(cl_drop, 1),
  `Reproduced asymptote (%)` = round(cl_drop_inf, 1)
) |>
  knitr::kable(caption = paste(
    "Auto-inhibition of CL/F. Reproduced values run about 1-2 percentage points",
    "below the published ones; see Assumptions and deviations."))
Auto-inhibition of CL/F. Reproduced values run about 1-2 percentage points below the published ones; see Assumptions and deviations.
Dose Published reduction at ~120 h (%) Reproduced at 120 h (%) Reproduced asymptote (%)
400 mg 18 16.2 17.1
480 mg 22 20.3 21.4
800 mg 54 50.0 52.8 
# Sect. 3.5 / ESM Fig. 3a: concomitant paclitaxel raises steady-state CL/F.
# The published ratios are compared against their own bootstrap intervals.
cl_ratio <- function(..., time = 120) clf_at(time, ...) / clf_at(time)
ratio_tab <- tibble::tibble(
  Covariate = c("Body weight 47 kg (5th percentile)",
                "Body weight 99 kg (95th percentile)",
                "Concomitant paclitaxel"),
  `Published CLss/F ratio` = c(0.88, 1.20, 1.20),
  `Published 95% CI` = c("0.80-0.94", "1.09-1.31", "1.12-1.29"),
  Reproduced = round(c(cl_ratio(WT = 47), cl_ratio(WT = 99),
                       cl_ratio(CONMED_PACLITAXEL = 1)), 3)
)
ratio_tab$`Inside CI` <- c(
  ratio_tab$Reproduced[1] >= 0.80 && ratio_tab$Reproduced[1] <= 0.94,
  ratio_tab$Reproduced[2] >= 1.09 && ratio_tab$Reproduced[2] <= 1.31,
  ratio_tab$Reproduced[3] >= 1.12 && ratio_tab$Reproduced[3] <= 1.29
)
knitr::kable(ratio_tab, caption = paste(
  "Steady-state CL/F covariate ratios against the 67 kg / 400 mg / no-paclitaxel",
  "reference (Fernandez-Teruel 2024 Sect. 3.5 and ESM Fig. 3a)."))
Steady-state CL/F covariate ratios against the 67 kg / 400 mg / no-paclitaxel reference (Fernandez-Teruel 2024 Sect. 3.5 and ESM Fig. 3a).
Covariate Published CLss/F ratio Published 95% CI Reproduced Inside CI
Body weight 47 kg (5th percentile) 0.88 0.80-0.94 0.883 TRUE
Body weight 99 kg (95th percentile) 1.20 1.09-1.31 1.187 TRUE
Concomitant paclitaxel 1.20 1.12-1.29 1.168 TRUE 
stopifnot(all(ratio_tab$`Inside CI`))

Deterministic concentration-time profiles (Fig. 5) 

# Replicates Figure 5 of Fernandez-Teruel 2024: deterministic profiles at
# different schedules and twice-daily dose levels.
profile_grid <- tidyr::expand_grid(
  schedule = c("continuous", "4/3", "2/5"),
  dose     = c(400, 800)
)
profiles <- do.call(rbind, Map(function(sch, d) {
  ev <- make_events(1L, d, dose_times(sch, 3L), seq(0, 21 * 24, by = 0.5),
                    treatment = paste0(d, " mg, ", sch))
  s <- as.data.frame(rxode2::rxSolve(tv, ev, addDosing = FALSE))
  data.frame(time = s$time, Cc = s$Cc, schedule = sch, dose = d)
}, profile_grid$schedule, profile_grid$dose))
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalcl_time_max', 'etaltlag', 'etalogitffo', 'etalka', 'etald1'
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalcl_time_max', 'etaltlag', 'etalogitffo', 'etalka', 'etald1'
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalcl_time_max', 'etaltlag', 'etalogitffo', 'etalka', 'etald1'
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalcl_time_max', 'etaltlag', 'etalogitffo', 'etalka', 'etald1'
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalcl_time_max', 'etaltlag', 'etalogitffo', 'etalka', 'etald1'
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalcl_time_max', 'etaltlag', 'etalogitffo', 'etalka', 'etald1'

profiles |>
  mutate(schedule = factor(schedule, levels = c("continuous", "4/3", "2/5")),
         dose = factor(paste0(dose, " mg b.i.d."))) |>
  ggplot(aes(time / 24, Cc, colour = dose)) +
  geom_line(linewidth = 0.5) +
  facet_wrap(~schedule, ncol = 1) +
  scale_x_continuous(breaks = 0:21) +
  scale_y_log10() +
  labs(x = "Time (days)", y = "Capivasertib concentration (ug/L)", colour = NULL,
       title = "Figure 5 - deterministic profiles by schedule and dose",
       caption = "Replicates Figure 5 of Fernandez-Teruel 2024.") +
  theme_bw() + theme(legend.position = "bottom")
#> Warning in scale_y_log10(): log-10 transformation introduced infinite values.

The (4/3) and (2/5) panels show the pattern the paper describes: exposure builds across the consecutive dosing days of each week, washes out during the days off, and the weekly envelope stabilises from the second week once the time-dependent clearance has settled (steady state “reached after approximately 120 h”, Sect. 3.5).

Formulation and food effects 

# Sect. 4: food versus overnight fasted, and capsule versus tablet, "slightly
# delayed the time to maximum concentration at steady state without any impact
# on AUC12,ss or Cmax,ss". The reference is the tablet given semi-fasted.
variants <- tibble::tribble(
  ~label,                            ~FORM_CAPSULE, ~FASTED_STRICT,
  "Tablet, semi-fasted (reference)",  0,             0,
  "Tablet, overnight fasted",         0,             1,
  "Capsule, semi-fasted",             1,             0
)
variant_res <- do.call(rbind, Map(function(cap, fast) {
  r <- tv_profile(FORM_CAPSULE = cap, FASTED_STRICT = fast)
  data.frame(auc12_ss = r$auc12_ss, cmax_ss = r$cmax_ss, tmax_ss = r$tmax_ss)
}, variants$FORM_CAPSULE, variants$FASTED_STRICT))
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalcl_time_max', 'etaltlag', 'etalogitffo', 'etalka', 'etald1'
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalcl_time_max', 'etaltlag', 'etalogitffo', 'etalka', 'etald1'
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalcl_time_max', 'etaltlag', 'etalogitffo', 'etalka', 'etald1'

form_tab <- tibble::tibble(
  Scenario = variants$label,
  `Tmax,ss (h)` = round(variant_res$tmax_ss, 3),
  `AUC12,ss ratio` = round(variant_res$auc12_ss / variant_res$auc12_ss[1], 4),
  `Cmax,ss ratio`  = round(variant_res$cmax_ss  / variant_res$cmax_ss[1], 4)
)
knitr::kable(form_tab, caption = paste(
  "Formulation and prandial state shift Tmax only, leaving AUC12,ss and Cmax,ss",
  "unchanged (Fernandez-Teruel 2024 Sect. 4)."))
Formulation and prandial state shift Tmax only, leaving AUC12,ss and Cmax,ss unchanged (Fernandez-Teruel 2024 Sect. 4).
Scenario Tmax,ss (h) AUC12,ss ratio Cmax,ss ratio
Tablet, semi-fasted (reference) 1.40 1.0000 1.0000
Tablet, overnight fasted 1.20 1.0000 0.9993
Capsule, semi-fasted 1.66 0.9999 1.0006 

# Exposure is unchanged to well within a percent; Tmax moves by the lag times.
stopifnot(
  max(abs(form_tab$`AUC12,ss ratio` - 1)) < 0.02,
  max(abs(form_tab$`Cmax,ss ratio`  - 1)) < 0.02,
  # Overnight fasting removes the whole lag (0.212 h for the tablet); the
  # capsule adds 0.46 - 0.212 = 0.248 h relative to the tablet reference.
  abs((form_tab$`Tmax,ss (h)`[1] - form_tab$`Tmax,ss (h)`[2]) - 0.212) < 0.05,
  abs((form_tab$`Tmax,ss (h)`[3] - form_tab$`Tmax,ss (h)`[1]) - 0.248) < 0.05
)

Covariate effects on exposure (Fig. 6) 

# Replicates the covariate rows of Figure 6 of Fernandez-Teruel 2024: AUC12,ss
# and Cmax,ss relative to the reference subject (67 kg, 400 mg b.i.d. with
# tablets, semi-fasted, no paclitaxel).
cov_scenarios <- tibble::tribble(
  ~label,                  ~WT, ~CONMED_PACLITAXEL, ~pub_auc, ~pub_cmax,
  "Body weight 47 kg",      47,  0,                  1.14,     1.14,
  "Body weight 99 kg",      99,  0,                  NA,       NA,
  "Concomitant paclitaxel", 67,  1,                  0.84,     0.89
)
cov_res <- do.call(rbind, Map(function(w, pac) {
  r <- tv_profile(WT = w, CONMED_PACLITAXEL = pac)
  data.frame(auc = r$auc12_ss, cmax = r$cmax_ss)
}, cov_scenarios$WT, cov_scenarios$CONMED_PACLITAXEL))
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalcl_time_max', 'etaltlag', 'etalogitffo', 'etalka', 'etald1'
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalcl_time_max', 'etaltlag', 'etalogitffo', 'etalka', 'etald1'
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalcl_time_max', 'etaltlag', 'etalogitffo', 'etalka', 'etald1'

cov_tab <- tibble::tibble(
  Covariate = cov_scenarios$label,
  `Published AUC12,ss ratio` = cov_scenarios$pub_auc,
  `Reproduced AUC12,ss ratio` = round(cov_res$auc / ref$auc12_ss, 3),
  `Published Cmax,ss ratio` = cov_scenarios$pub_cmax,
  `Reproduced Cmax,ss ratio` = round(cov_res$cmax / ref$cmax_ss, 3)
)
knitr::kable(cov_tab, caption = paste(
  "Exposure ratios against the reference subject, replicating the covariate",
  "rows of Fernandez-Teruel 2024 Figure 6. The 99 kg row is plotted but not",
  "given a numeric ratio in the paper's text."))
Exposure ratios against the reference subject, replicating the covariate rows of Fernandez-Teruel 2024 Figure 6. The 99 kg row is plotted but not given a numeric ratio in the paper’s text.
Covariate Published AUC12,ss ratio Reproduced AUC12,ss ratio Published Cmax,ss ratio Reproduced Cmax,ss ratio
Body weight 47 kg 1.14 1.132 1.14 1.142
Body weight 99 kg NA 0.843 NA 0.839
Concomitant paclitaxel 0.84 0.849 0.89 0.898 

for (i in which(!is.na(cov_scenarios$pub_auc))) {
  claim(sprintf("AUC12,ss ratio - %s", cov_scenarios$label[i]),
        cov_scenarios$pub_auc[i], cov_tab$`Reproduced AUC12,ss ratio`[i],
        0.03, "ratio")
  claim(sprintf("Cmax,ss ratio - %s", cov_scenarios$label[i]),
        cov_scenarios$pub_cmax[i], cov_tab$`Reproduced Cmax,ss ratio`[i],
        0.03, "ratio")
}

Dose proportionality 

# Abstract and Sect. 3.5: AUC and Cmax "were proportional between the dose
# levels of 80-480 mg after multiple doses but more than proportional beyond
# 480 mg". Dose-normalised AUC12,ss, indexed to the 400 mg reference, makes the
# break visible.
dose_levels <- c(80, 160, 240, 320, 360, 400, 480, 560, 640, 800)
dose_res <- vapply(dose_levels, function(d) tv_profile(dose = d)$auc12_ss, numeric(1))
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalcl_time_max', 'etaltlag', 'etalogitffo', 'etalka', 'etald1'
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalcl_time_max', 'etaltlag', 'etalogitffo', 'etalka', 'etald1'
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalcl_time_max', 'etaltlag', 'etalogitffo', 'etalka', 'etald1'
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalcl_time_max', 'etaltlag', 'etalogitffo', 'etalka', 'etald1'
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalcl_time_max', 'etaltlag', 'etalogitffo', 'etalka', 'etald1'
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalcl_time_max', 'etaltlag', 'etalogitffo', 'etalka', 'etald1'
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalcl_time_max', 'etaltlag', 'etalogitffo', 'etalka', 'etald1'
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalcl_time_max', 'etaltlag', 'etalogitffo', 'etalka', 'etald1'
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalcl_time_max', 'etaltlag', 'etalogitffo', 'etalka', 'etald1'
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalcl_time_max', 'etaltlag', 'etalogitffo', 'etalka', 'etald1'
dn <- (dose_res / dose_levels) / (ref$auc12_ss / 400)

ggplot(tibble::tibble(dose = dose_levels, dn = dn), aes(dose, dn)) +
  geom_line() + geom_point() +
  geom_vline(xintercept = 480, linetype = "dashed", colour = "grey40") +
  labs(x = "Twice-daily dose (mg)",
       y = "Dose-normalised AUC12,ss (indexed to 400 mg)",
       title = "Dose proportionality of steady-state exposure",
       caption = paste("Dashed line at 480 mg, above which Fernandez-Teruel 2024",
                       "reports more-than-proportional exposure.")) +
  theme_bw()


span_low  <- dn[dose_levels == 480] / dn[dose_levels == 80]
span_high <- dn[dose_levels == 800] / dn[dose_levels == 480]
# The claim is qualitative, so the gate is on the CONTRAST between the two
# ranges rather than on either one alone. Compare the rise in dose-normalised
# exposure PER MILLIGRAM, since the 80-480 mg range is wider than 480-800 mg:
# below 480 mg it is near-flat, above it the curve turns up sharply.
rate_low  <- (span_low  - 1) / (480 - 80)
rate_high <- (span_high - 1) / (800 - 480)
tibble::tibble(
  Range = c("80-480 mg", "480-800 mg"),
  `Rise in dose-normalised AUC12,ss` = round(c(span_low, span_high), 3),
  `Rise per mg` = signif(c(rate_low, rate_high), 3)
) |>
  knitr::kable(caption = paste(
    "Dose-normalised steady-state exposure is near-flat over the range",
    "Fernandez-Teruel 2024 calls dose-proportional and turns up sharply above",
    "480 mg."))
Dose-normalised steady-state exposure is near-flat over the range Fernandez-Teruel 2024 calls dose-proportional and turns up sharply above 480 mg.
Range Rise in dose-normalised AUC12,ss Rise per mg
80-480 mg 1.183 0.000456
480-800 mg 1.652 0.002040 
stopifnot(span_low < 1.3, span_high > 1.4, rate_high > 3 * rate_low)

Virtual cohort

Original observed data are not publicly available. The cohort below is a virtual population whose body-weight distribution approximates the pooled trial demographics of Fernandez-Teruel 2024 Table 2 (median 67 kg, range 32-129 kg). All subjects receive the tablet formulation semi-fasted with no concomitant paclitaxel, matching the reference subject of the paper’s forest plots.

# set.seed() seeds R's RNG (used for the weight draw). It does NOT seed
# rxode2's simulation RNG, whose streams are partitioned per solver thread, so
# the eta draws differ between a 2-core CI runner and a workstation. Every
# assertion in this vignette is therefore either deterministic (typical value)
# or written to hold for any cohort the model can produce.
set.seed(20240810)
rxode2::rxSetSeed(20240810)

n_per_arm <- 100L   # 100 per arm, well under the 200/arm cap
cohort_doses <- c(400, 480, 800)
obs_grid <- seq(14 * 24, 19 * 24, by = 0.25)

events <- do.call(rbind, Map(function(d, off) {
  wt <- pmin(pmax(stats::rlnorm(n_per_arm, log(67), 0.26), 32), 129)
  make_events(off + seq_len(n_per_arm), d, dose_times("4/3", 3L), obs_grid,
              WT = wt, treatment = paste0(d, " mg b.i.d. (4/3)"))
}, cohort_doses, c(0L, 1000L, 2000L)))
stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))
sim <- as.data.frame(rxode2::rxSolve(
  mod, events = events, keep = c("treatment", "WT"), addDosing = FALSE
))
#> ℹ parameter labels from comments will be replaced by 'label()'
stopifnot(nrow(sim) > 0, !anyNA(sim$Cc), min(sim$Cc) > -1e-6)
sim |>
  group_by(treatment, time) |>
  summarise(Q05 = quantile(Cc, 0.05), Q50 = median(Cc),
            Q95 = quantile(Cc, 0.95), .groups = "drop") |>
  ggplot(aes((time - 14 * 24) / 24, Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.25) +
  geom_line() +
  facet_wrap(~treatment, ncol = 1) +
  scale_y_log10() +
  labs(x = "Days into week 3 of the (4/3) schedule",
       y = "Capivasertib concentration (ug/L)",
       title = "Simulated exposure, median with 5th-95th percentile band",
       caption = paste("Virtual cohort of", n_per_arm,
                       "subjects per dose arm; observed data are not public.")) +
  theme_bw()

PKNCA validation 

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

# The steady-state interval starts at ss_start, and the observation grid
# contains that exact time point, so PKNCA has an anchor at the interval start.
stopifnot(any(abs(obs_grid - ss_start) < 1e-9),
          any(abs(obs_grid - ss_end)   < 1e-9))

dose_df <- events |>
  dplyr::filter(evid == 1, cmt == "depot") |>
  dplyr::select(id, time, amt, treatment)

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

intervals <- data.frame(
  start   = ss_start,
  end     = ss_end,
  cmax    = TRUE,
  tmax    = TRUE,
  auclast = TRUE,
  cav     = TRUE
)

nca_res <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals))
nca_tbl <- as.data.frame(nca_res$result)
stopifnot(nrow(nca_tbl) > 0, !anyNA(nca_tbl$PPORRES))

nca_tbl |>
  group_by(treatment, PPTESTCD) |>
  summarise(Median = median(PPORRES), `5th pctile` = quantile(PPORRES, 0.05),
            `95th pctile` = quantile(PPORRES, 0.95), .groups = "drop") |>
  mutate(Parameter = nlmixr2lib::ncaParamLabel(PPTESTCD), .before = PPTESTCD) |>
  select(-PPTESTCD) |>
  knitr::kable(digits = 1, caption = paste(
    "Steady-state NCA over the week-3, 4th-dosing-day interval",
    "(", ss_start, "-", ss_end, "h), full between-subject variability."))
Steady-state NCA over the week-3, 4th-dosing-day interval ( 408 - 420 h), full between-subject variability.
treatment Parameter Median 5th pctile 95th pctile
400 mg b.i.d. (4/3) AUClast 7579.5 4173.7 19297.5
400 mg b.i.d. (4/3) Cavg 631.6 347.8 1608.1
400 mg b.i.d. (4/3) Cmax 1254.4 675.8 2485.4
400 mg b.i.d. (4/3) Tmax 1.5 0.7 3.0
480 mg b.i.d. (4/3) AUClast 10779.3 4368.9 25292.2
480 mg b.i.d. (4/3) Cavg 898.3 364.1 2107.7
480 mg b.i.d. (4/3) Cmax 1763.9 696.4 3305.1
480 mg b.i.d. (4/3) Tmax 1.5 0.5 3.2
800 mg b.i.d. (4/3) AUClast 32969.0 9437.7 87224.0
800 mg b.i.d. (4/3) Cavg 2747.4 786.5 7268.7
800 mg b.i.d. (4/3) Cmax 4346.4 1544.0 9561.5
800 mg b.i.d. (4/3) Tmax 1.8 0.8 4.0

Comparison against published NCA

Fernandez-Teruel 2024 Sect. 3.5 reports median AUC12h,ss of 7730 ug*h/L and median Cmax,ss of 1340 ug/L at 400 mg b.i.d. (4/3), and Sect. 3.2 gives a steady-state Tmax of about 1.4 h. Those values are compared here against the typical-value profile – see the note in Assumptions and deviations for why the full-variability cohort median sits above them.

tv_events <- make_events(1L, 400, dose_times("4/3", 3L),
                         seq(ss_start, ss_end, by = 0.02),
                         treatment = "400 mg b.i.d. (4/3)")
tv_sim <- as.data.frame(rxode2::rxSolve(tv, tv_events, keep = "treatment",
                                        addDosing = FALSE))
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalcl_time_max', 'etaltlag', 'etalogitffo', 'etalka', 'etald1'
# rxSolve omits the `id` column entirely for a single-subject event table;
# PKNCA's grouping formula needs it back.
if (is.null(tv_sim$id)) tv_sim$id <- 1L

tv_conc <- PKNCA::PKNCAconc(
  tv_sim |> filter(!is.na(Cc)) |> select(id, time, Cc, treatment),
  Cc ~ time | treatment + id, concu = "ng/mL", timeu = "h")
tv_dose <- PKNCA::PKNCAdose(
  tv_events |> filter(evid == 1, cmt == "depot") |> select(id, time, amt, treatment),
  amt ~ time | treatment + id, doseu = "mg")
tv_res <- PKNCA::pk.nca(PKNCA::PKNCAdata(
  tv_conc, tv_dose,
  intervals = data.frame(start = ss_start, end = ss_end,
                         cmax = TRUE, tmax = TRUE, auclast = TRUE)))

published <- tibble::tibble(
  treatment = "400 mg b.i.d. (4/3)",
  cmax = 1340, tmax = 1.4, auclast = 7730
)

cmp <- nlmixr2lib::ncaComparisonTable(
  simulated = tv_res, reference = published, by = "treatment",
  units = c(cmax = "ug/L", tmax = "h", auclast = "ug*h/L"),
  tolerance_pct = 20
)
knitr::kable(cmp, caption = paste(
  "Typical-value steady-state NCA versus the values Fernandez-Teruel 2024",
  "reports. * marks a difference above 20%."),
  align = c("l", "l", "r", "r", "r"))
Typical-value steady-state NCA versus the values Fernandez-Teruel 2024 reports. * marks a difference above 20%.
NCA parameter treatment Reference Simulated % diff
Cmax (ug/L) 400 mg b.i.d. (4/3) 1340 1350 +1.0%
Tmax (h) 400 mg b.i.d. (4/3) 1.4 1.4 -0.0%
AUClast (ug*h/L) 400 mg b.i.d. (4/3) 7730 7690 -0.5%

Verification summary 

summary_tbl <- dplyr::bind_rows(acc$rows) |>
  mutate(`Abs. difference` = abs(Reproduced - Published)) |>
  select(Quantity, Unit, Published, Reproduced, `Abs. difference`,
         Tolerance, Pass, Deviation)

summary_tbl |>
  mutate(across(c(Published, Reproduced, `Abs. difference`, Tolerance),
                ~ signif(.x, 4))) |>
  knitr::kable(caption = paste(
    "Every published quantity checked against the packaged model. Rows marked",
    "Deviation = TRUE are discussed in Assumptions and deviations."))
Every published quantity checked against the packaged model. Rows marked Deviation = TRUE are discussed in Assumptions and deviations.
Quantity Unit Published Reproduced Abs. difference Tolerance Pass Deviation
Apparent volume of distribution at steady state (Vss = V2 + V3 + V4) L 255.60 255.6000 0.000e+00 0.20 TRUE FALSE
Fraction of the dose absorbed by the first-order route at 67 kg fraction 0.80 0.8022 2.184e-03 0.01 TRUE FALSE
Disposition half-life t1/2-alpha, first dose h 0.37 0.3699 5.340e-05 0.05 TRUE FALSE
Disposition half-life t1/2-alpha, multiple doses at 400 mg h 0.42 0.4145 5.489e-03 0.05 TRUE FALSE
Disposition half-life t1/2-beta, first dose h 4.20 4.1560 4.356e-02 0.20 TRUE FALSE
Disposition half-life t1/2-beta, multiple doses at 400 mg h 4.40 4.3880 1.223e-02 0.20 TRUE FALSE
Disposition half-life t1/2-gamma, first dose h 31.00 30.7800 2.212e-01 1.00 TRUE FALSE
Disposition half-life t1/2-gamma, multiple doses at 400 mg h 31.00 31.0500 5.371e-02 1.00 TRUE FALSE
Tmax at steady state, 400 mg b.i.d. (4/3) h 1.40 1.4000 0.000e+00 0.15 TRUE FALSE
AUC12,ss, 400 mg b.i.d. (4/3) ug*h/L 7730.00 7693.0000 3.690e+01 300.00 TRUE FALSE
Cmax,ss, 400 mg b.i.d. (4/3) ug/L 1340.00 1353.0000 1.344e+01 70.00 TRUE FALSE
Accumulation ratio, 400 mg b.i.d. (4/3) ratio 1.58 1.5800 1.097e-04 0.05 TRUE FALSE
Effective half-life, 400 mg b.i.d. (4/3) h 8.34 8.2990 4.109e-02 0.40 TRUE FALSE
Reduction in CL/F at 120 h, 400 mg % 18.00 16.2100 1.795e+00 4.50 TRUE TRUE
Reduction in CL/F at 120 h, 480 mg % 22.00 20.3000 1.697e+00 4.50 TRUE TRUE
Reduction in CL/F at 120 h, 800 mg % 54.00 50.0300 3.971e+00 4.50 TRUE TRUE
AUC12,ss ratio - Body weight 47 kg ratio 1.14 1.1320 8.000e-03 0.03 TRUE FALSE
Cmax,ss ratio - Body weight 47 kg ratio 1.14 1.1420 2.000e-03 0.03 TRUE FALSE
AUC12,ss ratio - Concomitant paclitaxel ratio 0.84 0.8490 9.000e-03 0.03 TRUE FALSE
Cmax,ss ratio - Concomitant paclitaxel ratio 0.89 0.8980 8.000e-03 0.03 TRUE FALSE 

stopifnot(all(summary_tbl$Pass))

Assumptions and deviations

  • Imax is on the log scale. Fernandez-Teruel 2024 never says so in words, and its Table 3 row is labelled “Imax” with no unit. The reading is forced by equation (e), which places Imax_i inside an exponential, and it is confirmed four times over: it reproduces the reported 18% / 22% / 54% reductions in CL/F, the +20% CLss/F with paclitaxel, the 7730 ug*h/L AUC12,ss, and the 1340 ug/L Cmax,ss. The alternative reading – -1.54 as a fraction – would make clearance rise by 154% over time and is excluded by every one of those.

  • The auto-inhibition reproduces about 1-2 percentage points shallower than published, and this is left as-is. Using Table 3’s printed Imax = -1.54 the model gives maximal reductions of 17.1% / 21.4% / 52.8% at 400 / 480 / 800 mg against the published 18% / 22% / 54%; at exactly 120 h the figures are 16.2% / 20.3% / 50.0%. An Imax of about -1.50 would reproduce all three to within 0.3 points, and -1.50 sits comfortably inside the paper’s own bootstrap interval of -1.85 to -1.29 (bootstrap median -1.51). The published percentages were read off the Fig. 4 simulation rather than tabulated, so the residual is consistent with rounding the point estimate to three significant figures. No parameter was tuned: the file keeps -1.54 exactly as printed and the summary table flags these three rows as a known deviation.

  • Between-subject variability is read as omega = CV / 100. Table 3 reports every BSV as a percent coefficient of variation, including Logit F1, whose random effect Sect. 3.2 describes as additive. A CV is only interpretable as 100 * sqrt(omega^2) for an additive random effect, so that convention – and not the log-normal CV = 100 * sqrt(exp(omega^2) - 1) – is applied uniformly. Under the alternative convention the log-normal omegas would be smaller (for example V2/F would be 0.913 rather than 1.14) while the additive one would be unchanged, which would make the table internally inconsistent.

  • The full-variability cohort median exceeds the published median by about 12-17% for AUC, while the typical-value profile matches it to within 0.5%. This follows from where the paper puts the random effect on Imax: equation (f) multiplies a negative log-scale quantity by exp(eta), an asymmetric transform. A subject with eta = -0.706 (one SD below) gets a 42% maximal reduction in CL/F, whereas one at eta = +0.706 gets only 3%; the downside is far larger than the upside, so the cohort’s clearance distribution is skewed low and its exposure distribution skewed high. That is a faithful property of the published parameterisation, not an encoding choice, so the comparison against the paper’s reported AUC12,ss / Cmax,ss / Tmax is made on the typical-value profile and the cohort NCA is reported descriptively.

  • Residual error is rendered on the linear scale. Sect. 3.2 states the model was fitted to log-transformed data with a combined proportional and additive residual error. nlmixr2’s Cc ~ prop(propSd) + add(addSd) is the linear-scale equivalent, with propSd = 0.439 (the reported 43.9% CV) and addSd = 0.504 ng/mL (the reported 0.504 ug/L; 1 ug/L = 1 ng/mL).

  • Steady-state window. The paper predicts steady state “on every third and fourth dosing day each week from the second week” under the (4/3) schedule (Sect. 3.2). The 12 h interval used throughout this vignette is the fourth dosing day of week three (408-420 h). Choosing the third dosing day instead lowers AUC12,ss by about 2%.

  • Covariates screened but not retained. Fernandez-Teruel 2024 tested age, sex, race, creatinine clearance, hepatic function, renal function, smoking status, schedule, and concomitant fulvestrant, CYP3A inducers, CYP3A inhibitors and acid-reducing agents, and retained none of them. They carry no published point estimate and so cannot be encoded; they are recorded in the model file’s covariatesDataExcluded metadata for provenance.

  • Absorption-route dosing requires two records per administration. The parallel first-order / zero-order input is a single NONMEM dose duplicated across two compartments (F1 into depot, F2 = 1 - F1 into central). Event tables must therefore carry two evid = 1 rows per administration with the same amt, and the central row must set rate = -2 so rxode2 uses the modelled duration D2. The make_events() helper above shows the pattern.

  • Virtual cohort demographics. Body weight is drawn log-normally with median 67 kg and truncated to the published 32-129 kg range; the paper reports the median and range but not the distributional form. Weight is the only covariate varied – formulation, prandial state and concomitant paclitaxel are held at the reference levels of the paper’s own forest plots.

  • Supplement. The Electronic Supplementary Material was not required: every final parameter estimate is in main-text Table 3, and every structural and covariate equation is in main-text Sect. 3.3. The ESM holds the per-study dose and sampling schedules (Table 1), additional baseline covariates (Table 2), the VPCs (Figs. 1-2), the CLss/F forest plot (Fig. 3) and the in vitro kinase-inhibition results (Figs. 4-9, Tables 4-7). ```