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Cobicistat PK boosting of olaparib (Overbeek 2025)

Source: vignettes/articles/Overbeek_2025_cobicistat_olaparib_boosting.Rmd
Overbeek_2025_cobicistat_olaparib_boosting.Rmd

Models and source

This paper contributes two models, extracted as two files because the authors fitted them as two sequential but independent analyses: a cobicistat model on 683 samples pooled across four trials, and an olaparib model on 261 samples from the single trial in which the two drugs were combined.

#> ℹ parameter labels from comments will be replaced by 'label()'
  • Overbeek_2025_cobicistat — Well-stirred liver model for oral cobicistat (CYP3A pharmacokinetic booster) pooling healthy volunteers, postpartum women with HIV, patients with rheumatoid arthritis and patients with solid tumours, with Erlang-type absorption through three transit compartments, a mechanistic hepatic-extraction central/liver disposition driven by unbound intrinsic clearance per litre of liver, a priori allometric scaling to 70 kg, and a higher intrinsic clearance in the PROACTIVE (olaparib-boosting) cohort (Overbeek 2025)
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etalclint_nocobicistat, etalclint_cobicistat
#> as a work-around try putting the mu-referenced expression on a simple line
  • Overbeek_2025_olaparib — Well-stirred liver model for oral olaparib in patients with solid tumours, with Erlang-type absorption through one transit compartment, a mechanistic hepatic-extraction central/liver disposition driven by unbound intrinsic clearance per litre of liver, a priori allometric scaling to 70 kg, and concomitant cobicistat raising prehepatic bioavailability 1.65-fold while lowering intrinsic clearance to 0.37-fold with its own reduced between-subject variability (Overbeek 2025)

Both models are well-stirred liver models. Rather than estimating a clearance directly, they estimate an unbound intrinsic clearance per litre of liver and let the hepatic physiology produce both the systemic clearance and the first-pass loss:

QHP=QH⋅(1−Ht)EH=CLint⋅fuQHP+CLint⋅fuCLH=EH⋅QHPQ_{HP} = Q_H \cdot (1 - Ht) \qquad E_H = \frac{CL_{int} \cdot f_u}{Q_{HP} + CL_{int} \cdot f_u} \qquad CL_H = E_H \cdot Q_{HP}

The absorbed dose is delivered into a liver compartment that exchanges with central at the hepatic plasma flow, so the fraction EHE_H is removed on first pass without any separate bioavailability term. This is what lets the paper separate cobicistat’s prehepatic effect on olaparib (intestinal CYP3A and P-glycoprotein inhibition, which raises f(depot)) from its hepatic effect (CYP3A inhibition, which lowers clint) — a distinction the earlier noncompartmental analysis of the same trial could not make.

Population

Cobicistat (Overbeek_2025_cobicistat): 683 samples from 66 subjects pooled over four trials — DATE-4 (16 healthy volunteers boosting atazanavir), PANNA (12 postpartum women living with HIV boosting elvitegravir), PRACTICAL (26 patients with rheumatoid arthritis boosting tofacitinib) and PROACTIVE (12 patients with solid tumours boosting olaparib). Median age 51.5 years (range 21-78), median weight 74 kg (range 52-124), 36% male. The first three studies used cobicistat 150 mg once daily; PROACTIVE used 150 mg twice daily. All used dense sampling over one dosing interval at steady state after at least 7 days (Overbeek 2025 Table 1). Only the postpartum PANNA occasion was included; the third-trimester data were excluded because pregnancy markedly altered cobicistat PK.

Olaparib (Overbeek_2025_olaparib): 261 samples from the 12 PROACTIVE patients, a randomised cross-over of olaparib 300 mg twice daily monotherapy against olaparib 100 mg twice daily boosted with cobicistat 150 mg twice daily. Median age 63 years (range 55-78), median weight 67 kg (range 54-104), 42% male.

The same information is available programmatically via each model’s population metadata, e.g. readModelDb("Overbeek_2025_olaparib")()$population.

Source trace

Per-parameter origins are recorded as in-file comments next to each ini() entry. The tables below collect them for review. “OR1” / “OR2” are Online Resource Materials 1 and 2 of the supplement, which contain the final NONMEM control streams; the $OMEGA and $SIGMA values there are variances, and Tables 2-3 present them as %CV through the table-footnote transformation sqrt(exp(omega^2) - 1).

Cobicistat

Equation / parameter Value Source location
lktr 3.92 /h Table 2 k_tr (RSE 12.3%); OR1 $THETA 1
lvc 69.7 L Table 2 V_c (RSE 5.6%); OR1 $THETA 2
lclint 322 L/h/L liver Table 2 CL_int (RSE 6.7%); OR1 $THETA 3
e_study_proactive_clint 1.21 Table 2 CL_int-olaparib (RSE 16.3%); OR1 $THETA 4
lfdepot log(1), fixed OR1 $PK F1=1*EXP(ETA(1)) with $OMEGA 1 = 0 FIX
q_liver 90 L/h, fixed Methods 2.3 “hepatic blood flood (QH) of 90 L/h”
hct 0.44, fixed Methods 2.3; sensitivity analysis 0.30-0.50 in Results 3.1
fu 0.025, fixed Methods 2.3 “unbound fraction in plasma (fu) of 0.025 for cobicistat”
v_liver_coef, e_wt_v_liver 0.10, 0.59, fixed Eq 5 VL = 0.10 * TBW^0.59 (ref. 31, Small 2017)
e_wt_fq, e_wt_vc, e_wt_ktr 0.75, 1, -0.25, fixed Methods 2.3 a priori allometry; OR1 ALLOQHP / ALLOV / ALLOKTR
etalktr, etalvc, etalclint 0.488, 0.129, 0.208 OR1 $OMEGA 2-4; Table 2 79.3% / 37.1% / 48.1%
propSd, addSd 0.172, 0.0332 OR1 $SIGMA 0.0296, 0.0011; Table 2 17.3%, 0.033 mg/L
QHP, EH, CLH n/a Eqs 1-3
Erlang chain depot -> transit1..3 -> liver n/a Results 3.1; OR1 K14 = K45 = K56 = K62 = KTR
liver <-> central exchange n/a OR1 K23 = QHP*(1-EH)/VL, K32 = QHP/V, K20 = CLH/VL

Olaparib

Equation / parameter Value Source location
lktr 3.51 /h Table 3 k_tr (RSE 15.2%); OR2 $THETA 2
lvc 31.6 L Table 3 V_c (RSE 8.7%); OR2 $THETA 3
lclint 45.6 L/h/L liver Table 3 Cl_int (RSE 14.4%); OR2 $THETA 4
e_conmed_cobicistat_fdepot 1.65 Table 3 F1 cobicistat (RSE 6%); Results 3.2 “65% increase”; OR2 $THETA 5
e_conmed_cobicistat_clint 0.37 Table 3 CL_int-cobicistat (RSE 6.5%); Results 3.2 “63% decrease”; OR2 $THETA 6
lfdepot log(1), fixed OR2 $THETA 1 = 1 FIX, $OMEGA 1 = 0 FIX
fu 0.181, fixed Methods 2.3 “0.181 for olaparib”
q_liver, hct, v_liver_coef, e_wt_v_liver 90, 0.44, 0.10, 0.59, fixed Methods 2.3, Eq 5 (shared with the cobicistat model)
e_wt_fq, e_wt_vc, e_wt_ktr 0.75, 1, -0.25, fixed Methods 2.3; OR2 ALLOCL / ALLOV / ALLOKA
etalktr, etalvc 0.249, 0.0477 OR2 $OMEGA 2-3; Table 3 53.2% / 22.1%
etalclint_nocobicistat 0.244 OR2 $OMEGA 4; Table 3 CL_int-without cobicistat 52.6%
etalclint_cobicistat 0.171 OR2 $OMEGA 5; Table 3 CL_int-with cobicistat 43.2%
propSd, addSd 0.1192, 0.3688 OR2 $SIGMA 0.0142, 0.136; Table 3 12.0%, 0.369 mg/L
Erlang chain depot -> transit1 -> liver n/a Results 3.2; OR2 K12 = K23 = KTR

Virtual cohort

Original observed data are not publicly available. The simulations below use virtual populations whose weight distributions approximate the per-study demographics of Table 1 (log-normal on the published median, scaled so the published range spans roughly the central 95%, then clamped to that range).

# `set.seed()` seeds R's RNG; `rxSetSeed()` seeds rxode2's, but only per solver
# thread, so the exact cohort differs between machines with different thread
# counts. Every assertion below is written to hold for any cohort this model
# can produce (see known-vignette-failure-patterns.md pattern 12).
set.seed(20250207)
rxode2::rxSetSeed(20250207)

N_PER_ARM <- 100L   # well under the 200/arm cap

draw_weights <- function(n, med, lo, hi) {
  sdlog <- (log(hi) - log(lo)) / (2 * 1.96)
  pmin(pmax(stats::rlnorm(n, log(med), sdlog), lo), hi)
}

# One arm: a steady-state dose at t = 0 (ss = 1) plus any further doses needed
# to cover the observation window, and observations on the `central` ODE state.
make_arm <- function(n, amt, ii, window, wt, covs, label, id_offset = 0L,
                     grid = 0.1) {
  do.call(rbind, lapply(seq_len(n), function(i) {
    id <- id_offset + i
    dose_times <- seq(0, window - ii, by = ii)
    dos <- data.frame(
      id = id, time = dose_times, evid = 1L, amt = amt, cmt = "depot",
      ii = c(ii, rep(0, length(dose_times) - 1L)),
      ss = c(1L, rep(0L, length(dose_times) - 1L))
    )
    obs <- data.frame(
      id = id, time = seq(0, window, by = grid), evid = 0L, amt = 0,
      cmt = "central", ii = 0, ss = 0L
    )
    e <- rbind(dos, obs)
    e$WT <- wt[i]                                   # covariates AFTER the
    for (nm in names(covs)) e[[nm]] <- covs[[nm]]   # canonical event columns
    e$arm <- label
    e[order(e$time, -e$evid), ]
  }))
}
# Four cobicistat cohorts, each with its own Table 1 weight distribution.
# All four are observed over 24 h so AUC0-24 is directly comparable, which is
# what Fig. 3 of the paper plots; PROACTIVE therefore receives two 12-hourly
# doses inside the window and the other three a single 24-hourly dose.
cobi_spec <- tibble::tribble(
  ~arm,        ~med, ~lo, ~hi, ~ii, ~proactive,
  "DATE-4",      73,  58,  90,  24,          0,
  "PANNA",       72,  52,  87,  24,          0,
  "PRACTICAL",   81,  54, 124,  24,          0,
  "PROACTIVE",   67,  54, 104,  12,          1
)

ev_cobi <- do.call(rbind, lapply(seq_len(nrow(cobi_spec)), function(k) {
  s <- cobi_spec[k, ]
  make_arm(
    n = N_PER_ARM, amt = 150, ii = s$ii, window = 24,
    wt = draw_weights(N_PER_ARM, s$med, s$lo, s$hi),
    covs = list(STUDY_PROACTIVE = s$proactive),
    label = s$arm, id_offset = (k - 1L) * N_PER_ARM
  )
}))

stopifnot(!anyDuplicated(ev_cobi[, c("id", "time", "evid")]))
# The two PROACTIVE cross-over arms, observed over one 12 h interval. The same
# 12 patients contributed both arms, so the two arms share a weight
# distribution; distinct ids are used because rxSolve treats id as the subject
# key and the arm-specific eta must be redrawn per arm-subject.
olap_wt <- draw_weights(N_PER_ARM, 67, 54, 104)

ev_olap <- rbind(
  make_arm(N_PER_ARM, amt = 300, ii = 12, window = 12, wt = olap_wt,
           covs = list(CONMED_COBICISTAT = 0),
           label = "Olaparib 300 mg BID (monotherapy)", id_offset = 0L),
  make_arm(N_PER_ARM, amt = 100, ii = 12, window = 12, wt = olap_wt,
           covs = list(CONMED_COBICISTAT = 1),
           label = "Olaparib 100 mg BID + cobicistat", id_offset = N_PER_ARM)
)

Simulation 

mod_cobi <- readModelDb("Overbeek_2025_cobicistat")
mod_olap <- readModelDb("Overbeek_2025_olaparib")

sim_cobi <- rxode2::rxSolve(mod_cobi, ev_cobi, keep = "arm", addDosing = FALSE)
#> ℹ parameter labels from comments will be replaced by 'label()'
sim_olap <- rxode2::rxSolve(mod_olap, ev_olap, keep = "arm", addDosing = FALSE)
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etalclint_nocobicistat, etalclint_cobicistat
#> as a work-around try putting the mu-referenced expression on a simple line

sim_cobi <- as.data.frame(sim_cobi)
sim_olap <- as.data.frame(sim_olap)

# The solve must have produced the observable and the derived well-stirred
# quantities; a silently-empty Cc column is the failure mode this guards.
stopifnot(
  nrow(sim_cobi) > 0, nrow(sim_olap) > 0,
  all(c("Cc", "clint", "clh", "eh", "vc") %in% names(sim_cobi)),
  all(is.finite(sim_cobi$Cc)), all(is.finite(sim_olap$Cc)),
  all(sim_cobi$Cc > 0), all(sim_olap$Cc > 0)
)

Structural identity: AUC over a dosing interval

The well-stirred algebra collapses to a exact closed form. Writing x=CLintfux = CL_{int} f_u, we have 1−EH=QHP/(QHP+x)1 - E_H = Q_{HP}/(Q_{HP} + x) and CLH=QHPx/(QHP+x)CL_H = Q_{HP} x/(Q_{HP}+x), so (1−EH)/CLH=1/x(1 - E_H)/CL_H = 1/x and the steady-state exposure over one dosing interval is

AUCτ=F1⋅Dose⋅(1−EH)CLH=F1⋅DoseCLint⋅fuAUC_\tau = \frac{F_1 \cdot Dose \cdot (1 - E_H)}{CL_H} = \frac{F_1 \cdot Dose}{CL_{int} \cdot f_u}

independent of hepatic flow. This is a check of the implementation rather than of the paper: both sides use each subject’s own drawn parameters, so the only difference is trapezoidal integration error and a tight bound is correct here.

trap <- function(t, y) sum(diff(t) * (head(y, -1) + tail(y, -1)) / 2)

closed_form_check <- function(sim, fu, dose, f1, n_dose) {
  sim |>
    group_by(id, arm) |>
    summarise(auc = trap(time, Cc), clint = first(clint), .groups = "drop") |>
    mutate(
      closed  = n_dose * f1 * dose / (clint * fu),
      pct     = 100 * (auc - closed) / closed
    )
}

cf <- bind_rows(
  closed_form_check(dplyr::filter(sim_cobi, arm != "PROACTIVE"),
                    fu = 0.025, dose = 150, f1 = 1,    n_dose = 1),
  closed_form_check(dplyr::filter(sim_cobi, arm == "PROACTIVE"),
                    fu = 0.025, dose = 150, f1 = 1,    n_dose = 2),
  closed_form_check(dplyr::filter(sim_olap, CONMED_COBICISTAT == 0),
                    fu = 0.181, dose = 300, f1 = 1,    n_dose = 1),
  closed_form_check(dplyr::filter(sim_olap, CONMED_COBICISTAT == 1),
                    fu = 0.181, dose = 100, f1 = 1.65, n_dose = 1)
)

# Pure numerical error on a 0.1 h grid; realised max was 0.006%. 0.5% still
# goes red on any mis-wired flow, volume or covariate term.
stopifnot(max(abs(cf$pct)) < 0.5)
sprintf("Closed-form agreement: max |%% difference| = %.4f%% over %d subjects",
        max(abs(cf$pct)), nrow(cf))
#> [1] "Closed-form agreement: max |% difference| = 0.0252% over 600 subjects"

Replicate published figures 

# Structural replication of Fig. 1 (cobicistat) and Fig. 4 (olaparib) model
# diagrams: the concentration-time shape each structure produces.
bind_rows(
  sim_cobi |> mutate(drug = "Cobicistat 150 mg"),
  sim_olap |> mutate(drug = "Olaparib")
) |>
  group_by(drug, arm, time) |>
  summarise(
    Q25 = quantile(Cc, 0.25), Q50 = median(Cc), Q75 = quantile(Cc, 0.75),
    .groups = "drop"
  ) |>
  ggplot(aes(time, Q50, colour = arm, fill = arm)) +
  geom_ribbon(aes(ymin = Q25, ymax = Q75), alpha = 0.20, colour = NA) +
  geom_line(linewidth = 0.7) +
  facet_wrap(~drug, scales = "free") +
  labs(
    x = "Time after dose (h)", y = "Concentration (mg/L)", colour = NULL,
    fill = NULL, title = "Steady-state profiles (median and interquartile band)",
    caption = "Structures of Fig. 1 (cobicistat) and Fig. 4 (olaparib) of Overbeek 2025."
  ) +
  theme(legend.position = "bottom")

# Replicates Figure 3 of Overbeek 2025: cobicistat AUC over 24 h per study.
auc24 <- sim_cobi |>
  group_by(id, arm) |>
  summarise(auc24 = trap(time, Cc), .groups = "drop")

# Medians read from the Fig. 3 box plot panel (mg.h/L). These are read off a
# figure, not printed values, so they anchor the comparison visually and are
# NOT used as a numeric gate.
fig3_median <- tibble::tibble(
  arm = c("DATE-4", "PANNA", "PRACTICAL", "PROACTIVE"),
  published_median = c(14, 27, 16.5, 30)
)

ggplot(auc24, aes(arm, auc24)) +
  geom_boxplot(outlier.size = 0.6) +
  geom_point(data = fig3_median, aes(arm, published_median),
             colour = "red", shape = 18, size = 4) +
  labs(
    x = NULL, y = "AUC cobicistat over 24 h (mg.h/L)",
    title = "Figure 3 --- cobicistat AUC0-24 by study",
    caption = paste("Boxes: simulated cohorts. Red diamonds: medians read from",
                    "Fig. 3 of Overbeek 2025.")
  )

The model carries a study covariate only for PROACTIVE, so it deliberately predicts one typical exposure for DATE-4, PANNA and PRACTICAL, differing only through their weight distributions. The observed PANNA median in Fig. 3 sits well above that common value. This is a property of the published model, not a transcription error: Results 3.1 states that all four study indicators improved the fit univariately, but that only PROACTIVE was retained after the covariate search, so the between-study spread among the three once-daily studies is left to between-subject variability by design. The elevation the model does capture — PROACTIVE above the rest — is reproduced.

PKNCA validation 

# Concentrations: filter on !is.na(Cc) only. Doses are steady-state (ss = 1),
# so the t = 0 record already carries the steady-state trough and no synthetic
# zero-concentration row may be inserted.
conc_olap <- sim_olap |>
  dplyr::filter(!is.na(Cc)) |>
  dplyr::select(id, time, Cc, arm)

dose_olap <- ev_olap |>
  dplyr::filter(evid == 1) |>
  dplyr::select(id, time, amt, arm)

conc_obj <- PKNCA::PKNCAconc(conc_olap, Cc ~ time | arm + id)
dose_obj <- PKNCA::PKNCAdose(dose_olap, amt ~ time | arm + id)

intervals_olap <- data.frame(
  start = 0, end = 12,
  cmax = TRUE, tmax = TRUE, auclast = TRUE, cav = TRUE, ctrough = TRUE
)

nca_olap <- PKNCA::pk.nca(
  PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals_olap)
)
olap_wide <- as.data.frame(nca_olap) |>
  dplyr::select(arm, id, PPTESTCD, PPORRES) |>
  tidyr::pivot_wider(names_from = PPTESTCD, values_from = PPORRES)

olap_summary <- olap_wide |>
  group_by(arm) |>
  summarise(across(c(cmax, tmax, auclast, cav, ctrough), median),
            .groups = "drop")

olap_summary |>
  dplyr::rename(
    "Arm"                  = arm,
    "Cmax (mg/L)"          = cmax,
    "Tmax (h)"             = tmax,
    "AUC0-12 (mg*h/L)"     = auclast,
    "Cav (mg/L)"           = cav,
    "Ctrough (mg/L)"       = ctrough
  ) |>
  knitr::kable(digits = 2,
               caption = "Simulated median steady-state olaparib NCA by arm.")
Simulated median steady-state olaparib NCA by arm.
Arm Cmax (mg/L) Tmax (h) AUC0-12 (mg*h/L) Cav (mg/L) Ctrough (mg/L)
Olaparib 100 mg BID + cobicistat 5.58 1.4 41.47 3.46 1.78
Olaparib 300 mg BID (monotherapy) 6.32 1.3 31.76 2.65 0.36 
conc_cobi <- sim_cobi |>
  dplyr::filter(!is.na(Cc)) |>
  dplyr::select(id, time, Cc, arm)

dose_cobi <- ev_cobi |>
  dplyr::filter(evid == 1) |>
  dplyr::select(id, time, amt, arm)

nca_cobi <- PKNCA::pk.nca(PKNCA::PKNCAdata(
  PKNCA::PKNCAconc(conc_cobi, Cc ~ time | arm + id),
  PKNCA::PKNCAdose(dose_cobi, amt ~ time | arm + id),
  intervals = data.frame(start = 0, end = 24,
                         cmax = TRUE, tmax = TRUE, auclast = TRUE)
))

cobi_summary <- as.data.frame(nca_cobi) |>
  dplyr::select(arm, id, PPTESTCD, PPORRES) |>
  tidyr::pivot_wider(names_from = PPTESTCD, values_from = PPORRES) |>
  group_by(arm) |>
  summarise(across(c(cmax, tmax, auclast), median), .groups = "drop") |>
  left_join(fig3_median, by = "arm")

cobi_summary |>
  dplyr::rename(
    "Study"                          = arm,
    "Cmax (mg/L)"                    = cmax,
    "Tmax (h)"                       = tmax,
    "AUC0-24 simulated (mg*h/L)"     = auclast,
    "AUC0-24 Fig. 3 median (mg*h/L)" = published_median
  ) |>
  knitr::kable(digits = 2,
               caption = paste("Simulated median steady-state cobicistat NCA",
                               "by study, against the Fig. 3 medians."))
Simulated median steady-state cobicistat NCA by study, against the Fig. 3 medians.
Study Cmax (mg/L) Tmax (h) AUC0-24 simulated (mg*h/L) AUC0-24 Fig. 3 median (mg*h/L)
DATE-4 1.55 2.0 15.14 14.0
PANNA 1.61 2.1 14.82 27.0
PRACTICAL 1.45 2.2 13.11 16.5
PROACTIVE 1.89 13.4 24.78 30.0

Comparison against published values

The paper reports its validation targets as text in the Discussion rather than as an NCA table, several of them quoted from the noncompartmental analysis of the same PROACTIVE trial (reference 16). Each is checked below against a typical-value solve with the random effects zeroed, which makes every row cohort-independent.

mod_cobi_t <- rxode2::zeroRe(mod_cobi)
#> ℹ parameter labels from comments will be replaced by 'label()'
mod_olap_t <- rxode2::zeroRe(mod_olap)
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etalclint_nocobicistat, etalclint_cobicistat
#> 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: etalclint_nocobicistat, etalclint_cobicistat
#> as a work-around try putting the mu-referenced expression on a simple line

typical <- function(mod, amt, ii, covs, wt = 70) {
  ev <- make_arm(1L, amt = amt, ii = ii, window = ii, wt = wt, covs = covs,
                 label = "typical", grid = 0.01)
  as.data.frame(rxode2::rxSolve(mod, ev, addDosing = FALSE))
}

t_cobi_od   <- typical(mod_cobi_t, 150, 24, list(STUDY_PROACTIVE = 0))
#> ℹ omega/sigma items treated as zero: 'etalktr', 'etalvc', 'etalclint'
t_cobi_pro  <- typical(mod_cobi_t, 150, 12, list(STUDY_PROACTIVE = 1))
#> ℹ omega/sigma items treated as zero: 'etalktr', 'etalvc', 'etalclint'
t_olap_mono <- typical(mod_olap_t, 300, 12, list(CONMED_COBICISTAT = 0))
#> ℹ omega/sigma items treated as zero: 'etalktr', 'etalvc', 'etalclint_nocobicistat', 'etalclint_cobicistat'
t_olap_boost<- typical(mod_olap_t, 100, 12, list(CONMED_COBICISTAT = 1))
#> ℹ omega/sigma items treated as zero: 'etalktr', 'etalvc', 'etalclint_nocobicistat', 'etalclint_cobicistat'

auc_mono  <- trap(t_olap_mono$time, t_olap_mono$Cc)
auc_boost <- trap(t_olap_boost$time, t_olap_boost$Cc)
claims <- tibble::tribble(
  ~Quantity, ~Source, ~Published, ~Model, ~Lower, ~Upper,

  "Cobicistat apparent hepatic clearance CL_H (L/h)",
  "Discussion, limitations",            8.3, first(t_cobi_od$clh),      7.5,  9.1,

  "Cobicistat apparent central volume V_c (L)",
  "Discussion, limitations",             70, first(t_cobi_od$vc),        63,   77,

  "Cobicistat CL_int ratio, PROACTIVE : other studies",
  "Table 2",                           1.21,
  first(t_cobi_pro$clint) / first(t_cobi_od$clint),                     1.15, 1.27,

  "Olaparib apparent hepatic clearance CL_H, unboosted (L/h)",
  "Discussion, paragraph 3",            8.4, first(t_olap_mono$clh),     7.6,  9.2,

  "Olaparib AUC0-12h, 300 mg BID monotherapy (mg*h/L)",
  "Discussion, paragraph 3 (ref. 16)", 29.4, auc_mono,                   26.5, 32.3,

  "Olaparib CL_int ratio, boosted : monotherapy",
  "Table 3",                           0.37,
  first(t_olap_boost$clint) / first(t_olap_mono$clint),                 0.35, 0.39,

  "Olaparib F1 ratio, boosted : monotherapy",
  "Table 3",                           1.65, 1.65,                      1.57, 1.73,

  "Dose-normalised olaparib AUC_tau ratio, boosted : mono",
  "Discussion, paragraph 5 (ref. 16)", 4.35,
  (auc_boost / 100) / (auc_mono / 300),                                 3.70, 5.00,

  "Olaparib Cmax ratio, boosted : mono ('similar')",
  "Discussion, paragraph 5 (ref. 16)", 1.00,
  max(t_olap_boost$Cc) / max(t_olap_mono$Cc),                           0.75, 1.35,

  "Olaparib Ctrough ratio, boosted : mono ('~fourfold')",
  "Discussion, paragraph 5 (ref. 16)", 4.00,
  t_olap_boost$Cc[nrow(t_olap_boost)] / t_olap_mono$Cc[nrow(t_olap_mono)],
                                                                        3.20, 5.20
) |>
  mutate(
    `% difference` = 100 * (Model - Published) / Published,
    Pass           = Model >= Lower & Model <= Upper
  )

# Bounds are absolute, taken from the published value with room for the
# read-precision of the quoted figure -- not from what this run happened to
# give. A mis-transcribed volume, dose, unbound fraction or covariate
# coefficient moves these by tens of percent and breaks them.
stopifnot(all(claims$Pass))

claims |>
  dplyr::select(Quantity, Source, Published, Model, `% difference`, Pass) |>
  knitr::kable(digits = c(0, 0, 2, 2, 1, 0),
               caption = paste("Model reproduction of every quantitative claim",
                               "Overbeek 2025 makes about these two models."))
Model reproduction of every quantitative claim Overbeek 2025 makes about these two models.
Quantity Source Published Model % difference Pass
Cobicistat apparent hepatic clearance CL_H (L/h) Discussion, limitations 8.30 8.26 -0.5 TRUE
Cobicistat apparent central volume V_c (L) Discussion, limitations 70.00 69.70 -0.4 TRUE
Cobicistat CL_int ratio, PROACTIVE : other studies Table 2 1.21 1.21 0.0 TRUE
Olaparib apparent hepatic clearance CL_H, unboosted (L/h) Discussion, paragraph 3 8.40 8.43 0.3 TRUE
Olaparib AUC0-12h, 300 mg BID monotherapy (mg*h/L) Discussion, paragraph 3 (ref. 16) 29.40 29.64 0.8 TRUE
Olaparib CL_int ratio, boosted : monotherapy Table 3 0.37 0.37 0.0 TRUE
Olaparib F1 ratio, boosted : monotherapy Table 3 1.65 1.65 0.0 TRUE
Dose-normalised olaparib AUC_tau ratio, boosted : mono Discussion, paragraph 5 (ref. 16) 4.35 4.46 2.5 TRUE
Olaparib Cmax ratio, boosted : mono (‘similar’) Discussion, paragraph 5 (ref. 16) 1.00 0.93 -7.4 TRUE
Olaparib Ctrough ratio, boosted : mono (‘~fourfold’) Discussion, paragraph 5 (ref. 16) 4.00 4.56 14.1 TRUE

Every claim the paper states as a number is reproduced within 3%. The last two rows check claims the paper makes only in words — olaparib Cmax is “similar despite a threefold dose reduction” and Ctrough “increased approximately fourfold” — so the Published column there is the round number those phrases stand for, and the model’s 0.93 and 4.56 are consistent with both.

Between-subject variability by arm

The paper’s central variability finding is that olaparib intrinsic-clearance variability is lower under boosting (%CV 43.2 with cobicistat versus 52.6 without, Table 3). Because AUCτ∝1/CLintAUC_\tau \propto 1/CL_{int} exactly, the simulated exposure %CV should track those omegas directly.

cv_pct <- function(x) 100 * sd(x) / mean(x)

var_tab <- olap_wide |>
  group_by(arm) |>
  summarise(`Simulated AUC0-12 %CV` = cv_pct(auclast), .groups = "drop") |>
  mutate(`Published CL_int %CV` = c(43.2, 52.6))   # PKNCA returns groups alphabetically

# An absolute band around each published omega, not a race between two noisy
# cohort statistics. Realised 39.6 / 49.9 at n = 100-200 per arm, against
# published 43.2 / 52.6; the sampling SE of a %CV at n = 100 is about 3.5
# points, so 15 admits the noise while still going red on a swapped or
# mis-transformed omega (the CV%-vs-variance confusion moves these by >30
# points).
stopifnot(
  all(abs(var_tab$`Simulated AUC0-12 %CV` - var_tab$`Published CL_int %CV`) < 15)
)

knitr::kable(var_tab, digits = 1,
             caption = paste("Simulated exposure variability against the",
                             "published arm-specific CL_int omegas."))
Simulated exposure variability against the published arm-specific CL_int omegas.
arm Simulated AUC0-12 %CV Published CL_int %CV
Olaparib 100 mg BID + cobicistat 47.8 43.2
Olaparib 300 mg BID (monotherapy) 52.3 52.6

Assumptions and deviations

  • Both models are apparent. No intravenous data existed, so every volume and clearance is relative to an unknown absolute bioavailability (Methods 2.3). lfdepot is fixed at log(1) in both models as the paper’s structural anchor, and the sole estimated bioavailability quantity is the cobicistat effect on olaparib.

  • The F1 inter-individual variability was fixed to zero by the authors ($OMEGA 1 = 0 FIX in both control streams), so no etalfdepot is carried. A zero-variance eta would risk a singular OMEGA at solve time and would add nothing.

  • STUDY_PROACTIVE is a cohort indicator, not a drug-drug interaction. Table 2 labels the coefficient CLint-olaparib and the NONMEM data item is named OLAP, but the paper attributes the 1.21-fold higher cobicistat intrinsic clearance to selection of a population with high CYP3A activity (Discussion, paragraph 3), and the indicator is simultaneously confounded with the twice-daily regimen and the solid-tumour population. It must not be read as olaparib perpetrating on cobicistat. The reciprocal, genuine interaction is carried by CONMED_COBICISTAT in the olaparib model.

  • The abstract and the final model disagree on one number. The abstract states cobicistat “decreased intrinsic clearance 0.34-fold”. Table 3, the Results text (“63% decrease”, i.e. 0.37) and $THETA 6 of the supplement’s final control stream all give 0.37, which is the value encoded here. The 0.34 in the abstract appears to be an error; it is the only place that value occurs. (A separate 76% decrease quoted in Results 3.2 is the univariate clearance-only model, superseded by the final combined model.)

  • Cobicistat AUC over 24 h in the PROACTIVE arm is simulated as two 12-hourly steady-state doses. The paper’s Eq 8 defines AUCtau = Dose / (CL_H/F), i.e. an apparent clearance that already contains the first-pass factor; the equivalent mechanistic form used here is AUCtau = F1 * Dose * (1 - E_H) / CL_H.

  • Haematocrit was assumed, not measured (hct fixed at 0.44), because haematocrit was unavailable in some studies. The paper’s own sensitivity analysis over 0.30-0.50 found negligible impact. hct is carried as an ini() parameter rather than a hard-coded constant so that sensitivity analysis is reproducible from the packaged model.

  • The cohort weight distributions are assumed. Table 1 reports only a median and range per study, so weights are drawn log-normally about the median with the range treated as an approximate 95% interval and clamped. Age, sex and race are not covariates in either model and are not simulated.

  • Fig. 3 medians are read from a plot panel, not from printed values, and are used only as visual anchors. They are excluded from the numeric gate.

  • covariatesDataExcluded. Cobicistat AUCtau was pre-specified as a candidate covariate on olaparib intrinsic clearance (Methods 2.5) but no relationship was found (Results 3.2, Online Resource Fig. 3), so it carries no coefficient and is documented rather than encoded.

  • A non-mu-referencing warning is emitted by the olaparib model. The arm-selected intrinsic-clearance eta (exp((1 - CONMED_COBICISTAT) * etalclint_nocobicistat + CONMED_COBICISTAT * etalclint_cobicistat)) is the faithful translation of the control stream’s IF (BOOST.EQ.0) ... / IF (BOOST.EQ.1) ... pair and cannot be written as a single mu-referenced line. The warning concerns estimation efficiency in a re-fit, not simulation correctness; the closed-form check above confirms both etas enter exactly as intended.