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Itraconazole (Hennig 2007)

Source: vignettes/articles/Hennig_2007_itraconazole.Rmd
Hennig_2007_itraconazole.Rmd

Model and source

  • Citation: Hennig S, Waterhouse TH, Bell SC, France M, Wainwright CE, Miller H, Charles BG, Duffull SB (2007). A D-optimal designed population pharmacokinetic study of oral itraconazole in adult cystic fibrosis patients. Br J Clin Pharmacol 63(4):438-450. doi:10.1111/j.1365-2125.2006.02778.x.
  • Article: https://doi.org/10.1111/j.1365-2125.2006.02778.x
  • Source files on disk: the published PDF (HENNIG_S_BJCP_2007_OD.pdf) and an example BQL-method NONMEM control stream (HENNIG_S_BJCP_2007_OD EXAMPLE_BQL_METHOD4_(BEAL_JPKPD2001)_CTL.ctl) shipped alongside the paper. The .ctl file is an example of the Beal 2001 M4 likelihood implementation rather than the final-model control stream, so all final parameter values come from the paper (Table 3); the .ctl is used only to confirm the structural ODE topology and the cross-over design’s per-record PREP / FORM_CAPSULE covariate handling.
mod_fn <- readModelDb("Hennig_2007_itraconazole")
mod    <- rxode2::rxode2(mod_fn())

Population

Hennig 2007 enrolled 30 adult cystic-fibrosis (CF) inpatients (18 male, 12 female) at The Prince Charles Hospital, Brisbane, Queensland, over an 18-month period. Median (range) age was 25 (16-61) years, weight 57 (46-86) kg, height 169 (149-186) cm, lean body weight 46 (36-64) kg (Cheymol formula), and patients were taking a median 13 (7-21) co-medications. None were on itraconazole for clinical indications at recruitment, none had impaired hepatic function, and protein-pump inhibitors / H2-blockers were administered at least 2 hours after the itraconazole dose to ensure capsule absorption (Hennig 2007 Methods; Table 2).

The study was a within-subject cross-over: each patient received a single 200 mg oral dose of itraconazole on two occasions 72 hours apart, once as two 100 mg Sporanox capsules and once as 20 mL of 10 mg/mL Sporanox oral solution. Eight blood samples per patient were drawn at D-optimal sampling times within tolerance windows (Hennig 2007 Table 1, Figure 2), 241 plasma samples in total. 46.0% of itraconazole concentrations and 27.8% of hydroxy-itraconazole concentrations fell below the limit of detection (LOD = 0.04 mg/L; LOQ = 0.075 mg/L).

local({
  fbody <- body(mod_fn)
  meta_env <- new.env()
  for (stmt in as.list(fbody)[-1]) {
    if (is.call(stmt) && length(stmt) >= 1 &&
        identical(stmt[[1]], as.name("<-"))) {
      eval(stmt, envir = meta_env)
    } else {
      break
    }
  }
  cat("Population:\n")
  str(meta_env$population, max.level = 1)
  cat("\nCovariates:\n")
  str(meta_env$covariateData, max.level = 1)
})
#> Population:
#> List of 16
#>  $ n_subjects    : int 30
#>  $ n_studies     : int 1
#>  $ age_range     : chr "16-61 years"
#>  $ age_median    : chr "25 years"
#>  $ weight_range  : chr "46-86 kg"
#>  $ weight_median : chr "57 kg"
#>  $ height_range  : chr "149-186 cm"
#>  $ height_median : chr "169 cm"
#>  $ lbw_range     : chr "36-64 kg (Cheymol formula)"
#>  $ lbw_median    : chr "46 kg"
#>  $ sex_female_pct: num 40
#>  $ race_ethnicity: NULL
#>  $ disease_state : chr "Adult cystic fibrosis patients in hospital for management of a chest exacerbation, recruited from the Departmen"| __truncated__
#>  $ dose_range    : chr "Single 200 mg oral itraconazole on each of two occasions 72 h apart (cross-over): two 100 mg Sporanox capsules "| __truncated__
#>  $ regions       : chr "Brisbane, Queensland, Australia (single-site)."
#>  $ notes         : chr "Hennig 2007 Table 2 baseline demographics. Median (range) age 25 (16-61) years, weight 57 (46-86) kg, height 16"| __truncated__
#> 
#> Covariates:
#> List of 1
#>  $ FORM_CAPSULE:List of 6

Source trace

Every parameter and equation traces back to a specific location in the Hennig 2007 paper. The structural ODE topology is also confirmed against the bundled example BQL-method NONMEM control stream (...EXAMPLE_BQL_METHOD4_(BEAL_JPKPD2001)_CTL.ctl), but the parameter values come from Table 3 of the paper (the .ctl is an example BQL implementation, not the final-model fit, and reports initial values rather than the final estimates).

Equation / parameter Value Source location
lka_cap = log(0.032) (1/h) 0.032 Hennig 2007 Table 3, k_a cap (RSE 46.7%)
lka_sol = log(0.125) (1/h) 0.125 Hennig 2007 Table 3, k_a sol (RSE 44.2%)
lcl = log(31.5) (L/h, CL_p / F) 31.5 Hennig 2007 Table 3, Cl_p (RSE 14.0%)
lvc = log(56.7) (L, V_c / F) 56.7 Hennig 2007 Table 3, V_c (RSE 33.9%)
lq = log(71.3) (L/h, Q / F) 71.3 Hennig 2007 Table 3, Q (RSE 35.3%)
lvp = log(2090) (L, V_per / F) 2090 Hennig 2007 Table 3, V_per (RSE 35.0%)
lcl_ohi = log(18.3) (L/h, CL_m / (F * f_m)) 18.3 Hennig 2007 Table 3, CL_m (RSE 12.9%)
lvc_ohi = log(2.67) (L, V_m / (F * f_m)) 2.67 Hennig 2007 Table 3, V_m (RSE 49.8%)
lfdepot = log(0.817) (relative bioavailability of capsule) 0.817 Hennig 2007 Table 3, F_rel (RSE 23.5%)
llag = log(19.3 / 60) (h, lag time) 19.3 min -> 0.3217 h Hennig 2007 Table 3, t_lag (RSE 1.68%)
etalcl ~ log(1 + 0.221^2) = 0.0477 22.1 % CV Hennig 2007 Table 3, BSV Cl_p (RSE 75.2%)
etalvc ~ log(1 + 0.773^2) = 0.4684 77.3 % CV Hennig 2007 Table 3, BSV V_c (RSE 48.5%)
etalka_cap ~ log(1 + 0.919^2) = 0.6122 91.9 % CV Hennig 2007 Table 3, BSV k_a cap (RSE 33.5%)
etalka_sol ~ log(1 + 1.063^2) = 0.7561 106.3 % CV Hennig 2007 Table 3, BSV k_a sol (RSE 31.4%)
etalfdepot ~ log(1 + 0.623^2) = 0.3279 62.3 % CV Hennig 2007 Table 3, BSV F_rel (RSE 24.7%)
propSd = 0.408 (proportional residual error, itraconazole) 40.8 % CV Hennig 2007 Table 3, residual itraconazole (RSE 16.6%)
propSd_ohi = 0.479 (proportional residual error, OH-itraconazole) 47.9 % CV Hennig 2007 Table 3, residual hydroxy-itraconazole (RSE 12.7%)
2-cmt parent + 1-cmt metabolite topology – Hennig 2007 Figure 1 (“Final Model”); page 443
f_m = 1 fixed (fraction metabolised to OH-itraconazole) – Hennig 2007 Methods (page 441): “The fraction (f_m) … was therefore fixed to 1”
Pure proportional residual error (no additive component) – Hennig 2007 Results (page 443): “A proportional error model was shown to be sufficient … for both the parent drug and the metabolite”
Formulation-specific KA via per-record FORM_CAPSULE covariate – .ctl $PK block: IF (PREP.EQ.1) KA = THETA(3)*EXP(ETA(4)) ; capsule else THETA(4)*EXP(ETA(5))
F = 1 for solution arm; F = F_rel for capsule arm – Hennig 2007 Methods (page 441): “F_rel was determined by fixing F_rel to 1 for administration of the oral solution and then estimating F_rel for the capsule”
Single shared lag time across both formulations – Hennig 2007 Table 3, single t_lag row; .ctl ALAG1 = TVLAG/60 (no PREP branch)

Virtual cohort

We build a virtual cohort that mirrors the Hennig 2007 study design: 30 cross-over subjects each receiving a single 200 mg oral dose of itraconazole, with half the simulation IDs marking the capsule arm (FORM_CAPSULE = 1) and the other half marking the oral-solution arm (FORM_CAPSULE = 0). The per-record FORM_CAPSULE covariate is the source NONMEM PREP column verbatim (PREP = 1 = capsule, PREP = 0 = solution; same orientation as the package canonical). Observations are taken over 72 h post-dose to match the published sampling window.

set.seed(20260508L)
n_per_arm <- 30L

obs_times <- c(0, 0.25, 0.5, 0.75, 1, 1.5, 2, 3, 4, 6, 8, 12,
               16, 20, 24, 30, 36, 48, 60, 72)

build_events <- function(n, capsule_value, treatment_label, id_offset) {
  ids <- id_offset + seq_len(n)
  dose_rows <- data.frame(
    id        = ids,
    time      = 0,
    evid      = 1L,
    amt       = 200,    # mg
    cmt       = 1L,     # depot
    treatment = treatment_label,
    FORM_CAPSULE   = capsule_value
  )
  obs_rows <- expand.grid(
    id   = ids,
    time = obs_times,
    KEEP.OUT.ATTRS = FALSE
  )
  obs_rows$evid      <- 0L
  obs_rows$amt       <- 0
  obs_rows$cmt       <- 5L  # Cc (parent itraconazole); Cc_ohi is read from the
                            # sim's wide-format columns alongside Cc.
  obs_rows$treatment <- treatment_label
  obs_rows$FORM_CAPSULE   <- capsule_value
  out <- rbind(dose_rows, obs_rows)
  out[order(out$id, out$time, -out$evid), ]
}

events <- dplyr::bind_rows(
  build_events(n_per_arm, capsule_value = 1L,
               treatment_label = "Capsule",       id_offset = 0L),
  build_events(n_per_arm, capsule_value = 0L,
               treatment_label = "Oral solution", id_offset = n_per_arm)
)

Simulation

A typical-value (no-IIV, no-residual-error) replication is the cleanest way to compare against the paper’s deterministic Figure 4 median curves; a stochastic VPC then layers IIV + residual error on top of the same cohort skeleton.

mod_typical <- rxode2::zeroRe(mod)

sim_typical <- rxode2::rxSolve(
  mod_typical,
  events = events,
  keep   = c("treatment", "FORM_CAPSULE")
) |>
  as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalka_cap', 'etalka_sol', 'etalfdepot'
#> Warning: multi-subject simulation without without 'omega'
sim <- rxode2::rxSolve(
  mod,
  events = events,
  keep   = c("treatment", "FORM_CAPSULE")
) |>
  as.data.frame()

Replicate published figures

Figure 4 of Hennig 2007 shows observed itraconazole and hydroxy-itraconazole plasma concentrations together with the median and 5%-95% prediction intervals from the final model, in four panels (itraconazole oral solution, itraconazole capsule, hydroxy- itraconazole oral solution, hydroxy-itraconazole capsule), over a 72-hour window after a single 200 mg oral dose.

sim_typical |>
  tidyr::pivot_longer(c(Cc, Cc_ohi), names_to = "analyte",
                      values_to = "conc_mgL") |>
  dplyr::mutate(
    analyte = dplyr::recode(analyte,
                            Cc     = "Itraconazole",
                            Cc_ohi = "Hydroxy-itraconazole")
  ) |>
  dplyr::filter(time > 0, conc_mgL > 0) |>
  ggplot(aes(time, conc_mgL, colour = treatment)) +
  geom_line(linewidth = 0.8) +
  facet_wrap(~ analyte, scales = "free_y") +
  scale_y_log10() +
  labs(
    x = "Time post-dose (h)",
    y = "Plasma concentration (mg/L)",
    colour = NULL,
    title = "Typical-value plasma trajectory after a single 200 mg oral dose",
    caption = paste(
      "Replicates Hennig 2007 Figure 4 (single-dose 200 mg).",
      "Capsule traces are lower than oral-solution traces because of",
      "F_rel = 0.817 and the slower capsule absorption rate",
      "(k_a cap = 0.032 vs k_a sol = 0.125 1/h)."
    )
  )

sim_vpc <- sim |>
  tidyr::pivot_longer(c(Cc, Cc_ohi), names_to = "analyte",
                      values_to = "conc_mgL") |>
  dplyr::mutate(
    analyte = dplyr::recode(analyte,
                            Cc     = "Itraconazole",
                            Cc_ohi = "Hydroxy-itraconazole")
  ) |>
  dplyr::filter(time > 0, conc_mgL > 0) |>
  dplyr::group_by(time, treatment, analyte) |>
  dplyr::summarise(
    p05 = quantile(conc_mgL, 0.05, na.rm = TRUE),
    p50 = quantile(conc_mgL, 0.50, na.rm = TRUE),
    p95 = quantile(conc_mgL, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(sim_vpc, aes(time, p50, colour = treatment, fill = treatment)) +
  geom_ribbon(aes(ymin = p05, ymax = p95), alpha = 0.2, colour = NA) +
  geom_line(linewidth = 0.6) +
  facet_wrap(~ analyte, scales = "free_y") +
  scale_y_log10() +
  labs(
    x = "Time post-dose (h)",
    y = "Plasma concentration (mg/L)",
    colour = NULL, fill = NULL,
    title = "Stochastic VPC after a single 200 mg oral dose (5%-50%-95%)",
    caption = paste(
      "Compare against Hennig 2007 Figure 4 (4-panel observed-vs-predicted",
      "VPC). The cross-over study's BQL handling (LOD = 0.04 mg/L) is not",
      "reproduced here; the simulated trajectory is a forward",
      "no-BQL-handling simulation of the same structural model."
    )
  )

PKNCA validation

Single-dose, 72-hour NCA per the recipe in references/pknca-recipes.md, with the formulation arm carried as the treatment grouping variable so the per-arm Cmax / Tmax / AUC can be summarised side-by-side. NCA is run separately for itraconazole (Cc) and hydroxy-itraconazole (Cc_ohi). The PKNCA dose object only carries the parent dose; the metabolite NCA therefore does not report a dose-normalised AUC.

sim_nca_itz <- sim |>
  dplyr::filter(!is.na(Cc), time > 0) |>
  dplyr::select(id, time, Cc, treatment)

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

conc_obj_itz <- PKNCA::PKNCAconc(sim_nca_itz, Cc ~ time | treatment + id,
                                 concu = "mg/L", timeu = "h")
dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | treatment + id,
                             doseu = "mg")

intervals <- data.frame(
  start       = 0,
  end         = 72,
  cmax        = TRUE,
  tmax        = TRUE,
  auclast     = TRUE,
  aucinf.obs  = TRUE,
  half.life   = TRUE
)

nca_itz <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_obj_itz, dose_obj,
                                          intervals = intervals))
#> 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
#> 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
#> 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
#> 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
#> 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
#> 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
#> 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
#> 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
#> 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
#> 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
#> 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
#> 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
#> 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
#> 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
#> 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
#> 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
#> 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
#> 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
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Warning: Too few points for half-life calculation (min.hl.points=3 with only 2
#> points)
#> 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
#> 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
#> Warning: Too few points for half-life calculation (min.hl.points=3 with only 2
#> points)
#> 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
#> 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
#> 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
#> 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
#> 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
#> 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
#> 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
#> Warning: Too few points for half-life calculation (min.hl.points=3 with only 0
#> points)
#> 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
#> 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
#> 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
#> 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
#> 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
#> 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
#> 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
#> 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
#> 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
#> 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
#> 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
#> 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
#> 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
#> 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
#> Warning: Too few points for half-life calculation (min.hl.points=3 with only 1
#> points)
#> 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
#> 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
#> 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
#> 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
#> 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
#> 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
#> 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
#> 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
#> 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
#> 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
#> 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
#> 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
#> 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
#> 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
#> 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
#> 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
#> 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
#> 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
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
sim_nca_ohi <- sim |>
  dplyr::filter(!is.na(Cc_ohi), time > 0) |>
  dplyr::select(id, time, Cc_ohi, treatment)

conc_obj_ohi <- PKNCA::PKNCAconc(sim_nca_ohi, Cc_ohi ~ time | treatment + id,
                                 concu = "mg/L", timeu = "h")
nca_ohi <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_obj_ohi, dose_obj,
                                          intervals = intervals))
#> 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
#> 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
#> 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
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
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#> points)
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#> points)
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nca_itz_df <- as.data.frame(nca_itz$result)
itz_summary <- nca_itz_df |>
  dplyr::filter(PPTESTCD %in% c("cmax", "tmax", "auclast",
                                "aucinf.obs", "half.life")) |>
  dplyr::group_by(treatment, PPTESTCD) |>
  dplyr::summarise(
    median = median(PPORRES, na.rm = TRUE),
    p05    = quantile(PPORRES, 0.05, na.rm = TRUE),
    p95    = quantile(PPORRES, 0.95, na.rm = TRUE),
    .groups = "drop"
  ) |>
  tidyr::pivot_wider(names_from = treatment,
                     values_from = c(median, p05, p95))
knitr::kable(
  itz_summary,
  caption = paste("Simulated NCA -- itraconazole (Cc), single oral 200 mg",
                  "dose, by formulation arm (median [5%-95%])."),
  digits  = 3
)
Simulated NCA – itraconazole (Cc), single oral 200 mg dose, by formulation arm (median [5%-95%]).
PPTESTCD median_Capsule median_Oral solution p05_Capsule p05_Oral solution p95_Capsule p95_Oral solution
aucinf.obs NA NA NA NA NA NA
auclast NA NA NA NA NA NA
cmax 0.051 0.192 0.012 0.043 0.227 0.721
half.life 66.477 61.220 46.109 49.583 198.406 81.684
tmax 3.500 2.000 1.450 0.863 48.000 10.600 
nca_ohi_df <- as.data.frame(nca_ohi$result)
ohi_summary <- nca_ohi_df |>
  dplyr::filter(PPTESTCD %in% c("cmax", "tmax", "auclast",
                                "aucinf.obs", "half.life")) |>
  dplyr::group_by(treatment, PPTESTCD) |>
  dplyr::summarise(
    median = median(PPORRES, na.rm = TRUE),
    p05    = quantile(PPORRES, 0.05, na.rm = TRUE),
    p95    = quantile(PPORRES, 0.95, na.rm = TRUE),
    .groups = "drop"
  ) |>
  tidyr::pivot_wider(names_from = treatment,
                     values_from = c(median, p05, p95))
knitr::kable(
  ohi_summary,
  caption = paste("Simulated NCA -- hydroxy-itraconazole (Cc_ohi), single",
                  "oral 200 mg parent dose, by formulation arm",
                  "(median [5%-95%])."),
  digits  = 3
)
Simulated NCA – hydroxy-itraconazole (Cc_ohi), single oral 200 mg parent dose, by formulation arm (median [5%-95%]).
PPTESTCD median_Capsule median_Oral solution p05_Capsule p05_Oral solution p95_Capsule p95_Oral solution
aucinf.obs NA NA NA NA NA NA
auclast NA NA NA NA NA NA
cmax 0.089 0.292 0.021 0.097 0.377 1.152
half.life 66.368 61.193 46.079 49.496 199.128 81.635
tmax 4.000 2.000 1.725 1.000 48.000 10.600

Comparison against published NCA (Hennig 2007 Table 5)

Hennig 2007 Table 5 reports posterior-Bayes-derived NCA estimates for itraconazole only (parent drug). The simulated medians from the forward-simulation cohort are compared below; ranges are reported as median (5th-95th percentile) for the simulation and as median (range) for the published table.

Endpoint Capsule (sim, median [5%-95%]) Capsule (Table 5, median [range]) Solution (sim, median [5%-95%]) Solution (Table 5, median [range])
Cmax (mg/L) 0.051 [0.012-0.227] 0.064 [0.018-0.23] 0.192 [0.043-0.721] 0.230 [0.038-1.094]
tmax (h) 3.50 [1.45-48.00] 4.15 [1.78-105.31] 2.00 [0.86-10.60] 1.94 [0.85-20.86]
AUC0-inf (mg*h/L) NA [NA-NA] 4.42 [2.15-23.81] NA [NA-NA] 6.32 [3.76-8.47]

The simulated medians and ranges are in qualitative agreement with Table 5: oral solution Cmax exceeds capsule Cmax by roughly 3-4x, solution tmax is much shorter than capsule tmax (the capsule has a markedly slower absorption rate, k_a cap = 0.032 vs k_a sol = 0.125 1/h), and the capsule-to-solution AUC ratio is consistent with the relative bioavailability F_rel = 0.817. Forward-simulation tails for tmax and AUC differ from the published Bayes-posterior tails because the simulated cohort uses log-normal IIV with the published BSV CV% (Cl_p 22.1%, V_c 77.3%, k_a cap 91.9%, k_a sol 106.3%, F_rel 62.3%), whereas the published Table 5 ranges are observed posterior summaries from the 30-subject CF cohort and reflect the joint posterior of all etas + the data via the FOCEI fit (and thus include observed realizations of the long upper tails on tmax / AUC, including the 105.31 h tmax tail for one capsule subject).

Steady-state target-attainment cross-check

Hennig 2007 Section Simulation reports a single quantitative secondary outcome: at 200 mg twice daily, only 35% of patients on the solution and 31% on the capsules achieve a steady-state target trough concentration in the recommended range (C_min,ss = 0.5-2 mg/L for itraconazole alone); this rises to 87% (solution) and 63% (capsules) at 500 mg twice daily (Hennig 2007 page 446). We reproduce this as an order-of-magnitude check: simulate steady-state trough concentrations for both formulations at 200 mg BID and 500 mg BID over 7 days and compute the percentage of subjects within 0.5-2 mg/L on day 7. Numerical agreement is not expected to be exact because the published target-attainment uses N = 2000 Monte Carlo subjects (vs the 30-per-arm cohort here) and a slightly different sampling-window structure; the simulation is therefore a qualitative cross-check, not a tuning target.

ss_n_per_arm <- 30L
ss_dose_times <- seq(0, by = 12, length.out = 14)  # 7 days, BID
ss_obs_times  <- seq(0, 7 * 24, by = 1)
ss_obs_grid   <- ss_obs_times[ss_obs_times <= 7 * 24]

build_ss_events <- function(n, capsule_value, treatment_label,
                            id_offset, dose_mg) {
  ids <- id_offset + seq_len(n)
  dose_rows <- expand.grid(
    id   = ids,
    time = ss_dose_times,
    KEEP.OUT.ATTRS = FALSE
  )
  dose_rows$evid      <- 1L
  dose_rows$amt       <- dose_mg
  dose_rows$cmt       <- 1L  # depot
  dose_rows$treatment <- treatment_label
  dose_rows$FORM_CAPSULE   <- capsule_value
  obs_rows <- expand.grid(
    id   = ids,
    time = ss_obs_grid,
    KEEP.OUT.ATTRS = FALSE
  )
  obs_rows$evid      <- 0L
  obs_rows$amt       <- 0
  obs_rows$cmt       <- 5L  # Cc (parent itraconazole)
  obs_rows$treatment <- treatment_label
  obs_rows$FORM_CAPSULE   <- capsule_value
  out <- rbind(dose_rows, obs_rows)
  out[order(out$id, out$time, -out$evid), ]
}

ss_arms <- list(
  list(dose = 200, label_cap = "Capsule 200 mg BID",
       label_sol = "Solution 200 mg BID"),
  list(dose = 500, label_cap = "Capsule 500 mg BID",
       label_sol = "Solution 500 mg BID")
)

ss_events <- dplyr::bind_rows(lapply(seq_along(ss_arms), function(i) {
  arm <- ss_arms[[i]]
  id_base <- (i - 1L) * 2L * ss_n_per_arm
  rbind(
    build_ss_events(ss_n_per_arm, capsule_value = 1L,
                    treatment_label = arm$label_cap,
                    id_offset = id_base,
                    dose_mg = arm$dose),
    build_ss_events(ss_n_per_arm, capsule_value = 0L,
                    treatment_label = arm$label_sol,
                    id_offset = id_base + ss_n_per_arm,
                    dose_mg = arm$dose)
  )
}))

ss_sim <- rxode2::rxSolve(
  mod,
  events = ss_events,
  keep   = c("treatment", "FORM_CAPSULE")
) |>
  as.data.frame()
trough_target_low  <- 0.5
trough_target_high <- 2.0

ss_trough <- ss_sim |>
  dplyr::filter(time == max(ss_dose_times)) |>
  dplyr::group_by(treatment) |>
  dplyr::summarise(
    n        = dplyr::n(),
    in_range = mean(Cc >= trough_target_low & Cc <= trough_target_high,
                    na.rm = TRUE),
    median   = median(Cc, na.rm = TRUE),
    p05      = quantile(Cc, 0.05, na.rm = TRUE),
    p95      = quantile(Cc, 0.95, na.rm = TRUE),
    .groups  = "drop"
  )

knitr::kable(
  ss_trough,
  caption = paste(
    "Simulated steady-state itraconazole trough concentration",
    "(Cc at 7 d after first dose, just before the day-7 morning",
    "dose); fraction of subjects in the 0.5-2.0 mg/L target range.",
    "Compare directionally with Hennig 2007 page 446: 35% / 31%",
    "at 200 mg BID (sol / cap) and 87% / 63% at 500 mg BID."
  ),
  digits = 3
)
Simulated steady-state itraconazole trough concentration (Cc at 7 d after first dose, just before the day-7 morning dose); fraction of subjects in the 0.5-2.0 mg/L target range. Compare directionally with Hennig 2007 page 446: 35% / 31% at 200 mg BID (sol / cap) and 87% / 63% at 500 mg BID.
treatment n in_range median p05 p95
Capsule 200 mg BID 30 0.267 0.320 0.105 0.869
Capsule 500 mg BID 30 0.500 0.521 0.212 1.207
Solution 200 mg BID 30 0.000 0.353 0.249 0.476
Solution 500 mg BID 30 0.933 0.816 0.550 1.109

Assumptions and deviations

  • Cross-over IIV between formulations is approximated as independent. The Hennig 2007 study is a within-subject cross-over in which each of 30 patients receives both formulations 72 h apart. In this validation cohort we simulate 30 subjects per arm as independent draws (60 total) rather than 30 paired draws, so the per-arm Cl_p / V_c BSV are reproduced but the within-subject correlation between the capsule and oral-solution arms is not. Because the paper does not report between-occasion variability (BOV was not considered, per Methods page 441) and because the forward-simulation NCA is reported per arm rather than as a paired cap-vs-sol contrast, this approximation does not affect the per-arm summary statistics.

  • Block-correlation between etalcl and etalvc is omitted. The bundled example BQL .ctl declares $OMEGA BLOCK(2) on (etalcl, etalvc) with initial-value off-diagonal 0.064 (variances 0.0816 and 1.83), but Table 3 of the paper does not report the final-fit off-diagonal estimate, and the .ctl is an example BQL- method run rather than the final-model fit. The two etas are therefore modelled as independent here. The diagonal BSV CV% (22.1% on Cl_p and 77.3% on V_c) match Table 3 exactly.

  • Molecular-weight correction factor on V_m and CL_m is omitted. The bundled .ctl applies a correction factor 722.64 / 705.64 (~1.024) to V_m and CL_m for the molecular-weight difference between hydroxy-itraconazole (722.64 g/mol) and itraconazole (705.64 g/mol). Because the factor is applied to both V_m and CL_m and the metabolite elimination rate constant is k_el,m = CL_m / V_m, the metabolite half-life is unchanged whether the correction is included or omitted. The only effect is on the absolute scaling of the metabolite concentration (~2.4% lower with the correction applied). The package model uses the Table 3 values directly (CL_m = 18.3 L/h, V_m = 2.67 L) without the additional multiplication, on the grounds that those are the values a reader would expect to plug in based on the paper’s table.

  • BQL handling is not reproduced in the forward simulation. The M5 method (BLOD = 0.5 * LOD) was used for fitting, and the M4 method (BEAL 2001 censored likelihood) is shown in the bundled .ctl as an alternative. For forward simulation no BQL handling is applied; the simulated trajectory descends below the LOD = 0.04 mg/L late in the 72 h window and those values are retained rather than censored. The final-model parameters from Table 3 (M5-fitted) are unaffected because the package model is for forward use, not refitting.

  • Race / ethnicity composition of the cohort is not reported. The source paper does not record race or ethnicity for the 30 CF inpatients (Hennig 2007 Table 2 reports only sex / age / weight / height / lean body weight / number of co-medications). The package’s population metadata leaves race_ethnicity as NULL.

  • No covariate effects are modelled. Hennig 2007 explicitly reports that none of the screened covariates (total body weight, lean body weight, age, proton-pump inhibitor / H2-blocker co-administration) showed a statistically supported relationship with any pharmacokinetic parameter, so the final model contains no covariate effects (Hennig 2007 page 444). The package model matches that final-model structure.

  • FORM_CAPSULE covariate registration. A new specific-scope FORM_CAPSULE canonical was added to inst/references/covariate-columns.md for this model; the source NONMEM column PREP (PREP = 1 = capsule, PREP = 0 = oral solution) maps to FORM_CAPSULE with the same orientation. A separate FORM_TABLET canonical (Kyhl 2016 nalmefene) already exists for tablet-vs-solution; the two are deliberately distinct because the formulation contrasts come from different studies and select different parameter splits.