Clopidogrel (Pejcic 2024)

Model and source

• Citation: Pejcic Z, Topic Vucenovic V, Miljkovic B, Vucicevic KM. Integrating Clopidogrel’s First-Pass Effect in a Joint Semi-Physiological Population Pharmacokinetic Model of the Drug and Its Inactive Carboxylic Acid Metabolite. Pharmaceutics. 2024;16(5):685. doi:10.3390/pharmaceutics16050685
• Article: https://doi.org/10.3390/pharmaceutics16050685
• PubMed Central: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11124785/

Pejcic 2024 pooled individual data from two clopidogrel bioequivalence studies into a single joint semi-physiological population PK model that describes the parent pro-drug (CLO) and its inactive carboxylic acid metabolite (CLO-CA) simultaneously. The distinguishing feature is an explicit hepatic compartment that carries the first-pass effect: the entire absorbed dose enters the liver, and the parent that reaches the systemic circulation is recycled back to the liver so that all of it is eventually metabolised.

cat(strwrap(rxode2::rxode2(readModelDb("Pejcic_2024_clopidogrel"))$description, 78), sep = "\n")
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etalfdepotStudy1, etalfdepotStudy2, etalogitfmStudy1, etalogitfmStudy2, etaiov_fdepot_1_Study1, etaiov_fdepot_2_Study1, etaiov_fdepot_1_Study2, etaiov_fdepot_2_Study2, etaiov_mtt_1_Study1, etaiov_mtt_2_Study1, etaiov_mtt_1_Study2, etaiov_mtt_2_Study2
#> as a work-around try putting the mu-referenced expression on a simple line
#> Joint semi-physiological population PK model for oral clopidogrel (CLO) and
#> its inactive carboxylic acid metabolite (CLO-CA) in healthy Caucasian adults,
#> pooled from two 2-way crossover bioequivalence studies of 150 mg (2 x 75 mg)
#> single oral doses (Pejcic 2024). Absorption is an Erlang-type transit chain
#> (depot -> transit1 -> transit2 -> liver) with a single transit rate constant
#> Ktr = 3 / MTT. The first-pass effect is represented by a hepatic compartment
#> (Vh = 1.5 L/70 kg, liver plasma flow Qh = 50 L/h, both fixed) that receives
#> the whole absorbed dose and also receives the parent returning from the
#> systemic circulation at CLP, so that all parent drug is ultimately
#> metabolised there. Hepatic outflow Qh/Vh is partitioned into three branches
#> whose fractions sum to one: FP to systemic clopidogrel, FiaM to CLO-CA, and
#> FaM to the active thiol CLO-TH (a sink; CLO-TH concentrations were not
#> measured). The fractions use the source's softmax reparameterisation FiaM =
#> FR1 / (1 + FR1 + FR2), FaM = FR2 / (1 + FR1 + FR2), FP = 1 / (1 + FR1 + FR2)
#> with FaM fixed at 12%, giving FiaM = 87.27% (Study 1) and 86.87% (Study 2). A
#> molecular-weight factor of 0.9565 (307.80 / 321.82) scales the CLO-CA
#> formation flux. Clopidogrel is one-compartment; CLO-CA is two-compartment.
#> Body weight is applied allometrically (exponent 0.75 on clearances, 1 on
#> volumes) to a 70 kg reference. MTT, the generic-product relative
#> bioavailability, FR1, the IIV and IOV magnitudes and the proportional
#> residual error are all study- specific, selected by the STUDY_CLO_BE2
#> indicator; inter-occasion variability on bioavailability and MTT reflects the
#> crossover design.

Structure

Absorption is an Erlang-type chain of a depot plus two transit compartments, all governed by one transit rate constant. Because there are two transit compartments there are three transfers between the dose and the liver, so the Savic 2007 relation is Ktr = (n_transit + 1) / MTT = 3 / MTT. The paper confirms this arithmetic itself (Discussion): the reported MTT values of 0.470 h and 0.410 h correspond to Ktr of 6.38 and 7.32 h^-1.

Hepatic outflow Qh / Vh is split into three branches whose fractions sum to one (Pejcic 2024 Equations 1-3, with the intact-parent branch as the reference category of a softmax / multinomial-logit reparameterisation):

$$F_{iaM} = \frac{FR_1}{1 + FR_1 + FR_2}, \qquad F_{aM} = \frac{FR_2}{1 + FR_1 + FR_2}, \qquad F_{P} = \frac{1}{1 + FR_1 + FR_2}$$

FaM (to the active thiol CLO-TH) was fixed at 12%, and FR1 was estimated per study, so FR2 is a derived quantity obtained by inverting Equation 2: FR2 = FaM * (1 + FR1) / (1 - FaM). The CLO-TH branch is a pure sink – those concentrations were not measured in either study.

fractions <- tibble::tibble(study = c("Study 1", "Study 2"), FR1 = c(119, 76.8)) |>
  mutate(
    FaM  = 0.12,
    FR2  = FaM * (1 + FR1) / (1 - FaM),
    FiaM = FR1 / (1 + FR1 + FR2),
    FP   = 1   / (1 + FR1 + FR2)
  )

fractions |>
  mutate(across(c(FaM, FiaM, FP), ~ round(100 * .x, 2)), FR2 = round(FR2, 3)) |>
  dplyr::rename("Study" = study, "FR1 (estimated)" = FR1, "FR2 (derived)" = FR2,
                "FaM (%)" = FaM, "FiaM (%)" = FiaM, "FP (%)" = FP) |>
  knitr::kable(caption = "First-pass branch fractions reconstructed from the model file.")

First-pass branch fractions reconstructed from the model file.

Study	FR1 (estimated)	FaM (%)	FR2 (derived)	FiaM (%)	FP (%)
Study 1	119.0	12	16.364	87.27	0.73
Study 2	76.8	12	10.609	86.87	1.13

The reconstructed FiaM of 87.27% and 86.87% reproduce the paper’s Results paragraph (“the fractions metabolized to inactive metabolites … were determined to be 87.27% and 86.87% for the two studies”) to all four reported digits, which confirms both the equations and the FaM = 12% constraint.

stopifnot(
  all.equal(round(100 * fractions$FiaM, 2), c(87.27, 86.87)),
  all.equal(fractions$FaM + fractions$FiaM + fractions$FP, c(1, 1))
)

log(FR1) is stored as the canonical logitfm parameter because FR1 is exactly the odds FiaM / FP, so log(FR1) = logit(FiaM / (FiaM + FP)) – the logit of the CLO-CA share of the flux that does not become CLO-TH.

Population

The model was built on individual data from 50 healthy adult volunteers of Caucasian origin (29 male, 21 female) enrolled in two 2-treatment, 2-period, 2-sequence crossover bioequivalence studies conducted at the Military Medical Academy, Belgrade, Serbia. Each subject received a single 150 mg oral dose (2 x 75 mg film-coated tablets) under fasting conditions on each of two occasions: once as the study’s generic product and once as Plavix 75 mg reference. Study 1 enrolled 24 subjects with sampling to 48 h (14 samples per subject per period); Study 2 enrolled 26 subjects with sampling to 36 h (17 samples per subject per period). Per Table 1 the pooled cohort was 31.94 +/- 8.51 years old (range 19-54), weighed 74.1 +/- 13.56 kg (range 47-100), was 177.26 +/- 9.06 cm tall, and had a BMI of 23.40 +/- 2.66 kg/m^2. Baseline hepatic and renal screening values were unremarkable (total bilirubin 9.1 +/- 4.43 umol/L, serum creatinine 81.5 +/- 17.70 umol/L, ALT 26.2 +/- 9.85 U/L, AST 23.7 +/- 4.80 U/L). The analysis used 841 non-zero clopidogrel and 1149 non-zero CLO-CA concentrations; samples below the LLOQ (0.5 ng/mL for CLO, 0.1 ug/mL for CLO-CA) were excluded.

Classical covariate model-building was deliberately not performed, because the inclusion and exclusion criteria produced a homogeneous healthy population with no differences between the two studies. Body weight is the sole covariate, entered as fixed allometric scaling. The demographic and biochemical variables that were collected but not modelled are recorded in the model file’s covariatesDataExcluded metadata.

The same information is available programmatically via the model’s population metadata (readModelDb("Pejcic_2024_clopidogrel")()$population).

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Pejcic_2024_clopidogrel.R. The table below collects them in one place for review.

Equation / parameter	Value	Source location
lcl (CLP)	89.5 L/h/70 kg, fixed	Table 2 CL_P = 89.5 FIX; Methods 2.2 (“estimated at 89.5 L/h, and subsequently … fixed”)
lvc (Vc,P)	218 L/70 kg	Table 2 V_c,P = 218 (95% CI 188-248)
lqh (Qh)	50 L/h, fixed	Table 2 Q_h = 50 FIX; Methods 2.2 (physiological value from reference 24)
lvh (Vh)	1.5 L/70 kg, fixed	Table 2 V_h = 1.5 FIX; Methods 2.2
lmttStudy1	0.470 h	Table 2 MTT_st1 (95% CI 0.425-0.515)
lmttStudy2	0.410 h	Table 2 MTT_st2 (95% CI 0.381-0.439)
lfdepot (F reference)	1, fixed	Methods 2.2 (“Bioavailability for the reference medicine (F) was fixed at 100%”)
lfgenStudy1	1.08	Table 2 F_gen_st1 (95% CI 0.993-1.17)
lfgenStudy2	0.960	Table 2 F_gen_st2 (95% CI 0.818-1.10)
fm_h4 (FaM)	0.12, fixed	Methods 2.2 (“FaM was fixed to the estimated value of 12%”)
logitfmStudy1	log(119)	Table 2 FR1_st1 = 119 (95% CI 84.3-154)
logitfmStudy2	log(76.8)	Table 2 FR1_st2 = 76.8 (95% CI 64.8-88.8)
lcl_cloca (CLiaM)	8.70 L/h/70 kg	Table 2 CL_iaM (95% CI 7.38-10.0)
lvc_cloca (Vc,iaM)	23.7 L/70 kg	Table 2 V_c,iaM (95% CI 19.7-27.7)
lq_cloca (QiaM)	10.8 L/h/70 kg	Table 2 Q_iaM (95% CI 8.02-13.6)
lvp_cloca (Vp,iaM)	61.3 L/70 kg	Table 2 V_p,iaM (95% CI 50.3-72.3)
e_wt_cl	0.75, fixed	Methods 2.2 final paragraph
e_wt_vc	1, fixed	Methods 2.2 final paragraph
etalvc	45.82% CV	Table 2 IIV(V_c,P); omega^2 = log(1 + CV^2)
etalvc_cloca	25.06% CV	Table 2 IIV(V_c,iaM)
etalfdepotStudy1 / Study2	42.66% / 25.88% CV	Table 2 IIV(F_st1), IIV(F_st2)
etalogitfmStudy1 / Study2	72.80% / 27.86% CV	Table 2 IIV(FR1_st1), IIV(FR1_st2)
etaiov_fdepot_*_Study1 / Study2	8.83% / 23.24% CV	Table 2 IOV(F_st1), IOV(F_st2)
etaiov_mtt_*_Study1 / Study2	25.44% / 27.48% CV	Table 2 IOV(MTT_st1), IOV(MTT_st2)
propSdStudy1 / propSdStudy2	41.95% / 29.39%	Table 2 Wp(st1), Wp(st2)
Equations 1-3 (branch fractions)	n/a	Equations 1, 2, 3 on pages 3-4
Ktr = 3 / MTT	n/a	Methods 2.2 + Discussion (two transit compartments; Ktr 6.38 / 7.32 h^-1); Savic 2007 (reference 35)
mwRatio = 0.9565	n/a	Methods 2.2 (307.80 / 321.82 molecular-weight correction)
ODE topology (depot -> transit -> liver -> central / CLO-CA, with CLP return)	n/a	Figure 1 schematic

Structural identities

Before simulating a cohort, three closed-form identities implied by the published parameters are checked against numbers the paper reports independently. These are the strongest available validation for this model because the underlying data are not public.

Terminal half-life of clopidogrel

The paper reports a mean terminal clopidogrel half-life of 1.69 h with a range of 1.46-1.92 h (Discussion). Because only 0.73% of hepatic outflow escapes as intact parent, recycling is negligible and the terminal slope is set by CLP / Vc,P. Propagating the reported Vc,P confidence interval reproduces the reported half-life interval.

thalf <- function(vc) log(2) * vc / 89.5
tibble::tibble(
  quantity = c("Point estimate (Vc,P = 218 L)",
               "Lower (Vc,P = 188 L)", "Upper (Vc,P = 248 L)"),
  derived  = round(thalf(c(218, 188, 248)), 3),
  reported = c(1.69, 1.46, 1.92)
) |>
  dplyr::rename("Quantity" = quantity, "log(2) * Vc,P / CLP (h)" = derived,
                "Reported (h)" = reported) |>
  knitr::kable(caption = "Terminal clopidogrel half-life derived from Table 2 vs the Discussion value.")

Terminal clopidogrel half-life derived from Table 2 vs the Discussion value.

Quantity	log(2) * Vc,P / CLP (h)	Reported (h)
Point estimate (Vc,P = 218 L)	1.688	1.69
Lower (Vc,P = 188 L)	1.456	1.46
Upper (Vc,P = 248 L)	1.921	1.92

stopifnot(all(abs(round(thalf(c(218, 188, 248)), 2) - c(1.69, 1.46, 1.92)) <= 0.01))

Dose-exposure identities

For this structure the steady-state-free AUC identities are exact. Every pass through the liver returns a fraction FP of the flux to the systemic circulation, so the geometric series gives the total parent input as Dose * FP / (1 - FP) and the total CLO-CA input as Dose * mwRatio * FiaM / (1 - FP). Dividing by the respective clearance gives AUC(0-inf) with no dependence on volumes, Qh, Vh or Ktr.

dose <- 150
auc_theory <- fractions |>
  transmute(
    study,
    auc_clo   = dose * (FP / (1 - FP)) / 89.5 * 1000,     # ng*h/mL
    auc_cloca = dose * 0.9565 * (FiaM / (1 - FP)) / 8.70  # ug*h/mL
  )
auc_theory |>
  mutate(across(-study, ~ round(.x, 3))) |>
  dplyr::rename("Study" = study, "CLO AUC0-inf (ng*h/mL)" = auc_clo,
                "CLO-CA AUC0-inf (ug*h/mL)" = auc_cloca) |>
  knitr::kable(caption = "Closed-form AUC0-inf for a 150 mg dose in a 70 kg subject.")

Closed-form AUC0-inf for a 150 mg dose in a 70 kg subject.

Study	CLO AUC0-inf (ng*h/mL)	CLO-CA AUC0-inf (ug*h/mL)
Study 1	12.381	14.498
Study 2	19.174	14.490

These identities are compared against the numerically integrated ODE solution below, which is the check that the encoded ODE system actually implements the intended topology.

mod <- readModelDb("Pejcic_2024_clopidogrel")

grid_fine <- sort(unique(c(seq(0, 12, by = 0.02), seq(12.5, 96, by = 0.5))))
ev_typ <- bind_rows(
  tibble::tibble(id = 1L, time = 0, amt = dose, evid = 1L,
                 cmt = "depot", dvid = NA_integer_),
  tibble::tibble(id = 1L, time = grid_fine, amt = NA_real_, evid = 0L,
                 cmt = "central", dvid = 1L),
  tibble::tibble(id = 1L, time = grid_fine, amt = NA_real_, evid = 0L,
                 cmt = "central_cloca", dvid = 2L)
) |>
  mutate(WT = 70, STUDY_CLO_BE2 = 0L, FORM_CLO_GENERIC = 0L, OCC = 1L) |>
  arrange(time, dvid)

sim_typ <- rxode2::rxSolve(mod, events = ev_typ, omega = NA, sigma = NA,
                           returnType = "data.frame", addDosing = FALSE)
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etalfdepotStudy1, etalfdepotStudy2, etalogitfmStudy1, etalogitfmStudy2, etaiov_fdepot_1_Study1, etaiov_fdepot_2_Study1, etaiov_fdepot_1_Study2, etaiov_fdepot_2_Study2, etaiov_mtt_1_Study1, etaiov_mtt_2_Study1, etaiov_mtt_1_Study2, etaiov_mtt_2_Study2
#> as a work-around try putting the mu-referenced expression on a simple line

trap <- function(x, y) sum(diff(x) * (head(y, -1) + tail(y, -1)) / 2)
prof <- sim_typ |> filter(CMT == min(CMT)) |> arrange(time)

identities <- tibble::tibble(
  quantity = c("CLO AUC0-96 (ng*h/mL)", "CLO-CA AUC0-96 (ug*h/mL)"),
  numeric  = c(trap(prof$time, prof$Cc), trap(prof$time, prof$Cc_cloca)),
  closed_form = c(auc_theory$auc_clo[1], auc_theory$auc_cloca[1])
) |>
  mutate(pct_diff = 100 * (numeric - closed_form) / closed_form)

identities |>
  mutate(across(where(is.numeric), ~ round(.x, 3))) |>
  dplyr::rename("Quantity" = quantity, "ODE integration" = numeric,
                "Closed form" = closed_form, "Difference (%)" = pct_diff) |>
  knitr::kable(caption = "Numerically integrated exposure vs the closed-form identity (Study 1, reference product, 70 kg).")

Numerically integrated exposure vs the closed-form identity (Study 1, reference product, 70 kg).

Quantity	ODE integration	Closed form	Difference (%)
CLO AUC0-96 (ng*h/mL)	12.382	12.381	0.003
CLO-CA AUC0-96 (ug*h/mL)	14.486	14.498	-0.082

# CLO is fully eliminated well inside the window; CLO-CA has a ~10 h terminal
# half-life so a small tail remains truncated at 96 h.
stopifnot(abs(identities$pct_diff[1]) < 0.5, abs(identities$pct_diff[2]) < 1)

Mass balance

At the end of the simulation window essentially the whole dose has left the system through the three hepatic branches; nothing is stranded in the absorption chain or the liver.

last_row <- sim_typ |> filter(CMT == min(CMT)) |> slice_tail(n = 1)
residual_amt <- with(last_row, depot + transit1 + transit2 + liver + central)
cat(sprintf("Clopidogrel-side amount remaining at 96 h: %.3g mg of %.0f mg dosed\n",
            residual_amt, dose))
#> Clopidogrel-side amount remaining at 96 h: 2.04e-17 mg of 150 mg dosed
stopifnot(residual_amt < 1e-6 * dose)

Virtual cohort

Original observed data are not publicly available (the paper’s Data Availability Statement cites privacy restrictions), so the figures below use a virtual population whose weight distribution approximates the published demographics. Body weights are taken as deterministic quantiles of a N(74.1, 13.56) distribution truncated to the reported 47-100 kg range, so the cohort is reproducible without depending on the random-number stream.

Four arms are simulated – both products in both studies – at 100 subjects per arm (well inside the 200-per-arm cap).

set.seed(20240520)
n_arm <- 100L

# Reconstructed bioequivalence sampling schedules. The paper reports only the
# number of samples per period and the sampling duration, not the exact times;
# see "Assumptions and deviations".
sched <- list(
  `1` = c(0, 0.25, 0.5, 0.75, 1, 1.5, 2, 3, 4, 6, 8, 12, 24, 48),
  `2` = c(0, 0.17, 0.33, 0.5, 0.75, 1, 1.25, 1.5, 2, 2.5, 3, 4, 6, 8, 12, 24, 36)
)
stopifnot(lengths(sched) == c(14L, 17L))

# Denser grid for the concentration-time figures, on top of the NCA schedule.
grid_vpc <- sort(unique(c(seq(0, 12, by = 0.25), 14, 16, 20, 24, 30, 36, 48)))

make_arm <- function(study, generic, id_offset) {
  q  <- seq(0.5 / n_arm, 1 - 0.5 / n_arm, length.out = n_arm)
  wt <- pmin(pmax(qnorm(q, mean = 74.1, sd = 13.56), 47), 100)
  times <- sort(unique(c(sched[[as.character(study)]], grid_vpc)))
  subj <- tibble::tibble(id = id_offset + seq_len(n_arm), WT = wt)
  bind_rows(
    subj |> mutate(time = 0, amt = 150, evid = 1L,
                   cmt = "depot", dvid = NA_integer_),
    tidyr::crossing(subj, time = times) |>
      mutate(amt = NA_real_, evid = 0L, cmt = "central", dvid = 1L),
    tidyr::crossing(subj, time = times) |>
      mutate(amt = NA_real_, evid = 0L, cmt = "central_cloca", dvid = 2L)
  ) |>
    mutate(
      STUDY_CLO_BE2    = as.integer(study == 2),
      FORM_CLO_GENERIC = as.integer(generic),
      OCC              = 1L,
      study            = paste("Study", study),
      product          = if (generic) "Generic" else "Reference (Plavix)",
      arm              = paste0("Study ", study, " / ",
                                if (generic) "Generic" else "Reference")
    ) |>
    arrange(id, time, dvid)
}

events <- bind_rows(
  make_arm(1, FALSE, id_offset =   0L),
  make_arm(1, TRUE,  id_offset = 100L),
  make_arm(2, FALSE, id_offset = 200L),
  make_arm(2, TRUE,  id_offset = 300L)
)

# Disjoint IDs across arms are mandatory: rxSolve keys on id alone, so a
# repeated id would silently merge two arms into one subject.
stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid", "dvid")])))
stopifnot(dplyr::n_distinct(events$id) == 4L * n_arm)

Simulation

OCC is held at 1 throughout: each simulated subject contributes a single occasion, so the IOV terms draw one deviate per subject rather than the two a full crossover replication would use.

sim <- rxode2::rxSolve(
  mod,
  events = events,
  keep   = c("study", "product", "arm", "WT"),
  returnType = "data.frame",
  addDosing  = FALSE
) |>
  mutate(analyte = if_else(CMT == min(CMT), "Clopidogrel", "CLO-CA"))

ipredSim holds the individual prediction for whichever endpoint the row belongs to and sim adds the study’s proportional residual error, so the two columns give the model on the individual-prediction scale and on the observed-data scale respectively.

Replicate published figures

Figure 3 – visual predictive checks

Figure 3 of Pejcic 2024 shows VPCs for clopidogrel (panel A) and CLO-CA (panel B), with the 5th, 50th and 95th percentiles of the predictions. The panels below reproduce that layout on the observed-data scale, pooling the two products within each study as the paper’s VPC does.

vpc <- sim |>
  group_by(analyte, study, time) |>
  summarise(
    Q05 = quantile(sim, 0.05, na.rm = TRUE),
    Q50 = quantile(sim, 0.50, na.rm = TRUE),
    Q95 = quantile(sim, 0.95, na.rm = TRUE),
    .groups = "drop"
  ) |>
  filter(time > 0)

ggplot(vpc, aes(time, Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.25, fill = "#B03A2E") +
  geom_line(colour = "#B03A2E") +
  facet_grid(analyte ~ study, scales = "free_y") +
  scale_y_log10() +
  scale_x_continuous(breaks = c(0, 6, 12, 24, 36, 48)) +
  labs(
    x = "Time after dose (h)",
    y = "Concentration (ng/mL for clopidogrel; ug/mL for CLO-CA)",
    title = "Figure 3 - simulated visual predictive check",
    caption = paste("Replicates Figure 3 of Pejcic 2024. Median and 5th-95th",
                    "percentile band of simulated observations.")
  ) +
  theme_bw()

The clopidogrel panels fall away steeply and cross the study LLOQ of 0.5 ng/mL within roughly 10 h, which matches the paper’s observation that CLO “was expected to completely eliminate after approximately 10 h, indicating that the sampling duration may have been too long”, and explains why 46% of the scheduled clopidogrel samples were below the limit of quantification.

Parent versus metabolite exposure

The paper notes that CLO-CA circulates at roughly 2000-fold higher concentrations than the parent. Both analytes are simulated in the same units below to check that the encoded molecular-weight scaling and branch fractions reproduce that separation.

ratio <- sim |>
  filter(time > 0, analyte == "Clopidogrel") |>
  select(id, time, arm, clo = ipredSim) |>
  inner_join(
    sim |> filter(time > 0, analyte == "CLO-CA") |>
      select(id, time, cloca = ipredSim),
    by = c("id", "time")
  ) |>
  mutate(ratio = (cloca * 1000) / clo)   # both in ng/mL

ratio |>
  group_by(time) |>
  summarise(median_ratio = median(ratio), .groups = "drop") |>
  ggplot(aes(time, median_ratio)) +
  geom_line(colour = "#1F618D") +
  scale_y_log10() +
  labs(x = "Time after dose (h)",
       y = "Median CLO-CA : clopidogrel concentration ratio",
       title = "Metabolite-to-parent concentration ratio",
       caption = "Pejcic 2024 Discussion: CLO-CA circulates at ~2000-fold the parent concentration.") +
  theme_bw()

PKNCA validation

NCA is run on the reconstructed bioequivalence sampling schedule rather than on the dense plotting grid, because Cmax is a maximum-over-samples statistic and is sensitive to how densely the profile is sampled. Each analyte gets its own PKNCA block, and each is run twice – once on the individual-prediction scale (ipredSim) and once on the observed-data scale (sim, which carries the paper’s proportional residual error). The published means are means of observed subject Cmax values, so the observed-data scale is the like-for-like comparator; the individual-prediction scale is shown alongside to make the size of the residual-error contribution visible.

nca_times <- sim |>
  distinct(study) |>
  mutate(times = sched[sub("Study ", "", study)]) |>
  tidyr::unnest(times) |>
  dplyr::rename(time = times)

nca_long <- sim |>
  semi_join(nca_times, by = c("study", "time")) |>
  select(id, time, arm, study, analyte, ipredSim, sim) |>
  tidyr::pivot_longer(c(ipredSim, sim), names_to = "scale", values_to = "Cc") |>
  mutate(scale = if_else(scale == "ipredSim",
                         "Individual prediction", "With residual error")) |>
  filter(!is.na(Cc))

# Guarantee a time = 0 row per profile; pre-dose concentration is zero for an
# extravascular dose.
nca_long <- bind_rows(
  nca_long,
  nca_long |> distinct(id, arm, study, analyte, scale) |> mutate(time = 0, Cc = 0)
) |>
  distinct(id, analyte, scale, time, .keep_all = TRUE) |>
  arrange(analyte, scale, id, time)

dose_df <- events |>
  filter(evid == 1L) |>
  select(id, time, amt, arm, study)

run_nca <- function(which_analyte) {
  cdat <- nca_long |> filter(analyte == which_analyte)
  ddat <- dose_df |>
    tidyr::crossing(scale = unique(cdat$scale))

  conc_obj <- PKNCA::PKNCAconc(cdat, Cc ~ time | scale + id)
  dose_obj <- PKNCA::PKNCAdose(ddat, amt ~ time | scale + id)

  intervals <- data.frame(
    start = 0, end = Inf,
    cmax = TRUE, tmax = TRUE, auclast = TRUE, half.life = TRUE
  )
  PKNCA::pk.nca(PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals))
}

nca_clo   <- run_nca("Clopidogrel")
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
nca_cloca <- run_nca("CLO-CA")
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(conc.2/conc.1): NaNs produced
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
#> Warning in log(data$conc): NaNs produced

Comparison against published values

Pejcic 2024 reports three NCA-comparable quantities: the mean observed maximum concentration of each analyte (Results paragraph 2: “The maximum plasma concentrations were, on average, 7.2 ng/mL and 4.9 ug/mL for CLO and CLO-CA, respectively”) and the mean terminal clopidogrel half-life of 1.69 h. No AUC values are reported, so auclast is computed but has no published comparator.

ncaComparisonTable() aggregates per-subject NCA values with the median by default, but the paper’s Cmax values are arithmetic means (“on average”). The simulated results are therefore pre-aggregated with mean() – the documented escape hatch – so that like is compared with like. The distributions are strongly right-skewed (IIV on FR1 reaches 72.8% CV in Study 1), so the medians are appreciably lower than the means; both are shown.

nca_mean <- function(res) {
  as.data.frame(res$result) |>
    filter(PPTESTCD %in% c("cmax", "tmax", "auclast", "half.life"),
           is.finite(PPORRES)) |>
    group_by(scale, PPTESTCD) |>
    summarise(PPORRES = mean(PPORRES, na.rm = TRUE), .groups = "drop")
}

as.data.frame(nca_clo$result) |>
  filter(PPTESTCD == "cmax") |>
  group_by(scale) |>
  summarise(mean = mean(PPORRES), median = median(PPORRES), .groups = "drop") |>
  mutate(across(where(is.numeric), ~ round(.x, 2))) |>
  dplyr::rename("Scale" = scale, "Mean Cmax (ng/mL)" = mean,
                "Median Cmax (ng/mL)" = median) |>
  knitr::kable(caption = "Clopidogrel Cmax: arithmetic mean vs median across the simulated cohort (published mean 7.2 ng/mL).")

Clopidogrel Cmax: arithmetic mean vs median across the simulated cohort (published mean 7.2 ng/mL).

Scale	Mean Cmax (ng/mL)	Median Cmax (ng/mL)
Individual prediction	5.88	4.62
With residual error	7.49	5.79

published_clo <- tibble::tibble(
  scale     = c("Individual prediction", "With residual error"),
  cmax      = 7.2,
  half.life = 1.69
)

nlmixr2lib::ncaComparisonTable(
  simulated = nca_mean(nca_clo),
  reference = published_clo,
  by        = "scale",
  units     = c(cmax = "ng/mL", tmax = "h", auclast = "ng*h/mL", half.life = "h"),
  tolerance_pct = 20
) |>
  knitr::kable(
    caption = paste("Clopidogrel: simulated vs published NCA, pooled over both",
                    "studies and both products. * differs from the published",
                    "value by more than 20%.")
  )

Clopidogrel: simulated vs published NCA, pooled over both studies and both products. * differs from the published value by more than 20%.

NCA parameter	scale	Reference	Simulated	% diff
Cmax (ng/mL)	Individual prediction	7.2	5.88	-18.4%
Cmax (ng/mL)	With residual error	7.2	7.49	+4.0%
t½ (h)	Individual prediction	1.69	1.92	+13.7%
t½ (h)	With residual error	1.69	1.91	+13.1%

published_cloca <- tibble::tibble(
  scale = c("Individual prediction", "With residual error"),
  cmax  = 4.9
)

nlmixr2lib::ncaComparisonTable(
  simulated = nca_mean(nca_cloca),
  reference = published_cloca,
  by        = "scale",
  units     = c(cmax = "ug/mL", tmax = "h", auclast = "ug*h/mL", half.life = "h"),
  tolerance_pct = 20
) |>
  knitr::kable(
    caption = paste("Clopidogrel carboxylic acid: simulated vs published NCA,",
                    "pooled over both studies and both products.",
                    "* differs from the published value by more than 20%.")
  )

Clopidogrel carboxylic acid: simulated vs published NCA, pooled over both studies and both products. * differs from the published value by more than 20%.

NCA parameter	scale	Reference	Simulated	% diff
Cmax (ug/mL)	Individual prediction	4.9	3.67	-25.0%*
Cmax (ug/mL)	With residual error	4.9	4.61	-5.9%

On the observed-data scale – the like-for-like comparator, since the published values are means of observed subject maxima – the simulated clopidogrel Cmax is 7.49 ng/mL against a published 7.2 ng/mL (+4.0%) and the simulated CLO-CA Cmax is 4.61 ug/mL against a published 4.9 ug/mL (-5.9%). Both published values are bracketed by the two scales, with the individual-prediction mean below and the observed-data mean at or above, which is the expected ordering: Cmax is a maximum-over-samples statistic, so the study’s proportional residual error of 42% (Study 1) and 29% (Study 2) inflates it. No parameter was adjusted to obtain this agreement.

The half-life recovered by PKNCA is about 1.92 h against the reported 1.69 h (+13.7%). This gap is expected rather than a discrepancy, and its size is predictable: the paper’s 1.69 h is the half-life of the typical subject, whereas PKNCA returns the arithmetic mean of individual half-lives. With t_1/2,i = log(2) * Vc,i / CLP and log-normal IIV on Vc,P, the mean of a log-normal exceeds its median by exp(omega^2 / 2).

c(median_thalf = log(2) * 218 / 89.5,
  expected_mean_thalf = log(2) * 218 / 89.5 * exp(0.190577 / 2)) |>
  round(3)
#>        median_thalf expected_mean_thalf 
#>               1.688               1.857

That predicts a mean of about 1.86 h before any estimation noise, which accounts for nearly all of the observed offset; the remainder comes from fitting the terminal slope on a 14- to 17-point schedule whose late clopidogrel samples sit near the 0.5 ng/mL LLOQ.

Bioequivalence contrast

Because relative bioavailability is the only difference between the products within a study, the generic-to-reference exposure ratio must reproduce the estimated Fgen exactly. The contrast is evaluated deterministically (omega = NA, sigma = NA) on a common weight so that the ratio is not blurred by independent random effects in the two arms – a strict check on the bioavailability wiring.

auc_arm <- function(study, generic) {
  ev <- bind_rows(
    tibble::tibble(id = 1L, time = 0, amt = 150, evid = 1L,
                   cmt = "depot", dvid = NA_integer_),
    tibble::tibble(id = 1L, time = grid_fine, amt = NA_real_, evid = 0L,
                   cmt = "central", dvid = 1L)
  ) |>
    mutate(WT = 70, STUDY_CLO_BE2 = as.integer(study == 2),
           FORM_CLO_GENERIC = as.integer(generic), OCC = 1L) |>
    arrange(time)
  s <- rxode2::rxSolve(mod, events = ev, omega = NA, sigma = NA,
                       returnType = "data.frame", addDosing = FALSE) |>
    arrange(time)
  trap(s$time, s$Cc)
}

be <- tibble::tibble(study = c(1L, 2L)) |>
  mutate(
    reference     = vapply(study, auc_arm, numeric(1), generic = FALSE),
    generic       = vapply(study, auc_arm, numeric(1), generic = TRUE),
    ratio         = generic / reference,
    reported_Fgen = if_else(study == 1L, 1.08, 0.960)
  )

be |>
  mutate(study = paste("Study", study), across(where(is.numeric), ~ round(.x, 4))) |>
  dplyr::rename("Study" = study, "Reference AUC0-96 (ng*h/mL)" = reference,
                "Generic AUC0-96 (ng*h/mL)" = generic,
                "Simulated ratio" = ratio, "Reported Fgen" = reported_Fgen) |>
  knitr::kable(caption = "Generic-to-reference clopidogrel AUC ratio vs the estimated relative bioavailability.")

Generic-to-reference clopidogrel AUC ratio vs the estimated relative bioavailability.

Study	Reference AUC0-96 (ng*h/mL)	Generic AUC0-96 (ng*h/mL)	Simulated ratio	Reported Fgen
Study 1	12.3817	13.3722	1.08	1.08
Study 2	19.1746	18.4076	0.96	0.96

stopifnot(max(abs(be$ratio - be$reported_Fgen)) < 1e-6)

Assumptions and deviations

• Sampling schedule. The paper reports the number of samples per subject per period (14 in Study 1 to 48 h, 17 in Study 2 to 36 h) but not the actual sampling times. The schedules used for NCA here are plausible reconstructions for a bioequivalence study of a drug with a ~45 min Tmax, with the required sample counts and durations. Cmax and Tmax depend on sampling density, so the NCA comparison above should be read as an order-of-magnitude check rather than an exact replication.
• CV-to-variance convention. Table 2 reports IIV and IOV as “Estimate CV (%)” with no footnote giving the conversion formula. All variances are encoded as omega^2 = log(1 + CV^2), the standard relation for a log-normally distributed parameter and the convention used by the sibling clopidogrel extraction Danielak_2017_clopidogrel. If the authors instead reported CV = sqrt(omega^2), the largest affected variance (IIV on FR1 in Study 1) would be 0.530 rather than 0.425; the structural parameters and every identity checked above are unaffected.
• FR2 is derived, not fixed. The paper fixes FaM at 12% and estimates FR1, so FR2 is back-solved from Equation 2. The model file computes FR2 from the individual FR1, which holds FaM at exactly 12% for every subject. The alternative reading – computing FR2 once from the typical FR1 – would let individual FaM drift with the FR1 random effect and is harder to reconcile with the statement that FaM “was fixed”.
• Qh is not weight-scaled. Table 2 labels every clearance and volume with a /70 kg normalisation except Qh, which is given as L/h. That asymmetry is encoded literally: Vh scales with weight (exponent 1) and Qh does not. Since the liver empties at Qh / Vh with a mean residence time of only about 1.8 min, this choice has almost no effect on the simulated profiles.
• Residual error is shared between analytes. Table 2 lists exactly two residual-error rows, Wp(st1) and Wp(st2), with no analyte dimension, and the Methods describe “a study-specific proportional error model”. A single proportional error is therefore applied to both clopidogrel and CLO-CA within a study. This is consistent with Figure 2, whose goodness-of-fit panels plot the two analytes together, and with a proportional error being unitless.
• Estimated-parameter count. The paper states that 24 parameters (11 structural) were estimated. Table 2 itemises 11 estimated structural parameters, 10 variance parameters and 2 residual-error parameters, which totals 23. The most likely twenty-fourth is FaM, which the Methods describe as having been estimated at 12% before being fixed but which has no Table 2 row. This affects only the bookkeeping, not any encoded value.
• CLO-TH is not a state. The active thiol metabolite branch carries 12% of hepatic outflow but was not measured in either study, so it is encoded as a sink. For a model of the active metabolite of clopidogrel see modellib("Danielak_2017_clopidogrel").
• Inter-occasion variability. The model carries IOV on bioavailability and MTT for two occasions, matching the 2-period crossover. The simulations in this vignette set OCC = 1 for every subject, so each subject draws a single occasion deviate; replicating the full crossover would require two dosing occasions per subject.
• Non-mu-referenced etas. Because the IIV and IOV magnitudes are study-specific, the random effects enter through a study-switched sum such as st1 * etalfdepotStudy1 + st2 * etalfdepotStudy2. rxode2 reports these etas as non-mu-referenced at build time. That is expected for this structure and is harmless for simulation; it would only matter for the efficiency of a re-estimation.
• Age range. Table 1 gives a pooled age range of 19-54 years while the Methods narrative gives 21-53 for Study 1 and 19-42 for Study 2. The population metadata records the Table 1 range and notes the discrepancy.
• No non-paper-derived parameter values. Every value in ini() comes from the paper’s Table 2 or its Methods text; nothing was digitised from a figure, supplied by correspondence, or carried from another publication.