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Anakinra (Urien 2013)

Source: vignettes/articles/Urien_2013_anakinra.Rmd
Urien_2013_anakinra.Rmd

Model and source

  • Citation: Urien S, Bardin C, Bader-Meunier B, Mouy R, Compeyrot-Lacassagne S, Foissac F, Florkin B, Wouters C, Neven B, Treluyer J-M, Quartier P (2013). Anakinra pharmacokinetics in children and adolescents with systemic-onset juvenile idiopathic arthritis and autoinflammatory syndromes. BMC Pharmacology and Toxicology 14:40. doi:10.1186/2050-6511-14-40.
  • Description: One-compartment population pharmacokinetic model for subcutaneous anakinra (recombinant nonglycosylated human IL-1 receptor antagonist) in 87 children and adolescents (8 months to 21 years, 4.3 to 83 kg) treated for systemic-onset juvenile idiopathic arthritis (SJIA) and diverse autoinflammatory syndromes (Urien 2013). First-order absorption (Ka) into a single central compartment with first-order elimination; apparent clearance CL/F and apparent volume V/F are allometrically scaled to body weight with estimated power exponents (0.47 on CL/F and 0.76 on V/F, reference 70 kg). Inter-individual variability is reported on CL/F and between-occasion variability on V/F; no other covariate effect (age, sex, co-administered anti-inflammatory drugs) was retained.
  • Article: https://doi.org/10.1186/2050-6511-14-40

Population

The model was developed in 87 children and adolescents (4.3-83 kg, 8 months to 21 years of age) drawn from two pooled cohorts: 22 systemic-onset juvenile idiopathic arthritis (SJIA) patients enrolled in the ANAJIS phase IIB trial (Quartier 2011) and 65 patients with diverse autoinflammatory conditions (cryopyrin-associated periodic syndromes, mevalonate kinase deficiency, TNF-receptor associated periodic syndromes, familial mediterranean fever, genetically undetermined autoinflammatory conditions) treated at the same centre. ANAJIS-trial SJIA patients received subcutaneous anakinra at 2 mg/kg once daily (maximum 100 mg); autoinflammatory patients received 2-10 mg/kg once daily. A total of 148 plasma anakinra concentrations were available for pharmacokinetic modelling, with four below-the-limit-of-quantification (40 ng/mL) observations treated as left-censored (Urien 2013 Results, Population pharmacokinetic modeling).

The same information is available programmatically via the model’s population metadata (readModelDb("Urien_2013_anakinra")$population).

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Urien_2013_anakinra.R. The table below collects them in one place for review.

Equation / parameter Value Source location
lka (Ka) 0.38 1/h Urien 2013 Table 1 (RSE 19 %)
lcl (CL/F at 70 kg) 6.24 L/h Urien 2013 Table 1 (RSE 8 %)
lvc (V/F at 70 kg) 65.2 L Urien 2013 Table 1 (RSE 12 %)
e_wt_cl (beta_CL) 0.47 Urien 2013 Table 1 (RSE 14 %)
e_wt_vc (beta_V) 0.76 Urien 2013 Table 1 (RSE 16 %)
etalcl (omega_CL) 0.28 (SD) -> 0.0784 (variance) Urien 2013 Table 1 (RSE 15 %)
etalvc (gamma_V) 0.47 (SD) -> 0.2209 (variance) Urien 2013 Table 1 (RSE 17 %); encoded as BSV (see Assumptions and deviations)
addSd (epsilon) 0.072 mg/L Urien 2013 Table 1 (RSE 10 %)
d/dt(depot) n/a Methods, Pharmacokinetic modelling (first-order SC absorption)
d/dt(central) n/a Methods, Pharmacokinetic modelling (linear elimination)
Allometric CL/F CL/F = 6.24 * (BW/70)^0.47 Urien 2013 Results, Population PK modeling (equivalent linear form CL/F = 0.847 * BW^0.47)
Allometric V/F V/F = 65.2 * (BW/70)^0.76 Urien 2013 Results, Population PK modeling (equivalent linear form V/F = 2.581 * BW^0.76)

Virtual cohort

Original observed concentrations are not publicly available. The simulations below use a virtual paediatric cohort whose body-weight distribution approximates the published range (4.3-83 kg, overall median 21 kg; Urien 2013 Results). To reproduce Figure 1 (anakinra time-courses following a single 2 mg/kg subcutaneous dose), a single dose is given at t = 0 and concentration is observed densely over 0-25 h. To reproduce Figure 4 (Css vs body weight at 2 mg/kg/day), once-daily dosing is given out to steady state.

set.seed(20130805L)  # Urien 2013 publication date

# Body weights spanning the reported range, with a roughly log-uniform
# spread to populate the small / large extremes that drive the
# allometric scaling.
n_subj  <- 200L
weights <- exp(runif(n_subj, log(5), log(80)))   # 5 to 80 kg

cohort <- tibble(id = seq_len(n_subj), WT = weights)
summary(cohort$WT)
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>   5.074  11.513  21.004  27.471  39.243  76.426
# Figure 1: single 2 mg/kg SC dose, observe 0-25 h post-dose.
sample_times <- seq(0, 25, by = 0.25)

events_single <- cohort |>
  rowwise() |>
  do({
    id_i <- .$id
    wt_i <- .$WT
    dose_i <- min(2 * wt_i, 100)              # 2 mg/kg, max 100 mg
    bind_rows(
      tibble(id = id_i, WT = wt_i, time = 0,
             evid = 1L, cmt = "depot", amt = dose_i),
      tibble(id = id_i, WT = wt_i, time = sample_times,
             evid = 0L, cmt = NA_character_, amt = 0)
    )
  }) |>
  ungroup() |>
  arrange(id, time, desc(evid))

Simulation 

mod <- readModelDb("Urien_2013_anakinra")

sim_single <- rxode2::rxSolve(
  mod, events = events_single,
  keep = c("WT")
) |>
  as.data.frame()
#> ℹ parameter labels from comments will be replaced by 'label()'

Replicate published figures

Figure 1 – anakinra concentration-time course after a single 2 mg/kg SC dose

Urien 2013 Figure 1 overlays the observed concentrations (87 children) on the model-predicted median and 5th / 95th percentiles after the once-daily 2 mg/kg SC dose. The simulation below uses the packaged model with between-subject variability (etalcl) and the BSV-encoded V/F variance (see Assumptions and deviations) to produce the same VPC bands.

fig1 <- sim_single |>
  filter(time > 0) |>
  group_by(time) |>
  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(fig1, aes(time, Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.25) +
  geom_line() +
  scale_y_log10() +
  labs(
    x = "Time after dose (hours)",
    y = "Plasma anakinra (mg/L)",
    title = "Figure 1 -- single-dose VPC at 2 mg/kg SC",
    caption = "Replicates Figure 1 of Urien 2013."
  )

Figure 4 – steady-state Css as a function of body weight at 2 mg/kg/day

Urien 2013 Figure 4 plots the mean anakinra steady-state concentration (Css) reached on once-daily SC dosing as a function of body weight, identifying the daily dose required to hit the recommended Css = 0.4 mg/L target. We reproduce the underlying Css-vs-BW relationship by simulating each subject to steady state at 2 mg/kg/day with the typical parameters (between-subject variability zeroed) and reading off the average concentration over the final dosing interval.

# Steady-state simulation at 2 mg/kg/day (max 100 mg) for 30 days; the
# absorption / elimination time scale (Ka = 0.38 1/h; kel = CL/F over V/F
# = 6.24 / 65.2 = 0.096 1/h; t1/2 = 7.2 h) reaches steady state in well
# under a week, so 30 days is conservative.
n_days  <- 30
tau_h   <- 24
ndoses  <- n_days

# Use a deterministic copy of the model for the typical-value sweep.
mod_typical <- rxode2::zeroRe(mod)
#> ℹ parameter labels from comments will be replaced by 'label()'

ss_events <- cohort |>
  rowwise() |>
  do({
    id_i <- .$id
    wt_i <- .$WT
    dose_i <- min(2 * wt_i, 100)
    dose_rows <- tibble(
      id = id_i, WT = wt_i,
      time = seq(0, by = tau_h, length.out = ndoses),
      evid = 1L, cmt = "depot", amt = dose_i
    )
    obs_rows <- tibble(
      id = id_i, WT = wt_i,
      time = seq((n_days - 1) * tau_h, n_days * tau_h, by = 0.5),
      evid = 0L, cmt = NA_character_, amt = 0
    )
    bind_rows(dose_rows, obs_rows)
  }) |>
  ungroup() |>
  arrange(id, time, desc(evid))

sim_ss <- rxode2::rxSolve(
  mod_typical, events = ss_events,
  keep = c("WT")
) |>
  as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc'
#> Warning: multi-subject simulation without without 'omega'

# Average Cc over the final 24-hour dosing interval is Css.
ss_summary <- sim_ss |>
  filter(time >= (n_days - 1) * tau_h, time <= n_days * tau_h) |>
  group_by(id, WT) |>
  summarise(Css = mean(Cc, na.rm = TRUE), .groups = "drop")

ggplot(ss_summary, aes(WT, Css)) +
  geom_point(alpha = 0.5) +
  geom_hline(yintercept = 0.4, linetype = "dashed") +
  scale_x_log10() +
  labs(
    x = "Body weight (kg)",
    y = "Steady-state anakinra Css (mg/L) at 2 mg/kg/day SC",
    title = "Figure 4 (underlying Css curve) -- 2 mg/kg/day SC",
    caption = paste(
      "Replicates the Css-vs-body-weight relationship",
      "from Figure 4 of Urien 2013.",
      "Dashed line: recommended Css = 0.4 mg/L."
    )
  )

PKNCA validation

Urien 2013 does not publish NCA parameters of its own (validation is via the prediction-vs-observation overlays in Figures 1 and 2, NPDE residuals, and the dosing simulations in Figures 3 and 4). We use PKNCA to compute single-dose Cmax / Tmax / AUC0-inf and steady-state AUC0-tau on simulated cohorts grouped by body-weight stratum so the resulting NCA table can be sanity-checked against the textbook relations AUC = dose / CL and Css = dose_rate / CL.

sim_single_nca <- sim_single |>
  filter(!is.na(Cc), time > 0) |>
  mutate(wt_stratum = cut(WT, c(0, 10, 25, 50, 100),
                          labels = c("<10 kg", "10-25 kg",
                                     "25-50 kg", ">50 kg"))) |>
  select(id, time, Cc, wt_stratum)

dose_single <- events_single |>
  filter(evid == 1) |>
  mutate(wt_stratum = cut(WT, c(0, 10, 25, 50, 100),
                          labels = c("<10 kg", "10-25 kg",
                                     "25-50 kg", ">50 kg"))) |>
  select(id, time, amt, wt_stratum)

conc_obj <- PKNCA::PKNCAconc(
  sim_single_nca, Cc ~ time | wt_stratum + id,
  concu = "mg/L", timeu = "h"
)
dose_obj <- PKNCA::PKNCAdose(
  dose_single, amt ~ time | wt_stratum + id,
  doseu = "mg"
)

intervals <- data.frame(
  start       = 0,
  end         = Inf,
  cmax        = TRUE,
  tmax        = TRUE,
  aucinf.obs  = TRUE,
  half.life   = TRUE
)

nca_res <- PKNCA::pk.nca(
  PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals)
)
#> Warning: Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
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#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
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#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
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#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
nca_summary <- summary(nca_res)
knitr::kable(
  nca_summary,
  caption = paste(
    "Single-dose NCA parameters by body-weight stratum",
    "(2 mg/kg SC, simulated cohort)."
  )
)
Single-dose NCA parameters by body-weight stratum (2 mg/kg SC, simulated cohort).
Interval Start Interval End wt_stratum N Cmax (mg/L) Tmax (h) Half-life (h) AUCinf,obs (h*mg/L)
0 Inf <10 kg 34 0.614 [36.6] 3.50 [2.25, 5.50] 3.99 [2.10] NC
0 Inf 10-25 kg 84 0.806 [32.3] 4.00 [1.75, 6.75] 5.39 [3.15] NC
0 Inf 25-50 kg 47 0.943 [32.3] 4.75 [2.75, 7.25] 8.15 [4.16] NC
0 Inf >50 kg 35 1.14 [33.8] 4.75 [2.50, 6.50] 7.27 [3.37] NC

Comparison against the textbook closed-form predictions

For a one-compartment linear model the relation AUC0-inf = dose / (CL/F) holds for any subject; at steady state on once-daily dosing the average concentration is Css = dose / (tau * (CL/F)). For the typical 21 kg patient (median weight of both cohorts), the model gives:

wt_typical  <- 21
cl_typical  <- 6.24 * (wt_typical / 70)^0.47       # L/h
vc_typical  <- 65.2 * (wt_typical / 70)^0.76       # L
dose        <- 2 * wt_typical                       # mg
tau_h       <- 24
auc_pred    <- dose / cl_typical                    # mg*h/L
css_pred    <- dose / (tau_h * cl_typical)          # mg/L
t_half_pred <- log(2) * vc_typical / cl_typical     # h

tibble::tibble(
  parameter = c("CL/F (L/h)", "V/F (L)",
                "AUC0-inf single dose (mg*h/L)",
                "Css at 2 mg/kg/day (mg/L)",
                "Terminal half-life (h)"),
  predicted = c(cl_typical, vc_typical,
                auc_pred, css_pred, t_half_pred)
) |>
  knitr::kable(digits = 3,
               caption = paste(
                 "Closed-form predictions for a 21 kg patient at",
                 "2 mg/kg SC daily."))
Closed-form predictions for a 21 kg patient at 2 mg/kg SC daily.
parameter predicted
CL/F (L/h) 3.543
V/F (L) 26.113
AUC0-inf single dose (mg*h/L) 11.853
Css at 2 mg/kg/day (mg/L) 0.494
Terminal half-life (h) 5.108

The predicted Css ~ 0.48 mg/L at 2 mg/kg/day in a 21 kg patient is consistent with the Urien 2013 Figure 4 dosing curve, which places the 2 mg/kg/day recommendation just above the 0.4 mg/L target across the 10-50 kg body-weight range.

Assumptions and deviations

  • PD model (CRP indirect response with mixture) deferred. Urien 2013 also reports a population PD model on C-reactive protein (CRP) in 22 ANAJIS SJIA patients (paper Methods “Pharmacodynamic modelling” and Table 2). The PD model is an indirect-response model with anakinra inhibiting the response production rate (kTR * R0 * [1 - C/(C50+C)]) combined with a mixture over two subpopulations: responders with high baseline (R0 = 141 mg/L) and large CRP decrease, and a second group with low baseline (R0 = 37.9 mg/L), small CRP decrease, and a delayed loss of effect modelled by an empirical resistance function Resis = exp(-kRESI * t) multiplying the inhibition term. Encoding this in nlmixr2 simultaneously requires (a) a covariate-flag representation of the Monolix subject-level mixture assignment (a non-trivial change of structure – see the precedent in Sherwin_2012_risperidone.R for a 3-subpopulation case), (b) a new canonical parameter name for the resistance rate constant kRESI (not in references/parameter-names.md), and (c) handling of the paper’s log10-additive residual error on CRP. The Urien 2013 PD model is therefore deferred to a follow-up extraction; the PK model is delivered here as the headline contribution of the paper (“This is the first pharmacokinetic study of anakinra in children”, Urien 2013 Discussion).
  • BOV on V/F encoded as BSV. Urien 2013 Table 1 reports a single between-occasion variability (omega 0.47 SD) on V/F and a single between-subject variability (omega 0.28 SD) on CL/F. The packaged model encodes the BOV on V/F as an extra BSV term (etalvc, variance 0.2209) so single-subject simulations exhibit V/F variability that is representative of the published spread. A faithful BOV encoding would require subject + occasion indexed random effects driven by an OCC covariate column; this is feasible (see Barnett_2018_coproporphyrin_I.R for the per-occasion-eta idiom) but out of scope for the present extraction. Users simulating from this model should treat the V/F spread as a simulation-level approximation, not a between-occasion forecast.
  • Allometric exponents estimated, not fixed at 0.75 / 1. Urien 2013 retained the estimated allometric exponents (0.47 on CL/F, 0.76 on V/F) rather than the theoretical 0.75 / 1.0 because anakinra is a 153-amino-acid peptide whose values diverged from the textbook expectations (Discussion). The model file encodes both exponents as point estimates without fixed() wrapping, mirroring the paper’s decision to treat them as estimated.
  • Cohort sex count discrepancy in the source. Urien 2013 Results reports “A total of 87 children (32 girls, 52 boys)” – 32 + 52 = 84 rather than 87. The population$sex_female_pct field uses the reported 32 girls / 87 total = 36.8 %, with a note in population$notes. Three patients with unknown / unreported sex is one possible explanation; the original record is not on disk to resolve.
  • Variability scale interpretation. Urien 2013 Table 1 reports eta and gamma without explicitly stating whether the column is SD or variance. The estimates (eta_CL 0.28, gamma_V 0.47) are interpreted as Monolix omega (SD of the log-normal random effect), consistent with Monolix v3.2 default output (the version named in the paper); the ini() entries store the corresponding variances (0.0784, 0.2209).
  • Residual error on plasma anakinra is additive only. Urien 2013 retained an additive residual variance (epsilon = 0.072 mg/L) without a proportional component for the PK model. The model observation equation is Cc ~ add(addSd). Concentrations below the 40 ng/mL LOQ were treated as left-censored in the paper’s fit; this is a feature of the estimation step and not reproduced for forward-simulation use.