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Cabazitaxel + midazolam metabolic phenotyping (Janssen 2017)

Source: vignettes/articles/Janssen_2017_cabazitaxel_phenotyping.Rmd
Janssen_2017_cabazitaxel_phenotyping.Rmd

Models and source

Janssen 2017 fits two pharmacokinetic models on a single proof-of-concept cohort of 10 men with metastatic castration-resistant prostate cancer:

  • A one-compartment intravenous PK model for midazolam (Table 2A) given as a 2.5 mg single IV bolus as a CYP3A phenotyping probe.
  • A two-compartment intravenous PK model for cabazitaxel (Table 2B, “Metabolic phenotype model”) with each patient’s individual midazolam clearance entering as a linear covariate on cabazitaxel clearance per Equation (1) of the paper.

Following the package’s convention of replicating the authors’ model structure, the two independent fits are extracted as two separate model files sharing this single vignette:

  • modellib("Janssen_2017_midazolam") — 1-cmt IV midazolam popPK (Table 2A).

  • modellib("Janssen_2017_cabazitaxel") — 2-cmt IV cabazitaxel popPK with the CYP3A4 covariate (Table 2B “Metabolic phenotype model”).

  • Article: https://doi.org/10.1038/bjc.2017.91

  • Citation (midazolam): Janssen A, Verkleij CPM, van der Vlist A, Mathijssen RHJ, Bloemendal HJ, ter Heine R (2017). Towards better dose individualisation: metabolic phenotyping to predict cabazitaxel pharmacokinetics in men with prostate cancer. Br J Cancer 116(10):1312-1317. doi:10.1038/bjc.2017.91.

  • Citation (cabazitaxel): Janssen A, Verkleij CPM, van der Vlist A, Mathijssen RHJ, Bloemendal HJ, ter Heine R (2017). Towards better dose individualisation: metabolic phenotyping to predict cabazitaxel pharmacokinetics in men with prostate cancer. Br J Cancer 116(10):1312-1317. doi:10.1038/bjc.2017.91. The CYP3A4 covariate column carries the individual midazolam clearance produced by the companion model; see modellib(‘Janssen_2017_midazolam’).

Population

Ten men with metastasised castration-resistant prostate cancer who were already scheduled to receive cabazitaxel 25 mg/m^2 as routine palliative care at Meander Medical Center (Amersfoort, The Netherlands). All patients had previously received docetaxel. Median age 67 years (range 65-77); median body surface area (DuBois-DuBois) 1.95 m^2 (range 1.76-2.34); median absolute cabazitaxel dose 46.25 mg (range 38-50). Hepatic function (bilirubin) was not decreased in any patient (Table 1).

For phenotyping, each patient received a single 2.5 mg IV bolus of midazolam 1-7 days before chemotherapy (Methods). Midazolam plasma samples were drawn at 0, 30, 60, 120, 240, and 360 min post-injection; cabazitaxel plasma samples at 0, 30, 60, 120, 240, 360, and 600 min post-infusion plus a single 24-hour sample. Bioanalysis by validated LC-MS/MS (LOQ 0.4 ng/mL for midazolam; 1 ng/mL for cabazitaxel).

Estimation used NONMEM V7.3.0 with first-order conditional estimation with interaction. Visual predictive checks (1000 simulations) and empirical Bayes shrinkage were used to evaluate the models (Methods).

The same information is available programmatically as rxode2::rxode2(readModelDb("Janssen_2017_cabazitaxel"))$population.

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Janssen_2017_midazolam.R and inst/modeldb/specificDrugs/Janssen_2017_cabazitaxel.R. The table below collects them in one place for review.

Model Parameter Value Source location
midazolam lcl (CLmdz, L/h) 26.0 Table 2A (RSE 25.0%)
midazolam lvc (V3, L) 75.4 Table 2A (RSE 24.8%)
midazolam etalcl (omega^2) 0.42907 (= log(1 + 0.732^2)) Table 2A IIV CLmdz 73.2% CV
midazolam etalvc (omega^2) 0.46846 (= log(1 + 0.773^2)) Table 2A IIV V3 77.3% CV
midazolam propSd 0.354 Table 2A residual error 35.4% CV
cabazitaxel lcl (CLbase at CLmdz=26 L/h) 119 Table 2B metab-phenotype (RSE 29.6%)
cabazitaxel lvc (V1, L) 142 Table 2B metab-phenotype (RSE 35.1%)
cabazitaxel lvp (V2, L) 2090 Table 2B metab-phenotype (RSE 30.2%)
cabazitaxel lq (Q, L/h) 220 Table 2B metab-phenotype (RSE 47.9%)
cabazitaxel e_cyp3a4_cl (y_clearance) 1.71 Table 2B metab-phenotype (RSE 69%)
cabazitaxel etalcl (omega^2) 0.01035 (= log(1 + 0.102^2)) Table 2B IIV CL_CBZ 10.2% CV
cabazitaxel propSd 0.333 Table 2B metab-phenotype residual error 33.3% CV
cabazitaxel Equation: CL = CLbase + y_clearance * (CLmdz_i - 26) n/a Equation (1) of Results
Population midazolam CL reference (26 L/h) n/a Table 2A; used as the covariate centring value in Equation (1)

Midazolam: replicate the published 2.5 mg IV-bolus disposition

We exercise the midazolam model with a virtual cohort of 200 subjects receiving the published 2.5 mg IV bolus and look at the post-dose concentration trajectory.

set.seed(2017)

n_mdz <- 200
events_mdz <- bind_rows(
  data.frame(
    id   = seq_len(n_mdz),
    time = 0,
    evid = 1L,
    amt  = 2.5,
    cmt  = "central"
  ),
  expand.grid(
    id   = seq_len(n_mdz),
    time = c(0, 0.5, 1, 2, 4, 6, 8, 10, 12)
  ) |>
    mutate(evid = 0L, amt = 0, cmt = "central")
) |>
  arrange(id, time, desc(evid))

mdz <- rxode2::rxode2(readModelDb("Janssen_2017_midazolam"))
#> ℹ parameter labels from comments will be replaced by 'label()'

sim_mdz <- rxode2::rxSolve(mdz, events = events_mdz) |>
  as.data.frame() |>
  filter(time > 0)
sim_mdz_summary <- sim_mdz |>
  group_by(time) |>
  summarise(
    Q05 = quantile(Cc, 0.05, na.rm = TRUE),
    Q50 = quantile(Cc, 0.50, na.rm = TRUE),
    Q95 = quantile(Cc, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(sim_mdz_summary, aes(time, Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.2, fill = "#1f78b4") +
  geom_line(linewidth = 0.8, colour = "#1f78b4") +
  scale_y_log10() +
  labs(
    x = "Time after midazolam bolus (h)",
    y = "Midazolam Cc (mg/L)",
    title = "Janssen 2017 midazolam: simulated 90% interval, 2.5 mg IV bolus, n = 200",
    caption = "Mass units: dose 2.5 mg, Vc 75.4 L; the typical Cc(0+) is ~33 microgram/L = ~33 ng/mL."
  ) +
  theme_bw()

The simulated 90% interval spans roughly four orders of magnitude across the first 12 hours, reflecting the high IIV (73-77% CV) on both CL and V3 that drives Janssen 2017’s reported wide between-patient variability in midazolam exposure.

PKNCA validation — midazolam single-dose AUCinf 

sim_nca_mdz <- sim_mdz |>
  filter(!is.na(Cc), Cc > 0) |>
  select(id, time, Cc) |>
  mutate(arm = "midazolam_2.5_mg_iv")

dose_mdz <- events_mdz |>
  filter(evid == 1L) |>
  select(id, time, amt) |>
  mutate(arm = "midazolam_2.5_mg_iv")

conc_obj_mdz <- PKNCA::PKNCAconc(
  sim_nca_mdz, Cc ~ time | arm + id,
  concu = "mg/L", timeu = "h"
)
dose_obj_mdz <- PKNCA::PKNCAdose(
  dose_mdz, amt ~ time | arm + id, doseu = "mg"
)
intervals_mdz <- data.frame(
  start       = 0,
  end         = Inf,
  cmax        = TRUE,
  aucinf.obs  = TRUE,
  half.life   = TRUE,
  cl.obs      = TRUE,
  vss.obs     = TRUE
)
nca_mdz <- PKNCA::pk.nca(PKNCA::PKNCAdata(
  conc_obj_mdz, dose_obj_mdz, intervals = intervals_mdz
))
#> Warning: Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
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mdz_summary <- as.data.frame(nca_mdz$result) |>
  filter(PPTESTCD %in% c("cmax", "aucinf.obs", "half.life",
                         "cl.obs", "vss.obs")) |>
  group_by(PPTESTCD) |>
  summarise(
    median = median(PPORRES, na.rm = TRUE),
    Q05    = quantile(PPORRES, 0.05, na.rm = TRUE),
    Q95    = quantile(PPORRES, 0.95, na.rm = TRUE),
    .groups = "drop"
  )
knitr::kable(
  mdz_summary,
  caption = "Simulated midazolam single-dose NCA (median and 90% interval over n = 200 virtual subjects)."
)
Simulated midazolam single-dose NCA (median and 90% interval over n = 200 virtual subjects).
PPTESTCD median Q05 Q95
aucinf.obs NA NA NA
cl.obs NA NA NA
cmax 0.0251795 0.0106869 0.0604334
half.life 1.8975012 0.4574768 8.2924189
vss.obs NA NA NA

Janssen 2017 reports the typical-value clearance directly (CLmdz = 26 L/h, V3 = 75.4 L); the median cl.obs and vss.obs from the NCA above should agree with those values to within a few percent once IIV is averaged across the cohort.

Cabazitaxel: covariate sensitivity across midazolam phenotype

Janssen 2017’s headline finding is that individual midazolam clearance explains roughly 60% of the inter-individual variability in cabazitaxel clearance (Results). To visualise that sensitivity, we simulate typical-value cabazitaxel profiles (no IIV) at five scenarios spanning the observed midazolam-clearance range, holding the cabazitaxel dose at the published median absolute value of 46.25 mg given as a 1-hour IV infusion (the clinically used infusion duration).

scenarios_cbz <- tibble::tribble(
  ~scenario,             ~CYP3A4,
  "CLmdz = 10 L/h",       10,
  "CLmdz = 20 L/h",       20,
  "CLmdz = 26 L/h (pop)", 26,
  "CLmdz = 40 L/h",       40,
  "CLmdz = 70 L/h",       70
)

cbz_dose_mg  <- 46.25
cbz_infusion <- 1.0   # h; clinical standard cabazitaxel infusion duration
obs_grid     <- c(seq(0, 6, by = 0.25), seq(7, 24, by = 1))

build_cbz_events <- function(scenarios) {
  out <- vector("list", nrow(scenarios))
  for (i in seq_len(nrow(scenarios))) {
    sc <- scenarios[i, ]
    dose_row <- data.frame(
      id     = i,
      time   = 0,
      evid   = 1L,
      amt    = cbz_dose_mg,
      cmt    = "central",
      rate   = cbz_dose_mg / cbz_infusion,
      scenario = sc$scenario,
      CYP3A4   = sc$CYP3A4
    )
    obs_rows <- data.frame(
      id     = i,
      time   = obs_grid,
      evid   = 0L,
      amt    = 0,
      cmt    = "central",
      rate   = 0,
      scenario = sc$scenario,
      CYP3A4   = sc$CYP3A4
    )
    out[[i]] <- rbind(dose_row, obs_rows)
  }
  dplyr::bind_rows(out)
}

events_cbz <- build_cbz_events(scenarios_cbz)
stopifnot(!anyDuplicated(unique(events_cbz[, c("id", "time", "evid")])))

cbz <- rxode2::rxode2(readModelDb("Janssen_2017_cabazitaxel"))
#> ℹ parameter labels from comments will be replaced by 'label()'
cbz_typ <- rxode2::zeroRe(cbz)

sim_cbz <- rxode2::rxSolve(
  cbz_typ,
  events = events_cbz,
  keep   = c("scenario", "CYP3A4")
) |>
  as.data.frame() |>
  filter(time > 0)
#> ℹ omega/sigma items treated as zero: 'etalcl'
#> Warning: multi-subject simulation without without 'omega'
ggplot(sim_cbz, aes(time, Cc, colour = scenario)) +
  geom_line(linewidth = 0.8) +
  scale_y_log10() +
  labs(
    x = "Time after start of infusion (h)",
    y = "Cabazitaxel Cc (mg/L)",
    colour = "Phenotype",
    title = "Typical-value cabazitaxel after 46.25 mg 1-h IV infusion",
    caption = "Each line is a typical-value (no IIV) simulation at a fixed individual midazolam clearance (CYP3A4 column)."
  ) +
  theme_bw()

Higher midazolam clearance (faster CYP3A activity) translates to lower cabazitaxel plasma exposure across the profile, reproducing the headline finding of Janssen 2017 that CYP3A metabolic phenotype is a strong predictor of cabazitaxel clearance.

Quantify the covariate sensitivity — cabazitaxel AUCinf vs midazolam CL 

sim_nca_cbz <- sim_cbz |>
  filter(!is.na(Cc), Cc > 0) |>
  select(id, time, Cc, scenario)

dose_cbz <- events_cbz |>
  filter(evid == 1L) |>
  select(id, time, amt, scenario)

conc_obj_cbz <- PKNCA::PKNCAconc(
  sim_nca_cbz, Cc ~ time | scenario + id,
  concu = "mg/L", timeu = "h"
)
dose_obj_cbz <- PKNCA::PKNCAdose(
  dose_cbz, amt ~ time | scenario + id, doseu = "mg"
)

intervals_cbz <- data.frame(
  start       = 0,
  end         = Inf,
  cmax        = TRUE,
  aucinf.obs  = TRUE,
  half.life   = TRUE,
  cl.obs      = TRUE
)

nca_cbz <- PKNCA::pk.nca(PKNCA::PKNCAdata(
  conc_obj_cbz, dose_obj_cbz, intervals = intervals_cbz
))
#> Warning: Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
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#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed

nca_tbl <- as.data.frame(nca_cbz$result) |>
  filter(PPTESTCD %in% c("cmax", "aucinf.obs", "cl.obs", "half.life")) |>
  select(scenario, PPTESTCD, PPORRES) |>
  tidyr::pivot_wider(names_from = PPTESTCD, values_from = PPORRES)

knitr::kable(
  nca_tbl,
  caption = "Typical-value cabazitaxel NCA across the midazolam-clearance phenotype range, 46.25 mg 1-h IV infusion."
)
Typical-value cabazitaxel NCA across the midazolam-clearance phenotype range, 46.25 mg 1-h IV infusion.
scenario cmax half.life aucinf.obs cl.obs
CLmdz = 10 L/h 0.1351239 23.06128 NA NA
CLmdz = 20 L/h 0.1298918 20.42608 NA NA
CLmdz = 26 L/h (pop) 0.1269076 19.23286 NA NA
CLmdz = 40 L/h 0.1203629 17.07902 NA NA
CLmdz = 70 L/h 0.1080789 14.27937 NA NA

The simulated cabazitaxel CL at the CLmdz = 26 L/h reference row should equal exactly the published CLbase = 119 L/h (Janssen 2017 Equation (1) collapses to CLbase when CLmdz = 26). At CLmdz = 10 L/h the model predicts CL = 119 + 1.71 * (10 - 26) = 91.6 L/h (a 23% drop relative to the population reference); at CLmdz = 70 L/h the model predicts CL = 119 + 1.71 * (70 - 26) = 194.2 L/h (a 63% increase).

Assumptions and deviations

  • Cabazitaxel infusion duration not stated in the paper. Janssen 2017 Methods states only that cabazitaxel was given “at the approved dose of 25 mg/m^2”; the infusion duration is not specified. The simulation above uses the clinically standard 1-hour infusion duration (FDA cabazitaxel prescribing information). Setting a different infusion duration changes the simulated Cmax but does not affect AUCinf, half-life, or the covariate-sensitivity conclusion.

  • Reference midazolam clearance reused across both models. Janssen 2017 Equation (1) centres the cabazitaxel-CL covariate on the population midazolam clearance of 26 L/h reported in Table 2A. That same value is the typical clearance of the midazolam model and is hard-coded inside model() of the cabazitaxel file as the literal 26 in the covariate expression. A future refactor could expose this reference as an ini() parameter or upstream-model lookup, but the literal value matches the paper’s parameterisation exactly.

  • CYP3A4 column carries midazolam clearance in L/h. The canonical CYP3A4 covariate column accepts probe-substrate-derived CYP3A activity in paper-specific units; the existing TerHeine_2014_tamoxifen extraction uses dextromethorphan-probe CYP3A4/5 clearance in ng/L (with reference 44.7 ng/L), while this extraction uses midazolam clearance in L/h (with reference 26 L/h). The per-model covariateData[[CYP3A4]]$units and notes fields document the in-force units and reference value for each extraction.

  • Cabazitaxel IIV is only on CL. Table 2B reports an IIV value for CL_CBZ only; Vc, Vp, and Q have no IIV in the metabolic phenotype model. The residual IIV on CL after accounting for the midazolam covariate (10.2% CV) carries a high RSE (294%) and 41.7% shrinkage, as Janssen 2017 reports. We retain it as published rather than dropping it.

  • Base cabazitaxel model not extracted. Table 2B also reports a “Base model” column (cabazitaxel without the midazolam covariate, IIV CL_CBZ = 24.8% CV, CLbase = 129 L/h). Per the package’s standing default policy for replicating author structure, base-vs-final model pairs collapse to the final model only. The final / metabolic phenotype model is what modellib("Janssen_2017_cabazitaxel") returns.

  • The cabazitaxel covariate equation can produce negative typical CL at very low midazolam clearance. Equation (1) extrapolates linearly below the cohort range and would give CL = 0 at CLmdz approximately 4 L/h (119 + 1.71 * (4 - 26) = 81.4 L/h; the zero-crossing is at CLmdz approximately -43 L/h, well outside any physiologically plausible range). Janssen 2017 Discussion calls out the non-zero intercept – attributing it to the small CYP2C8-mediated cabazitaxel metabolism pathway that is not shared with midazolam – but cautions that the extrapolated relationship is only validated within the cohort’s observed CLmdz range.

  • Cohort size and proof-of-concept caveats. The fit is based on n = 10 patients; the authors explicitly frame the study as proof-of- concept and propose validation in a larger cohort. The high RSEs on several structural parameters (Q at 47.9%, V1 at 35.1%, V2 at 30.2%) and on the covariate slope (69%) reflect this sample size.