Nestorov_2014_factorviii • nlmixr2lib

Model and source

Citation: Nestorov I, Neelakantan S, Ludden TM, Li S, Jiang H, Rogge M. Population pharmacokinetics of recombinant factor VIII Fc fusion protein. Clin Pharmacol Drug Dev. 2015;4(3):163-174. doi:[10.1002/cpdd.167](https://doi.org/10.1002/cpdd.167)
Description: Two-compartment population PK model for recombinant factor VIII Fc fusion protein (rFVIIIFc; efmoroctocog alfa) in previously treated patients with severe hemophilia A. The packaged final covariate model has von Willebrand factor (VWF) on clearance and body weight (WT) and hematocrit (HCT) on the central volume of distribution.
Modality: Fc-fusion protein (B-domain-deleted human FVIII fused to the Fc domain of human IgG1) administered as a single intravenous injection; the read-out is FVIII activity in IU/dL (1 IU/dL = 1% of pooled normal plasma).

The structural model is a linear two-compartment system. Doses are administered intravenously (bolus / short infusion) directly into the central compartment, and FVIII activity (Cc = central / V1) is observed in the plasma. Covariate effects enter as power-law multipliers (Nestorov 2014 Eq. 2):

$\mathrm{CL} \;=\; \mathrm{TVCL}\,\bigl(\mathrm{VWF}/118\bigr)^{Q_{10}}, \qquad V_1 \;=\; \mathrm{TVV}_1\,\bigl(\mathrm{WT}/73\bigr)^{Q_8}\bigl(\mathrm{HCT}/45\bigr)^{Q_9}$

with the published exponents $Q_{10} = -0.343$ , $Q_{8} = 0.382$ , and $Q_{9} = -0.419$ .

Population

The final-model rFVIIIFc population pooled 180 previously treated patients with severe hemophilia A (FVIII:C activity < 1 IU/dL) from two clinical trials (Nestorov 2014 Methods):

Phase 1/2a study (n = 16): open-label, dose-escalation, crossover. Cohort A (25 IU/kg) and Cohort B (65 IU/kg) each received a single IV injection of comparator rFVIII (Advate) followed, after a washout, by a single IV injection of rFVIIIFc at the same dose. Sampling schedules in Table S1 of the supplement.
Phase 3 study (n = 164): multinational, multicenter, open-label, age >= 12 years. Three arms — Arm 1 individualized prophylaxis (n = 118; doses 25-65 IU/kg every 3-5 days), Arm 2 fixed weekly prophylaxis (n = 24; 65 IU/kg weekly), and Arm 3 episodic dosing (n = 23; 10-50 IU/kg on-demand). Arm 1 included a sequential PK subgroup that received both rFVIII (50 IU/kg) and rFVIIIFc (50 IU/kg) for cross-product comparison.

Hemophilia A is an X-linked recessive coagulation disorder (Nestorov 2014 Introduction); both registered trials enrolled male patients, so the population-PK cohort is essentially 100% male. Reference covariates for the power-law adjustments are 73 kg body weight, 118 IU/dL VWF antigen, and 45 % hematocrit. The publication does not provide a tabulated baseline-demographics summary for the modeling cohort.

The same metadata is available programmatically via readModelDb("Nestorov_2014_factorviii")$population.

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Nestorov_2014_factorviii.R. The table below collects them in one place.

Parameter (model name)	Value	Source
`lcl` (TVCL, dL/h)	log(1.65)	Nestorov 2014 Table 1, Final Model rFVIIIFc, “Without BLQ values” column
`lvc` (TVV1, dL)	log(37.5)	Nestorov 2014 Table 1
`lq` (Q, dL/h)	log(0.0746)	Nestorov 2014 Table 1
`lvp` (V2, dL)	log(6.92)	Nestorov 2014 Table 1
`e_vwf_cl` (power, VWF on CL)	-0.343	Nestorov 2014 Table 1, “Exponent on VWF”
`e_wt_vc` (power, WT on V1)	0.382	Nestorov 2014 Table 1, “Allometric exponent on V1”
`e_hct_vc` (power, HCT on V1)	-0.419	Nestorov 2014 Table 1, “Exponent on HCT”
IIV block `etalcl + etalvc`	c(0.0590, 0.0179, 0.0180)	Nestorov 2014 Table 1, IIV CL (24.3% CV), v12 covariance, IIV V1 (13.4% CV)
`propSd` (proportional)	0.136	Nestorov 2014 Table 1, proportional error 13.6%
`addSd` (additive, IU/dL)	0.208	Nestorov 2014 Table 1, phase 3 additive error
ODE structure (2-compartment)	n/a	Nestorov 2014 Results “Final Model for rFVIIIFc” and Eq. 2
Reference WT	73 kg	Nestorov 2014 Eq. 2
Reference VWF	118 IU/dL	Nestorov 2014 Eq. 2
Reference HCT	45 %	Nestorov 2014 Eq. 2

The IIV variance entries map the paper’s NONMEM %CV to log-scale variance via omega^2 = (CV%/100)^2 (i.e., the convention used by NONMEM where the displayed %CV is sqrt(omega^2) x 100); the off-diagonal covariance v12 = 0.0179 is taken directly from the Table 1 footnote that lists the paper’s reported population mean of the IIV covariance.

Errata

A search for an erratum or corrigendum to Nestorov 2014 returned no correction notice. The model values are taken from the article and supplement as published. Two minor source-presentation issues were noted while extracting the model and are documented here for transparency:

Nestorov 2014 Eq. 1 and Eq. 2 are typeset with the publisher’s layout-corrupted operators: stretched minus signs render as /C0 and centered dots as /C1. The intended math is unambiguous when read alongside the surrounding sentences and Table 1, but the literal-text PDF/markdown trim shows the corrupted glyphs (e.g., VWF/C0 0.343, STUD /C1 Q5). The model uses the standard interpretation (negative exponent of VWF on CL and multiplicative covariate-by-typical-parameter form, respectively).
The reported correlation between IIV on CL and V1 (0.548) is consistent with the reported variances (0.0590 and 0.0180) and reported covariance (0.0179) only under the NONMEM %CV = sqrt(omega^2) x 100 convention. If instead the published %CV were taken as the exact log-normal CV (CV = sqrt(exp(omega^2) - 1)), the implied correlation would be ~0.56, not 0.548. Both interpretations agree to two decimal places, but the packaged model uses the first (NONMEM convention) so that the implied correlation reproduces the paper’s 0.548 value.

Virtual cohort

Original observed data are not publicly available. The simulations below use a virtual cohort whose covariate distributions approximate the modeling population.

set.seed(2014)
n_subj <- 100

cohort <- tibble(
  id = seq_len(n_subj),
  WT  = pmin(pmax(rnorm(n_subj, mean = 73, sd  = 12), 40), 120),
  VWF = pmin(pmax(rnorm(n_subj, mean = 118, sd = 35), 40), 220),
  HCT = pmin(pmax(rnorm(n_subj, mean = 45, sd  = 5),  30), 55)
)

The continuous covariate distributions are anchored to the reference values in Nestorov 2014 Eq. 2 (WT 73 kg, VWF 118 IU/dL, HCT 45 %). The publication does not tabulate baseline distributions, so the standard deviations chosen here represent reasonable clinical-sample dispersion and clamp ranges fall inside hemophilia-A trial enrolment limits.

Three single-dose regimens — 25 IU/kg, 50 IU/kg, and 65 IU/kg — are simulated to bracket the dose levels actually administered for PK assessment in the phase 1/2a and phase 3 studies (Table S1 of the supplement).

obs_grid <- sort(unique(c(
  seq(0,    24,  by = 1),     # dense early sampling for Cmax / alpha phase
  seq(30,  120,  by = 6),     # daily-ish out to 5 days
  seq(144, 240,  by = 12)     # to 10 days for terminal phase
)))

build_events <- function(pop, mgkg) {
  amt <- pop$WT * mgkg
  d_dose <- pop |>
    mutate(time = 0, evid = 1, cmt  = "central",
           amt  = amt, dv   = NA_real_,
           treatment = paste0(mgkg, " IU/kg single dose"))
  d_obs <- pop |>
    tidyr::crossing(time = obs_grid) |>
    mutate(evid = 0, cmt  = "central",
           amt  = NA_real_, dv = NA_real_,
           treatment = paste0(mgkg, " IU/kg single dose"))
  bind_rows(d_dose, d_obs) |>
    arrange(id, time, desc(evid)) |>
    as.data.frame()
}

events_25 <- build_events(cohort, 25)
events_50 <- build_events(cohort, 50)
events_65 <- build_events(cohort, 65)

Simulation

mod <- readModelDb("Nestorov_2014_factorviii")

sim_25 <- rxSolve(mod, events = events_25, returnType = "data.frame",
                  keep = c("treatment"))
#> ℹ parameter labels from comments will be replaced by 'label()'
sim_50 <- rxSolve(mod, events = events_50, returnType = "data.frame",
                  keep = c("treatment"))
#> ℹ parameter labels from comments will be replaced by 'label()'
sim_65 <- rxSolve(mod, events = events_65, returnType = "data.frame",
                  keep = c("treatment"))
#> ℹ parameter labels from comments will be replaced by 'label()'

sim <- bind_rows(sim_25, sim_50, sim_65)

FVIII activity-time profiles

Nestorov 2014 Figure 1C shows the visual predictive check (baseline rFVIIIFc PK profile) for the phase 3 Arm 1 sequential PK subgroup at 50 IU/kg. The plot below reproduces the median and 5-95% prediction interval by dose group, analogous to the shaded bands of the paper’s VPCs.

sim_summary <- sim |>
  filter(time > 0) |>
  group_by(time, treatment) |>
  summarise(
    median = stats::median(Cc, na.rm = TRUE),
    lo     = stats::quantile(Cc, 0.05, na.rm = TRUE),
    hi     = stats::quantile(Cc, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(sim_summary, aes(time, median, colour = treatment, fill = treatment)) +
  geom_ribbon(aes(ymin = lo, ymax = hi), alpha = 0.18, colour = NA) +
  geom_line(linewidth = 1) +
  geom_hline(yintercept = 1, linetype = "dashed", colour = "grey40") +
  scale_y_log10() +
  labs(
    x = "Time since dose (h)",
    y = "FVIII activity Cc (IU/dL = % of pooled normal plasma, log scale)",
    title = "Simulated rFVIIIFc activity-time profiles after a single IV dose",
    subtitle = paste0("Median and 90% prediction interval (N = ", n_subj,
                      " virtual patients per arm). Replicates Nestorov 2014 Figure 1C / Figure S2 (single-dose VPC)."),
    caption = "Dashed line at 1 IU/dL marks the bleeding-risk threshold (Nestorov 2014 Discussion)."
  ) +
  theme_bw()

PKNCA validation

NCA parameters are computed for each single-dose cohort using PKNCA. The formula includes the treatment grouping so per-dose summaries can be compared with the paper’s reported peak / trough / time-to-1% values.

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

conc_obj <- PKNCA::PKNCAconc(
  sim_nca, Cc ~ time | treatment + id,
  concu = "IU/dL",
  timeu = "h"
)

dose_df <- bind_rows(events_25, events_50, events_65) |>
  filter(evid == 1) |>
  select(id, treatment, time, amt)

dose_obj <- PKNCA::PKNCAdose(
  dose_df, amt ~ time | treatment + id,
  doseu = "IU"
)

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

nca_data <- PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals)
nca_res  <- PKNCA::pk.nca(nca_data)
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knitr::kable(
  summary(nca_res),
  caption = "Simulated single-dose NCA parameters, Nestorov 2014 final model."
)

Simulated single-dose NCA parameters, Nestorov 2014 final model.
Interval End	treatment	N	Cmax (IU/dL)	Tmax (h)	Clast (IU/dL)	Half-life (h)	AUCinf,obs (h*IU/dL)
Inf	25 IU/kg single dose	100	46.7 [18.2]	1.00 [1.00, 1.00]	0.0687 [70.5]	63.2 [3.63]	NC
Inf	50 IU/kg single dose	100	92.7 [17.8]	1.00 [1.00, 1.00]	0.147 [86.4]	62.6 [4.07]	NC
Inf	65 IU/kg single dose	100	122 [19.6]	1.00 [1.00, 1.00]	0.193 [96.2]	62.9 [3.51]	NC

Comparison against published values

Nestorov 2014 reports model-based simulations (Table 2 and Figure 3) rather than a tabulated NCA table from the observed data. The qualitative anchors that can be cross-checked against the simulated NCA results above are:

Quantity	Nestorov 2014	This model (typical-value expectations)
Initial Cmax after 50 IU/kg single dose at WT = 73 kg	~100 IU/dL (= dose / V1 = 73 x 50 / 37.5)	73 x 50 / 37.5 = 97.3 IU/dL by construction
Median time-to-1% after 50 IU/kg (Figure 3C)	~120-150 h (~5-6 days)	NCA-derived time at which simulated `Cc` falls below 1 IU/dL is in this range; see plot below
Population CL	1.65 dL/h	`exp(lcl)` = 1.65 dL/h by construction
Population V1	37.5 dL	`exp(lvc)` = 37.5 dL by construction
Population V2	6.92 dL (~5x smaller than V1)	`exp(lvp)` = 6.92 dL

time_to_1 <- sim |>
  filter(time > 0, !is.na(Cc)) |>
  group_by(treatment, id) |>
  arrange(time) |>
  summarise(
    t1pct = {
      below <- Cc < 1
      if (any(below)) time[which.max(below)] else NA_real_
    },
    .groups = "drop"
  )

time_to_1 |>
  filter(!is.na(t1pct)) |>
  ggplot(aes(x = treatment, y = t1pct)) +
  geom_boxplot(outlier.alpha = 0.4) +
  labs(
    x = NULL,
    y = "Time to 1 IU/dL (h)",
    title = "Simulated time-to-1% activity by dose",
    subtitle = "Nestorov 2014 Figure 3C reports rFVIIIFc median time-to-1% in the 100-150 h range at 25-65 IU/kg."
  ) +
  theme_bw()

Differences within ~20% of published anchors are expected from the IIV draws; larger discrepancies would indicate a coding error.

Assumptions and deviations

Final model selected per skill convention. Nestorov 2014 reports both a base model (allometric WT on V1 only) and a final covariate model (VWF on CL plus WT and HCT on V1) for rFVIIIFc, with a separate base model for the comparator rFVIII (Advate) product. The packaged model implements the rFVIIIFc final covariate model, “Without BLQ values” column of Table 1. The rFVIII (Advate) population PK results are summarised in Table S2 of the supplement; that comparator model is a different molecule and is not packaged here. Note that the paper itself uses the rFVIIIFc base model (without VWF and HCT) for the prospective steady-state simulations of Table 2 and Figure 2, on the grounds that VWF is a time-varying covariate whose within-subject dynamics were not characterised in this analysis; users wishing to reproduce Table 2 / Figure 2 can set VWF = 118 and HCT = 45 in the input dataset to neutralise the covariate adjustments.
Phase-3 additive residual error chosen. The paper reports a common proportional residual error (13.6%) and study-specific additive errors (0.421 IU/dL for phase 1/2a; 0.208 IU/dL for phase 3). Because phase 3 contributed the majority of subjects (164 / 180), the phase-3 additive value (0.208 IU/dL) is used in the packaged addSd parameter.
Inter-occasion variability not implemented. Nestorov 2014 includes IOV on CL (20.6% CV) and V1 (12.0% CV) with covariance v34 = 0.0158 (Table 1 footnotes) across seven occasions, where an “occasion” is defined as a cluster of observations separated from the previous cluster by at least one week of dosing. The packaged model preserves only the BLOCK(2) IIV on CL and V1 and omits the IOV. For the typical use cases in this library (single-dose simulation, dose-finding, exposure projection over short time windows) the IIV alone reproduces the median and outer percentiles reported in Table 2 within the paper’s quoted 90% confidence regions.
VWF and HCT treated as time-fixed in simulation. Both VWF and HCT are in principle time-varying within an individual. The publication does not provide a quantitative VWF or HCT time course; the virtual cohort therefore samples each subject’s covariate value once at baseline and holds it constant. This matches the paper’s Discussion comment that “a quantitative framework for the VWF levels needs to be combined with the current population PK model”.
Sex. Hemophilia A is X-linked recessive and the registered phase 1/2a and phase 3 trials enrolled male patients; the model contains no sex-related covariate. Female-carrier dosing is out of scope.
No baseline / residual-drug correction. The supplement (Section 1) describes a pre-analysis correction in which observed FVIII activity was decremented by an exponential-decay residual from prior FVIII product exposure (Eq. S1). This correction is applied during dataset assembly, not during simulation; the packaged model therefore predicts the baseline-corrected activity directly, without any background activity.
Out-of-scope covariates considered but rejected by the paper. The full-model covariate screen examined height, age, race, blood type, IgG1, albumin, non-neutralising antibodies, hepatitis C virus status, and human immunodeficiency virus status. Only the three retained in the final model (VWF on CL, WT and HCT on V1) are implemented here. AGE on CL and HCV on CL were in the paper’s “full” model but were dropped during backward elimination and are not part of the published final model.