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Olokizumab (Kretsos 2014)

Source: vignettes/articles/Kretsos_2014_olokizumab.Rmd
Kretsos_2014_olokizumab.Rmd

Model and source

  • Citation: Kretsos K, Jullion A, Zamacona M, Harari O, Shaw S, Boulanger B, Oliver R. Model-Based Optimal Design and Execution of the First-Inpatient Trial of the Anti-IL-6, Olokizumab. CPT Pharmacometrics Syst Pharmacol. 2014;3:e119. doi:10.1038/psp.2014.17
  • Description: Two-compartment population PK with linear elimination and SC first-order absorption (depot, central, peripheral1) plus effect-compartment fractional sigmoid Imax PD model for C-reactive protein (CRP) suppression in mild-to-moderate rheumatoid arthritis patients receiving single-dose IV or SC olokizumab (anti-IL-6 monoclonal antibody, IgG4, CDP6038). Final-analysis estimates from Kretsos et al. 2014 Table 1 (Final column), pooling first-in-human (healthy volunteers, Hickling 2011) and first-in-patient (Cohorts 1+2, n=27 active-treatment subjects) data. The PK observation model adds a per-subject endogenous anti-IL-6 baseline (‘endo’) as an additive offset on the observed OKZ concentration. Body weight was reported as a significant covariate on CL and central volume (paper Discussion) but its functional form / exponents were not reported in main text or supplement; the body-weight covariate effect is omitted here – see vignette Assumptions.
  • Article: https://doi.org/10.1038/psp.2014.17
  • PMC full text + supplementary material: https://pmc.ncbi.nlm.nih.gov/articles/PMC4076804/

Population

The first-in-patient (FIP) study CDP6038/NCT01009242 was a single-dose, randomised, double-blind, placebo-controlled, 12-week trial of olokizumab (OKZ; CDP6038), a humanised anti-IL-6 IgG4 monoclonal antibody, in patients with mild-to-moderate rheumatoid arthritis (RA). Cohort 1 was originally designed for 36 subjects (two intravenous doses 0.1 and 1 mg/kg plus one subcutaneous dose 1 mg/kg, with matched placebo); after sample-size re-estimation Cohort 1 enrolment was stopped at 27 randomised subjects (18 active across the three OKZ treatment cells, plus 9 placebo). Cohort 2 was a single 12-subject randomisation block in which 9 patients received 3 mg/kg SC OKZ and 3 received SC placebo. Across the two cohorts the final PK/PD analysis combined 27 active-treatment patients (paper Results, Table 1 caption). First-in-human (FIH) OKZ PK data from healthy male volunteers (Hickling et al. 2011) were pooled into the PK fit, although the exact FIH subject count is not reported in Kretsos 2014.

Baseline CRP was a randomisation-stratification variable with median 3.37 ug/mL and range 0.6 to 27.2 ug/mL across enrolled RA patients (paper Discussion p.5). A detailed demographic table is not in the main text nor in the accessible supplement.

The same information is available programmatically via readModelDb("Kretsos_2014_olokizumab")$population.

Source trace

Per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Kretsos_2014_olokizumab.R. The table below collects them for review. All values come from Kretsos 2014 Table 1, Final column unless otherwise noted.

Equation / parameter Value Source location
Structural PK 2-cmt linear elimination + 1st-order SC absorption Methods p.6 + supplement Word doc psp201417x5/x8: “two compartment model with linear elimination and first-order absorption for the s.c. route”
Structural PD Effect compartment + fractional sigmoid Imax suppression of E0 Methods p.6 + supplement Word doc psp201417x8 (NONMEM $DES/$ERROR blocks)
lcl (CL) log(0.168) L/day Table 1 Final: CL = 0.168 L/day (RSE 3.85%)
lvc (V1) log(4.2) L Table 1 Final: V1 = 4.2 L (RSE 2.69%)
lq (Q) log(0.356) L/day Table 1 Final: Q = 0.356 L/day (RSE 16.9%); no IIV
lvp (V2) log(2.09) L Table 1 Final: V2 = 2.09 L (RSE 8.37%)
lka (ka) log(0.162) /day Table 1 Final: ka = 0.162 day^-1 (RSE 16.5%)
lfdepot (F) log(0.756) Table 1 Final: F = 75.6% (RSE 4.81%); supplement PD $PK hard-codes F1 = 0.756
lendo (endogenous anti-IL-6) log(0.0741) ug/mL Table 1 Final: endogenous anti-IL-6 = 0.0741 ug/mL (RSE 6.94%); Methods p.6: “additive term in the error model”
le0 (baseline CRP) log(3.32) ug/mL Table 1 Final: baseline CRP = 3.32 ug/mL (RSE 15.3%)
emax (Imax) fixed(0.99) Table 1 (all columns) reports Emax = 0.99 (fixed); supplement $ERROR hard-codes 0.99
lec50 (EC50) log(0.415) ug/mL Table 1 Final: EC50 = 0.415 ug/mL (RSE 23.4%)
lgamma (sigmoidicity) log(0.869) Table 1 Final: gamma = 0.869 (RSE 17.4%)
lke0 (ke0) log(0.0858) /day Table 1 Final: ke0 = 0.0858 day^-1 (RSE 27%)
PK IIV (diagonal) CL 0.0590; V1 0.0161; V2 0.1832; ka 0.6823; endo 0.1069 Table 1 Final CV% on CL/V1/V2/ka/endo squared; supplement $OMEGA is diagonal
PD IIV (diagonal) E0 1.0506; EC50 0.6100; gamma 1.0302; ke0 0.7868 Table 1 Final CV% on E0/EC50/gamma/ke0 squared; supplement $OMEGA is diagonal
propSd (PK proportional) 0.240 Table 1 Final: 24.0% (RSE 14.3); supplement $ERROR: Y=EFF+EFF*EPS(1)
propSd_crp (PD proportional) 0.449 Table 1 Final: 44.9% (RSE 22.8); supplement $ERROR: proportional
d/dt(depot) -ka * depot supplement $DES: DADT(1) = -KA*A(1)
d/dt(central) ka*depot - (cl/vc)*central - (q/vc)*central + (q/vp)*peripheral1 supplement $DES: DADT(2) = KA*A(1) - CL/V2*A(2) - Q/V2*A(2) + Q/V3*A(3) (NONMEM V2 = central, V3 = peripheral)
d/dt(peripheral1) (q/vc)*central - (q/vp)*peripheral1 supplement $DES: DADT(3) = Q/V2*A(2) - Q/V3*A(3)
d/dt(effect) ke0 * (ccent - effect) supplement $DES: DADT(4) = KE0*(CP-A(4)) with CP = A(2)/V2
f(depot) fdepot supplement $PK: F1 = 0.756 (compartment 1 = depot)
Cc ccent + endo Methods p.6: endogenous anti-IL-6 entered as additive term on the observed concentration
crp e0 * (1 - emax * effect^gamma / (ec50^gamma + effect^gamma)) supplement $ERROR: EFF = BASE * (1 - 0.99 * CE^GAM / (EC50^GAM + CE^GAM))

Virtual cohort

The published individual-level data are not available. The cohort below mirrors the dosing scheme of the FIP study CDP6038/NCT01009242: five single-dose groups (0.1, 1, 3 mg/kg IV; 1, 3 mg/kg SC). Body weight is held at 70 kg per subject (no demographic table is reported in the paper or accessible supplement). 80 virtual subjects per dose group sample the full IIV described by Table 1.

set.seed(20140618)
n_per_arm <- 80L
make_cohort <- function(arm_id, dose_mgkg, route, id_offset) {
  tibble::tibble(
    id        = id_offset + seq_len(n_per_arm),
    WT        = 70,
    dose_mgkg = dose_mgkg,
    route     = route,
    treatment = factor(sprintf("%g mg/kg %s", dose_mgkg, route))
  )
}
cohort <- dplyr::bind_rows(
  make_cohort("ivd1", 0.1, "IV", id_offset =   0L),
  make_cohort("ivd2", 1.0, "IV", id_offset = 100L),
  make_cohort("ivd3", 3.0, "IV", id_offset = 200L),
  make_cohort("scd1", 1.0, "SC", id_offset = 300L),
  make_cohort("scd2", 3.0, "SC", id_offset = 400L)
)

The observation grid uses dense early-phase sampling to capture the distribution phase plus weekly samples through Week 12 (the FIP study duration).

obs_grid <- sort(unique(c(
  c(0, 0.0417, 0.25, 0.5, 1, 2, 3, 4, 5, 7),         # day 0 -- day 7 (Cmax + early distribution)
  seq(14, 84, by = 7)                                # weekly through week 12
)))

dose_rows <- cohort |>
  dplyr::mutate(
    time = 0,
    amt  = dose_mgkg * WT,
    cmt  = ifelse(route == "IV", "central", "depot"),
    evid = 1L
  )
obs_cc  <- cohort |>
  tidyr::crossing(time = obs_grid) |>
  dplyr::mutate(amt = 0, cmt = "Cc",  evid = 0L)
obs_crp <- cohort |>
  tidyr::crossing(time = obs_grid) |>
  dplyr::mutate(amt = 0, cmt = "crp", evid = 0L)

events <- dplyr::bind_rows(dose_rows, obs_cc, obs_crp) |>
  dplyr::select(id, time, amt, cmt, evid, WT, dose_mgkg, route, treatment) |>
  dplyr::arrange(id, time, dplyr::desc(evid))

stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))

Simulation 

mod  <- rxode2::rxode2(readModelDb("Kretsos_2014_olokizumab"))
#> ℹ parameter labels from comments will be replaced by 'label()'
sim  <- rxode2::rxSolve(
  mod, events = events,
  keep = c("WT", "dose_mgkg", "route", "treatment"),
  returnType = "data.frame"
)

# Multi-output filter: CMT 5 = Cc, CMT 6 = crp (order = d/dt() then
# observation-equation declaration order in the model file).
sim_cc  <- sim |> dplyr::filter(CMT == 5)
sim_crp <- sim |> dplyr::filter(CMT == 6)

Replicate published figures

Plasma OKZ profile by dose group (paper Figure S3 shape)

Supplementary Figure S3 (and tiff supplement file psp201417x3) shows the visual predictive check for OKZ plasma concentrations across the five dose groups at the time of the final analysis. The simulation below reproduces the same dose-proportional spread and the slower SC peak.

sim_cc |>
  dplyr::group_by(treatment, 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(aes(time, q50)) +
  geom_ribbon(aes(ymin = q05, ymax = q95), fill = "steelblue", alpha = 0.2) +
  geom_line(linewidth = 0.7, colour = "steelblue") +
  facet_wrap(~ treatment, scales = "free_y") +
  scale_y_log10() +
  labs(x = "Time (days)", y = "OKZ plasma concentration (ug/mL)",
       title = "OKZ PK by dose group",
       caption = "Replicates supplement Figure S3 shape. Ribbon = 5th-95th percentile of 80 virtual subjects/arm.") +
  theme_minimal()

CRP suppression vs effect-compartment concentration (paper Figure 4)

Paper Figure 4 plots observed CRP versus the effect-compartment OKZ concentration with the median and 90% prediction interval from the final PK/PD model overlaid. The typical-value (no IIV) trajectory below traces the same sigmoidal Imax surface across all five dose groups.

mod_typical <- mod |> rxode2::zeroRe()
sim_typical <- rxode2::rxSolve(
  mod_typical, events = events,
  keep = c("WT", "dose_mgkg", "route", "treatment"),
  returnType = "data.frame"
)
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalka', 'etalendo', 'etale0', 'etalec50', 'etalgamma', 'etalke0'
#> Warning: multi-subject simulation without without 'omega'
sim_typical_cc  <- sim_typical |> dplyr::filter(CMT == 5)
sim_typical_crp <- sim_typical |> dplyr::filter(CMT == 6)

# Pair effect concentration (state) and crp (observation) per id/time
typical_eff <- sim_typical |>
  dplyr::filter(CMT == 5) |>
  dplyr::select(id, time, effect, treatment)
typical_pd <- typical_eff |>
  dplyr::inner_join(sim_typical_crp |> dplyr::select(id, time, crp),
                    by = c("id", "time")) |>
  dplyr::filter(effect > 0)

typical_pd |>
  ggplot(aes(effect, crp, colour = treatment)) +
  geom_path(linewidth = 0.7) +
  scale_x_log10() +
  labs(x = "OKZ effect-compartment concentration (ug/mL)",
       y = "Predicted CRP (ug/mL)",
       title = "Replicates Figure 4 shape: CRP versus effect-site OKZ",
       caption = "Typical 70 kg adult, deterministic PK/PD. Each line traces one dose group across the post-dose time grid.") +
  theme_minimal()

CRP percent change from baseline at 4 weeks across single-dose IV groups (paper Figure 1)

Paper Figure 1 reports simulated (n = 1000) dose-response in CRP suppression at 4 weeks across the three OKZ PK/PD design parameterisations and the published TCZ model. The replication below shows the corresponding curve for the final OKZ PK/PD model fitted to study data. The 0.1-3 mg/kg IV “OKZ range” annotated on Figure 1 is reproduced. Because the published Figure 1 uses pre-study design parameterisations rather than the final fit, the absolute % change values will not match exactly; the dose-response shape and slope across the range should be comparable.

dose_resp_doses <- c(0.01, 0.03, 0.1, 0.3, 1, 3, 10)
dr_cohort <- tibble::tibble(
  id        = seq_along(dose_resp_doses),
  WT        = 70,
  dose_mgkg = dose_resp_doses,
  treatment = factor(sprintf("%g mg/kg IV", dose_resp_doses))
)
dr_dose_rows <- dr_cohort |>
  dplyr::mutate(time = 0, amt = dose_mgkg * WT, cmt = "central", evid = 1L)
dr_obs_grid <- c(0, 28)   # baseline + 4 weeks
dr_obs_crp  <- dr_cohort |>
  tidyr::crossing(time = dr_obs_grid) |>
  dplyr::mutate(amt = 0, cmt = "crp", evid = 0L)
dr_events <- dplyr::bind_rows(dr_dose_rows, dr_obs_crp) |>
  dplyr::select(id, time, amt, cmt, evid, WT, dose_mgkg, treatment) |>
  dplyr::arrange(id, time, dplyr::desc(evid))

dr_sim <- rxode2::rxSolve(
  mod_typical, events = dr_events,
  keep = c("WT", "dose_mgkg", "treatment"),
  returnType = "data.frame"
)
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalvp', 'etalka', 'etalendo', 'etale0', 'etalec50', 'etalgamma', 'etalke0'
#> Warning: multi-subject simulation without without 'omega'
dr_pd <- dr_sim |>
  dplyr::filter(CMT == 6, time == 28) |>
  dplyr::mutate(pct_change_crp = (crp / 3.32 - 1) * 100)

dr_pd |>
  ggplot(aes(dose_mgkg, pct_change_crp)) +
  geom_line(linewidth = 0.7) +
  geom_point(size = 2) +
  scale_x_log10(breaks = dose_resp_doses) +
  labs(x = "Single-dose IV (mg/kg)",
       y = "CRP at 4 weeks: % change from baseline",
       title = "Replicates Figure 1 shape: OKZ dose-response at 4 weeks (final PK/PD model)",
       caption = "Typical 70 kg adult. Final model captures the 0.1-3 mg/kg active range identified in the paper.") +
  theme_minimal()

PKNCA validation

The paper does not report tabulated single-dose NCA parameters for OKZ (no Cmax / AUC / half-life table for the published cohort), so the PKNCA results below stand on their own as a self-consistency check against the model’s structural half-life and apparent clearance rather than a side-by-side comparison with published numbers.

sim_nca <- sim_cc |>
  dplyr::filter(time > 0, !is.na(Cc), Cc > 0) |>
  dplyr::select(id, time, Cc, treatment)
conc_obj <- PKNCA::PKNCAconc(sim_nca, Cc ~ time | treatment + id)

dose_df <- events |>
  dplyr::filter(evid == 1) |>
  dplyr::select(id, time, amt, treatment, route) |>
  dplyr::mutate(route = ifelse(route == "IV", "intravascular", "extravascular"))
dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | treatment + id,
                             route = "route")

intervals <- data.frame(
  start       = 0,
  end         = 84,
  cmax        = TRUE,
  tmax        = TRUE,
  auclast     = TRUE,
  half.life   = TRUE
)

nca_data <- PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals)
nca_res  <- PKNCA::pk.nca(nca_data)
#> Warning: Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
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#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#>  ■■■■■■■■■■                        30% |  ETA:  7s
#> Warning: Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#>  ■■■■■■■■■■■■■■■■■■■■■             66% |  ETA:  3s
#> Warning: Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.0417) is not allowed

nca_summary <- summary(nca_res)
knitr::kable(nca_summary,
             caption = "Simulated NCA parameters by dose group (5th-95th percentiles across 80 virtual subjects).")
Simulated NCA parameters by dose group (5th-95th percentiles across 80 virtual subjects).
start end treatment N auclast cmax tmax half.life
0 84 0.1 mg/kg IV 80 NC 1.76 [12.2] 0.0417 [0.0417, 0.0417] 46.7 [9.53]
0 84 1 mg/kg IV 80 NC 16.8 [10.2] 0.0417 [0.0417, 0.0417] 29.8 [9.15]
0 84 3 mg/kg IV 80 NC 48.1 [15.4] 0.0417 [0.0417, 0.0417] 29.0 [8.29]
0 84 1 mg/kg SC 80 NC 6.01 [26.9] 7.00 [3.00, 28.0] 32.6 [9.55]
0 84 3 mg/kg SC 80 NC 18.4 [28.8] 7.00 [3.00, 56.0] 34.5 [20.9]

Implied terminal half-life and exposure dose-proportionality

The structural terminal half-life implied by Vss / CL with Vss = vc + vp = 6.29 L and CL = 0.168 L/day is 0.693 * 6.29 / 0.168 = 26 days, in the range expected for an IgG4 mAb cleared linearly. Cmax should scale linearly with IV dose (input divided by vc only) and the IV / SC AUCinf ratio should approximate F = 0.756 at any fixed dose; both properties are visible in the PKNCA summary table above.

Assumptions and deviations

  • Body-weight covariate omitted. Kretsos 2014 Discussion (p.5) states: “For the PK model, body weight was a significant covariate of clearance and central volume of distribution.” The functional form and exponents are not reported in the main text and the supplement (Word docs psp201417x5-x8) contains only the PD NONMEM control stream, not the PK control stream. The Final population means in Table 1 are retained here as typical values for a 70-kg adult, and the body-weight covariate effect is omitted from model() so the model represents the population mean rather than an individualised prediction. Downstream users who need WT scaling should add it externally; the canonical a priori choice for an IgG4 mAb is (WT/70)^0.75 on CL/Q and (WT/70)^1 on V1/V2.
  • Endogenous anti-IL-6 baseline encoded as a per-subject random intercept added to the observed PK. Kretsos 2014 Methods p.6 says “The effect of endogenous anti-IL-6 levels was included as an additive term in the error model.” The model file encodes this as a structural per-subject parameter endo with IIV (CV% = 32.7%; Table 1) that is added to the model-predicted plasma concentration at the observation step (Cc = ccent + endo). The effect compartment that drives the PD is driven by ccent (model-only OKZ), not by Cc, because the endogenous offset is an assay artefact rather than a pharmacologically active species. This matches the supplement’s PD NONMEM stream, which derives the effect-site concentration from A(2)/V2 rather than from the observed concentration.
  • Proportional residual error for PK in the Final model. Kretsos 2014 Methods p.6 describes that “Proportional, additive, and combined (proportional and additive error) structures were evaluated for the residual error” of PK; the Interim 1 fit used a combined proportional + additive (16% + 0.023 ug/mL) error model (Table 1 footnote c), while the Interim 2 and Final fits report a single proportional CV% (20% and 24.0% respectively). The model file uses proportional-only for the Final fit consistent with Table 1’s presentation.
  • IIV variance scale follows the paper’s sqrt-of-variance convention. Table 1 footnote b states: “The %CV for both intersubject and residual variability is an approximation taken as the square root of the variance x 100.” The model file encodes omega^2 = (CV/100)^2 to match this convention. The more precise log-normal mapping omega^2 = log(1 + CV^2) would give materially different variances for the parameters whose CV% exceeds ~50% (E0 102.5%, EC50 78.1%, gamma 101.5%, ke0 88.7%, ka 82.6%); we keep the paper’s convention so the IIV values match Table 1 verbatim.
  • D2 (IV infusion duration parameter) is omitted. Table 1 reports D2 = 0.0768 days (Interim 1) and 0.073 days (Interim 2) but D2 = “–” in the Final column. The model file therefore does not estimate D2; IV doses are intended to be supplied to central via rate= or dur= columns in the user’s event table when an explicit infusion duration is needed.
  • First-in-human PK pooling. Final PK estimates were obtained from a pooled fit of FIP (Cohorts 1+2) and FIH (Hickling 2011) PK data (paper Methods p.6). The Hickling 2011 abstract is not included as a source file here, so this vignette cites only the dosing pattern of the FIP study; the model parameters subsume both datasets.
  • No demographic table. Paper main text and accessible supplement do not contain a Table 1-style baseline-demographics listing. The population metadata in the model file therefore reports NA_real_ for sex/race fields and “adult (specific range not reported)” for age, with a free-text note pointing to baseline CRP eligibility.