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Narwal_2013_sifalimumab

Source: vignettes/articles/Narwal_2013_sifalimumab.Rmd
Narwal_2013_sifalimumab.Rmd

Model and source

  • Citation: Narwal R, Roskos LK, Robbie GJ. Population pharmacokinetics of sifalimumab, an investigational anti-interferon-alpha monoclonal antibody, in systemic lupus erythematosus. Clin Pharmacokinet. 2013;52(11):1017-1027. doi:[10.1007/s40262-013-0085-2](https://doi.org/10.1007/s40262-013-0085-2)
  • Article (open access): https://pmc.ncbi.nlm.nih.gov/articles/PMC3824374/
  • Description: Two-compartment linear population PK model for sifalimumab (anti-IFN-alpha IgG1 monoclonal antibody) in adult patients with systemic lupus erythematosus (SLE).
  • Modality: Fully human IgG1-kappa therapeutic monoclonal antibody, intravenous infusion over 30-60 minutes.

Sifalimumab is a fully human IgG1-kappa mAb that neutralises a majority of the subtypes of human interferon-alpha. Narwal 2013 developed the population PK model from the phase Ib MI-CP152 study (NCT00482989), a multicentre, randomised, placebo-controlled, dose-escalation trial in which 121 SLE patients received escalating IV doses of 0.3, 1, 3, or 10 mg/kg every 14 days for up to 14 doses. The final model is the single structural model of record in the paper — the authors describe a base model and one final model with covariates; no alternative candidate models are presented.

The structural model is a two-compartment linear model with first-order elimination (NONMEM ADVAN3 / TRANS4; Narwal 2013 Section 2.3). A target-mediated elimination component was not necessary because the soluble target (IFN-alpha) is in stoichiometric excess only at sub-therapeutic concentrations.

Population

The final-model population was 120 SLE patients from the MI-CP152 phase Ib study (Narwal 2013 Table 1 / Section 3.1):

  • Treatment cohorts: 26 at 0.3 mg/kg, 25 at 1 mg/kg, 27 at 3 mg/kg, 42 at 10 mg/kg.
  • Sex: 114 female (95%), 6 male.
  • Region: 85 from North America (71%), 35 from South America (29%).
  • Baseline body weight: 43.1-120 kg (median 73, mean 76 +/- 19).
  • Age: 18-71 years (median 43, mean 42 +/- 11).
  • Baseline SLEDAI score: 2-34 (median 10).
  • Baseline 21-gene IFN signature (BGENE21): 0.63-87 (median 33).
  • One 10 mg/kg subject was excluded from the analysis due to very low observed serum concentrations.

A total of 2,370 serum concentrations were available (mean ~20 samples per subject over up to 1 year). The lower limit of quantitation was 1.25 ug/mL (Narwal 2013 Section 2.2).

The same metadata is available programmatically via readModelDb("Narwal_2013_sifalimumab")$population.

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Narwal_2013_sifalimumab.R. The table below collects them in one place for review.

Parameter (model name) Value Source
lcl (CL, L/day) log(0.176) Table 2, theta1 = 0.176 L/day (reported as 176 mL/day)
lvc (V1, L) log(2.90) Table 2, theta2 = 2.90 L
lvp (V2, L) log(2.12) Table 2, theta3 = 2.12 L
lq (Q, L/day) log(0.171) Table 2, theta4 = 0.171 L/day
e_wt_cl 0.481 Table 2, theta5 (Eq. 3)
e_bgene21_cl 0.0558 Table 2, theta6 (Eq. 3)
e_cohdose_cl 0.0542 Table 2, theta7 (Eq. 3)
e_steroid_cl 0.195 Table 2, theta8 (Eq. 3)
e_wt_v1 0.489 Table 2, theta9 (Eq. 4)
e_wt_v2 0.646 Table 2, theta10 (Eq. 5)
IIV block etalcl/etalvc/etalvp lower-tri c(0.075478, 0.046354, 0.091758, 0, 0.021369, 0.289979) Table 2 %CVs (28/31/58) and correlations (CL-V1 0.557, V1-V2 0.131)
etalq 0.408195 Table 2, Q %CV = 71%
propSd 0.275 Table 2, residual error CV 27.5%
d/dt(central) + d/dt(peripheral1) two-compartment IV Section 2.3 (NONMEM ADVAN3 TRANS4)

Narwal 2013 final-model equations (paper’s numbering):

CL=θ1⋅(WT/75)θ5⋅(BGENE21/32)θ6⋅(Dose/1)θ7⋅(1+θ8⋅BSTEROID)(Eq. 3) \text{CL} = \theta_1 \cdot (\text{WT}/75)^{\theta_5} \cdot (\text{BGENE21}/32)^{\theta_6} \cdot (\text{Dose}/1)^{\theta_7} \cdot (1 + \theta_8 \cdot \text{BSTEROID}) \quad (\text{Eq. 3})

V1=θ2⋅(WT/75)θ9(Eq. 4) V_1 = \theta_2 \cdot (\text{WT}/75)^{\theta_9} \quad (\text{Eq. 4})

V2=θ3⋅(WT/75)θ10(Eq. 5) V_2 = \theta_3 \cdot (\text{WT}/75)^{\theta_{10}} \quad (\text{Eq. 5})

Q=θ4(Eq. 6) Q = \theta_4 \quad (\text{Eq. 6})

The %CV-to-variance conversion uses ω2=log(1+CV2)\omega^2 = \log(1 + CV^2) and covariances use cov=r⋅ωi2⋅ωj2\operatorname{cov} = r \cdot \sqrt{\omega^2_i \cdot \omega^2_j}. The CL-V2 correlation is not reported in Table 2 and is therefore taken as zero in the 3x3 OMEGA block.

Virtual cohort

Original observed concentrations are not publicly available. The simulations below use a virtual cohort whose body-weight distribution approximates the MI-CP152 population (median 73 kg, range 43.1-120). All subjects are assigned the median BGENE21 of 33, set to STEROID = 0 (no baseline steroid use), and stratified into the four dose cohorts that matched the phase Ib design.

set.seed(2013)
n_per_cohort <- 50
cohorts <- c(0.3, 1, 3, 10)

cohort <- tibble::tibble(
  ID       = seq_len(length(cohorts) * n_per_cohort),
  COHDOSE  = rep(cohorts, each = n_per_cohort),
  WT       = pmin(pmax(rlnorm(length(cohorts) * n_per_cohort,
                              meanlog = log(73), sdlog = 0.22),
                       43.1), 120),
  BGENE21  = 33,
  STEROID  = 0
)

A Q14D dosing schedule of 14 infusions (to match MI-CP152) is used. Concentration observations are dense in the first dose interval (every 2 hours) and daily thereafter to capture terminal decline through Day 350.

infusion_dur_d <- 45 / 60 / 24  # 45-minute infusion, in days
dose_times_d   <- seq(0, by = 14, length.out = 14)
obs_times_d    <- sort(unique(c(
  seq(0, 1, by = 2/24),
  seq(1, 14, by = 0.5),
  seq(14, 196, by = 1),
  seq(196, 350, by = 7)
)))

build_events <- function(pop) {
  d_dose <- pop |>
    dplyr::mutate(AMT = WT * COHDOSE) |>
    tidyr::crossing(TIME = dose_times_d) |>
    dplyr::mutate(EVID = 1, CMT = "central",
                  DUR = infusion_dur_d, DV = NA_real_)
  d_obs <- pop |>
    tidyr::crossing(TIME = obs_times_d) |>
    dplyr::mutate(AMT = NA_real_, EVID = 0, CMT = "central",
                  DUR = NA_real_, DV = NA_real_)
  dplyr::bind_rows(d_dose, d_obs) |>
    dplyr::arrange(ID, TIME, dplyr::desc(EVID)) |>
    as.data.frame()
}

events <- build_events(cohort)

Simulation 

mod <- readModelDb("Narwal_2013_sifalimumab")
sim <- rxode2::rxSolve(mod, events = events, returnType = "data.frame")
#> ℹ parameter labels from comments will be replaced by 'label()'
sim$treatment <- paste0(sim$COHDOSE, " mg/kg Q14D")

For deterministic typical-value profiles (Narwal 2013 Fig. 2 median line), the random effects are zeroed out:

mod_typical <- rxode2::zeroRe(mod)
#> ℹ parameter labels from comments will be replaced by 'label()'
sim_typical <- rxode2::rxSolve(mod_typical, events = events,
                               returnType = "data.frame")
#> ℹ omega/sigma items treated as zero: 'etalvp', 'etalvc', 'etalcl', 'etalq'
#> Warning: multi-subject simulation without without 'omega'
sim_typical$treatment <- paste0(sim_typical$COHDOSE, " mg/kg Q14D")

Replicate Figure 2 — VPC by dose cohort

Narwal 2013 Fig. 2 displays a visual predictive check of serum concentrations stratified by dose cohort (0.3, 1, 3, 10 mg/kg Q14D) with observed median and 5th/95th percentiles overlaid on simulated 90% prediction intervals. The chunk below reproduces the simulation side of the VPC.

sim_vpc <- sim |>
  dplyr::filter(time > 0, !is.na(Cc)) |>
  dplyr::group_by(treatment, time) |>
  dplyr::summarise(
    q05 = stats::quantile(Cc, 0.05, na.rm = TRUE),
    q50 = stats::quantile(Cc, 0.50, na.rm = TRUE),
    q95 = stats::quantile(Cc, 0.95, na.rm = TRUE),
    .groups = "drop"
  ) |>
  dplyr::mutate(treatment = factor(
    treatment,
    levels = c("0.3 mg/kg Q14D", "1 mg/kg Q14D",
               "3 mg/kg Q14D", "10 mg/kg Q14D")
  ))

ggplot(sim_vpc, aes(time, q50)) +
  geom_ribbon(aes(ymin = q05, ymax = q95), alpha = 0.2, fill = "steelblue") +
  geom_line(colour = "steelblue", linewidth = 0.8) +
  facet_wrap(~ treatment, scales = "free_y") +
  labs(
    x = "Time (days)",
    y = expression(Sifalimumab~concentration~(mu*g/mL)),
    title = "Simulated VPC by dose cohort (Replicates Fig. 2 of Narwal 2013)",
    subtitle = "Median and 90% prediction interval from the packaged model"
  ) +
  theme_bw()

Replicate Table 3 — steady-state exposure for fixed monthly dosing

Narwal 2013 Table 3 reports predicted median steady-state pharmacokinetic parameters following fixed monthly IV dosing of 200, 600, or 1,200 mg with a loading dose at Day 14:

Dose Cmax_ss (ug/mL) Ctrough_ss (ug/mL) AUC_ss (ug*day/mL)
200 mg 89 18 1,110
600 mg 268 53 3,329
1,200 mg 536 106 6,659

The simulation below reproduces this calculation with a typical 75 kg subject (zeroRe) and monthly dosing (every 28 days) with an additional loading dose on Day 14, sampled densely within the last dosing interval.

# Doses: Day 0, loading dose at Day 14, then monthly (every 28 days).
# Simulate through Day 406 so the interval between the last two monthly
# doses (378 -> 406) is an accumulation-stabilized steady-state window.
monthly_dose_times <- c(0, 14, seq(42, 406, by = 28))
obs_ss_times       <- sort(unique(c(
  monthly_dose_times,
  seq(378, 406, by = 0.25)   # dense grid across the final interval
)))
ss_start <- 378
ss_end   <- 406

build_ss_events <- function(dose_mg) {
  d_dose <- data.frame(
    ID = 1L, TIME = monthly_dose_times, AMT = dose_mg, EVID = 1,
    DUR = infusion_dur_d, CMT = "central", DV = NA_real_
  )
  d_obs <- data.frame(
    ID = 1L, TIME = obs_ss_times, AMT = NA_real_, EVID = 0,
    DUR = NA_real_, CMT = "central", DV = NA_real_
  )
  rbind(d_dose, d_obs) |>
    dplyr::arrange(ID, TIME, dplyr::desc(EVID))
}
ss_dose_mg <- c(200, 600, 1200)
mod_ref <- rxode2::zeroRe(mod)
#> ℹ parameter labels from comments will be replaced by 'label()'

ss_results <- lapply(ss_dose_mg, function(d) {
  ev <- build_ss_events(d)
  ev$WT <- 75
  ev$BGENE21 <- 33
  ev$COHDOSE <- d / 75   # per-subject cohort dose in mg/kg (reference subject)
  ev$STEROID <- 0
  sim_ss <- rxode2::rxSolve(mod_ref, events = ev, returnType = "data.frame")
  last <- sim_ss |>
    dplyr::filter(time >= ss_start, time <= ss_end)
  tibble::tibble(
    regimen    = paste(d, "mg monthly"),
    Cmax_ss    = max(last$Cc, na.rm = TRUE),
    Ctrough_ss = last$Cc[which.max(last$time)],  # last observation pre-next dose
    AUC_ss     = PKNCA::pk.calc.auc(conc  = last$Cc,
                                     time  = last$time,
                                     interval = c(ss_start, ss_end),
                                     method = "linear")
  )
}) |> dplyr::bind_rows()
#> ℹ omega/sigma items treated as zero: 'etalvp', 'etalvc', 'etalcl', 'etalq'
#> ℹ omega/sigma items treated as zero: 'etalvp', 'etalvc', 'etalcl', 'etalq'
#> ℹ omega/sigma items treated as zero: 'etalvp', 'etalvc', 'etalcl', 'etalq'

published <- tibble::tibble(
  regimen      = paste(ss_dose_mg, "mg monthly"),
  Cmax_pub     = c(89, 268, 536),
  Ctrough_pub  = c(18, 53, 106),
  AUC_pub      = c(1110, 3329, 6659)
)

comparison <- published |>
  dplyr::left_join(ss_results, by = "regimen") |>
  dplyr::mutate(
    Cmax_pct_diff    = round(100 * (Cmax_ss     - Cmax_pub)    / Cmax_pub, 1),
    Ctrough_pct_diff = round(100 * (Ctrough_ss  - Ctrough_pub) / Ctrough_pub, 1),
    AUC_pct_diff     = round(100 * (AUC_ss      - AUC_pub)     / AUC_pub, 1)
  )

knitr::kable(comparison,
             caption = "Simulated vs published steady-state parameters (Narwal 2013 Table 3). Percent differences within ~20% are consistent with the typical-value fit.",
             digits = c(0, 0, 0, 0, 1, 1, 1, 1, 1, 1))
Simulated vs published steady-state parameters (Narwal 2013 Table 3). Percent differences within ~20% are consistent with the typical-value fit.
regimen Cmax_pub Ctrough_pub AUC_pub Cmax_ss Ctrough_ss AUC_ss Cmax_pct_diff Ctrough_pct_diff AUC_pct_diff
200 mg monthly 89 18 1110 86.0 19.1 1068.2 -3.4 6.2 -3.8
600 mg monthly 268 53 3329 252.2 51.8 3018.0 -5.9 -2.2 -9.3
1200 mg monthly 536 106 6659 497.7 97.1 5811.7 -7.1 -8.4 -12.7

PKNCA validation — single-dose NCA across the 4 cohorts

Single-dose NCA parameters (Cmax, Tmax, AUC over 14 days, half-life) across the 4 dose cohorts. The paper does not publish per-cohort NCA values, so this block serves primarily as a sanity check that the simulated profiles reproduce dose-proportional exposure with the expected mAb-like half-life (~2-4 weeks) on log-linear terminal decline.

first_interval_end <- 14

sim_nca <- sim |>
  dplyr::filter(!is.na(Cc),
                time >= 0,
                time <= first_interval_end) |>
  dplyr::select(id, treatment, time, Cc)

dose_df <- events |>
  dplyr::filter(EVID == 1, TIME == 0) |>
  dplyr::select(id = ID, time = TIME, amt = AMT) |>
  dplyr::left_join(
    cohort |>
      dplyr::transmute(
        id = ID,
        treatment = paste0(COHDOSE, " mg/kg Q14D")
      ),
    by = "id"
  )

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

intervals <- data.frame(
  start     = 0,
  end       = first_interval_end,
  cmax      = TRUE,
  tmax      = TRUE,
  auclast   = TRUE,
  half.life = TRUE
)

nca_data <- PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals)
nca_res  <- suppressWarnings(PKNCA::pk.nca(nca_data))
#>  ■■■■■■■■■■■■■                     41% |  ETA:  4s
#>  ■■■■■■■■■■■■■■■■■■■■■■■■■■■       86% |  ETA:  1s

knitr::kable(summary(nca_res),
             caption = "Simulated single-dose NCA across the MI-CP152 cohorts (first 14 days).")
Simulated single-dose NCA across the MI-CP152 cohorts (first 14 days).
start end treatment N auclast cmax tmax half.life
0 14 0.3 mg/kg Q14D 50 58.5 [28.6] 7.81 [36.6] 0.0833 [0.0833, 0.0833] 12.9 [3.78]
0 14 1 mg/kg Q14D 50 178 [24.1] 23.8 [31.8] 0.0833 [0.0833, 0.0833] 13.3 [4.03]
0 14 10 mg/kg Q14D 50 1880 [28.6] 264 [31.2] 0.0833 [0.0833, 0.0833] 11.2 [3.60]
0 14 3 mg/kg Q14D 50 543 [35.3] 74.5 [44.0] 0.0833 [0.0833, 0.0833] 12.9 [4.26]

Assumptions and deviations

  • Reference weight 75 kg. Narwal 2013 uses 75 kg as the reference body weight in Eqs. 3-5 (the population median was 73 kg; 75 kg was chosen as a round-number reference). The packaged model uses 75 kg directly.
  • CL-V2 correlation = 0. Narwal 2013 Table 2 reports the CL-V1 (0.557) and V1-V2 (0.131) correlations but does not report a CL-V2 correlation, indicating the NONMEM OMEGA block did not include this off-diagonal element. The 3x3 IIV block in the packaged model therefore uses cov(CL, V2) = 0 and is positive-definite.
  • Dose as subject-level covariate (COHDOSE). The paper’s Eq. 3 treats dose (mg/kg) as a power-term covariate on CL. Because every MI-CP152 subject was randomised to a single dose cohort that was maintained across all 14 infusions, this is a subject-level rather than an event-level covariate. For the COHDOSE column in the events data, use the cohort assignment (0.3, 1, 3, 10 mg/kg for the phase Ib design; dose/WT for phase IIb fixed-dose simulations). The paper’s Discussion (p. 1024) notes that the apparent dose effect may be a data artifact of the escalating design — single-dose data in MI-CP126 were linear across 0.3-30 mg/kg.
  • STEROID default. The phase IIb simulations in the paper set BSTEROID = 0 (no baseline steroid use) as the reference. The virtual cohort above does the same; set STEROID = 1 per subject to simulate the +19.5% CL effect for concomitant-steroid users.
  • Monthly dosing interval for Table 3. Narwal 2013 Table 3 is labelled “monthly” without a numeric dosing-interval definition. The replication above uses every 28 days with an additional loading dose at Day 14, which matches the description in Section 3.2.2 and the phase IIb study protocol NCT01283139.
  • Residual error magnitude. The model uses propSd = 0.275 directly (Table 2 reports the residual-error %CV as 27.5%). If the paper’s NONMEM control stream used SIGMA on variance scale, the equivalent is sigma = 0.27547^2 = 0.07588; this is numerically equivalent because nlmixr2’s propSd is a standard deviation.
  • BLQ handling. Simulated concentrations are continuous; the clinical assay’s LOQ of 1.25 ug/mL is not imposed.
  • No inter-occasion variability (IOV). Narwal 2013 did not report IOV on any PK parameter.