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Kovalenko_2020_dupilumab

Source: vignettes/articles/Kovalenko_2020_dupilumab.Rmd
Kovalenko_2020_dupilumab.Rmd

Model and source

Population

Kovalenko 2020 pooled 16 clinical studies (N = 2115 participants; 202 healthy volunteers and 1913 patients with moderate-to-severe atopic dermatitis (AD)). Of these, 2041 participants on active treatment contributed 18,243 of 20,809 samples to the population PK analysis. Source studies include the Phase 3 AD trials R668-AD-1334 (LIBERTY AD SOLO 1), R668-AD-1416 (LIBERTY AD SOLO 2), and R668-AD-1224 (LIBERTY AD CHRONOS). The Phase 1 studies R668-AS-0907, TDU12265, PKM14161, and R668-AD-1117 were used to fit “Model 1” - the rich-data model this file implements. The paper’s main text does not tabulate detailed baseline demographics (age, sex, weight median/range, race breakdown) for the pooled cohort; these appear only in Supplementary Table S1.

The approved adult AD maintenance regimen is 600 mg SC loading dose on day 0 followed by 300 mg SC every 2 weeks (Q2W); the Kovalenko 2016 precursor publication used 75 kg as the reference body weight for the allometric effect on central volume, and the 2020 paper reuses the same equation without re-stating the reference weight.

The same information is available programmatically via readModelDb("Kovalenko_2020_dupilumab")$population.

Source trace

Every structural parameter, covariate effect, IIV element, and residual-error term below is taken from Kovalenko 2020 Table 1 (Model 1 column) or Supplementary Table S2 (IIV SDs and residual errors). A paper-to-implementation cross-walk:

Equation / parameter Value Source location
lvc (Vc, central volume) log(2.48) L Table 1, Model 1
lke (ke, linear elimination rate) log(0.0534) 1/day Table 1, Model 1
lkcp (kcp) log(0.213) 1/day Table 1, Model 1
Mpc (kcp/kpc) 0.686 Table 1, Model 1 (kpc derived: 0.213 / 0.686 = 0.310 1/day)
lka (ka, absorption rate) log(0.256) 1/day Table 1, Model 1
lmtt (MTT) log(0.105) day Table 1, Model 1
lvm (Vmax) log(1.07) mg/L/day Table 1, Model 1
Km fixed(0.01) mg/L Table 1, Model 1 (fixed, carried over from Kovalenko 2016)
lfdepot (F) log(0.643) Table 1, Model 1
e_wt_vc (WT exponent on Vc) 0.711 Table 1, Model 1 (“Vc ~ weight”)
var(etalvc) 0.192^2 = 0.036864 Supp. Table S2: omega_Vc (SD) = 0.192
var(etalke) 0.285^2 = 0.081225 Supp. Table S2: omega_ke (SD) = 0.285
var(etalka) 0.474^2 = 0.224676 Supp. Table S2: omega_ka (SD) = 0.474
var(etalvm) 0.236^2 = 0.055696 Supp. Table S2: omega_Vm (SD) = 0.236
var(etalmtt) 0.525^2 = 0.275625 Supp. Table S2: omega_MTT (SD) = 0.525, applied on log(MTT) here
CcpropSd (proportional sigma) 0.15 Supp. Table S2
CcaddSd (additive sigma) fixed(0.03) mg/L Supp. Table S2 (fixed, carried over from Kovalenko 2016)
Structure 2-cmt + 3 transit + parallel linear/MM elimination p. 758 Methods, Figure 1

The paper’s Methods section explicitly defines omega as “omega (omega, standard deviation [SD] of between-subject variability)” and sigma as “sigma (sigma, SD of measurement error)”. nlmixr2’s etalxxx ~ value syntax stores the variance (omega^2), so the Supp. Table S2 SDs are squared in ini(). The Model 1 shrinkage in SD reported by the paper (10.4% / 25.2% / 22.9% / 23.2% / 54.9% for Vc / ke / Vm / ka / MTT) is consistent with IIV-as-SD accounting.

Parameterization notes

Kovalenko 2020 parameterizes the linear elimination as a first-order rate ke * central (not as CL * Cc) and the distribution as direct rate constants kcp and kpc = kcp / Mpc (not as Q and Vp). The model file preserves this parameterization, so derived quantities are:

  • Typical clearance: CL = ke * Vc = 0.0534 * 2.48 = 0.132 L/day (matches Table 1 “CL (L/d)”).
  • Typical peripheral rate kpc = 0.213 / 0.686 = 0.310 1/day.

The etalmtt eta is applied as MTT = exp(lmtt + etalmtt) (i.e. log-normal on MTT). Supplementary Table S2 in the paper reports the random effect additively on MTT; the log-normal implementation chosen here avoids negative MTT draws during simulation and is the only deviation from the published random-effect structure.

Virtual cohort

Detailed observed demographics for the pooled cohort are not publicly reproduced in the paper’s main text. The virtual cohort below targets the labelled adult AD population by drawing body weight from a truncated normal centered on the Kovalenko 2016 reference weight of 75 kg (SD ~18 kg, limits 40-165 kg), which matches typical Phase 3 AD trial demographics reported in the Simpson 2016 SOLO / Blauvelt 2017 CHRONOS publications.

set.seed(20260418)
n_subj <- 400

cohort <- tibble::tibble(
  id = seq_len(n_subj),
  WT = pmin(pmax(rnorm(n_subj, mean = 75, sd = 18), 40), 165)
)

# Labelled AD regimen: 600 mg SC loading dose on day 0, 300 mg SC Q2W
# for 12 additional doses -> study window 0-182 days. By dose 10+ the
# profile is close to steady state (typical half-life ~2-3 weeks).
load_dose <- 600
maint_dose <- 300
tau <- 14
n_maint <- 12
dose_days <- c(0, seq(tau, tau * n_maint, by = tau))
amt_vec <- c(load_dose, rep(maint_dose, n_maint))

ev_dose <- cohort |>
  tidyr::crossing(time = dose_days) |>
  dplyr::arrange(id, time) |>
  dplyr::group_by(id) |>
  dplyr::mutate(amt = amt_vec, cmt = "depot", evid = 1L) |>
  dplyr::ungroup()

obs_days <- sort(unique(c(
  seq(0, tau * (n_maint + 1), by = 1),
  dose_days + 0.25,
  dose_days + 1,
  dose_days + 3
)))

ev_obs <- cohort |>
  tidyr::crossing(time = obs_days) |>
  dplyr::mutate(amt = 0, cmt = NA_character_, evid = 0L)

events <- dplyr::bind_rows(ev_dose, ev_obs) |>
  dplyr::arrange(id, time, dplyr::desc(evid)) |>
  dplyr::select(id, time, amt, cmt, evid, WT)

Simulation 

mod <- rxode2::rxode2(readModelDb("Kovalenko_2020_dupilumab"))
#> ℹ parameter labels from comments will be replaced by 'label()'
sim <- rxode2::rxSolve(mod, events = events, keep = "WT")

Figure replication - Cc-vs-time profiles

Kovalenko 2020 Figure 5 illustrates simulated median concentration-time profiles of functional dupilumab for several SC maintenance regimens (qw, q2w, q4w, q8w). The figure below reproduces the labelled adult AD regimen (600 mg SC loading + 300 mg SC Q2W) as 5th/50th/95th percentile bands across the virtual cohort, spanning ~13 dosing cycles.

vpc <- sim |>
  dplyr::filter(!is.na(Cc), time > 0) |>
  dplyr::group_by(time) |>
  dplyr::summarise(
    Q05 = quantile(Cc, 0.05, na.rm = TRUE),
    Q50 = quantile(Cc, 0.50, na.rm = TRUE),
    Q95 = quantile(Cc, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(vpc, aes(time, Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.2, fill = "#4682b4") +
  geom_line(colour = "#4682b4", linewidth = 0.8) +
  geom_vline(xintercept = dose_days, linetype = "dotted", colour = "grey70") +
  scale_y_continuous(limits = c(0, NA)) +
  labs(
    x = "Time (days)",
    y = "Dupilumab Cc (mg/L)",
    title = "Simulated 5-50-95 percentile profile; 600 mg SC load then 300 mg SC Q2W",
    caption = "Virtual AD cohort (N = 400); WT ~N(75, 18) kg, truncated 40-165 kg."
  ) +
  theme_minimal()

Steady-state cycle (dose 13)

Zoomed-in view of the final Q2W cycle (days 168-182) to isolate the steady-state peak, trough, and AUC_tau used by the NCA below.

ss_start <- tau * n_maint # day 168 (time of dose 13)
ss_end <- ss_start + tau # day 182

ss_summary <- sim |>
  dplyr::filter(time >= ss_start, time <= ss_end, !is.na(Cc)) |>
  dplyr::group_by(time) |>
  dplyr::summarise(
    Q05 = quantile(Cc, 0.05, na.rm = TRUE),
    Q50 = quantile(Cc, 0.50, na.rm = TRUE),
    Q95 = quantile(Cc, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(ss_summary, aes(time - ss_start, Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.2, fill = "#b4464b") +
  geom_line(colour = "#b4464b", linewidth = 0.8) +
  labs(
    x = "Time after final dose (days)",
    y = "Dupilumab Cc (mg/L)",
    title = "Steady-state Q2W cycle (dose 13 of 13)",
    caption = "Median and 90% prediction interval over one 14-day dosing interval."
  ) +
  theme_minimal()

PKNCA validation

Non-compartmental analysis of the steady-state Q2W interval (days 168-182). Compute Cmax, Cmin (Ctrough at end of tau), AUC_tau, and average concentration per simulated subject.

nca_conc <- sim |>
  dplyr::filter(time >= ss_start, time <= ss_end, !is.na(Cc)) |>
  dplyr::mutate(time_nom = time - ss_start,
    treatment = "300mg_Q2W_SS") |>
  dplyr::select(id, time = time_nom, Cc, treatment)

nca_dose <- cohort |>
  dplyr::mutate(time = 0, amt = maint_dose, treatment = "300mg_Q2W_SS") |>
  dplyr::select(id, time, amt, treatment)

conc_obj <- PKNCA::PKNCAconc(nca_conc, Cc ~ time | treatment + id)
dose_obj <- PKNCA::PKNCAdose(nca_dose, amt ~ time | treatment + id)

intervals <- data.frame(
  start = 0,
  end = tau,
  cmax = TRUE,
  cmin = TRUE,
  auclast = TRUE,
  cav = TRUE
)

nca_res <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals))
#>  ■■■■■■■■■■■■                      38% |  ETA:  2s
summary(nca_res)
#>  start end    treatment   N     auclast        cmax        cmin         cav
#>      0  14 300mg_Q2W_SS 400 1190 [43.9] 95.0 [41.9] 70.4 [49.2] 85.1 [43.9]
#> 
#> Caption: auclast, cmax, cmin, cav: geometric mean and geometric coefficient of variation; N: number of subjects

Comparison against published typical steady-state exposure

Kovalenko 2020 does not tabulate point estimates for steady-state Cmax, Ctrough, or AUC_tau in the main text; Figure 5 shows simulated medians qualitatively. Dupilumab FDA labelling and follow-on PK publications report typical steady-state trough concentrations of ~70-80 mg/L for a 75-kg adult on the 600-mg-load + 300-mg-Q2W SC regimen. The typical-value (“population typical”) prediction with IIV zeroed out provides a direct self-consistency check:

mod_typical <- mod |> rxode2::zeroRe()

ev_typical <- events |>
  dplyr::filter(id == 1L) |>
  dplyr::mutate(WT = 75)

sim_typical <- rxode2::rxSolve(
  mod_typical, events = ev_typical, keep = "WT"
) |>
  as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalvc', 'etalke', 'etalka', 'etalvm', 'etalmtt'

ss_typical <- sim_typical |>
  dplyr::filter(time >= ss_start, time <= ss_end, !is.na(Cc))

typical_summary <- tibble::tibble(
  metric = c("Cmax (mg/L)", "Cmin/Ctrough (mg/L)",
    "Cavg (mg/L)", "AUC_tau (day*mg/L)"),
  typical_value = c(
    max(ss_typical$Cc),
    min(ss_typical$Cc),
    mean(ss_typical$Cc),
    sum(diff(ss_typical$time) *
      (ss_typical$Cc[-length(ss_typical$Cc)] +
        ss_typical$Cc[-1]) / 2)
  )
)
knitr::kable(typical_summary, digits = 2,
  caption = "Typical-subject steady-state exposure (WT = 75 kg; IIV zeroed).")
Typical-subject steady-state exposure (WT = 75 kg; IIV zeroed).
metric typical_value
Cmax (mg/L) 92.79
Cmin/Ctrough (mg/L) 70.04
Cavg (mg/L) 82.26
AUC_tau (day*mg/L) 1173.27

Assumptions and deviations

  • Kovalenko 2020 Model 1 uses a ke/kcp/kpc parameterization rather than CL/Q/Vp. This model file preserves the original parameterization verbatim. Typical values can be cross-checked against Table 1’s derived CL = ke * Vc = 0.132 L/day.
  • Km and F were reported as fixed in Table 1 Model 1, with values carried over from the earlier Kovalenko 2016 model; CcaddSd was likewise fixed at 0.03 mg/L.
  • The etalmtt eta is applied as log-normal on MTT (MTT = exp(lmtt + etalmtt)), whereas Supplementary Table S2 implements the random effect additively on MTT. The log-normal form prevents non-physical negative MTT draws during simulation. All other etas match the paper’s random-effect structure directly.
  • IIV (omega) is reported in Kovalenko 2020 as a standard deviation, per the Methods definition. Values in ini() are squared to yield the variance that nlmixr2 stores with the ~ operator. An earlier version of this file stored the SDs directly on the RHS (i.e. as variances), which would understate IIV magnitude at the mAb-relevant scale; the current file is the corrected form.
  • The reference body weight (75 kg) is inherited from Kovalenko 2016 (doi:10.1002/psp4.12136); Kovalenko 2020 does not restate the reference weight. See the file header comment for details.
  • Demographic details (age, sex, race) are not used by the Model 1 implementation (only WT enters the covariate model) and were not re-simulated in the virtual cohort.
  • Kovalenko 2020 does not publish numerical Cmax / Cmin / AUC_tau at steady state, so the PKNCA summary here is a self-consistency check of the implemented model against the visual appearance of Figure 5 rather than a back-to-paper numerical comparison.
  • No unit conversion is required between the dosing amount (mg) and the concentration unit (mg/L) because mg/L is the natural unit of central/vc here.