Skip to contents

HuHMFG1 (Royer 2010)

Source: vignettes/articles/Royer_2010_HuHMFG1.Rmd
Royer_2010_HuHMFG1.Rmd

Model and source

  • Citation: Royer B, Yin W, Pegram M, Ibrahim N, Villanueva C, Mir D, Erlandsson F, Pivot X. Population pharmacokinetics of the humanised monoclonal antibody, HuHMFG1 (AS1402), derived from a phase I study on breast cancer. Br J Cancer. 2010;102(5):827-832. doi:10.1038/sj.bjc.6605560
  • Description: Two-compartment population PK model with linear elimination for HuHMFG1 (AS1402), a humanised anti-MUC1 monoclonal antibody, in patients with metastatic breast cancer; serum AST enters the typical clearance equation additively (Royer 2010)
  • Article: https://doi.org/10.1038/sj.bjc.6605560
  • PubMed (PMID 20160731): https://pubmed.ncbi.nlm.nih.gov/20160731/

HuHMFG1 (AS1402) is a humanised IgG1 monoclonal antibody that targets the MUC1 tumour-associated antigen. Royer et al. (2010) fit a linear two-compartment model to 435 serum concentrations from 26 patients enrolled in the Pegram 2009 phase I dose-escalation study (1, 3, 9, and 16 mg/kg IV infusion) in metastatic breast cancer. The NONMEM ADVAN3 TRANS4 macro was used (CL, V1, Q, V2 parameterisation), with FOCE-INTERACTION estimation.

Inter-patient variability was modelled with exponential random effects on V1 and CL only (no estimable random effects on Q or V2). Residual variability used a combined proportional + fixed additive model. The only retained covariate was serum aspartate aminotransferase (AST), which entered the typical-CL equation additively rather than via the more common power form.

Population

The development cohort comprised 26 patients with locally advanced or metastatic breast cancer (Royer 2010 Table 2). Median (min-max) baseline characteristics: age 55 (32-72) years, weight 73.1 (50-108) kg, height 165 (155-179) cm, BMI 25.75 (18.00-40.65) kg/m^2, total protein 68 (54-82) g/L, albumin 41 (27-48) g/L, creatinine clearance 85.3 (37.2-648.9) mL/min, ALP 86 (47-1127) U/L, ALT 27 (6-252) U/L, AST 29 (14-1392) U/L, GGT 37 (9-1386) U/L, CA15-3 45 (9-16400), CA27.29 31.3 (3.5-1723). Patients were enrolled across cohorts of 3, 9, 6, and 8 individuals at the 1, 3, 9, and 16 mg/kg dose levels respectively; up to 10 administrations were observed in one patient. Human anti-human antibody (HAHA) testing was negative in every assessable patient (0 of 23) and was not further investigated. The same information is available programmatically via readModelDb("Royer_2010_HuHMFG1")$population.

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Royer_2010_HuHMFG1.R. The table below collects the mapping in one place for reviewer audit.

Element Source location Value / form
Linear two-compartment model, IV input into central Royer 2010 Results page 829 (“ADVAN3 TRANS4 subroutine”) d/dt(central) = -kel*central - k12*central + k21*peripheral1
Typical V1 (central volume) Royer 2010 Table 3 3.31 L
Typical CL intercept (theta_CL) Royer 2010 Table 3 0.016 L/h
Typical Q (inter-compartmental CL) Royer 2010 Table 3 0.017 L/h
Typical V2 (peripheral volume) Royer 2010 Table 3 2.33 L
AST coefficient (COV_CL) Royer 2010 Table 3, Results page 829 0.0036 (additive on CL, in L/h per unit AST/ASTmed)
ASTmed (study median used for normalisation) Royer 2010 Table 2 29 U/L
CL equation form Royer 2010 Results page 829 CL = 0.016 + 0.0036 * (AST / 29) (additive, NOT power)
IIV on V1 (omega^2) Royer 2010 Table 3 0.042 (exponential, log-normal)
IIV on CL (omega^2) Royer 2010 Table 3 0.062 (exponential, log-normal)
IIV on Q, V2 Royer 2010 Table 3 / Results page 829 Not estimable; omitted from the model
Proportional residual error (sigma^2) Royer 2010 Table 3 0.034 (stored as propSd = sqrt(0.034) = 0.184)
Additive residual error (sigma^2, FIXED) Royer 2010 Table 3 2.26 (mg/L)^2 (stored as addSd = fixed(sqrt(2.26)) = 1.503 mg/L)
Published median distribution half-life Royer 2010 Results page 829 1.87 days (0.49-2.29)
Published median terminal half-life Royer 2010 Results page 829 11.04 days (4.38-15.04)

Covariate column naming

Source column Canonical column used here Notes
AST AST (U/L) Baseline aspartate aminotransferase activity; additive form on typical CL with ASTmed = 29 U/L (study median, Table 2).

Virtual cohort

The source paper does not publish per-subject baseline covariates. The cohort below approximates the Royer 2010 Table 2 marginals so that simulated NCA metrics can be compared with the paper’s published median half-lives. Body weight is drawn so that its 5th-95th percentiles cover the Table 2 range; AST is drawn from a log-normal centred at the study median.

set.seed(2010L)
n_subj <- 200L

# Per-dose-cohort layout matching Royer 2010 patient counts (3 / 9 / 6 / 8)
# scaled to n_subj. Each cohort gets a distinct id_offset so the IDs are
# disjoint when bound together for multi-cohort simulation.
royer_cohorts <- tibble::tribble(
  ~cohort,      ~dose_mg_per_kg, ~infusion_dur_min, ~n_paper,
  "1 mg/kg",                  1,                60,        3,
  "3 mg/kg",                  3,                60,        9,
  "9 mg/kg",                  9,               120,        6,
  "16 mg/kg",                16,               180,        8
) |>
  mutate(n_sim     = round(n_subj * n_paper / sum(n_paper)),
         id_offset = c(0L, head(cumsum(n_sim), -1)))

make_cohort <- function(n, dose_mg_per_kg, infusion_dur_min, id_offset,
                        cohort_label) {
  tibble(
    id             = id_offset + seq_len(n),
    WT             = pmin(pmax(rnorm(n, mean = 73.1, sd = 14), 50), 108),
    AST            = pmin(pmax(rlnorm(n, log(29), 0.5), 14), 200),
    cohort         = cohort_label,
    dose_mg_per_kg = dose_mg_per_kg,
    infusion_dur_h = infusion_dur_min / 60
  )
}

pop <- do.call(
  rbind,
  Map(make_cohort,
      n                = royer_cohorts$n_sim,
      dose_mg_per_kg   = royer_cohorts$dose_mg_per_kg,
      infusion_dur_min = royer_cohorts$infusion_dur_min,
      id_offset        = royer_cohorts$id_offset,
      cohort_label     = royer_cohorts$cohort)
)

Dosing dataset (single dose, dense sampling)

The paper’s NCA-relevant comparator is the median single-dose terminal half-life (~11 days) and distribution half-life (~1.87 days). We simulate a single IV infusion at each cohort’s labelled dose level with sampling schedule mirroring Table 1 (pre-dose, end of infusion, 1.5-840 h).

obs_times_h <- sort(unique(c(
  0,
  1.5, 4, 6, 12, 24, 48, 72,
  seq(96, 240, by = 24),
  seq(264, 840, by = 24)
)))

d_dose <- pop |>
  mutate(
    time = 0,
    amt  = dose_mg_per_kg * WT,                  # mg
    rate = amt / infusion_dur_h,                 # mg/h
    evid = 1L,
    cmt  = "central",
    dv   = NA_real_
  )

d_obs <- tidyr::crossing(pop, time = obs_times_h) |>
  mutate(amt = NA_real_, rate = NA_real_, evid = 0L,
         cmt = "central", dv = NA_real_)

events <- bind_rows(d_dose, d_obs) |>
  arrange(id, time, desc(evid)) |>
  as.data.frame()

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

Simulation 

mod <- readModelDb("Royer_2010_HuHMFG1")
sim <- rxode2::rxSolve(mod, events = events,
                       keep = c("cohort", "dose_mg_per_kg", "WT", "AST"))
#> ℹ parameter labels from comments will be replaced by 'label()'
sim_df <- as.data.frame(sim)

Typical-subject profiles by dose cohort (replicates Royer 2010 Figure 1)

Royer 2010 Figure 1 shows semi-logarithmic concentration-time profiles during the first administration at each dose level. The panel below uses the same dose cohorts under zero residual variability and at the cohort median AST (=29 U/L) to reproduce the typical-subject behaviour.

mod_typical <- rxode2::zeroRe(mod)
#> ℹ parameter labels from comments will be replaced by 'label()'

typical_subjects <- royer_cohorts |>
  mutate(id = seq_len(nrow(royer_cohorts)),
         WT = 73.1,
         AST = 29,
         time = 0,
         amt  = dose_mg_per_kg * WT,
         rate = amt / (infusion_dur_min / 60),
         evid = 1L,
         cmt  = "central",
         dv   = NA_real_)

typical_dose <- typical_subjects |>
  dplyr::select(id, WT, AST, cohort, time, amt, rate, evid, cmt, dv)

typical_obs <- tidyr::crossing(
  typical_subjects |> dplyr::select(id, WT, AST, cohort),
  time = c(seq(0, 24, by = 0.5), seq(24, 840, by = 6))
) |>
  mutate(amt = NA_real_, rate = NA_real_, evid = 0L,
         cmt = "central", dv = NA_real_)

events_typical <- bind_rows(typical_dose, typical_obs) |>
  arrange(id, time, desc(evid)) |>
  as.data.frame()

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

ggplot(sim_typical |> dplyr::filter(time > 0),
       aes(x = time, y = Cc, colour = cohort)) +
  geom_line(linewidth = 1) +
  scale_y_log10() +
  labs(
    x = "Time (h)",
    y = "HuHMFG1 serum concentration (mg/L)",
    title = "Typical-subject HuHMFG1 profile after a single IV infusion",
    subtitle = "Replicates Royer 2010 Figure 1 (1, 3, 9, 16 mg/kg single dose; WT=73.1 kg, AST=29 U/L)",
    colour = "Dose cohort"
  ) +
  theme_bw()

VPC-style simulation across the virtual cohort 

vpc_summary <- sim_df |>
  dplyr::filter(time > 0) |>
  group_by(cohort, time) |>
  summarise(
    median = median(Cc, na.rm = TRUE),
    lo     = quantile(Cc, 0.05, na.rm = TRUE),
    hi     = quantile(Cc, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(vpc_summary, aes(x = time, colour = cohort, fill = cohort)) +
  geom_ribbon(aes(ymin = lo, ymax = hi), alpha = 0.2, colour = NA) +
  geom_line(aes(y = median), linewidth = 1) +
  scale_y_log10() +
  labs(
    x = "Time (h)",
    y = "HuHMFG1 serum concentration (mg/L)",
    title = "Simulated HuHMFG1 profile after a single IV infusion (virtual cohort)",
    subtitle = paste0("Median and 90% prediction interval, N = ", n_subj, " virtual subjects"),
    caption = "Patterned after Royer 2010 Figure 3A (first administration VPC).",
    colour = "Dose cohort", fill = "Dose cohort"
  ) +
  theme_bw()

PKNCA validation

Run a single-dose NCA on the virtual cohort using PKNCA. The Royer 2010 paper reports median (range) distribution half-life 1.87 (0.49-2.29) days and terminal half-life 11.04 (4.38-15.04) days, calculated from the final-model parameter estimates rather than from a non-compartmental analysis. We compute terminal half-life via PKNCA’s half.life parameter and compare against the published terminal estimate.

sim_nca <- sim_df |>
  dplyr::filter(!is.na(Cc), Cc > 0) |>
  dplyr::transmute(id, time, Cc, cohort)

dose_df <- events |>
  dplyr::filter(evid == 1L) |>
  dplyr::transmute(id, time, amt, cohort)

conc_obj <- PKNCA::PKNCAconc(sim_nca, Cc ~ time | cohort + id,
                             concu = "mg/L", timeu = "h")
dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | cohort + 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 (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1.5) is not allowed

nca_summary <- summary(nca_res)
knitr::kable(nca_summary,
             caption = "PKNCA single-dose summary by cohort (terminal half-life reported in hours).")
PKNCA single-dose summary by cohort (terminal half-life reported in hours).
Interval Start Interval End cohort N Cmax (mg/L) Tmax (h) Half-life (h) AUCinf,obs (h*mg/L)
0 Inf 1 mg/kg 23 22.5 [31.0] 1.50 [1.50, 1.50] 255 [46.0] NC
0 Inf 16 mg/kg 62 321 [26.5] 4.00 [4.00, 4.00] 255 [61.2] NC
0 Inf 3 mg/kg 69 62.3 [27.4] 1.50 [1.50, 1.50] 253 [57.4] NC
0 Inf 9 mg/kg 46 175 [30.1] 4.00 [4.00, 4.00] 257 [63.6] NC

Comparison against published terminal half-life 

hl_by_id <- nca_res$result |>
  dplyr::as_tibble() |>
  dplyr::filter(PPTESTCD == "half.life") |>
  dplyr::transmute(cohort, id, half_life_h = PPORRES,
                   half_life_day = PPORRES / 24)

hl_summary <- hl_by_id |>
  group_by(cohort) |>
  summarise(
    `Median t1/2 (day)` = median(half_life_day, na.rm = TRUE),
    `5th pct (day)`     = quantile(half_life_day, 0.05, na.rm = TRUE),
    `95th pct (day)`    = quantile(half_life_day, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

published <- tibble::tibble(
  cohort = unique(hl_summary$cohort),
  `Published median t1/2 (day)` = 11.04,
  `Published min (day)`         = 4.38,
  `Published max (day)`         = 15.04
)

knitr::kable(
  hl_summary |> dplyr::left_join(published, by = "cohort"),
  digits = 2,
  caption = "Simulated vs. published terminal half-life. Royer 2010 reports a single global summary (11.04 days, 4.38-15.04) calculated from the final-model parameters; the simulation column is dose-cohort-stratified."
)
Simulated vs. published terminal half-life. Royer 2010 reports a single global summary (11.04 days, 4.38-15.04) calculated from the final-model parameters; the simulation column is dose-cohort-stratified.
cohort Median t1/2 (day) 5th pct (day) 95th pct (day) Published median t1/2 (day) Published min (day) Published max (day)
1 mg/kg 10.42 8.45 13.99 11.04 4.38 15.04
16 mg/kg 10.15 7.79 15.61 11.04 4.38 15.04
3 mg/kg 10.14 7.09 14.30 11.04 4.38 15.04
9 mg/kg 10.40 7.55 14.29 11.04 4.38 15.04

The simulated terminal half-life across cohorts is expected to track the paper’s 11.04-day published median within ~20%. Larger differences would reflect interaction between virtual covariate distributions (AST, WT) and the additive AST-on-CL term rather than a structural error.

Assumptions and deviations

Royer 2010 does not publish per-subject baseline covariates, so the virtual cohort above approximates rather than reproduces the source sample:

  • Body weight ~ Normal(73.1, 14) kg, clipped to 50-108 kg. The median matches Table 2; the tails cover the Table 2 range.
  • AST ~ log-Normal(log 29, 0.5) U/L, clipped to 14-200 U/L. The median matches the Table 2 study median (ASTmed = 29 U/L); the upper clip stops short of the most extreme reported value (1392 U/L, likely a small subset with hepatic metastasis) to keep the AST-on-CL effect inside a clinically meaningful range. Royer 2010 retained AST despite hepatic enzymes being correlated; the additive form is preserved exactly as published.
  • Sex distribution is not tabulated in Royer 2010. Pegram 2009 enrolled women with metastatic breast cancer; the model has no sex effect, so simulation is insensitive to the assumption.
  • Dose levels and infusion durations follow Pegram 2009 / Royer 2010 Methods page 828: 60 min infusion at 1 and 3 mg/kg, 120 min at 9 mg/kg, 180 min at 16 mg/kg. Single-dose simulations omit the multi-cycle schedule (the paper’s first-administration data already drive the reported half-lives).
  • CL covariate model is additive, not power. The Royer 2010 equation CL (L/h) = 0.016 + 0.0036 * (AST / 29) is reproduced exactly. The intercept (0.016 L/h, Table 3 theta_CL) is stored as lcl = log(0.016); the additive AST coefficient (0.0036 L/h, Table 3 COV_CL) is stored on the linear scale as e_ast_cl. The inter-individual random effect is applied multiplicatively (cl = tvcl * exp(etalcl)), matching the paper’s “exponential random effect” description.
  • Residual error variances vs SDs. Royer 2010 Table 3 reports proportional and additive residual error as variances (sigma^2). The packaged values are stored as SDs (propSd = sqrt(0.034), addSd = fixed(sqrt(2.26)) mg/L) to match the nlmixr2 prop() / add() convention.
  • Random effects on Q and V2 could not be obtained per Royer 2010 Results page 829 (“Random effects could not be obtained for either Q or V2”). They are therefore omitted from the model rather than fixed at zero.
  • Inter-occasion variability was assessed and found insignificant (Royer 2010 Results page 829); no IOV term is included.
  • Errata search: no erratum, corrigendum, or correction notice was located for DOI 10.1038/sj.bjc.6605560 via PubMed (PMID 20160731) at the time of this extraction. The reference field will be amended if a later correction surfaces.

Reference

  • Royer B, Yin W, Pegram M, Ibrahim N, Villanueva C, Mir D, Erlandsson F, Pivot X. Population pharmacokinetics of the humanised monoclonal antibody, HuHMFG1 (AS1402), derived from a phase I study on breast cancer. Br J Cancer. 2010;102(5):827-832. doi:10.1038/sj.bjc.6605560