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Isavuconazole (Cojutti 2021)

Source: vignettes/articles/Cojutti_2021_isavuconazole.Rmd
Cojutti_2021_isavuconazole.Rmd

Model and source

  • Citation: Cojutti PG, Carnelutti A, Lazzarotto D, Sozio E, Candoni A, Fanin R, Tascini C, Pea F. Population Pharmacokinetics and Pharmacodynamic Target Attainment of Isavuconazole against Aspergillus fumigatus and Aspergillus flavus in Adult Patients with Invasive Fungal Diseases: Should Therapeutic Drug Monitoring for Isavuconazole Be Considered as Mandatory as for the Other Mold-Active Azoles? Pharmaceutics. 2021;13(12):2099. doi:10.3390/pharmaceutics13122099. PMCID PMC8708495.
  • Description: Two-compartment population PK model for isavuconazole (dosed as the prodrug isavuconazonium sulfate, doses expressed as isavuconazole) in hospitalized adults treated for invasive fungal disease, mostly invasive pulmonary aspergillosis, with first-order oral absorption, oral bioavailability, 1-h intravenous infusion into the central compartment, and linear elimination (Cojutti 2021). No covariates were retained. Fitted non-parametrically with the NPAG algorithm in Pmetrics; the Table 3 medians are encoded as lognormal medians and the tabulated CV percentages as independent lognormal marginal variances.
  • Article: https://doi.org/10.3390/pharmaceutics13122099 (PMC8708495; open access, CC BY)

Isavuconazole is a second-generation triazole approved for invasive aspergillosis and, in Europe, invasive mucormycosis. Cojutti and colleagues fitted a population PK model to routine therapeutic drug monitoring (TDM) data from 50 hospitalized adults at Udine, Italy, using the non-parametric adaptive grid (NPAG) algorithm in Pmetrics. They then ran Monte Carlo simulations of a 200 mg every 8 h loading dose for two days followed by 100, 200 or 300 mg once daily. The simulations report the probability that the trough falls below 1 mg/L or above the 5.13 mg/L toxicity threshold, and the probability of attaining AUC24h/MIC > 33.4 against Aspergillus fumigatus and A. flavus. The final model is a two-compartment model with first-order oral absorption, oral bioavailability and linear elimination. It has no covariates.

No erratum or correction was found on the journal landing page or in Europe PMC (checked 2026-09-30).

Population 

knitr::kable(
  data.frame(
    Characteristic = c(
      "Patients", "Age (years)", "Male / female", "Body weight (kg)",
      "Albumin (g/L)", "Total bilirubin (mg/dL)", "Invasive pulmonary aspergillosis",
      "Oncohaematological malignancy", "Oral administration",
      "Troughs / peaks", "Observed Ctrough (mg/L)", "Observed Cpeak (mg/L)",
      "Treatment duration (days)"
    ),
    Value = c(
      "50", "61.5 (IQR 51.3-72.0)", "31 / 19", "65.0 (IQR 55.5-71.5)",
      "35.0 (IQR 28.4-40.0)", "0.28 (IQR 0.2-0.4)", "40 (80%)", "25 (50%)",
      "38 (76%)", "175 / 24", "3.68 (IQR 2.07-5.38)", "4.67 (IQR 3.78-5.96)",
      "48 (IQR 19-91)"
    )
  ),
  caption = "Cojutti 2021 Table 1 and Results."
)
Cojutti 2021 Table 1 and Results.
Characteristic Value
Patients 50
Age (years) 61.5 (IQR 51.3-72.0)
Male / female 31 / 19
Body weight (kg) 65.0 (IQR 55.5-71.5)
Albumin (g/L) 35.0 (IQR 28.4-40.0)
Total bilirubin (mg/dL) 0.28 (IQR 0.2-0.4)
Invasive pulmonary aspergillosis 40 (80%)
Oncohaematological malignancy 25 (50%)
Oral administration 38 (76%)
Troughs / peaks 175 / 24
Observed Ctrough (mg/L) 3.68 (IQR 2.07-5.38)
Observed Cpeak (mg/L) 4.67 (IQR 3.78-5.96)
Treatment duration (days) 48 (IQR 19-91)

All patients received the labelled regimen of 200 mg every 8 h for 48 h followed by 200 mg once daily, orally or as a 1-h intravenous infusion. Troughs were drawn about 5 min before the daily dose, from at least 72 h after the start of therapy. Peaks were drawn 2 h after an oral dose or 0.5 h after the end of an infusion. No patient received a strong CYP3A4 inhibitor or inducer. Ten received mild or moderate CYP3A4 inhibitors. Race and ethnicity are not reported.

Source trace 

knitr::kable(
  data.frame(
    Item = c(
      "lka", "lcl", "lvc", "lq", "lvp", "lfdepot",
      "etalka / etalcl / etalvc / etalq / etalvp",
      "IIV on Fos (not encoded)",
      "addSd", "propSd", "combined1()",
      "Two-compartment ODE, first-order oral input",
      "1-h intravenous infusion into central",
      "Cc = central / vc",
      "AGE, CONMED_CYP3A4_INH (excluded)",
      "WT, SEXF, ALB, TBILI, ALT, AST, GGT (excluded)"
    ),
    Value = c(
      "log(22.64) 1/h", "log(1.33) L/h", "log(102.58) L", "log(5.08) L/h",
      "log(385.93) L", "log(1.00)",
      "0.02423 / 0.3436 / 0.2023 / 0.7867 / 0.5558",
      "CV 7.42%",
      "0.012 mg/L", "0.378", "linear sum of SDs",
      "depot -> central <-> peripheral1",
      "dosing only", "mg / L = mg/L",
      "tested on CL, not retained",
      "Ctrough regression only"
    ),
    Source = c(
      rep("Table 3, Median row", 6),
      "Table 3, CV (%) row, omega^2 = log(CV^2 + 1)",
      "Table 3, CV (%) row; see Assumptions",
      "Methods 2.2: C0 = 0.006 x G = 2",
      "Methods 2.2: C1 = 0.189 x G = 2",
      "Methods 2.2: SD = C0 + C1 x C (Pmetrics polynomial)",
      "Methods 2.2; Results 3.2",
      "Methods 2.1 ('0.5 h after a 1 h intravenous infusion')",
      "Units declaration",
      "Results 3.2",
      "Table 2 (mixed-effect regression on Ctrough)"
    )
  )
)
Item Value Source
lka log(22.64) 1/h Table 3, Median row
lcl log(1.33) L/h Table 3, Median row
lvc log(102.58) L Table 3, Median row
lq log(5.08) L/h Table 3, Median row
lvp log(385.93) L Table 3, Median row
lfdepot log(1.00) Table 3, Median row
etalka / etalcl / etalvc / etalq / etalvp 0.02423 / 0.3436 / 0.2023 / 0.7867 / 0.5558 Table 3, CV (%) row, omega^2 = log(CV^2 + 1)
IIV on Fos (not encoded) CV 7.42% Table 3, CV (%) row; see Assumptions
addSd 0.012 mg/L Methods 2.2: C0 = 0.006 x G = 2
propSd 0.378 Methods 2.2: C1 = 0.189 x G = 2
combined1() linear sum of SDs Methods 2.2: SD = C0 + C1 x C (Pmetrics polynomial)
Two-compartment ODE, first-order oral input depot -> central <-> peripheral1 Methods 2.2; Results 3.2
1-h intravenous infusion into central dosing only Methods 2.1 (‘0.5 h after a 1 h intravenous infusion’)
Cc = central / vc mg / L = mg/L Units declaration
AGE, CONMED_CYP3A4_INH (excluded) tested on CL, not retained Results 3.2
WT, SEXF, ALB, TBILI, ALT, AST, GGT (excluded) Ctrough regression only Table 2 (mixed-effect regression on Ctrough)

Choice of typical values

Table 3 prints the mean, SD, CV and median of each parameter’s NPAG distribution, and the two columns differ a lot for the two distribution parameters. For Q the mean is 16.78 L/h and the median 5.08 L/h. For Vp the mean is 735 L and the median 386 L. The text uses both columns. The Discussion quotes the mean CL (1.52 L/h) as “the median CL estimate”. It also quotes “the wide median volume of distribution (488.51 L)”, which is the sum of the two medians (102.58 + 385.93) and not of the two means (824.74 L).

The paper’s own Monte Carlo output decides which column to use. Below, the Table 4 simulation is re-run with each column. The CV is the same in both runs, because Table 3’s CV is SD / mean for every row. The residual error is left out, because the paper’s Table 4 describes true troughs. The oral route is used, because Methods does not give the simulation route and F is 1 at the median.

md_levels <- c(100, 200, 300)
days <- c(2, 7, 14, 21, 28, 60)
# AUC24 needs a within-day grid; the trough is the value at the day's end
# (24 * day h), which is also the time of the next oral dose. An oral dose
# enters the depot, so Cc at that instant is still the pre-dose trough.
grid <- sort(unique(c(0, unlist(lapply(days, function(d) {
  24 * (d - 1) + c(0, 0.25, 0.5, 1, 1.5, 2, 3, 4, 6, 8, 12, 16, 20, 24)
})))))

make_events <- function(md) {
  rxode2::et(amt = 200, ii = 8, addl = 5, cmt = "depot") |>
    rxode2::et(time = 48, amt = md, ii = 24, addl = 60, cmt = "depot") |>
    rxode2::et(grid, cmt = "central")
}

n_per_arm <- 200
simulate_arms <- function(model, label) {
  bind_rows(lapply(md_levels, function(md) {
    s <- rxode2::rxSolve(model, make_events(md), nSub = n_per_arm,
                         returnType = "data.frame")
    # A single event table replicated with nSub returns the subject index as
    # sim.id rather than id.
    if (!"id" %in% names(s)) s$id <- s$sim.id
    s$md <- md
    s$column <- label
    s
  }))
}

# The mean column. Fos mean 0.95; no IIV on Fos in either run.
mod_mean <- mod |>
  ini(lka = log(22.64), lcl = log(1.52), lvc = log(89.50), lq = log(16.78),
      lvp = log(735.24), lfdepot = log(0.95))
#> ℹ parameter labels from comments will be replaced by 'label()'
#> ℹ change initial estimate of `lka` to `3.11971825333498`
#> ℹ change initial estimate of `lcl` to `0.418710334858185`
#> ℹ change initial estimate of `lvc` to `4.49423862528081`
#> ℹ change initial estimate of `lq` to `2.82018770103906`
#> ℹ change initial estimate of `lvp` to `6.60019697652556`
#> ℹ change initial estimate of `lfdepot` to `-0.0512932943875506`

rxode2::rxSetSeed(20211206)
sim_med <- simulate_arms(mod, "Median (encoded)")
#> ℹ parameter labels from comments will be replaced by 'label()'
rxode2::rxSetSeed(20211206)
sim_mean <- simulate_arms(mod_mean, "Mean")
sim_all <- bind_rows(sim_med, sim_mean)
troughs <- sim_all |>
  filter(time %in% (24 * days)) |>
  mutate(day = time / 24)

sim_t4 <- troughs |>
  group_by(column, md, day) |>
  summarise(
    lt1 = 100 * mean(Cc < 1),
    mid = 100 * mean(Cc >= 1 & Cc <= 5.13),
    gt5 = 100 * mean(Cc > 5.13),
    .groups = "drop"
  )

# Cojutti 2021 Table 4. The Day 2 (end of loading) column is common to all
# three maintenance doses.
pub_t4 <- tibble::tribble(
  ~md, ~day, ~lt1_pub, ~mid_pub, ~gt5_pub,
  100, 2, 1.7, 85.2, 13.1,
  100, 7, 21.7, 76.4, 1.9,
  100, 14, 16.4, 81.5, 2.1,
  100, 21, 12.9, 84.6, 2.5,
  100, 28, 12.0, 83.8, 4.2,
  100, 60, 11.7, 81.1, 7.2,
  200, 2, 1.7, 85.2, 13.1,
  200, 7, 4.1, 84.3, 11.6,
  200, 14, 1.8, 80.4, 17.8,
  200, 21, 1.3, 73.6, 25.1,
  200, 28, 1.0, 71.3, 27.7,
  200, 60, 1.1, 59.7, 39.2,
  300, 2, 1.7, 85.2, 13.1,
  300, 7, 0.8, 76.9, 22.3,
  300, 14, 0.2, 60.6, 39.2,
  300, 21, 0.2, 48.6, 51.2,
  300, 28, 0.1, 46.9, 53.0,
  300, 60, 0.1, 26.6, 73.2
)

t4 <- sim_t4 |>
  left_join(pub_t4, by = c("md", "day")) |>
  mutate(abs_diff = (abs(lt1 - lt1_pub) + abs(mid - mid_pub) + abs(gt5 - gt5_pub)) / 3)

knitr::kable(
  t4 |>
    filter(column == "Median (encoded)") |>
    transmute(md, day,
              lt1 = sprintf("%.1f (%.1f)", lt1, lt1_pub),
              mid = sprintf("%.1f (%.1f)", mid, mid_pub),
              gt5 = sprintf("%.1f (%.1f)", gt5, gt5_pub)) |>
    dplyr::rename("MD (mg/day)" = md, "Day" = day,
                  "Ctrough < 1 mg/L, % (published)" = lt1,
                  "1-5.13 mg/L, % (published)" = mid,
                  "> 5.13 mg/L, % (published)" = gt5),
  caption = paste("Replicates Table 4 of Cojutti 2021 with the encoded (median)",
                  "parameters; published values in parentheses.")
)
Replicates Table 4 of Cojutti 2021 with the encoded (median) parameters; published values in parentheses.
MD (mg/day) Day Ctrough < 1 mg/L, % (published) 1-5.13 mg/L, % (published) > 5.13 mg/L, % (published)
100 2 0.5 (1.7) 80.0 (85.2) 19.5 (13.1)
100 7 14.0 (21.7) 84.5 (76.4) 1.5 (1.9)
100 14 12.5 (16.4) 83.5 (81.5) 4.0 (2.1)
100 21 12.0 (12.9) 83.0 (84.6) 5.0 (2.5)
100 28 12.0 (12.0) 82.0 (83.8) 6.0 (4.2)
100 60 8.5 (11.7) 81.0 (81.1) 10.5 (7.2)
200 2 0.0 (1.7) 76.0 (85.2) 24.0 (13.1)
200 7 3.5 (4.1) 82.5 (84.3) 14.0 (11.6)
200 14 1.5 (1.8) 76.0 (80.4) 22.5 (17.8)
200 21 1.0 (1.3) 66.0 (73.6) 33.0 (25.1)
200 28 1.0 (1.0) 59.5 (71.3) 39.5 (27.7)
200 60 1.0 (1.1) 44.5 (59.7) 54.5 (39.2)
300 2 1.5 (1.7) 78.5 (85.2) 20.0 (13.1)
300 7 0.5 (0.8) 81.0 (76.9) 18.5 (22.3)
300 14 0.5 (0.2) 51.0 (60.6) 48.5 (39.2)
300 21 0.5 (0.2) 42.5 (48.6) 57.0 (51.2)
300 28 0.5 (0.1) 36.5 (46.9) 63.0 (53.0)
300 60 0.5 (0.1) 23.5 (26.6) 76.0 (73.2) 

fit_summary <- t4 |>
  group_by(column) |>
  summarise(
    mean_abs_diff = mean(abs_diff),
    lt1_end_of_loading = mean(lt1[day == 2]),
    .groups = "drop"
  )
knitr::kable(
  fit_summary |>
    dplyr::rename("Table 3 column" = column,
                  "Mean |difference| from Table 4 (points)" = mean_abs_diff,
                  "Ctrough < 1 mg/L at end of loading, % (published 1.7)" = lt1_end_of_loading),
  digits = 1,
  caption = "Agreement of each Table 3 column with the published Monte Carlo output."
)
Agreement of each Table 3 column with the published Monte Carlo output.
Table 3 column Mean |difference| from Table 4 (points) Ctrough < 1 mg/L at end of loading, % (published 1.7)
Mean 7.8 17.3
Median (encoded) 4.4 0.7

The median column reproduces Table 4 closely. Both the fraction of troughs below 1 mg/L at the end of loading and the build-up of troughs above 5.13 mg/L over two months come out close to the published values. The mean column puts many more troughs below 1 mg/L at the end of loading, because its larger Vp and Q move more drug into the peripheral compartment during loading. So the medians are encoded.

fs <- setNames(fit_summary$mean_abs_diff, fit_summary$column)
lt <- setNames(fit_summary$lt1_end_of_loading, fit_summary$column)
stopifnot(
  # Centre of agreement over all 18 cells. Realised 3.0-5.1 over seven seeds
  # and at 1 and 4 threads (the mean column gives 7.8-9.9), so 7 leaves room
  # for the draw.
  fs[["Median (encoded)"]] < 7,
  # End of loading, Ctrough < 1 mg/L: realised 0.2-1.5 percent with the
  # median column and 17-20 percent with the mean column over the same runs.
  # The 8 percent split sits well clear of both.
  lt[["Median (encoded)"]] < 8,
  lt[["Mean"]] > 8
)

Replicate Figure 4 

fig4 <- troughs |>
  filter(column == "Median (encoded)") |>
  group_by(md, day) |>
  summarise(
    q05 = quantile(Cc, 0.05), q25 = quantile(Cc, 0.25), q50 = median(Cc),
    q75 = quantile(Cc, 0.75), q95 = quantile(Cc, 0.95), .groups = "drop"
  ) |>
  mutate(day = factor(day), md = paste("MD", md, "mg daily"))

ggplot(fig4, aes(x = day)) +
  geom_boxplot(aes(ymin = q05, lower = q25, middle = q50, upper = q75, ymax = q95),
               stat = "identity", fill = "grey85") +
  geom_hline(yintercept = 5.13, linetype = "dashed") +
  facet_wrap(~md) +
  labs(x = "Day of treatment", y = "Isavuconazole Ctrough (mg/L)") +
  theme_bw()

Replicates Figure 4 of Cojutti 2021: boxes are the median and 25th-75th percentiles, whiskers the 5th-95th percentiles, and the dashed line is the 5.13 mg/L toxicity threshold. Troughs build up over the whole two months, as the paper reports. The typical terminal half-life of this parameter set is about 300 h, so steady state is reached only after several weeks.

Probability of target attainment

Figure 5 reports that the standard 200 mg maintenance dose “achieved optimal PTAs” (at least 90%) at the 1 mg/L EUCAST breakpoint on Day 7, for a target of AUC24h/MIC > 33.4. The Table 5 cumulative fractions of response need the EUCAST MIC distributions, which the paper does not tabulate, so they are not recomputed here.

nca_in <- sim_med |>
  filter(!is.na(Cc)) |>
  mutate(treatment = paste("MD", md, "mg"), id = paste(md, id)) |>
  select(id, time, Cc, treatment)

# Dose records per subject: LD at 0, 8, ..., 40 h, then MD every 24 h from 48 h.
dose_times <- c(seq(0, 40, by = 8), seq(48, 48 + 24 * 60, by = 24))
doses <- nca_in |>
  distinct(id, treatment) |>
  tidyr::crossing(time = dose_times) |>
  mutate(amt = ifelse(time < 48, 200, as.numeric(sub("MD ([0-9]+) mg", "\\1", treatment))))

conc_obj <- PKNCA::PKNCAconc(nca_in, Cc ~ time | treatment + id)
dose_obj <- PKNCA::PKNCAdose(doses, amt ~ time | treatment + id)
intervals <- data.frame(
  start = 24 * (days - 1), end = 24 * days,
  auclast = TRUE, cmax = TRUE, cmin = TRUE
)
nca_res <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals))

nca_tab <- as.data.frame(nca_res$result) |>
  filter(PPTESTCD %in% c("auclast", "cmax", "cmin")) |>
  mutate(day = end / 24)

pta <- nca_tab |>
  filter(PPTESTCD == "auclast") |>
  group_by(treatment, day) |>
  summarise(
    median_auc24 = median(PPORRES),
    pta_mic1 = 100 * mean(PPORRES / 1 > 33.4),
    .groups = "drop"
  )
knitr::kable(
  pta |>
    dplyr::rename("Regimen" = treatment, "Day" = day,
                  "Median AUC24 (mg*h/L)" = median_auc24,
                  "PTA at MIC 1 mg/L (%)" = pta_mic1),
  digits = 1,
  caption = "Simulated AUC24 and PTA of AUC24/MIC > 33.4 at MIC = 1 mg/L."
)
Simulated AUC24 and PTA of AUC24/MIC > 33.4 at MIC = 1 mg/L.
Regimen Day Median AUC24 (mg*h/L) PTA at MIC 1 mg/L (%)
MD 100 mg 2 87.4 99.5
MD 100 mg 7 58.6 86.5
MD 100 mg 14 61.3 87.5
MD 100 mg 21 63.6 87.5
MD 100 mg 28 65.8 87.0
MD 100 mg 60 69.0 89.0
MD 200 mg 2 84.9 100.0
MD 200 mg 7 83.6 99.0
MD 200 mg 14 99.9 100.0
MD 200 mg 21 112.4 100.0
MD 200 mg 28 122.8 100.0
MD 200 mg 60 148.7 100.0
MD 300 mg 2 84.3 98.5
MD 300 mg 7 111.1 99.5
MD 300 mg 14 140.8 99.5
MD 300 mg 21 161.7 99.5
MD 300 mg 28 175.5 99.5
MD 300 mg 60 210.8 99.5 

pta200 <- pta$pta_mic1[pta$treatment == "MD 200 mg" & pta$day == 7]
# Figure 5: at least 90 percent at MIC 1 mg/L with 200 mg on Day 7. Allow
# 3-4 Monte Carlo SE at n = 200 below the claim.
stopifnot(pta200 > 85)

The simulated PTA at 1 mg/L on Day 7 with 200 mg daily is 99.0%, in line with the paper’s statement that the standard dose reaches at least 90% at the breakpoint.

Comparison with observed TDM values

The paper reports no NCA of its own. The nearest thing is the Table 1 summary of observed TDM concentrations under 200 mg daily, which pools troughs and peaks drawn at different times from Day 3 to several months. The table below compares these with the simulated Day 14 dosing interval under 200 mg daily. For an oral dose absorbed with a half-life of about 2 minutes, the 2-h post-dose peak is close to Cmax. This is a descriptive check and is not used as a gate.

published_tdm <- data.frame(
  treatment = "MD 200 mg",
  cmin = 3.68,
  cmax = 4.67
)
sim_day14 <- nca_res
sim_day14$result <- sim_day14$result |>
  filter(end == 24 * 14, PPTESTCD %in% c("cmin", "cmax"))

knitr::kable(
  nlmixr2lib::ncaComparisonTable(
    simulated = sim_day14,
    reference = published_tdm,
    by = "treatment",
    units = c(cmin = "mg/L", cmax = "mg/L"),
    tolerance_pct = 20
  ),
  caption = paste("Simulated Day 14 cmin / cmax (200 mg daily) against the observed",
                  "Table 1 TDM medians. * differs by >20%.")
)
Simulated Day 14 cmin / cmax (200 mg daily) against the observed Table 1 TDM medians. * differs by >20%.
NCA parameter treatment Reference Simulated % diff
Cmax (mg/L) MD 200 mg 4.67 5.42 +16.1%
Cmin (mg/L) MD 200 mg 3.68 3.49 -5.2%

Steady-state closed-form check

For a linear model the steady-state AUC over a dosing interval equals F x Dose / CL. The typical patient is run for 150 days of 200 mg daily, which is more than 10 terminal half-lives, and PKNCA is applied to the last interval.

ev_ss <- rxode2::et(amt = 200, ii = 24, addl = 149, cmt = "depot") |>
  rxode2::et(c(0, 24 * 149 + c(0, 0.25, 0.5, 1, 2, 4, 8, 12, 16, 20, 24)), cmt = "central")
ss <- rxode2::rxSolve(rxode2::zeroRe(mod), ev_ss, returnType = "data.frame") |>
  filter(!is.na(Cc)) |>
  mutate(id = 1, treatment = "200 mg daily, typical")
#> ℹ parameter labels from comments will be replaced by 'label()'
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalcl', 'etalvc', 'etalq', 'etalvp'
ss_dose <- data.frame(id = 1, treatment = "200 mg daily, typical",
                      time = seq(0, 24 * 149, by = 24), amt = 200)
ss_nca <- PKNCA::pk.nca(PKNCA::PKNCAdata(
  PKNCA::PKNCAconc(ss, Cc ~ time | treatment + id),
  PKNCA::PKNCAdose(ss_dose, amt ~ time | treatment + id),
  intervals = data.frame(start = 24 * 149, end = 24 * 150, auclast = TRUE)
))
auc_ss <- as.data.frame(ss_nca$result)$PPORRES[1]
auc_closed <- 1.00 * 200 / 1.33
c(PKNCA = auc_ss, closed_form = auc_closed)
#>       PKNCA closed_form 
#>    150.2819    150.3759
# Deterministic; the only difference is trapezoidal error on the fast
# absorption peak and the few percent of steady state not yet reached.
stopifnot(abs(auc_ss / auc_closed - 1) < 0.05)

Assumptions and deviations

  • Median column encoded. Table 3 gives both a mean and a median for each parameter. The medians are encoded because they reproduce the paper’s own Table 4 Monte Carlo output and the means do not (see “Choice of typical values”). The Discussion’s “median CL (1.52 L/h)” is the Table 3 mean.
  • Lognormal marginals for a non-parametric fit. NPAG estimates a discrete joint distribution. The CV column is carried as independent lognormal marginals with omega^2 = log(CV^2 + 1), because covariances are not reported. Any multimodality in the NPAG distribution cannot be recovered from Table 3. The simulated trough distribution builds up a little faster than Table 4 after Day 21 (for example, 200 mg Day 60 above 5.13 mg/L). This is the expected sign of lognormal tails on Q and Vp. It is not a transcription error.
  • No IIV on bioavailability. Fos has median 1.00, mean 0.95 and CV 7.42%. With the median at the upper bound of 1, a lognormal marginal would give F > 1 to half of the patients, and a logit-normal marginal is undefined. Bioavailability is therefore fixed at its typical value of 1 for every simulated patient. The Table 3 column header says “Fos (%)”, but the values are fractions.
  • Ka. Table 3 gives the same mean and median for Ka (22.64 1/h, an absorption half-life of about 2 minutes). The data were troughs and a few 2-h peaks, so they carry almost no information on absorption. The value is encoded as printed.
  • Residual error. Methods gives the assay polynomial SD = 0.006 + 0.189 x C and a gamma of 2. Pmetrics multiplies the assay SD by gamma, so the encoded residual is 0.012 mg/L + 37.8% with the two parts summed linearly (combined1()). The 0.189 slope is larger than the “< 10%” inter-assay CV that Methods quotes. The paper does not say whether C1 absorbs extra variability, and the value is encoded as printed.
  • Monte Carlo settings. Methods does not give the route or the error model of the Table 4 simulation. Here the simulation is oral with no residual error, and the trough is taken at the end of each named day (24 x day h). Troughs with added residual error fit Table 4 worse; for example, they put about 5% below 1 mg/L at the end of loading against the published 1.7%.
  • Covariates. The population model retained none. Age and mild or moderate CYP3A4 inhibitors were tested on CL and did not improve the fit. The other Table 2 variables come from a separate mixed-effect regression on Ctrough and were never part of the PK model. All of them are listed in covariatesDataExcluded.
  • Dose units. Doses are isavuconazole equivalents (200 mg isavuconazole = 372 mg isavuconazonium sulfate), as in the paper.