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Itraconazole nanocrystal formulation (Jansen 2023)

Source: vignettes/articles/Jansen_2023_itraconazole.Rmd
Jansen_2023_itraconazole.Rmd

Model and source

  • Citation: Jansen AME, Ter Heine R, Donnelly JP, Blijlevens N, Bruggemann RJM. Repurposing antifungals: population pharmacokinetics of itraconazole and hydroxy-itraconazole following administration of a nanocrystal formulation. J Antimicrob Chemother. 2023;78(5):1172-1178. doi:10.1093/jac/dkad072
  • Description: Semi-mechanistic population PK model for intravenous itraconazole nanocrystal formulation (NCF) and its active metabolite hydroxy-itraconazole in allogeneic haematopoietic cell transplant recipients (Jansen 2023). A nanocrystal-bound itraconazole compartment receives the infusion and dissolves by a fixed first-order rate constant into a two-compartment dissolved-itraconazole disposition model; all eliminated itraconazole (fraction metabolised fixed to 1) enters a one-compartment hydroxy-itraconazole model. Observed itraconazole is the sum of nanocrystal-bound and dissolved concentrations. Allometric weight scaling with fixed exponents 0.75 on clearances and 1 on volumes. All amounts and concentrations are molar, as the source data were converted to molar equivalents before fitting.
  • Article: https://doi.org/10.1093/jac/dkad072
  • Supplement (figures S1-S5 and the final model NONMEM control stream): https://www.ebi.ac.uk/europepmc/webservices/rest/PMC10154123/supplementaryFiles

Population

Ten adults (median age 47.5 years, range 22.0-59.0; 50% female; median weight 78.3 kg, range 60.0-92.5 kg) received a matched allogeneic bone marrow transplant after conditioning with idarubicin, cyclophosphamide and total body irradiation, and took part in a prospective open-label Phase II study of itraconazole nanocrystal formulation (NCF) for prophylaxis of invasive fungal disease at Radboud University Medical Center, Nijmegen (Jansen 2023, Table 1). Underlying diseases were acute lymphatic leukaemia (30%), acute myeloid leukaemia (20%), chronic myelomonocytic leukaemia (20%), non-Hodgkin lymphoma (20%) and myelofibrosis (10%).

Every subject received itraconazole NCF 200 mg as a 2 h intravenous infusion twice daily for 2 days, then 200 mg once daily until day 14. Full pharmacokinetic curves were drawn on days 7 and 14, with pre- and post-infusion samples until day 6, pre-infusion samples on days 10 and 12, and washout samples on days 16, 17, 18, 19 and 28. This yielded 471 itraconazole and 471 paired hydroxy-itraconazole concentrations, all above the LLOQ. The study was explicitly not powered to identify covariates, so body weight - entered a priori as fixed allometric scaling - is the only covariate in the model.

The same information is available programmatically via readModelDb("Jansen_2023_itraconazole")()$population.

Model structure

The published model is a semi-mechanistic parent-metabolite model (Jansen 2023 Figure S2, and the $MODEL / $PK blocks of the supplementary final model control stream):

  • The infusion enters a nanocrystal-bound itraconazole compartment (central_np), from which drug dissolves by a first-order rate constant kN fixed at 4.62 /h (a 9 min dissolution half-life in human plasma).
  • Dissolved itraconazole follows two-compartment disposition (central, peripheral1).
  • The fraction of itraconazole metabolised to hydroxy-itraconazole was fixed to 1, so the whole of CL_P feeds the one-compartment hydroxy-itraconazole model (central_ohi); there is no K10 in the control stream.
  • The nanocrystal-bound volume V_N is set equal to the itraconazole central volume V_P1 (an explicit assumption of the paper, made in the absence of nanocrystal-bound concentration measurements).
  • The observed itraconazole concentration is the sum of the nanocrystal-bound and dissolved concentrations ($ERROR: IPRED = LOG(C1 + C4)), which is what Cc returns here.

All concentrations in the source analysis were converted to molar equivalents before fitting, so that the fixed fm = 1 conversion is mole-for-mole. The packaged model therefore works in mmol and mmol/L, matching the y-axis of Jansen 2023 Figure 1. This vignette converts to mg/L for comparison against the paper’s reported trough concentrations and therapeutic-drug-monitoring targets.

# Molecular weights are chemical constants, NOT taken from the paper (the paper
# does not print them). Itraconazole C35H38Cl2N8O4 = 705.6 g/mol (PubChem CID
# 55283); hydroxy-itraconazole C35H38Cl2N8O5 = 721.6 g/mol (PubChem CID 108222).
MW_ITZ <- 705.6
MW_OHI <- 721.6

# 200 mg itraconazole per infusion, expressed in the model's molar dose unit.
dose_mmol <- 200 / MW_ITZ
dose_mmol
#> [1] 0.2834467

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Jansen_2023_itraconazole.R. The table below collects them in one place for review. “Control stream” refers to the FINAL MODEL CONTROL STREAM printed at the end of the supplementary data document.

Equation / parameter Value Source location
lcl (CL_P) 4.29 L/h Table 2 (95% CI 3.85-4.80); control stream $THETA TVCLP
lvc (V_P1 = V_N) 14.1 L Table 2 (95% CI 11.8-17.2); control stream $THETA TVVP1/TVVN
lq (Q_P) 53.0 L/h Table 2 (95% CI 45.3-63.4); control stream $THETA TVQP
lvp (V_P2) 1660 L Table 2 (95% CI 1558-1775); control stream $THETA TVVP2
lcl_ohi (CL_M) 2.86 L/h Table 2 (95% CI 2.43-3.33); control stream $THETA TVCLM
lvc_ohi (V_M) 43.1 L Table 2 (95% CI 36.9-50.4); control stream $THETA TVVM
lkdiss (kN) 4.62 /h, fixed Methods, “Population pharmacokinetic analysis”; control stream $PK KN = 4.62
e_wt_cl 0.75, fixed Methods, “a fixed exponent of 3/4 for (intercompartmental) clearance”; control stream (WT/70)**0.75
e_wt_vc 1.0, fixed Methods, “and 1 for volumes of distribution”; control stream (WT/70)**1
etalcl var 0.0126 Control stream $OMEGA “IIV CLP”; Table 2 reports 11.3% = sqrt(exp(0.0126) - 1)
etalcl_ohi var 0.0506 Control stream $OMEGA “IIV CLM”; Table 2 reports 22.8% = sqrt(exp(0.0506) - 1)
expSd sqrt(0.214) Control stream $SIGMA BLOCK(2) first diagonal; Table 2 Error_P 48.8% = sqrt(exp(0.214) - 1)
expSd_ohi sqrt(0.0358) Control stream $SIGMA BLOCK(2) second diagonal; Table 2 Error_M 19.1% = sqrt(exp(0.0358) - 1)
d/dt(central_np) n/a Control stream $PK K41 = KN; dose administered into COMP=(NANO)
d/dt(central), d/dt(peripheral1) n/a Control stream $PK K12 = QP/VP1, K21 = QP/VP2, K13 = CLP/VP1 (no K10)
d/dt(central_ohi) n/a Control stream $PK K13 = CLP/VP1, K30 = CLM/VM; Methods, fm assumed 1
Cc = (central + central_np)/vc n/a Control stream $ERROR: C1 = A(1)/VP1, C4 = A(4)/VN, IPRED = LOG(C1+C4)
Cc_ohi = central_ohi/vc_ohi n/a Control stream $ERROR: C3 = A(3)/VM, IPRED = LOG(C3); $PK S3 = VM

Dosing regimens used below 

mod <- readModelDb("Jansen_2023_itraconazole")

# Trial protocol: 200 mg NCF over 2 h, q12h x 4 doses (days 1-2), then q24h
# until day 14 (12 further doses, last at t = 312 h).
trial_doses <- rxode2::et(amt = dose_mmol, dur = 2, ii = 12, addl = 3,
                          cmt = "central_np") |>
  rxode2::et(amt = dose_mmol, dur = 2, time = 48, ii = 24, addl = 11,
             cmt = "central_np")

# Observation rows name an ODE state in `cmt` and select the model endpoint
# with `dvid`. rxode2 requires an observation record of a multi-endpoint model
# to resolve to one of the endpoint compartments; `dvid` does that without
# writing an algebraic observable name into `cmt` (which would inject a
# compartment slot and renumber the states). Every algebraic observable
# (`Cc`, `Cc_np`, `Cc_ohi`) is returned as a column regardless of `dvid`.
obs_rows <- function(times) {
  data.frame(time = times, evid = 0L, amt = NA_real_,
             cmt = "central", dvid = 1L)
}

add_obs <- function(doses, times) {
  bind_rows(as.data.frame(doses), obs_rows(times)) |>
    arrange(time)
}

Replicate Figure 1

Figure 1 of Jansen 2023 shows simulated nanocrystal-bound itraconazole (dotted), itraconazole (solid) and hydroxy-itraconazole (dashed) for a typical individual given the study protocol, on a log y-axis in mmol/L over 144 h. The nanocrystal-bound curve spikes and collapses within minutes of each infusion (dissolution half-life 9 min), so it appears as a near-vertical excursion at each dose.

ev_typ <- add_obs(trial_doses, seq(0, 144, by = 0.05)) |>
  mutate(WT = 70)

sim_typ <- rxode2::rxSolve(mod, ev_typ, omega = NA, addDosing = FALSE,
                           returnType = "data.frame")
#> ℹ parameter labels from comments will be replaced by 'label()'

fig1 <- sim_typ |>
  transmute(
    time,
    `Nanocrystal-bound itraconazole` = Cc_np,
    `Itraconazole (dissolved)`       = Cc - Cc_np,
    `Hydroxy-itraconazole`           = Cc_ohi
  ) |>
  pivot_longer(-time, names_to = "Analyte", values_to = "conc") |>
  filter(conc > 0)

ggplot(fig1, aes(time, conc, linetype = Analyte)) +
  geom_line() +
  scale_y_log10(limits = c(1e-4, 1e-2)) +
  scale_x_continuous(breaks = seq(0, 144, by = 24)) +
  scale_linetype_manual(values = c(
    "Nanocrystal-bound itraconazole" = "dotted",
    "Itraconazole (dissolved)"       = "solid",
    "Hydroxy-itraconazole"           = "dashed"
  )) +
  labs(x = "Time (h)", y = "Concentration (mmol/L)", linetype = NULL,
       caption = "Replicates Figure 1 of Jansen 2023.") +
  theme(legend.position = "bottom")
#> Warning: Removed 444 rows containing missing values or values outside the scale range
#> (`geom_line()`).
Replicates Figure 1 of Jansen 2023: typical-individual (70 kg) profiles over the first 6 days of the study protocol.

Replicates Figure 1 of Jansen 2023: typical-individual (70 kg) profiles over the first 6 days of the study protocol.

The reproduced curves match the published panel in both level and shape: the itraconazole trough climbs from roughly 1.5e-4 mmol/L after the first inter-dose interval to roughly 9e-4 mmol/L by 144 h, while hydroxy-itraconazole rises smoothly past the parent from about 40 h onward.

tr <- function(t) sim_typ[which.min(abs(sim_typ$time - t)), ]
# Deterministic (typical-value) quantities: a tight bound is appropriate.
stopifnot(
  # Itraconazole trough at 144 h, read off Figure 1 as ~9e-4 mmol/L.
  abs(tr(144)$Cc / 9.0e-4 - 1) < 0.15,
  # Hydroxy-itraconazole overtakes itraconazole partway through the profile
  # and stays above it thereafter, as in Figure 1.
  tr(24)$Cc_ohi  > tr(24)$Cc,
  tr(144)$Cc_ohi > tr(144)$Cc,
  # The nanocrystal-bound term is spent long before the next dose: at the 144 h
  # trough it contributes nothing measurable to the observed itraconazole.
  tr(144)$Cc_np / tr(144)$Cc < 1e-6
)

Virtual cohort

Original observed data are not publicly available. The cohort below reproduces the trial’s body-weight distribution (median 78.3 kg, observed range 60.0-92.5 kg; Jansen 2023 Table 1) and uses the model’s own IIV on itraconazole and hydroxy-itraconazole clearance.

# `set.seed()` seeds R's RNG, not rxode2's, and rxode2's streams are
# partitioned per solver thread -- so this cohort differs between a 2-core CI
# runner and a 16-thread workstation. Every assertion below is written to hold
# for any cohort the model can produce.
set.seed(20230501)

n_sub <- 100  # well under the 200-per-arm cap

cohort <- tibble(
  id = seq_len(n_sub),
  # Log-normal about the published median; SD chosen so the central 95% of the
  # distribution spans roughly the published 60.0-92.5 kg range.
  WT = 78.3 * exp(rnorm(n_sub, 0, 0.12)),
  treatment = "200 mg NCF IV"
)

base_ev <- add_obs(trial_doses, seq(0, 336, by = 0.5))

events <- tidyr::expand_grid(cohort, base_ev) |>
  arrange(id, time)

stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))
sim <- rxode2::rxSolve(mod, events, keep = c("WT", "treatment"),
                       addDosing = FALSE, returnType = "data.frame")
if (is.null(sim$id)) sim$id <- 1L

Steady-state trough concentrations

Jansen 2023 reports a mean (SD) trough concentration at steady state (after day 7) of 0.79 mg/L (0.35) for itraconazole and 1.31 mg/L (0.29) for hydroxy-itraconazole. Pre-dose samples in that window were drawn on days 7, 10, 12 and 14, i.e. at 144, 216, 264 and 312 h after the first infusion.

The primary comparison uses the typical-value profile at the study’s median weight, which is a deterministic quantity and can therefore be gated tightly.

trough_times <- c(144, 216, 264, 312)

ev_med <- add_obs(trial_doses, trough_times) |>
  mutate(WT = 78.3)

sim_med <- rxode2::rxSolve(mod, ev_med, omega = NA, addDosing = FALSE,
                           returnType = "data.frame")

trough_cmp <- tibble(
  Analyte    = c("Itraconazole", "Hydroxy-itraconazole"),
  Published  = c(0.79, 1.31),
  Simulated  = c(mean(sim_med$Cc) * MW_ITZ, mean(sim_med$Cc_ohi) * MW_OHI)
) |>
  mutate(`% diff` = 100 * (Simulated - Published) / Published)

trough_cmp |>
  rename("Published mean Cmin (mg/L)" = Published,
         "Simulated typical Cmin (mg/L)" = Simulated) |>
  knitr::kable(digits = c(0, 2, 3, 1),
               caption = "Mean trough concentration over days 7, 10, 12 and 14 at the study median weight (78.3 kg), against the observed means of Jansen 2023 Results.")
Mean trough concentration over days 7, 10, 12 and 14 at the study median weight (78.3 kg), against the observed means of Jansen 2023 Results.
Analyte Published mean Cmin (mg/L) Simulated typical Cmin (mg/L) % diff
Itraconazole 0.79 0.778 -1.5
Hydroxy-itraconazole 1.31 1.288 -1.7 
# Structural gate: a mis-transcribed clearance, dose, molecular weight or unit
# moves these by tens of percent. The typical-value solve is deterministic, so
# the bound does not have to absorb cohort noise.
stopifnot(max(abs(trough_cmp$`% diff`)) < 10)

For context the same window is summarised over the virtual cohort. Note that these are individual predictions: the published means are arithmetic means of observations, which the log-scale residual error would inflate by exp(sigma^2 / 2) (about 11% for itraconazole and 2% for hydroxy-itraconazole) relative to a noise-free prediction.

cohort_troughs <- sim |>
  filter(time %in% trough_times) |>
  summarise(
    .by = id,
    ITZ = mean(Cc) * MW_ITZ,
    OHI = mean(Cc_ohi) * MW_OHI
  )

tibble(
  Analyte = c("Itraconazole", "Hydroxy-itraconazole"),
  Median  = c(median(cohort_troughs$ITZ), median(cohort_troughs$OHI)),
  P05     = c(quantile(cohort_troughs$ITZ, 0.05), quantile(cohort_troughs$OHI, 0.05)),
  P95     = c(quantile(cohort_troughs$ITZ, 0.95), quantile(cohort_troughs$OHI, 0.95))
) |>
  rename("Median (mg/L)" = Median, "5th pct" = P05, "95th pct" = P95) |>
  knitr::kable(digits = 3,
               caption = "Virtual-cohort mean trough over days 7, 10, 12 and 14 (individual predictions).")
Virtual-cohort mean trough over days 7, 10, 12 and 14 (individual predictions).
Analyte Median (mg/L) 5th pct 95th pct
Itraconazole 0.78 0.635 0.902
Hydroxy-itraconazole 1.26 0.911 1.929 
# Cohort-derived: assert the centre and a robust quantile, never an extreme.
stopifnot(
  abs(median(cohort_troughs$ITZ) / 0.79 - 1) < 0.25,
  abs(median(cohort_troughs$OHI) / 1.31 - 1) < 0.25
)

PKNCA validation

Steady-state exposure over the day-14 dosing interval

PKNCA is used for every NCA quantity. The paper reports no NCA table, so the values below characterise the packaged model rather than reproducing a published table.

tau      <- 24
start_ss <- 312          # last dose of the protocol
end_ss   <- start_ss + tau

nca_conc <- function(df, col) {
  out <- df |>
    filter(!is.na(.data[[col]]), time >= start_ss, time <= end_ss) |>
    transmute(id, time, Cc = .data[[col]], treatment)
  out
}

intervals_ss <- data.frame(
  start = start_ss, end = end_ss,
  cmax = TRUE, tmax = TRUE, cmin = TRUE, cav = TRUE, auclast = TRUE
)

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

nca_for <- function(col, concu) {
  conc_obj <- PKNCA::PKNCAconc(nca_conc(sim, col), Cc ~ time | treatment + id,
                               concu = concu, timeu = "h")
  dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | treatment + id,
                               doseu = "mmol")
  PKNCA::pk.nca(PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals_ss))
}

nca_itz <- nca_for("Cc", "mmol/L")
nca_ohi <- nca_for("Cc_ohi", "mmol/L")
nca_tbl <- function(res, analyte, mw) {
  as.data.frame(res$result) |>
    filter(PPTESTCD %in% c("cmax", "tmax", "cmin", "cav", "auclast")) |>
    mutate(
      value = if_else(PPTESTCD == "tmax", PPORRES, PPORRES * mw),
      Analyte = analyte
    ) |>
    summarise(.by = c(Analyte, PPTESTCD),
              Median = median(value),
              P05 = quantile(value, 0.05),
              P95 = quantile(value, 0.95)) |>
    mutate(Parameter = nlmixr2lib::ncaParamLabel(PPTESTCD),
           Units = if_else(PPTESTCD == "tmax", "h",
                           if_else(PPTESTCD == "auclast", "mg*h/L", "mg/L"))) |>
    select(Analyte, Parameter, Units, Median, P05, P95)
}

bind_rows(nca_tbl(nca_itz, "Itraconazole", MW_ITZ),
          nca_tbl(nca_ohi, "Hydroxy-itraconazole", MW_OHI)) |>
  rename("5th pct" = P05, "95th pct" = P95) |>
  knitr::kable(digits = 3,
               caption = "PKNCA over the day-14 dosing interval (312-336 h) of the virtual cohort, converted from molar to mass units.")
PKNCA over the day-14 dosing interval (312-336 h) of the virtual cohort, converted from molar to mass units.
Analyte Parameter Units Median 5th pct 95th pct
Itraconazole AUClast mg*h/L 29.518 24.299 34.031
Itraconazole Cmax mg/L 3.984 3.372 4.573
Itraconazole Cmin mg/L 0.922 0.746 1.064
Itraconazole Tmax h 2.000 2.000 2.000
Itraconazole Cavg mg/L 1.230 1.012 1.418
Hydroxy-itraconazole AUClast mg*h/L 39.207 28.795 58.725
Hydroxy-itraconazole Cmax mg/L 1.764 1.312 2.579
Hydroxy-itraconazole Cmin mg/L 1.480 1.074 2.256
Hydroxy-itraconazole Tmax h 3.000 3.000 3.000
Hydroxy-itraconazole Cavg mg/L 1.634 1.200 2.447

Exact internal identities at true steady state

The terminal half-life implied by the published disposition parameters is log(2) / beta with beta from the two-compartment micro-constants; it is long enough (roughly 12 days) that the 14-day protocol has not reached true steady state, which is why the troughs above are still climbing at day 14. At true steady state the model satisfies three exact mass-balance identities, which are checked here against PKNCA’s AUC over one dosing interval:

  • AUCtau(Cc - Cc_np) = Dose / CL_P - every molecule leaving the dissolved itraconazole compartment does so through CL_P.
  • AUCtau(Cc_np) = Dose / (kN * V_P1) - the nanocrystal-bound compartment has dissolution as its only exit.
  • AUCtau(Cc_ohi) = Dose / CL_M - fm is fixed to 1.
n_days <- 120  # about 10 terminal half-lives
t_last <- (n_days - 1) * 24

ev_ss <- add_obs(
  rxode2::et(amt = dose_mmol, dur = 2, ii = 24, addl = n_days - 1,
             cmt = "central_np"),
  seq(t_last, t_last + tau, by = 0.05)
) |>
  mutate(WT = 70, id = 1L, treatment = "200 mg QD to steady state")

sim_ss <- rxode2::rxSolve(mod, ev_ss, omega = NA, addDosing = FALSE,
                          maxsteps = 200000L, atol = 1e-12, rtol = 1e-10,
                          returnType = "data.frame")
if (is.null(sim_ss$id)) sim_ss$id <- 1L
sim_ss$treatment <- "200 mg QD to steady state"

auc_ss <- function(col) {
  conc <- sim_ss |> transmute(id, time, Cc = .data[[col]], treatment)
  conc_obj <- PKNCA::PKNCAconc(conc, Cc ~ time | treatment + id,
                               concu = "mmol/L", timeu = "h")
  dose_obj <- PKNCA::PKNCAdose(
    tibble(id = 1L, time = t_last, amt = dose_mmol,
           treatment = "200 mg QD to steady state"),
    amt ~ time | treatment + id, doseu = "mmol")
  res <- PKNCA::pk.nca(PKNCA::PKNCAdata(
    conc_obj, dose_obj,
    intervals = data.frame(start = t_last, end = t_last + tau, auclast = TRUE)))
  as.data.frame(res$result) |> filter(PPTESTCD == "auclast") |> pull(PPORRES)
}

# The nanocrystal-bound concentration decays through 40 orders of magnitude
# within one dosing interval and its far tail sits in solver round-off, where a
# value can go very slightly negative. PKNCA's log-down trapezoid takes log() of
# it and returns NaN, so clamp the round-off to zero first.
sim_ss$Cc_np   <- pmax(sim_ss$Cc_np, 0)
sim_ss$Cc_free <- sim_ss$Cc - sim_ss$Cc_np
p <- sim_ss[1, ]

identities <- tibble(
  Quantity = c("AUCtau(itraconazole, dissolved)",
               "AUCtau(itraconazole, nanocrystal-bound)",
               "AUCtau(hydroxy-itraconazole)"),
  `Closed form`  = c("Dose / CL_P", "Dose / (kN * V_P1)", "Dose / CL_M"),
  Predicted = c(dose_mmol / p$cl,
                dose_mmol / (p$kdiss * p$vc),
                dose_mmol / p$cl_ohi),
  `PKNCA AUCtau` = c(auc_ss("Cc_free"), auc_ss("Cc_np"), auc_ss("Cc_ohi"))
) |>
  mutate(Ratio = `PKNCA AUCtau` / Predicted)

identities |>
  knitr::kable(digits = c(0, 0, 5, 5, 5),
               caption = "Model-internal mass-balance identities at true steady state (200 mg QD, 70 kg, mmol*h/L).")
Model-internal mass-balance identities at true steady state (200 mg QD, 70 kg, mmol*h/L).
Quantity Closed form Predicted PKNCA AUCtau Ratio
AUCtau(itraconazole, dissolved) Dose / CL_P 0.06607 0.06601 0.99900
AUCtau(itraconazole, nanocrystal-bound) Dose / (kN * V_P1) 0.00435 0.00435 0.99952
AUCtau(hydroxy-itraconazole) Dose / CL_M 0.09911 0.09900 0.99896 
# Deterministic: the only error sources are the ODE solver tolerance, the
# trapezoidal AUC rule on a 0.05 h grid, and the residual approach to steady
# state after 120 daily doses. 0.5% is generous for all three together and
# still catches any structural error (a missing elimination path, a wrong
# scaling volume, or an fm that is not 1 move these by tens of percent).
stopifnot(max(abs(identities$Ratio - 1)) < 0.005)

Therapeutic drug monitoring targets

Jansen 2023 simulated day-14 trough concentrations for the standard 200 mg once-daily NCF regimen and compared them against the itraconazole targets of > 0.5 mg/L (prophylaxis) and > 1.0 mg/L (treatment), the itraconazole plus hydroxy-itraconazole targets of > 1.0 mg/L (prophylaxis) and > 2.0 mg/L (treatment), and the itraconazole concentration of > 4.0 mg/L associated with toxicity. The published attainment was 100% / 54.4% for itraconazole, 100% / 91.8% for the sum, and none above the toxicity threshold. This is a partial replication: the published Monte Carlo used the demographics of 1576 haematology patients from the authors’ department, which are not published, so the cohort here uses the trial’s own weight distribution instead.

day14 <- sim |>
  filter(time == 312) |>
  transmute(id,
            ITZ = Cc * MW_ITZ,
            SUM = Cc * MW_ITZ + Cc_ohi * MW_OHI)

targets <- tibble(
  Target = c("Itraconazole Cmin > 0.5 mg/L (prophylaxis)",
             "Itraconazole Cmin > 1.0 mg/L (treatment)",
             "Itraconazole + hydroxy Cmin > 1.0 mg/L (prophylaxis)",
             "Itraconazole + hydroxy Cmin > 2.0 mg/L (treatment)",
             "Itraconazole Cmin > 4.0 mg/L (toxicity)"),
  Published = c(100, 54.4, 100, 91.8, 0),
  Simulated = c(100 * mean(day14$ITZ > 0.5),
                100 * mean(day14$ITZ > 1.0),
                100 * mean(day14$SUM > 1.0),
                100 * mean(day14$SUM > 2.0),
                100 * mean(day14$ITZ > 4.0))
)

targets |>
  rename("Published (%)" = Published, "Simulated (%)" = Simulated) |>
  knitr::kable(digits = 1,
               caption = "Day-14 trough target attainment. The published column comes from a Monte Carlo over 1576 haematology patients whose demographics are not reported; the simulated column uses the trial's own weight distribution.")
Day-14 trough target attainment. The published column comes from a Monte Carlo over 1576 haematology patients whose demographics are not reported; the simulated column uses the trial’s own weight distribution.
Target Published (%) Simulated (%)
Itraconazole Cmin > 0.5 mg/L (prophylaxis) 100.0 100
Itraconazole Cmin > 1.0 mg/L (treatment) 54.4 23
Itraconazole + hydroxy Cmin > 1.0 mg/L (prophylaxis) 100.0 100
Itraconazole + hydroxy Cmin > 2.0 mg/L (treatment) 91.8 87
Itraconazole Cmin > 4.0 mg/L (toxicity) 0.0 0 
# Only the claims the paper states as absolutes are gated, and as proportions
# with headroom rather than as exact 0 / 100 (see pattern 12 of
# known-vignette-failure-patterns.md). The two treatment-target percentages are
# NOT gated: they depend on a covariate distribution the paper does not report.
stopifnot(
  mean(day14$ITZ > 0.5) > 0.95,
  mean(day14$SUM > 1.0) > 0.95,
  mean(day14$ITZ > 4.0) < 0.05
)

The itraconazole treatment target is the one row that does not reproduce, and the reason is visible in the weight sensitivity below. The day-14 trough sits almost exactly on the 1.0 mg/L threshold, so the percentage above it is set by where the simulated population’s weight distribution is centred - the one input this replication cannot reproduce, because the demographics of the paper’s 1576-patient database are not published. A cohort centred near 70 kg puts the typical trough at 1.02 mg/L and therefore roughly half the population above the threshold, which is what the published 54.4% implies; the trial’s own median of 78.3 kg puts it at 0.92 mg/L and only 23% above.

tibble(WT = c(70, 75, 78.3)) |>
  rowwise() |>
  mutate(res = list(rxode2::rxSolve(
    mod, add_obs(trial_doses, 312) |> mutate(WT = WT),
    omega = NA, addDosing = FALSE, returnType = "data.frame"))) |>
  mutate(`Itraconazole (mg/L)` = res$Cc[1] * MW_ITZ,
         `Itraconazole + hydroxy (mg/L)` = res$Cc[1] * MW_ITZ + res$Cc_ohi[1] * MW_OHI) |>
  ungroup() |>
  select(-res) |>
  rename("Body weight (kg)" = WT) |>
  knitr::kable(digits = 3,
               caption = "Typical-value day-14 trough as a function of body weight, showing the sensitivity of the 1.0 mg/L treatment target to the simulated population's weight distribution.")
Typical-value day-14 trough as a function of body weight, showing the sensitivity of the 1.0 mg/L treatment target to the simulated population’s weight distribution.
Body weight (kg) Itraconazole (mg/L) Itraconazole + hydroxy (mg/L)
70.0 1.021 2.699
75.0 0.959 2.537
78.3 0.923 2.441

Assumptions and deviations

  • Correlated residual error is not reproduced. The published $SIGMA is a BLOCK(2) with off-diagonal 0.0185, i.e. a correlation of 0.211 between the itraconazole and hydroxy-itraconazole log-scale residuals. Table 2 reports this as 48.5%, which is the same sqrt(exp(x) - 1) back-transformation the paper applies to its variance terms, evaluated at 0.211 - the two printings are consistent once that is recognised. nlmixr2 has no syntax for a correlated residual-error block across endpoints, so the two residuals are encoded independently. This affects the width of a joint predictive interval for the two analytes, not the typical-value predictions or either marginal residual magnitude.
  • Zero-variance IIV terms are omitted. The control stream declares $OMEGA entries for V_P1/V_N, Q_P, V_P2 and V_M and fixes all four to 0 FIX. Carrying them would make the OMEGA matrix singular and break rxSolve’s Cholesky sampler, so only the two estimated IIV terms (on CL_P and CL_M) are declared. The model is unchanged.
  • Molar units, and the molecular weights used here. The packaged model is in mmol and mmol/L because the source data were converted to molar equivalents before fitting (Methods) and Figure 1 is plotted in mmol/L. The molecular weights used in this vignette to convert to mg/L (705.6 g/mol for itraconazole, 721.6 g/mol for hydroxy-itraconazole) are chemical constants from PubChem, not values printed in the paper.
  • Body-weight distribution of the virtual cohort, and the one target that does not reproduce. The paper reports only the median (78.3 kg) and range (60.0-92.5 kg) of the trial’s weights, and does not report the demographics of the 1576-patient database used for its own Monte Carlo. The cohort here samples a log-normal with median 78.3 kg and a log-SD of 0.12, which puts the central 95% of the distribution over roughly 62-99 kg. Against that cohort the itraconazole treatment target (Cmin > 1.0 mg/L) is met by about 23% of subjects versus the published 54.4%. This is a known, documented deviation rather than a transcription problem: the day-14 trough is 1.02 mg/L at 70 kg and 0.92 mg/L at 78.3 kg, so the published 54.4% is what a cohort centred near 70 kg would give. Every other published attainment figure reproduces. The two treatment-target rows are deliberately excluded from the vignette’s assertions for this reason.
  • V_N = V_P1 is the paper’s own assumption, stated in the Discussion: nanocrystal-bound concentrations were never measured, so the volume of the nanocrystal compartment is not identifiable and was set equal to the itraconazole central volume.
  • fm = 1 is the paper’s own assumption, made in the absence of metabolic conversion data. Every hydroxy-itraconazole parameter is therefore apparent to the fraction metabolised.
  • The published trough summary is compared against individual predictions. The paper’s mean Cmin values are arithmetic means of observed concentrations and so include residual error; the typical-value comparison above is noise-free. The log-scale residual would inflate a simulated arithmetic mean by about 11% (itraconazole) and 2% (hydroxy-itraconazole).
  • No erratum or corrigendum was found for this article at the time of extraction.