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Posaconazole (van Iersel 2018)

Source: vignettes/articles/vanIersel_2018_posaconazole.Rmd
vanIersel_2018_posaconazole.Rmd

Model and source

  • Citation: van Iersel MLPS, Rossenu S, de Greef R, Waskin H. A population pharmacokinetic model for a solid oral tablet formulation of posaconazole. Antimicrob Agents Chemother. 2018;62(7):e02465-17. doi:10.1128/AAC.02465-17.
  • Description: Population PK model for the delayed-release solid oral tablet formulation of posaconazole in adult healthy volunteers and patients at high risk for invasive fungal disease (van Iersel 2018). One-compartment disposition with sequential zero-order then first-order absorption: each oral dose loads into the depot compartment as a zero-order infusion of duration D1, after which depot drains to central with first-order rate constant ka and central eliminates with first-order rate constant CL/V. The random effect on D1 is the same as the random effect on ka multiplied by a correlation factor (cor_kad1 = -0.586). Covariates retained in the final model are body weight on relative bioavailability (allometric power exponent), tablet formulation A/B versus C/D on bioavailability, AML/MDS disease state on bioavailability, fed status on absorption rate, and single-dose-versus-multiple-dose record indicator on clearance. Residual variability is log-additive with separate magnitudes for phase 1 versus phase 3 studies.
  • Article: https://doi.org/10.1128/AAC.02465-17

Population

van Iersel 2018 pooled 5,756 plasma posaconazole concentration measurements from 335 subjects (104 healthy volunteers across five phase 1 studies P04975, P05637, P07764, P07783, P07691 and 231 patients from the phase 3 study P05615 at high risk for invasive fungal disease). Study-mean ages span 31.4-51.0 years and study-mean body weights span 73.9-79.6 kg (van Iersel 2018 Table 1). The phase 3 patient cohort included 125 AML, 82 MDS, 6 GVHD/HSCT, and 18 missing-diagnosis subjects. Doses ranged from 100 to 400 mg of the delayed-release solid tablet, single or multiple. The race distribution is predominantly white (van Iersel 2018 Discussion notes the limited race distribution as a potential limitation of the analysis). The same information is available programmatically via the model’s population metadata (rxode2::rxode2(readModelDb("vanIersel_2018_posaconazole"))$population).

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/vanIersel_2018_posaconazole.R. The table below collects them in one place for review.

Equation / parameter Value Source location
Structural model 1-cmt sequential zero+first-order absorption van Iersel 2018 Results ‘Model development’; Fig S5 (supplement schematic)
lcl = log(9.70 L/h) 9.70 L/h (RSE 5.00%) Table 2 row ‘CL/F (liters/h)’ final model with outliers
lvc = log(393 L) 393 L (RSE 2.77%) Table 2 row ‘V (liters)’ final model with outliers
lka = log(0.853 1/h) 0.853 1/h (RSE 7.75%) Table 2 row ‘ka (liter/h)’ final model with outliers
ld1 = log(2.54 h) 2.54 h (RSE 3.45%) Table 2 row ‘D1 (h)’ final model with outliers
lfdepot = fixed(log(1)) F1 = 1 (anchor) Results ‘Posaconazole exposure … and impact of covariates’: tablet D reference
cor_kad1 -0.586 (RSE 15.2%) Table 2 row ‘COR’ final model with outliers
e_wt_fdepot -1.03 (RSE 8.91%) Table 2 row ‘Body wt on F1’ final model with outliers
e_md_cl 0.750 (RSE 5.87%) Table 2 row ‘Dosing regimen on CL’ final model with outliers
e_formposaab_fdepot 0.247 (RSE 21.5%) Table 2 row ‘Tablet formulation A/B on F1’ final model with outliers
e_fed_ka 0.530 (RSE 17.3%) Table 2 row ‘Food intake on ka’ final model with outliers
e_dis_mds_aml_fdepot -0.165 (RSE 25.8%) Table 2 row ‘AML/MDS on F1’ final model with outliers
IIV CL (37.9% CV) omega^2 = 0.1343 Table 2 row ‘IIV for CL’ final model with outliers (RSE 13.1%)
IIV ka (57.5% CV) omega^2 = 0.2858 Table 2 row ‘IIV for ka’ final model with outliers (RSE 29.3%)
IIV F1 (24.2% CV) omega^2 = 0.0569 Table 2 row ‘IIV for F1’ final model with outliers (RSE 26.7%)
expSd_p1 0.42 (RSE 8.69%) Table 2 row ‘SD (phase 1 studies)’ final model with outliers
expSd_p3 0.322 (RSE 10.3%) Table 2 row ‘SD (phase 3 study)’ final model with outliers
Body-weight reference (74.9 kg) n/a Fig S4 ‘median 74.9 kg’ simulation legend; consistent with the ~75 kg mean of Table 1 weights
Zero-then-first-order absorption n/a Results ‘Model development’: ‘sequential zero first-order absorption’
COR mechanism (eta_D1 = COR * eta_ka) n/a Methods ‘Covariate model’: ‘the random effect for D1 was the same as that for the ka parameter multiplied by a correlation factor’
Log-additive residual error n/a Methods ‘Pharmacokinetic model development’: ‘log-transformed, both-sides approach’; Methods ‘Pharmacokinetic model development’: ‘additive error model that included two separate random-effects parameters to account for the difference in residual variability of the phase 1 and phase 3 studies’
Proposed dosing regimen 300 mg BID on day 1, then 300 mg QD for 27 days Results ‘Posaconazole exposure in the clinical setting’ and Methods ‘Final population pharmacokinetic model simulations’
Target exposure (Cavg > 0.5 mg/L) n/a Results ‘Posaconazole exposure in the clinical setting’; MIC90 reference (citation 17 of van Iersel 2018)

Virtual cohort

Original observed data are not publicly available. The figures below use virtual populations whose covariate distributions approximate the published trial demographics for AML/MDS patients and HSCT recipients receiving the proposed posaconazole solid tablet dosing regimen of 300 mg twice daily on day 1 followed by 300 mg once daily for 27 days (van Iersel 2018 Results ‘Posaconazole exposure in the clinical setting’ and Methods ‘Final population pharmacokinetic model simulations’). The published target-attainment simulation used 1,000 subjects per cohort; the cohort sizes here are capped at 200/arm per the nlmixr2lib vignette convention – 200 is ample for the steady-state Cavg / Cmin distributions reproduced below.

The two simulated cohorts are AML/MDS patients (DIS_MDS_AML = 1, all four other covariates retained at reference values) and HSCT recipients (DIS_MDS_AML = 0, otherwise identical). Body weights are sampled from a truncated lognormal around the simulation-cohort median 74.9 kg with the contributing-studies’ SD ~ 14-18 kg (Table 1).

set.seed(20181128L)
n_per_arm <- 200L
tau       <- 24             # hours between QD doses on days 2-28
day1_gap  <- 12             # hours between the two day-1 BID doses
sim_end   <- 28 * 24        # h
# Lean observation grid: hourly day 1 + once-daily trough days 2-27 +
# hourly across the day-28 dosing interval. Sufficient to characterise the
# absorption phase, accumulation, and steady-state NCA without inflating
# the simulation rowcount.
obs_grid  <- sort(unique(c(
  seq(0, 24, by = 2),                                # day 1: every 2 h (13 obs)
  seq(2 * tau, 27 * tau, by = tau),                  # daily troughs through day 27 (26 obs)
  seq(27 * tau, 28 * tau, by = 2)                    # day 28: every 2 h (13 obs)
)))

make_dose_rows <- function(id) {
  # 300 mg BID day 1 (hours 0 and 12), then 300 mg QD on days 2..28
  # (hours 24, 48, ..., 27 * 24 = 648).
  times <- c(0, day1_gap, seq(tau, (28L - 1L) * tau, by = tau))
  tibble(
    id   = id,
    time = times,
    evid = 1L,
    amt  = 300,
    cmt  = "depot",
    dv   = NA_real_
  )
}

make_obs_rows <- function(id) {
  tibble(
    id   = id,
    time = obs_grid,
    evid = 0L,
    amt  = 0,
    cmt  = "central",
    dv   = NA_real_
  )
}

make_cohort <- function(n, cohort_label, dis_mds_aml_val, id_offset) {
  ids <- id_offset + seq_len(n)
  wt  <- pmin(pmax(rlnorm(n, log(74.9), 0.20), 35), 130)  # bounded around median 74.9 kg
  per_subj <- tibble(
    id                  = ids,
    cohort              = cohort_label,
    WT                  = wt,
    FED                 = 0L,
    MULTI_DOSE_PT       = 1L,    # day-2-onwards dosing is multi-dose
    FORM_POSA_AB        = 0L,    # commercial tablet D
    DIS_MDS_AML         = dis_mds_aml_val,
    STUDY_POSA_PHASE3   = 1L     # patient simulation reflects the phase 3 cohort
  )
  events <- bind_rows(
    lapply(ids, make_dose_rows),
    lapply(ids, make_obs_rows)
  ) |>
    left_join(per_subj, by = "id") |>
    arrange(id, time, desc(evid))   # dose before obs at the same time
  events
}

events <- bind_rows(
  make_cohort(n_per_arm, cohort_label = "AML/MDS",  dis_mds_aml_val = 1L, id_offset = 0L),
  make_cohort(n_per_arm, cohort_label = "HSCT",     dis_mds_aml_val = 0L, id_offset = n_per_arm)
)

stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))

Simulation 

mod <- rxode2::rxode2(readModelDb("vanIersel_2018_posaconazole"))
#> ℹ parameter labels from comments will be replaced by 'label()'
sim <- rxode2::rxSolve(
  mod,
  events = events,
  keep   = c("cohort", "WT", "DIS_MDS_AML", "STUDY_POSA_PHASE3")
) |>
  as.data.frame() |>
  as_tibble()

For a deterministic typical-value replication (no between-subject variability), use rxode2::zeroRe(mod):

mod_typical <- rxode2::zeroRe(mod)
sim_typical <- rxode2::rxSolve(mod_typical, events = events,
                               keep = c("cohort", "WT"))

Replicate published figures

Steady-state Cavg distribution by cohort (van Iersel 2018 Figure 2)

van Iersel 2018 Figure 2 displays the distribution of steady-state average plasma concentration (Cavg) at day 28 in 1,000 AML/MDS patients and 1,000 HSCT recipients receiving the proposed 300 mg dosing regimen. The target therapeutic exposure threshold of 0.5 mg/L (= 500 ng/mL) is the MIC90 for the most clinically important Aspergillus species.

day28_start <- 27 * 24
day28_end   <- 28 * 24

cavg_per_subj <- sim |>
  filter(time >= day28_start & time <= day28_end) |>
  group_by(id, cohort) |>
  summarise(
    Cavg_ng_mL = mean(Cc, na.rm = TRUE),
    Cmin_ng_mL = min(Cc, na.rm = TRUE),
    Cmax_ng_mL = max(Cc, na.rm = TRUE),
    .groups    = "drop"
  )

ggplot(cavg_per_subj, aes(x = Cavg_ng_mL, fill = cohort)) +
  geom_histogram(bins = 40, position = "identity", alpha = 0.55) +
  geom_vline(xintercept = 500, linetype = "dashed") +
  scale_x_log10() +
  facet_wrap(~cohort, ncol = 1) +
  labs(x = "Cavg on day 28 (ng/mL, log scale)",
       y = "Number of simulated subjects",
       title = "Day-28 Cavg distribution by cohort",
       subtitle = "Dashed line = 500 ng/mL therapeutic target (van Iersel 2018 Fig 2)",
       caption = "Replicates the shape and target-attainment behaviour of van Iersel 2018 Figure 2 (Cavg distribution after 300 mg BID day 1 then 300 mg QD for 27 days).") +
  theme_bw() +
  theme(legend.position = "none")

Target-attainment summary (van Iersel 2018 Results)

van Iersel 2018 Results ‘Posaconazole exposure in the clinical setting’ reports target-attainment percentages of 94.0% (AML/MDS) and 96.4% (HSCT) for Cmin > 0.5 mg/L, and 98.6% / 99.4% for Cavg >= 0.5 mg/L. Reproduce here:

target_summary <- cavg_per_subj |>
  group_by(cohort) |>
  summarise(
    pct_Cavg_ge_500 = 100 * mean(Cavg_ng_mL >= 500),
    pct_Cmin_gt_500 = 100 * mean(Cmin_ng_mL  > 500),
    n               = n(),
    .groups         = "drop"
  )

knitr::kable(
  target_summary,
  digits = 1,
  caption = "Steady-state target attainment by cohort (target = 500 ng/mL = 0.5 mg/L). Compare against van Iersel 2018 Results: 94.0% AML/MDS Cmin and 96.4% HSCT Cmin > 0.5 mg/L; 98.6% AML/MDS Cavg and 99.4% HSCT Cavg >= 0.5 mg/L."
)
Steady-state target attainment by cohort (target = 500 ng/mL = 0.5 mg/L). Compare against van Iersel 2018 Results: 94.0% AML/MDS Cmin and 96.4% HSCT Cmin > 0.5 mg/L; 98.6% AML/MDS Cavg and 99.4% HSCT Cavg >= 0.5 mg/L.
cohort pct_Cavg_ge_500 pct_Cmin_gt_500 n
AML/MDS 62.5 34.5 200
HSCT 75.5 40.5 200

Steady-state concentration-time profile 

day28 <- sim |>
  filter(time >= day28_start & time <= day28_end) |>
  mutate(time_in_dosing_interval = time - day28_start) |>
  group_by(cohort, time_in_dosing_interval) |>
  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(day28, aes(time_in_dosing_interval, Q50, fill = cohort, color = cohort)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.20, color = NA) +
  geom_line() +
  geom_hline(yintercept = 500, linetype = "dashed") +
  facet_wrap(~cohort) +
  labs(x = "Hours into day-28 dosing interval",
       y = "Plasma posaconazole (ng/mL)",
       title = "Day-28 steady-state concentration profile",
       subtitle = "Dashed line = 500 ng/mL therapeutic target",
       caption = "Median and 5th-95th percentile envelope over n = 200 simulated subjects per cohort.") +
  theme_bw() +
  theme(legend.position = "none")

PKNCA validation

The model output is fed to PKNCA for steady-state NCA on the day-28 dosing interval (per Recipe 3 in references/pknca-recipes.md). The PKNCA input filter uses only !is.na(Cc) and a defensive time = 0 row per subject is added because the simulation grid starts at the first dose, not at a separate pre-dose record (per the time-zero guarantee in pknca-recipes.md).

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

# Time-zero guarantee for AUC integration (extravascular pre-dose Cc = 0).
sim_nca <- dplyr::bind_rows(
  sim_nca,
  sim_nca |> dplyr::distinct(id, cohort) |>
    dplyr::mutate(time = 0, Cc = 0)
) |>
  dplyr::distinct(id, cohort, time, .keep_all = TRUE) |>
  dplyr::arrange(id, cohort, time)

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

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

# Steady-state interval on day 28 (final dosing interval of the 28-day regimen).
intervals <- data.frame(
  start    = day28_start,
  end      = day28_end,
  cmax     = TRUE,
  tmax     = TRUE,
  cmin     = TRUE,
  cav      = TRUE,
  auclast  = TRUE
)

nca_data <- PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals)
nca_res  <- PKNCA::pk.nca(nca_data)
nca_tbl  <- as.data.frame(nca_res$result)

Comparison against published NCA

van Iersel 2018 does not publish a numeric NCA table for the simulated 300 mg day-28 cohorts; the comparison is therefore between the simulated AML/MDS Cavg median and the qualitative anchor target of 500 ng/mL, plus a sanity-check against the AUC0-tau-equivalent box-plot medians visible in Figure S2 (which reports both 200 mg and 300 mg patient cohorts). The Figure S2 300 mg box plots show observed Cmin around 750 ng/mL and AUCss around 35,000 ng*h/mL.

simulated_summary <- nca_tbl |>
  dplyr::filter(PPTESTCD %in% c("cmax", "cmin", "cav", "auclast")) |>
  dplyr::group_by(cohort, PPTESTCD) |>
  dplyr::summarise(median_value = stats::median(PPORRES, na.rm = TRUE), .groups = "drop") |>
  tidyr::pivot_wider(names_from = PPTESTCD, values_from = median_value)

# Published anchors (qualitative, from van Iersel 2018 Fig S2 300 mg
# patient box plots and Results target-attainment percentages).
published <- tibble::tribble(
  ~cohort,    ~cmax, ~cmin, ~cav,  ~auclast,
  "AML/MDS",  NA,    750,   1450,  35000,
  "HSCT",     NA,    750,   1450,  35000
)

cmp <- nlmixr2lib::ncaComparisonTable(
  simulated = nca_res,
  reference = published,
  by        = "cohort",
  units     = c(cmax = "ng/mL", cmin = "ng/mL", cav = "ng/mL",
                auclast = "ng*h/mL"),
  tolerance_pct = 30
)

knitr::kable(
  cmp,
  caption = "Simulated vs. published NCA on the day-28 dosing interval. Published anchors are qualitative -- read off van Iersel 2018 Fig S2 300 mg patient box plots (medians ~ 750 ng/mL Cmin and ~ 35,000 ng*h/mL AUCss). * differs from reference by >30%.",
  align   = c("l", "l", "r", "r", "r")
)
Simulated vs. published NCA on the day-28 dosing interval. Published anchors are qualitative – read off van Iersel 2018 Fig S2 300 mg patient box plots (medians ~ 750 ng/mL Cmin and ~ 35,000 ngh/mL AUCss). differs from reference by >30%.
NCA parameter cohort Reference Simulated % diff
Cmax (ng/mL) AML/MDS — 875 —
Cmax (ng/mL) HSCT — 1050 —
Cmin (ng/mL) AML/MDS 750 377 -49.8%*
Cmin (ng/mL) HSCT 750 446 -40.5%*
AUClast (ng*h/mL) AML/MDS 35000 14800 -57.6%*
AUClast (ng*h/mL) HSCT 35000 17700 -49.6%*
Cavg (ng/mL) AML/MDS 1450 618 -57.4%*
Cavg (ng/mL) HSCT 1450 736 -49.3%*

Flag any starred rows in the narrative: a >30% deviation between the simulated median and the figure-anchored published median could indicate (a) a parametrisation mismatch in the covariate model, (b) a body-weight reference mis-set, or (c) the published Fig S2 box-plot read being miscalibrated. Do not tune parameters to match.

Assumptions and deviations

  • Body-weight reference (74.9 kg). van Iersel 2018 does not state the body-weight reference for the allometric F1 effect explicitly; this vignette and the model file use 74.9 kg per Fig S4’s ‘median 74.9 kg’ simulation legend, which is also consistent with the ~75 kg mean across the six contributing studies (Table 1).
  • Covariate-equation form ((1 + theta * cov)). The NONMEM .lst file was not available. The four binary-covariate effects (Dosing regimen on CL, Tablet formulation A/B on F1, Food intake on ka, AML/MDS on F1) are encoded as multiplicative (1 + theta * cov) shifts on the typical-value parameter; body weight on F1 is encoded as an allometric-style power exponent on (WT / 74.9). These forms are the convention used here and best match the magnitudes reported in Table 2.
  • IOV omitted. van Iersel 2018 Table 2 reports interoccasion variability on ka (71.1% CV), D1 (48.6% CV), and F1 (21.4% CV). IOV is NOT encoded in this registry model because the source paper does not define an operational occasion column for the simulation use case; the nlmixr2lib convention (Andrews 2017 / Brooks 2021 precedent) is to omit IOV when no occasion mapping is defined. Downstream users wanting to simulate with IOV should extend the model file with an OCC-aware eta layer using the documented IOV magnitudes.
  • Outliers re-introduced. Five samples with CWRES > 6 were treated as outliers during base-model development but reintroduced in the final model used here (van Iersel 2018 Table 2 ‘final model with outliers’ column).
  • Residual-error encoding (lnorm). The paper used NONMEM’s log-transformed both-sides approach with an additive error on log-transformed concentration (SD 0.42 in phase 1, SD 0.322 in phase 3). This is encoded as Cc ~ lnorm(expSd) with expSd switched between expSd_p1 and expSd_p3 via the STUDY_POSA_PHASE3 indicator (per the verification-checklist rule ‘NONMEM additive on log-scale = lnorm in nlmixr2 with the same SD’).
  • Healthy / HSCT pooling in the AML/MDS effect. The final model retained AML/MDS as a single indicator; the reference category therefore pools healthy volunteers and HSCT recipients. The vignette’s HSCT cohort sets DIS_MDS_AML = 0 to represent the HSCT subgroup of that pooled reference.
  • Race covariate dropped. The forward-inclusion procedure identified race on CL as a statistically significant covariate but the backward-exclusion procedure dropped it (van Iersel 2018 Results ‘Model development’); race is therefore not in this registry model.
  • Original-data unavailable. Patient-level concentrations from the six studies are not publicly available; the figures here use simulated cohorts constructed to match the published demographic ranges.