Skip to contents

Viloxazine (Nasser 2021)

Source: vignettes/articles/Nasser_2021_viloxazine.Rmd
Nasser_2021_viloxazine.Rmd

Model and source

  • Citation: Nasser A, Gomeni R, Wang Z, Kosheleff AR, Xie L, Adeojo LW, Schwabe S. Population Pharmacokinetics of Viloxazine Extended-Release Capsules in Pediatric Subjects With Attention Deficit/Hyperactivity Disorder. J Clin Pharmacol. 2021;61(12):1626-1637. doi:10.1002/jcph.1940.
  • Description: Joint parent (viloxazine) + metabolite (5-hydroxyviloxazine glucuronide, 5-HVLX-gluc) population PK model for once-daily oral viloxazine extended-release capsules in children (6-11 years) and adolescents (12-17 years) with ADHD (Nasser 2021, pooled phase 3 studies P301-P304). Viloxazine is one-compartment with first-order absorption (ka = 0.068 1/h, so the terminal phase is absorption-limited) and two parallel first-order elimination routes from the central compartment: formation of 5-HVLX-gluc (CLV) and all remaining viloxazine elimination (CLL). 5-HVLX-gluc is one-compartment with first-order elimination (CLM) and shares the viloxazine apparent volume (assumed by the authors for identifiability). Body weight enters as power functions centred on the 36.35 kg median on the shared volume, CLV and CLM; F is fixed to 1.
  • Article: https://doi.org/10.1002/jcph.1940 (open access; supplementary Tables S1-S3 and Figures S1-S3 in the online supporting information)

Population

Nasser 2021 pooled sparse steady-state samples from four phase 3, randomized, double-blind, placebo-controlled trials of once-daily viloxazine extended-release (ER) capsules in ADHD: P301 and P303 in children aged 6-11 years (100, 200 or 400 mg/day) and P302 and P304 in adolescents aged 12-17 years (200, 400 or 600 mg/day). 495 subjects contributed samples (86 at 100 mg, 197 at 200 mg, 164 at 400 mg, 48 at 600 mg): 263 children and 232 adolescents, mean age 11.2 years, mean weight 44.5 kg (range 20-92.5 kg; median 36.35 kg), 68% male, 52% White and 43% Black or African American, 23% Hispanic or Latino (Table 1). Up to five samples per subject (pre-dose and 1, 2, 4 and 6 h post-dose) were assayed for viloxazine and its major metabolite 5-hydroxyviloxazine glucuronide (5-HVLX-gluc).

The same information is available programmatically via readModelDb("Nasser_2021_viloxazine")()$population.

Source trace

Every ini() entry in inst/modeldb/specificDrugs/Nasser_2021_viloxazine.R carries an in-file comment naming its source; the table below collects them.

Equation / parameter Value Source location
lka (ka) log(0.068) 1/h Table 2
lvc (V2/F = V3/F) log(14.60) L at 36.35 kg Table 2; Methods ‘Population Pharmacokinetic Analysis’ (V2/F and V3/F identical)
lcl_nonmet (CLL, viloxazine clearance) log(0.87) L/h Table 2; Figure 1
lcl_met (CLV, viloxazine metabolic clearance) log(4.72) L/h at 36.35 kg Table 2; Figure 1
lcl_gluc (CLM, 5-HVLX-gluc clearance) log(6.75) L/h at 36.35 kg Table 2; Figure 1
e_wt_vc (WT,V) 0.78 Table 2
e_wt_cl_met (WT,CLV) 0.59 Table 2
e_wt_cl_gluc (WT,CLM) 0.70 Table 2
etalvc, etalcl_nonmet, etalka, etalcl_met, etalcl_gluc 0.10, 3.03, 0.17, 0.11, 0.08 (variances) Table 2 ‘Random effect’
addSd, addSd_gluc 0.12 ug/mL Table 2 ‘Residual error, Additive’
propSd, propSd_gluc 0.29 Table 2 ‘Residual error, Proportional’
P = Pref * (WT / 36.35)^g n/a Methods ‘Covariate Analysis’ equation; median weight 36.35 kg
Weight on V, CLV, CLM only n/a Results; Table S1 model 10 (final)
d/dt(depot), d/dt(central), d/dt(central_gluc) n/a Figure 1; Methods (1-compartment parent, first-order absorption, first-order formation and elimination of the metabolite)
F = 1 n/a Methods ‘Population Pharmacokinetic Analysis’

Simulation design

The paper’s own validation targets are its Monte Carlo drug-holiday simulations (Tables S2 and S3, Figure 5): 10 days of once-daily dosing, 1-4 missed days, then dosing resumed, with weight fixed at the median of each age group (children 31.5 kg, adolescents 57.25 kg; Methods ‘Impact of Missed Doses’). The vignette simulates the same design at 400 mg/day for both age groups, 200 virtual subjects per scenario, without residual error (the tables report medians of the predicted concentrations).

mod <- readModelDb("Nasser_2021_viloxazine")

tau <- 24
n_per_arm <- 200L

# One scenario = age group x number of missed days. Doses on days 1-10, then
# `missed` days without a dose, then 10 more daily doses.
make_holiday <- function(age_group, wt, missed, dose, id_offset) {
  dose_times <- c(seq(0, 9) * tau, (10 + missed + seq(0, 9)) * tau)
  # Observe only the windows the tables summarise: the last steady-state
  # interval (day 10), the holiday, and the three days after restarting.
  t_ss <- 9 * tau
  t_end <- (10 + missed + 3) * tau
  obs_times <- seq(t_ss, t_end, by = 1)
  ids <- id_offset + seq_len(n_per_arm)
  doses <- expand.grid(id = ids, time = dose_times) |>
    mutate(evid = 1L, amt = dose, cmt = "depot", dvid = NA_integer_)
  obs <- expand.grid(id = ids, time = obs_times) |>
    mutate(evid = 0L, amt = NA_real_, cmt = "central", dvid = 1L)
  bind_rows(doses, obs) |>
    mutate(
      WT = wt, age_group = age_group, missed = missed, dose = dose,
      scenario = paste0(age_group, ", ", missed, " missed")
    ) |>
    arrange(id, time, desc(evid))
}

scen <- expand.grid(
  age_group = c("Children", "Adolescents"), missed = 1:4,
  stringsAsFactors = FALSE
) |>
  mutate(
    wt = ifelse(age_group == "Children", 31.5, 57.25),
    id_offset = (seq_len(n()) - 1L) * n_per_arm
  )

events <- bind_rows(lapply(seq_len(nrow(scen)), function(i) {
  make_holiday(
    scen$age_group[i], scen$wt[i], scen$missed[i],
    dose = 400, id_offset = scen$id_offset[i]
  )
}))
stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))
rxode2::rxSetSeed(20211201)
sim <- rxode2::rxSolve(
  rxode2::zeroRe(mod, "sigma"),
  events = events,
  keep = c("age_group", "missed", "dose", "WT", "scenario")
) |>
  as.data.frame()
#> ℹ parameter labels from comments will be replaced by 'label()'

Typical-value check against the closed form

Viloxazine is linear, so the typical steady-state average concentration is Dose / ((CLL + CLV) * tau) and the metabolite average is Dose * CLV / ((CLL + CLV) * CLM * tau) (equal parent and metabolite volumes, 1:1 mass formation). Both sides use the same parameters, so the difference is pure numerical error and the bound is tight.

typ <- rxode2::rxSolve(
  rxode2::zeroRe(mod),
  events = events |> filter(missed == 1, (id - 1) %% n_per_arm == 0),
  keep = c("age_group")
) |>
  as.data.frame() |>
  filter(time >= 9 * tau, time <= 10 * tau) |>
  group_by(age_group, WT) |>
  summarise(
    cav_sim = mean(Cc[time < 10 * tau]),
    cav_gluc_sim = mean(Cc_gluc[time < 10 * tau]),
    .groups = "drop"
  ) |>
  mutate(
    cl_par = 0.87 + 4.72 * (WT / 36.35)^0.59,
    cl_met = 4.72 * (WT / 36.35)^0.59,
    cl_gluc = 6.75 * (WT / 36.35)^0.70,
    cav_closed = 400 / (cl_par * tau),
    cav_gluc_closed = 400 * cl_met / (cl_par * cl_gluc * tau)
  )
#> ℹ parameter labels from comments will be replaced by 'label()'
#> ℹ omega/sigma items treated as zero: 'etalvc', 'etalcl_nonmet', 'etalka', 'etalcl_met', 'etalcl_gluc'
#> Warning: multi-subject simulation without without 'omega'

typ |>
  select(age_group, WT, cav_sim, cav_closed, cav_gluc_sim, cav_gluc_closed) |>
  rename(
    "Age group" = age_group, "WT (kg)" = WT,
    "Viloxazine Cavg sim (ug/mL)" = cav_sim,
    "Viloxazine Cavg closed form" = cav_closed,
    "5-HVLX-gluc Cavg sim (ug/mL)" = cav_gluc_sim,
    "5-HVLX-gluc Cavg closed form" = cav_gluc_closed
  ) |>
  knitr::kable(digits = 3, caption = "Typical-value steady-state Cavg at 400 mg/day.")
Typical-value steady-state Cavg at 400 mg/day.
Age group WT (kg) Viloxazine Cavg sim (ug/mL) Viloxazine Cavg closed form 5-HVLX-gluc Cavg sim (ug/mL) 5-HVLX-gluc Cavg closed form
Adolescents 57.25 2.363 2.367 1.575 1.575
Children 31.50 3.193 3.200 2.273 2.273 

# Day 10 is not fully at steady state for the slow absorption phase and the
# 1-h grid mean is a rectangle rule, so allow 2%.
stopifnot(
  all(abs(typ$cav_sim / typ$cav_closed - 1) < 0.02),
  all(abs(typ$cav_gluc_sim / typ$cav_gluc_closed - 1) < 0.02)
)

Replicate Tables S2 and S3 (drug holidays)

The windows are read from the tables’ structure: “Steady-state” is the dosing interval before the holiday (day 10); “Holiday” is the whole off-drug period (the holiday Cavg falls roughly as 1 / number of days, and the holiday Cmin falls by the one-day decay factor per extra day, so it is the concentration at the end of the holiday); “Day k after” is the k-th dosing interval after restarting. Cavg (PKNCA cav) and Cmin, taken as the concentration at the end of each window (PKNCA clast.obs, i.e. the trough before the next dose), are computed per subject with PKNCA, one call per scenario. PKNCA’s cmin is not used here: it includes the first time point of the window, which after a holiday is the pre-restart trough.

holiday_windows <- function(missed) {
  t_ss <- 9 * tau
  t_restart <- (10 + missed) * tau
  data.frame(
    window = c("Steady-state", "Holiday", "Day 1 after", "Day 2 after", "Day 3 after"),
    start = c(t_ss, 10 * tau, t_restart, t_restart + tau, t_restart + 2 * tau),
    end = c(10 * tau, t_restart, t_restart + tau, t_restart + 2 * tau, t_restart + 3 * tau)
  )
}

run_nca <- function(sim_df, conc_col) {
  out <- list()
  for (sc in unique(sim_df$scenario)) {
    d <- sim_df |> filter(scenario == sc)
    d$conc <- d[[conc_col]]
    d <- d |> filter(!is.na(conc))
    missed <- d$missed[1]
    w <- holiday_windows(missed)
    conc_obj <- PKNCA::PKNCAconc(d, conc ~ time | scenario + id)
    dose_df <- events |>
      filter(scenario == sc, evid == 1) |>
      select(id, time, amt, scenario)
    dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | scenario + id)
    intervals <- data.frame(start = w$start, end = w$end, cav = TRUE, clast.obs = TRUE)
    res <- as.data.frame(PKNCA::pk.nca(PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals)))
    res$window <- w$window[match(res$start, w$start)]
    res$missed <- missed
    res$age_group <- d$age_group[1]
    out[[sc]] <- res
  }
  bind_rows(out)
}

nca_hol <- run_nca(sim, "Cc")

sim_hol <- nca_hol |>
  group_by(age_group, missed, window, PPTESTCD) |>
  summarise(sim = median(PPORRES, na.rm = TRUE), .groups = "drop")

The paper tabulates the medians at 100, 200, 400 and 600 mg/day, each from a separate Monte Carlo draw. Viloxazine is linear, so all four are estimates of the same dose-normalised median; their spread (about +/-7% between doses) is the paper’s own Monte Carlo noise. The comparison below uses the 400 mg/day column and, as a less noisy reference, the mean of the four dose-normalised columns scaled to 400 mg/day.

windows <- c("Steady-state", "Holiday", "Day 1 after", "Day 2 after", "Day 3 after")
# Table S2 (Cavg, ug/mL) and Table S3 (Cmin, ug/mL); columns are
# 1/2/3/4 missed doses x Child/Adol, rows are the five windows.
s2 <- list(
  `100` = c(0.70, 0.51, 0.67, 0.52, 0.71, 0.57, 0.71, 0.53,
            0.17, 0.12, 0.09, 0.07, 0.06, 0.05, 0.05, 0.04,
            0.55, 0.41, 0.49, 0.39, 0.52, 0.43, 0.52, 0.38,
            0.66, 0.48, 0.62, 0.49, 0.66, 0.54, 0.67, 0.49,
            0.69, 0.50, 0.65, 0.51, 0.70, 0.56, 0.70, 0.51),
  `200` = c(1.34, 1.07, 1.27, 1.03, 1.50, 1.03, 1.45, 1.10,
            0.28, 0.30, 0.16, 0.14, 0.13, 0.11, 0.12, 0.10,
            1.10, 0.84, 0.98, 0.79, 1.07, 0.72, 1.02, 0.76,
            1.28, 1.01, 1.21, 0.98, 1.38, 0.94, 1.32, 1.00,
            1.32, 1.06, 1.26, 1.02, 1.46, 1.00, 1.40, 1.07),
  `400` = c(2.97, 2.05, 2.61, 1.98, 2.78, 2.05, 2.79, 2.17,
            0.67, 0.45, 0.35, 0.25, 0.26, 0.19, 0.17, 0.14,
            2.42, 1.64, 1.93, 1.52, 1.99, 1.46, 2.11, 1.60,
            2.84, 1.94, 2.42, 1.88, 2.57, 1.90, 2.63, 2.05,
            2.94, 2.01, 2.54, 1.95, 2.71, 2.02, 2.76, 2.13),
  `600` = c(4.26, 3.19, 4.15, 3.03, 4.13, 3.20, 4.25, 3.11,
            0.89, 0.72, 0.56, 0.44, 0.35, 0.33, 0.32, 0.26,
            3.46, 2.56, 3.16, 2.26, 3.12, 2.30, 3.03, 2.15,
            4.09, 3.03, 3.94, 2.81, 3.90, 2.96, 3.89, 2.78,
            4.20, 3.13, 4.08, 2.96, 4.05, 3.13, 4.13, 2.98)
)
s3 <- list(
  `100` = c(0.344, 0.240, 0.308, 0.235, 0.315, 0.254, 0.332, 0.240,
            0.066, 0.048, 0.010, 0.007, 0.002, 0.001, 0.001, 0.000,
            0.290, 0.202, 0.242, 0.191, 0.241, 0.208, 0.258, 0.172,
            0.333, 0.229, 0.294, 0.221, 0.303, 0.236, 0.317, 0.220,
            0.342, 0.234, 0.305, 0.232, 0.311, 0.250, 0.327, 0.233),
  `200` = c(0.582, 0.567, 0.536, 0.498, 0.707, 0.520, 0.704, 0.553,
            0.101, 0.130, 0.019, 0.013, 0.004, 0.005, 0.002, 0.001,
            0.512, 0.460, 0.456, 0.385, 0.542, 0.394, 0.540, 0.433,
            0.565, 0.539, 0.521, 0.466, 0.655, 0.471, 0.651, 0.517,
            0.576, 0.559, 0.528, 0.492, 0.686, 0.496, 0.690, 0.547),
  `400` = c(1.389, 0.918, 1.173, 0.866, 1.275, 0.991, 1.200, 0.951,
            0.261, 0.163, 0.054, 0.028, 0.010, 0.008, 0.001, 0.002,
            1.152, 0.831, 0.958, 0.689, 1.030, 0.789, 0.985, 0.776,
            1.338, 0.898, 1.105, 0.823, 1.213, 0.943, 1.171, 0.902,
            1.372, 0.904, 1.154, 0.852, 1.250, 0.986, 1.194, 0.927),
  `600` = c(1.812, 1.429, 1.760, 1.420, 1.823, 1.588, 1.974, 1.520,
            0.364, 0.270, 0.087, 0.068, 0.010, 0.013, 0.003, 0.004,
            1.563, 1.228, 1.447, 1.108, 1.520, 1.206, 1.521, 1.164,
            1.751, 1.378, 1.639, 1.345, 1.734, 1.490, 1.845, 1.432,
            1.798, 1.409, 1.686, 1.406, 1.784, 1.563, 1.966, 1.491)
)
to_long <- function(tab, testcd) {
  bind_rows(lapply(names(tab), function(d) {
    expand.grid(
      age_group = c("Children", "Adolescents"), missed = 1:4, window = windows,
      stringsAsFactors = FALSE
    ) |>
      mutate(dose = as.numeric(d), value = tab[[d]], PPTESTCD = testcd)
  }))
}
paper <- bind_rows(to_long(s2, "cav"), to_long(s3, "clast.obs")) |>
  group_by(age_group, missed, window, PPTESTCD) |>
  summarise(
    paper_400 = value[dose == 400],
    paper_pooled = mean(value / dose) * 400,
    .groups = "drop"
  )

cmp_hol <- paper |>
  inner_join(sim_hol, by = c("age_group", "missed", "window", "PPTESTCD")) |>
  mutate(
    pct_vs_pooled = 100 * (sim - paper_pooled) / paper_pooled,
    window = factor(window, levels = windows)
  ) |>
  arrange(PPTESTCD, age_group, missed, window)

cmp_hol |>
  mutate(PPTESTCD = ifelse(PPTESTCD == "cav", "Cavg", "Cmin")) |>
  select(PPTESTCD, age_group, missed, window, paper_400, paper_pooled, sim, pct_vs_pooled) |>
  rename(
    "Metric" = PPTESTCD, "Age group" = age_group, "Missed days" = missed,
    "Window" = window, "Paper, 400 mg (ug/mL)" = paper_400,
    "Paper, pooled doses (ug/mL)" = paper_pooled,
    "Simulated median (ug/mL)" = sim, "Difference vs pooled (%)" = pct_vs_pooled
  ) |>
  knitr::kable(
    digits = 3,
    caption = "Median viloxazine Cavg (Table S2) and Cmin (Table S3) at 400 mg/day: paper vs. simulation."
  )
Median viloxazine Cavg (Table S2) and Cmin (Table S3) at 400 mg/day: paper vs. simulation.
Metric Age group Missed days Window Paper, 400 mg (ug/mL) Paper, pooled doses (ug/mL) Simulated median (ug/mL) Difference vs pooled (%)
Cavg Adolescents 1 Steady-state 2.050 2.089 1.999 -4.325
Cavg Adolescents 1 Holiday 0.450 0.502 0.459 -8.684
Cavg Adolescents 1 Day 1 after 1.640 1.667 1.622 -2.651
Cavg Adolescents 1 Day 2 after 1.940 1.975 1.899 -3.860
Cavg Adolescents 1 Day 3 after 2.010 2.054 1.990 -3.136
Cavg Adolescents 2 Steady-state 1.980 2.035 2.170 6.646
Cavg Adolescents 2 Holiday 0.250 0.276 0.279 1.177
Cavg Adolescents 2 Day 1 after 1.520 1.542 1.648 6.922
Cavg Adolescents 2 Day 2 after 1.880 1.918 2.058 7.276
Cavg Adolescents 2 Day 3 after 1.950 2.001 2.149 7.390
Cavg Adolescents 3 Steady-state 2.050 2.131 2.289 7.422
Cavg Adolescents 3 Holiday 0.190 0.208 0.235 13.281
Cavg Adolescents 3 Day 1 after 1.460 1.538 1.653 7.429
Cavg Adolescents 3 Day 2 after 1.900 1.978 2.126 7.459
Cavg Adolescents 3 Day 3 after 2.020 2.087 2.238 7.261
Cavg Adolescents 4 Steady-state 2.170 2.141 1.982 -7.403
Cavg Adolescents 4 Holiday 0.140 0.168 0.128 -23.887
Cavg Adolescents 4 Day 1 after 1.600 1.518 1.465 -3.506
Cavg Adolescents 4 Day 2 after 2.050 1.966 1.878 -4.469
Cavg Adolescents 4 Day 3 after 2.130 2.074 1.962 -5.422
Cavg Children 1 Steady-state 2.970 2.822 3.077 9.001
Cavg Children 1 Holiday 0.670 0.626 0.646 3.208
Cavg Children 1 Day 1 after 2.420 2.282 2.526 10.712
Cavg Children 1 Day 2 after 2.840 2.692 2.946 9.446
Cavg Children 1 Day 3 after 2.940 2.785 3.027 8.705
Cavg Children 2 Steady-state 2.610 2.649 2.815 6.270
Cavg Children 2 Holiday 0.350 0.351 0.409 16.583
Cavg Children 2 Day 1 after 1.930 1.989 2.119 6.541
Cavg Children 2 Day 2 after 2.420 2.487 2.631 5.793
Cavg Children 2 Day 3 after 2.540 2.595 2.758 6.273
Cavg Children 3 Steady-state 2.780 2.843 2.946 3.611
Cavg Children 3 Holiday 0.260 0.248 0.273 9.753
Cavg Children 3 Day 1 after 1.990 2.073 2.162 4.332
Cavg Children 3 Day 2 after 2.570 2.642 2.770 4.814
Cavg Children 3 Day 3 after 2.710 2.782 2.905 4.402
Cavg Children 4 Steady-state 2.790 2.841 2.970 4.549
Cavg Children 4 Holiday 0.170 0.206 0.199 -3.312
Cavg Children 4 Day 1 after 2.110 2.062 2.261 9.623
Cavg Children 4 Day 2 after 2.630 2.636 2.825 7.164
Cavg Children 4 Day 3 after 2.760 2.778 2.961 6.574
Cmin Adolescents 1 Steady-state 0.918 0.991 0.870 -12.261
Cmin Adolescents 1 Holiday 0.163 0.199 0.182 -8.628
Cmin Adolescents 1 Day 1 after 0.831 0.844 0.767 -9.118
Cmin Adolescents 1 Day 2 after 0.898 0.953 0.843 -11.507
Cmin Adolescents 1 Day 3 after 0.904 0.974 0.861 -11.592
Cmin Adolescents 2 Steady-state 0.866 0.937 1.016 8.462
Cmin Adolescents 2 Holiday 0.028 0.032 0.044 38.154
Cmin Adolescents 2 Day 1 after 0.689 0.740 0.846 14.305
Cmin Adolescents 2 Day 2 after 0.823 0.884 0.975 10.325
Cmin Adolescents 2 Day 3 after 0.852 0.925 1.000 8.101
Cmin Adolescents 3 Steady-state 0.991 1.026 1.111 8.242
Cmin Adolescents 3 Holiday 0.008 0.008 0.009 12.186
Cmin Adolescents 3 Day 1 after 0.789 0.803 0.835 3.959
Cmin Adolescents 3 Day 2 after 0.943 0.956 1.047 9.520
Cmin Adolescents 3 Day 3 after 0.986 1.005 1.108 10.233
Cmin Adolescents 4 Steady-state 0.951 1.008 0.884 -12.307
Cmin Adolescents 4 Holiday 0.002 0.002 0.001 -51.594
Cmin Adolescents 4 Day 1 after 0.776 0.776 0.654 -15.807
Cmin Adolescents 4 Day 2 after 0.902 0.943 0.838 -11.063
Cmin Adolescents 4 Day 3 after 0.927 0.987 0.869 -11.962
Cmin Children 1 Steady-state 1.389 1.284 1.354 5.423
Cmin Children 1 Holiday 0.261 0.242 0.236 -2.519
Cmin Children 1 Day 1 after 1.152 1.094 1.146 4.660
Cmin Children 1 Day 2 after 1.338 1.242 1.293 4.160
Cmin Children 1 Day 3 after 1.372 1.273 1.330 4.530
Cmin Children 2 Steady-state 1.173 1.163 1.232 5.990
Cmin Children 2 Holiday 0.054 0.048 0.053 11.679
Cmin Children 2 Day 1 after 0.958 0.951 1.013 6.515
Cmin Children 2 Day 2 after 1.105 1.104 1.186 7.402
Cmin Children 2 Day 3 after 1.154 1.138 1.226 7.700
Cmin Children 3 Steady-state 1.275 1.291 1.415 9.625
Cmin Children 3 Holiday 0.010 0.008 0.012 42.564
Cmin Children 3 Day 1 after 1.030 1.023 1.070 4.651
Cmin Children 3 Day 2 after 1.213 1.223 1.291 5.547
Cmin Children 3 Day 3 after 1.250 1.264 1.393 10.244
Cmin Children 4 Steady-state 1.200 1.313 1.363 3.793
Cmin Children 4 Holiday 0.001 0.003 0.002 -35.308
Cmin Children 4 Day 1 after 0.985 1.028 1.056 2.771
Cmin Children 4 Day 2 after 1.171 1.243 1.276 2.690
Cmin Children 4 Day 3 after 1.194 1.298 1.329 2.365

The holiday Cmin after three or four missed days is 0.001-0.01 ug/mL in the paper, below the assay LLOQ and printed to one significant figure, so those cells are reported but kept out of the gate. Everything else enters it.

gate_hol <- cmp_hol |>
  filter(!(PPTESTCD == "clast.obs" & window == "Holiday" & missed >= 3))
gate_hol |>
  group_by(PPTESTCD) |>
  summarise(
    n_cells = n(),
    median_pct = median(pct_vs_pooled),
    p90_abs_pct = unname(quantile(abs(pct_vs_pooled), 0.9)),
    .groups = "drop"
  ) |>
  rename(
    "Metric" = PPTESTCD, "Cells" = n_cells,
    "Median difference (%)" = median_pct,
    "90th percentile of |difference| (%)" = p90_abs_pct
  ) |>
  knitr::kable(digits = 1)
Metric Cells Median difference (%) 90th percentile of |difference| (%)
cav 40 6.3 9.8
clast.obs 36 4.7 12.3 

# A transcription error in a clearance, the volume or ka moves every cell by
# tens of percent; the paper's own dose-to-dose Monte Carlo spread is about
# +/-7%, and n = 200 per scenario adds about 4% on a median.
stopifnot(
  abs(median(gate_hol$pct_vs_pooled[gate_hol$PPTESTCD == "cav"])) < 10,
  abs(median(gate_hol$pct_vs_pooled[gate_hol$PPTESTCD == "clast.obs"])) < 12,
  quantile(abs(gate_hol$pct_vs_pooled), 0.9) < 25
)

Figure 5 (children, 400 mg/day) 

sim |>
  filter(age_group == "Children") |>
  group_by(missed, time) |>
  summarise(
    Q05 = quantile(Cc, 0.05), Q50 = median(Cc), Q95 = quantile(Cc, 0.95),
    .groups = "drop"
  ) |>
  mutate(missed = paste(missed, "missed dose(s)")) |>
  ggplot(aes(time / 24 + 1, Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), fill = "grey80") +
  geom_line() +
  facet_wrap(~missed) +
  labs(
    x = "Day of dosing", y = "Viloxazine (ug/mL)",
    title = "Drug holidays in children, 400 mg/day (median and 90% PI)",
    caption = "Replicates Figure 5 of Nasser 2021 (WT = 31.5 kg)."
  )

As in the paper, the median returns to within about 10% of its steady-state level after two doses whatever the length of the holiday.

restart <- cmp_hol |>
  filter(PPTESTCD == "cav", window %in% c("Steady-state", "Day 2 after")) |>
  select(age_group, missed, window, sim) |>
  pivot_wider(names_from = window, values_from = sim) |>
  mutate(ratio = `Day 2 after` / `Steady-state`)
knitr::kable(
  restart |> rename("Age group" = age_group, "Missed days" = missed, "Day 2 / steady state" = ratio),
  digits = 3
)
Age group Missed days Steady-state Day 2 after Day 2 / steady state
Adolescents 1 1.999 1.899 0.950
Adolescents 2 2.170 2.058 0.948
Adolescents 3 2.289 2.126 0.929
Adolescents 4 1.982 1.878 0.947
Children 1 3.077 2.946 0.958
Children 2 2.815 2.631 0.934
Children 3 2.946 2.770 0.940
Children 4 2.970 2.825 0.951 
# Paper: 'reached nominal steady-state levels after approximately 2 days';
# its own Table S2 ratios are 0.87-0.97.
stopifnot(all(restart$ratio > 0.8 & restart$ratio < 1.02))

Table 3: steady-state NCA

Table 3 reports mean (SD) steady-state viloxazine exposures for children (31.5 kg) and adolescents (57.25 kg) at each dose. Those values come from the empirical Bayes estimates of the observed subjects (Results ‘Final Model Evaluation’), not from a fresh draw of the population model, so they are a weaker target than Tables S2 and S3. The simulation uses the last pre-holiday interval (day 10) scaled to each dose (the model is linear).

ss_sim <- sim |> filter(missed == 1, time >= 9 * tau, time <= 10 * tau)
conc_ss <- PKNCA::PKNCAconc(ss_sim, Cc ~ time | age_group + id)
dose_ss <- events |>
  filter(missed == 1, evid == 1) |>
  select(id, time, amt, age_group)
dose_obj_ss <- PKNCA::PKNCAdose(dose_ss, amt ~ time | age_group + id)
int_ss <- data.frame(
  start = 9 * tau, end = 10 * tau,
  cmax = TRUE, cmin = TRUE, cav = TRUE, auclast = TRUE
)
nca_ss <- as.data.frame(PKNCA::pk.nca(PKNCA::PKNCAdata(conc_ss, dose_obj_ss, intervals = int_ss)))

# Arithmetic means per age group at 400 mg, scaled to each dose.
sim_means <- nca_ss |>
  group_by(age_group, PPTESTCD) |>
  summarise(m400 = mean(PPORRES), .groups = "drop") |>
  tidyr::crossing(dose = c(100, 200, 400, 600)) |>
  mutate(
    PPORRES = m400 * dose / 400,
    group = paste0(age_group, ", ", dose, " mg")
  ) |>
  select(group, PPTESTCD, PPORRES)

published_t3 <- tibble::tribble(
  ~group,                   ~cmax, ~cmin, ~cav, ~auclast,
  "Children, 100 mg",        1.60,  0.21, 0.80,    19.29,
  "Children, 200 mg",        2.83,  0.49, 1.45,    34.72,
  "Children, 400 mg",        5.61,  0.94, 2.83,    68.00,
  "Children, 600 mg",        8.89,  1.50, 4.46,   106.96,
  "Adolescents, 100 mg",     1.16,  0.14, 0.59,    14.15,
  "Adolescents, 200 mg",     2.06,  0.36, 1.07,    25.78,
  "Adolescents, 400 mg",     4.08,  0.70, 2.12,    50.80,
  "Adolescents, 600 mg",     6.49,  1.15, 3.33,    79.97
)

cmp_t3 <- nlmixr2lib::ncaComparisonTable(
  simulated = sim_means,
  reference = published_t3,
  by = "group",
  params = c("cmax", "cmin", "cav", "auclast"),
  units = c(cmax = "ug/mL", cmin = "ug/mL", cav = "ug/mL", auclast = "ug*h/mL"),
  tolerance_pct = 20
)
knitr::kable(
  cmp_t3,
  caption = "Mean steady-state viloxazine NCA: simulation vs. Table 3. * differs by >20%."
)
Mean steady-state viloxazine NCA: simulation vs. Table 3. * differs by >20%.
NCA parameter group Reference Simulated % diff
Cmax (ug/mL) Children, 100 mg 1.6 1.17 -26.9%*
Cmax (ug/mL) Children, 200 mg 2.83 2.34 -17.3%
Cmax (ug/mL) Children, 400 mg 5.61 4.68 -16.6%
Cmax (ug/mL) Children, 600 mg 8.89 7.02 -21.0%*
Cmax (ug/mL) Adolescents, 100 mg 1.16 0.771 -33.6%*
Cmax (ug/mL) Adolescents, 200 mg 2.06 1.54 -25.2%*
Cmax (ug/mL) Adolescents, 400 mg 4.08 3.08 -24.4%*
Cmax (ug/mL) Adolescents, 600 mg 6.49 4.62 -28.7%*
Cmin (ug/mL) Children, 100 mg 0.21 0.379 +80.7%*
Cmin (ug/mL) Children, 200 mg 0.49 0.759 +54.8%*
Cmin (ug/mL) Children, 400 mg 0.94 1.52 +61.4%*
Cmin (ug/mL) Children, 600 mg 1.5 2.28 +51.8%*
Cmin (ug/mL) Adolescents, 100 mg 0.14 0.264 +88.4%*
Cmin (ug/mL) Adolescents, 200 mg 0.36 0.528 +46.6%*
Cmin (ug/mL) Adolescents, 400 mg 0.7 1.06 +50.7%*
Cmin (ug/mL) Adolescents, 600 mg 1.15 1.58 +37.6%*
AUClast (ug*h/mL) Children, 100 mg 19.3 18.6 -3.4%
AUClast (ug*h/mL) Children, 200 mg 34.7 37.3 +7.3%
AUClast (ug*h/mL) Children, 400 mg 68 74.5 +9.6%
AUClast (ug*h/mL) Children, 600 mg 107 112 +4.5%
AUClast (ug*h/mL) Adolescents, 100 mg 14.2 12.6 -11.2%
AUClast (ug*h/mL) Adolescents, 200 mg 25.8 25.1 -2.5%
AUClast (ug*h/mL) Adolescents, 400 mg 50.8 50.2 -1.1%
AUClast (ug*h/mL) Adolescents, 600 mg 80 75.4 -5.7%
Cavg (ug/mL) Children, 100 mg 0.8 0.776 -3.0%
Cavg (ug/mL) Children, 200 mg 1.45 1.55 +7.1%
Cavg (ug/mL) Children, 400 mg 2.83 3.11 +9.7%
Cavg (ug/mL) Children, 600 mg 4.46 4.66 +4.4%
Cavg (ug/mL) Adolescents, 100 mg 0.59 0.523 -11.3%
Cavg (ug/mL) Adolescents, 200 mg 1.07 1.05 -2.2%
Cavg (ug/mL) Adolescents, 400 mg 2.12 2.09 -1.2%
Cavg (ug/mL) Adolescents, 600 mg 3.33 3.14 -5.7% 
t3_long <- sim_means |>
  inner_join(
    published_t3 |> pivot_longer(-group, names_to = "PPTESTCD", values_to = "paper"),
    by = c("group", "PPTESTCD")
  ) |>
  mutate(pct = 100 * (PPORRES - paper) / paper)
# Exposure (AUC0-24 and Cavg) is set by CL/F alone and reproduces Table 3.
expo <- t3_long |> filter(PPTESTCD %in% c("auclast", "cav"))
stopifnot(abs(median(expo$pct)) < 10, quantile(abs(expo$pct), 0.9) < 20)
t3_long |>
  group_by(PPTESTCD) |>
  summarise(median_pct = median(pct), .groups = "drop") |>
  rename("Parameter" = PPTESTCD, "Median difference vs. Table 3 (%)" = median_pct) |>
  knitr::kable(digits = 1)
Parameter Median difference vs. Table 3 (%)
auclast -1.8
cav -1.7
cmax -24.8
cmin 53.3

AUC0-24 and Cavg agree with Table 3 on the model’s predicted concentrations, but Cmax is about 25% lower and Cmin about 50% higher, i.e. the predicted profiles fluctuate less (about 100% versus the 160-190% that Table 3 prints). The paper’s own Monte Carlo trough medians in Table S3 are reproduced (previous section), so the model’s trough is not the problem.

The pattern is the one produced by taking Cmax and Cmin over concentrations that carry residual error: the maximum of several noisy points is biased up, the minimum biased down, while AUC and Cavg average the noise out. The check below adds the packaged combined residual error to the day-10 profiles and repeats the NCA. The paper does not state the time grid of its NCA; a 2-h grid is used here (a 1-h grid gives about 7% higher Cmax and 9% lower Cmin). The additive part does not scale with dose, so only the simulated 400 mg/day cohorts are compared.

set.seed(20211204)
ss_ruv <- ss_sim |>
  filter(time %% 2 == 0) |>
  mutate(Cc_obs = Cc * (1 + 0.29 * rnorm(n())) + 0.12 * rnorm(n()))
conc_ruv <- PKNCA::PKNCAconc(ss_ruv, Cc_obs ~ time | age_group + id)
#> Warning in assert_conc(conc, any_missing_conc = any_missing_conc): Negative
#> concentrations found
nca_ruv <- as.data.frame(PKNCA::pk.nca(PKNCA::PKNCAdata(
  conc_ruv, dose_obj_ss,
  intervals = data.frame(start = 9 * tau, end = 10 * tau, cmax = TRUE, cmin = TRUE)
)))
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc = conc): Negative concentrations found
#> Warning in assert_conc(conc = conc): Negative concentrations found
ruv_tab <- nca_ruv |>
  filter(PPTESTCD %in% c("cmax", "cmin")) |>
  group_by(age_group, PPTESTCD) |>
  summarise(sim_mean = mean(PPORRES), sim_sd = sd(PPORRES), .groups = "drop") |>
  left_join(
    tibble::tribble(
      ~age_group,    ~PPTESTCD, ~paper_mean, ~paper_sd,
      "Children",    "cmax",    5.61,        2.48,
      "Children",    "cmin",    0.94,        0.63,
      "Adolescents", "cmax",    4.08,        1.67,
      "Adolescents", "cmin",    0.70,        0.47
    ),
    by = c("age_group", "PPTESTCD")
  ) |>
  mutate(pct = 100 * (sim_mean - paper_mean) / paper_mean)
ruv_tab |>
  rename(
    "Age group" = age_group, "Parameter" = PPTESTCD,
    "Simulated mean (ug/mL)" = sim_mean, "Simulated SD" = sim_sd,
    "Table 3 mean (ug/mL)" = paper_mean, "Table 3 SD" = paper_sd,
    "Difference in mean (%)" = pct
  ) |>
  knitr::kable(digits = 2, caption = "400 mg/day steady-state Cmax and Cmin with residual error added, vs. Table 3.")
400 mg/day steady-state Cmax and Cmin with residual error added, vs. Table 3.
Age group Parameter Simulated mean (ug/mL) Simulated SD Table 3 mean (ug/mL) Table 3 SD Difference in mean (%)
Adolescents cmax 3.90 1.74 4.08 1.67 -4.43
Adolescents cmin 0.69 0.56 0.70 0.47 -2.09
Children cmax 5.77 2.45 5.61 2.48 2.80
Children cmin 1.04 0.74 0.94 0.63 10.59 
# The predicted-concentration comparison above is 25% (Cmax) and 50% (Cmin)
# off; with residual error both close to within a few percent. Read as
# variances, the residual rows push the mean Cmin to about zero.
stopifnot(all(abs(ruv_tab$pct) < 20))

Adding the residual error closes both gaps and reproduces the Table 3 SDs as well, so Table 3’s Cmax and Cmin are read as NCA over residual-perturbed concentrations. Reading the Table 2 residual rows as variances instead drives the mean Cmin to about zero, which Table 3 rules out.

Figure 2 and Figure S2: visual predictive check

Figure 2A shows the 90% prediction interval for children on 200 mg/day in study P303. The paper’s VPCs are simulations of 100 subjects from the final model, stratified by age group because weight is the retained covariate (Methods ‘Model Diagnostics’; Results ‘Final Model Evaluation’), so the vignette simulates 200 children at the children’s median weight of 31.5 kg. The VPC includes residual error. The maintainers read the band off the figure at steady state: median peak about 1.95 ug/mL, median trough about 0.55 ug/mL, 95th percentile at the peak about 4.4 ug/mL, and a 5th percentile that reaches zero at each trough.

make_vpc <- function(n, dose, wt, id_offset) {
  ids <- id_offset + seq_len(n)
  doses <- expand.grid(id = ids, time = seq(0, 13) * tau) |>
    mutate(evid = 1L, amt = dose, cmt = "depot", dvid = NA_integer_)
  obs <- expand.grid(id = ids, time = seq(13 * tau, 14 * tau, by = 0.5)) |>
    mutate(evid = 0L, amt = NA_real_, cmt = "central", dvid = 1L)
  bind_rows(doses, obs) |>
    mutate(WT = wt) |>
    arrange(id, time, desc(evid))
}
ev_vpc <- make_vpc(200, dose = 200, wt = 31.5, id_offset = 0L)

rxode2::rxSetSeed(20211203)
vpc_ipred <- rxode2::rxSolve(rxode2::zeroRe(mod, "sigma"), events = ev_vpc) |>
  as.data.frame()
#> ℹ parameter labels from comments will be replaced by 'label()'

# Add the combined residual error, Y = IPRED * (1 + propSd * e1) + addSd * e2,
# under the packaged reading (Table 2 rows are SDs) and the alternative one
# (rows are variances), with the same standard-normal draws for both.
set.seed(20211202)
e1 <- rnorm(nrow(vpc_ipred))
e2 <- rnorm(nrow(vpc_ipred))
vpc_obs <- vpc_ipred |>
  mutate(
    tad = time - 13 * tau,
    y_sd = Cc * (1 + 0.29 * e1) + 0.12 * e2,
    y_var = Cc * (1 + sqrt(0.29) * e1) + sqrt(0.12) * e2
  )

vpc_summary <- function(d, col, label) {
  d |>
    group_by(tad) |>
    summarise(
      Q05 = quantile(.data[[col]], 0.05), Q50 = median(.data[[col]]),
      Q95 = quantile(.data[[col]], 0.95), .groups = "drop"
    ) |>
    mutate(reading = label)
}
vpc_both <- bind_rows(
  vpc_summary(vpc_obs, "y_sd", "Residual rows as SD (packaged)"),
  vpc_summary(vpc_obs, "y_var", "Residual rows as variances")
)

ggplot(vpc_both, aes(tad, Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), fill = "grey80") +
  geom_line() +
  geom_hline(yintercept = 4.4, linetype = 2, colour = "red") +
  facet_wrap(~reading) +
  labs(
    x = "Time after dose at steady state (h)", y = "Viloxazine (ug/mL)",
    title = "Children, 200 mg/day: 90% prediction interval with residual error",
    caption = "Compare with Figure 2A of Nasser 2021; dashed line = digitised 95th percentile at the peak."
  )


peak_tab <- vpc_both |>
  group_by(reading) |>
  summarise(
    median_peak = max(Q50), median_trough = Q50[tad == 0],
    p95_peak = max(Q95), p05_trough = Q05[tad == 0], .groups = "drop"
  )
knitr::kable(
  peak_tab |>
    rename(
      "Reading" = reading, "Median peak" = median_peak,
      "Median trough" = median_trough, "95th pct at peak" = p95_peak,
      "5th pct at trough" = p05_trough
    ),
  digits = 2,
  caption = "Figure 2A digitised: median peak ~1.95, trough ~0.55, 95th percentile at peak ~4.4 ug/mL."
)
Figure 2A digitised: median peak ~1.95, trough ~0.55, 95th percentile at peak ~4.4 ug/mL.
Reading Median peak Median trough 95th pct at peak 5th pct at trough
Residual rows as SD (packaged) 2.14 0.59 4.75 0.05
Residual rows as variances 2.05 0.57 5.57 -0.29 
# For the gate, pool the peak window (3-6 h after the dose) rather than take
# the maximum over time points of a 200-subject percentile, which is biased up
# and varies with the simulated cohort.
peak_win <- vpc_obs |> filter(tad >= 3, tad <= 6)
p95_sd <- unname(quantile(peak_win$y_sd, 0.95))
p95_var <- unname(quantile(peak_win$y_var, 0.95))
round(c("95th pct, 3-6 h, SD reading" = p95_sd, "95th pct, 3-6 h, variance reading" = p95_var), 2)
#>       95th pct, 3-6 h, SD reading 95th pct, 3-6 h, variance reading 
#>                              4.18                              4.96
med_peak <- peak_tab$median_peak[peak_tab$reading == "Residual rows as SD (packaged)"]
# Digitising the figure is good to about 0.1-0.2 ug/mL at these levels.
stopifnot(
  abs(med_peak / 1.95 - 1) < 0.15,
  abs(p95_sd / 4.4 - 1) < 0.15,
  abs(p95_var / 4.4 - 1) > abs(p95_sd / 4.4 - 1)
)

In the metabolite VPC of Figure S2 (study P303, 200 mg/day) the median oscillates between about 0.55 and 1.3 ug/mL over each dosing interval at steady state.

met_band <- vpc_obs |>
  group_by(tad) |>
  summarise(Q50 = median(Cc_gluc), .groups = "drop") |>
  summarise(min_median = min(Q50), max_median = max(Q50))
met_band |>
  rename("Lowest median (ug/mL)" = min_median, "Highest median (ug/mL)" = max_median) |>
  knitr::kable(digits = 2, caption = "Simulated 5-HVLX-gluc median over the steady-state interval, children 200 mg/day.")
Simulated 5-HVLX-gluc median over the steady-state interval, children 200 mg/day.
Lowest median (ug/mL) Highest median (ug/mL)
0.61 1.49 
# Digitised Figure S2: about 0.55 to 1.3 ug/mL. A molar-mass factor between the
# analytes (429/237 = 1.8) would move both ends by 80%.
stopifnot(
  abs(met_band$min_median / 0.55 - 1) < 0.3,
  abs(met_band$max_median / 1.3 - 1) < 0.3
)

Assumptions and deviations

  • IIV scale. Table 2 prints the random effects without a scale. The maintainers read them as log-scale variances (NONMEM OMEGA). On that reading the closed-form median steady-state Cavg at 400 mg/day is 2.85 ug/mL for children and 2.13 ug/mL for adolescents, against Table S2 means of 2.79 and 2.06; reading them as SDs gives 3.08 and 2.26, and a mean CL/F above 100 L/h against the 6-8 L/h of Table 3.
  • Residual error scale and sharing. Table 2 prints one Additive (0.12) and one Proportional (0.29) row for the joint parent + metabolite fit. They are read as SDs, because the Figure 2A prediction interval is reproduced on that reading at the children’s median weight and overshot on the variance reading (section above). Drawing weights from the children’s distribution in Table 1 (mean 32.8, SD 8.9 kg) instead widens both bands, to a 95th percentile at the peak of about 5.1 (SD reading) and 5.9 ug/mL (variance reading), so the SD reading remains the closer one. Table 3’s Cmax and Cmin, which carry the residual error, independently support the SD reading (Table 3 section). The same pair is applied to both analytes as separate parameters with equal values; the paper does not say whether the analytes shared one error model.
  • Metabolite units. The paper states no molecular-weight correction between viloxazine (237.3 g/mol) and 5-HVLX-gluc. The metabolite state is formed 1:1 in mass and Cc_gluc is in ug/mL, as reported; the fitted CLV and CLM absorb any molar ratio. The Figure S2 metabolite median is reproduced on this basis.
  • Table 3. Table 3’s Cmax and Cmin are reproduced only when residual error is added to the profiles before the NCA (2-h grid assumed; the paper does not state its grid). On the model’s predicted concentrations Cmax is about 25% lower and Cmin about 50% higher, while AUC and Cavg agree either way.
  • Holiday windows. Tables S2 and S3 do not define their windows. The vignette uses the dosing interval before the holiday, the whole holiday period (Cavg) or its end (Cmin), and the first three dosing intervals after restarting, which is what the tables’ day-to-day pattern implies.
  • Figure 2 cohort. P303 used a 3-week titration before maintenance; the VPC here simulates steady state on a fixed 200 mg/day at the children’s median weight (31.5 kg).
  • No erratum or correction notice for doi:10.1002/jcph.1940 was found as of 2026-10-02.