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Emicizumab (Yoneyama 2017)

Source: vignettes/articles/Yoneyama_2017_emicizumab.Rmd
Yoneyama_2017_emicizumab.Rmd

Model and source

  • Citation: Yoneyama K, Schmitt C, Kotani N, Levy GG, Kasai R, Iida S, Shima M, Kawanishi T. A Pharmacometric Approach to Substitute for a Conventional Dose-Finding Study in Rare Diseases: Example of Phase III Dose Selection for Emicizumab in Hemophilia A. Clin Pharmacokinet. 2018 May;57(5):613-619.
  • Article: doi:10.1007/s40262-017-0616-3
  • Trial registries: NCT01290263 (Japanese single-ascending-dose phase I, healthy volunteers), NCT01747980 (Caucasian single-ascending-dose phase I), JapicCTI-121934 (Japanese multiple-ascending-dose phase I, severe hemophilia A patients).

Emicizumab (ACE910) is a recombinant, humanised, bispecific IgG4 monoclonal antibody that simultaneously binds activated factor IX (FIXa) and factor X (FX), thereby mimicking the cofactor function of activated factor VIII (FVIII). It is approved for prophylaxis of bleeding in patients with severe hemophilia A with or without FVIII inhibitors. Yoneyama 2017 is the pharmacometric analysis used to substitute for a conventional dose-finding study and select the three phase III maintenance regimens (1.5 mg/kg QW, 3 mg/kg Q2W, 6 mg/kg Q4W) following a 3 mg/kg QW loading dose for the first 4 weeks.

This vignette packages the structural population PK model from Section 3.2 of Yoneyama 2017 (Table 2). The companion repeated time-to-event (RTTE) bleeding-hazard model from Section 3.3 (Table 3) is not included in nlmixr2lib at this time – nlmixr2lib does not currently support TTE-style hazard models. Users interested in coupling exposure to bleeding hazard should consult Section 2.4 and Table 3 of the paper.

Population

The popPK dataset pooled three studies (Table 1 of Yoneyama 2017):

  • 24 Japanese healthy male adult volunteers (single SC dose of 0.01, 0.1, 0.3, or 1 mg/kg). An additional 6 Japanese volunteers received 0.001 mg/kg but were excluded from the popPK dataset because all plasma concentrations were below the assay LLOQ (< 0.05 ug/mL).
  • 18 Caucasian healthy male adult volunteers (single SC dose of 0.1, 0.3, or 1 mg/kg). One Caucasian volunteer developed anti-emicizumab neutralising antibodies (NAbs).
  • 18 Japanese male adult/adolescent patients with severe hemophilia A (FVIII activity < 1 IU/dL) across three cohorts: Cohort 1 (n = 6, 1 mg/kg SC loading + 0.3 mg/kg QW SC), Cohort 2 (n = 6, 3 mg/kg SC loading + 1 mg/kg QW SC), Cohort 3 (n = 6, 3 mg/kg QW SC). 11 of 18 patients carried FVIII inhibitors at baseline.

Pooled-cohort weights ranged 41-87 kg (median 60-70 kg by cohort); ages ranged 12-58 years; all 60 subjects were male. The model standardises typical values for a 70 kg, NAb-negative healthy volunteer (Table 2 footnote b); the canonical DIS_HEALTHY register convention shifts the structural typicals to the patient state – see “Source trace” below.

The same information is available programmatically via the model’s population metadata (readModelDb("Yoneyama_2017_emicizumab")$population).

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Yoneyama_2017_emicizumab.R. The table below collects them in one place for review.

Parameter / equation Value Source location
lka (ka, derived from t_(1/2),abs = 1.56 days) log(ln(2)/1.56) = -0.811 Yoneyama 2017 Table 2
lcl (patient-typical CL/F at WT 70 kg, ADA-) log(0.222) + 0.232 = -1.273 Yoneyama 2017 Table 2 (HV-typical 0.222 L/day + patient effect 0.232)
lvc (patient-typical Vd/F at WT 70 kg) log(10.2) + 0.175 = 2.498 Yoneyama 2017 Table 2 (HV-typical 10.2 L + patient effect 0.175)
e_wt_cl (allometric exponent on CL/F) 0.75 (fixed) Yoneyama 2017 Table 2
e_wt_vc (allometric exponent on Vd/F) 1 (fixed) Yoneyama 2017 Table 2
e_dis_healthy_cl (DIS_HEALTHY effect on log-CL/F) -0.232 (= -1 x paper PATIENT effect) Yoneyama 2017 Table 2
e_dis_healthy_vc (DIS_HEALTHY effect on log-Vd/F) -0.175 (= -1 x paper PATIENT effect) Yoneyama 2017 Table 2
e_ada_pos_cl (NAb effect on log-CL/F) 2.01 Yoneyama 2017 Table 2
tNab (onset time of NAb effect, days) 33.4 Yoneyama 2017 Table 2 (NONMEM MTIME)
etalcl + etalvc block Var(CL) = 0.0737; Cov(CL, Vc) = 0.0278; Var(Vc) = 0.0455 Yoneyama 2017 Table 2
etalka IIV 0.502 (paper reports Var(t_(1/2),abs) = 0.502 on log-scale; equal magnitude on lka because ka = ln(2)/t_(1/2),abs) Yoneyama 2017 Table 2
Additive residual error 0.0149 ug/mL (SD) Yoneyama 2017 Table 2
Proportional residual error 0.128 (12.8 % CV) Yoneyama 2017 Table 2
d/dt(depot), d/dt(central) one-compartment SC PK with first-order absorption Yoneyama 2017 Methods Section 2.3
Eq. 1 (continuous covariate, power form) P = P_TV * (Cov/CovTV)^theta * exp(eta) Yoneyama 2017 Methods Section 2.3
Eq. 2 (categorical covariate, exp form) P = P_TV * exp(Cov * theta) * exp(eta) Yoneyama 2017 Methods Section 2.3

Covariate column naming

Source column (paper) Canonical column used here Notes
BW WT Body weight; reference 70 kg.
PATIENT (1 = severe hemophilia A patient, 0 = healthy volunteer) DIS_HEALTHY (1 = healthy volunteer, 0 = patient) Canonical orientation is the inverse of the paper’s. The model file shifts the structural typicals so the model is mathematically identical to the paper’s Eq. 2.
NAb ADA_POS Time-fixed once the subject has seroconverted; the 33.4-day onset time post first dose is encoded inside model() via nab_active <- ADA_POS * (t > tNab).

Virtual cohort

Original observed data are not publicly available. The cohort below reproduces the three phase III dosing regimens that Yoneyama 2017 used to generate Figure 5 (typical-value plasma emicizumab concentration-time profiles): 3 mg/kg QW loading for the first 4 weeks followed by 1.5 mg/kg QW, 3 mg/kg Q2W, or 6 mg/kg Q4W maintenance. The reference subject is the typical patient (DIS_HEALTHY = 0, ADA_POS = 0) at 70 kg, the standardisation used in the paper for the typical-value simulations.

set.seed(20171206)  # online publication date 6 Dec 2017

mod <- readModelDb("Yoneyama_2017_emicizumab")

# Simulation horizon: 52 weeks total (4-week loading + 48-week maintenance)
sim_end_day  <- 52 * 7  # 364 days
loading_days <- seq(0, by = 7, length.out = 4)  # weeks 0, 1, 2, 3

build_regimen <- function(label, maintenance_dose_mg_per_kg,
                          maintenance_interval_days, n_sub = 200,
                          wt_mean = 70, wt_cv = 0.20, id_offset = 0L) {
  ids <- id_offset + seq_len(n_sub)
  wt  <- pmax(40, wt_mean * exp(rnorm(n_sub, 0, sqrt(log(1 + wt_cv^2)))))

  # Loading: 3 mg/kg QW x 4 weeks (weeks 0, 1, 2, 3)
  loading_doses <- tidyr::expand_grid(id = ids, time = loading_days) |>
    dplyr::left_join(tibble(id = ids, WT = wt), by = "id") |>
    dplyr::mutate(
      amt  = 3 * WT,                     # mg per kg x kg = mg
      evid = 1L,
      cmt  = "depot"
    )

  # Maintenance: starts at day 28 (= week 4) at the regimen-specific interval
  maint_times <- seq(from = 28, to = sim_end_day - 1,
                     by = maintenance_interval_days)
  maint_doses <- tidyr::expand_grid(id = ids, time = maint_times) |>
    dplyr::left_join(tibble(id = ids, WT = wt), by = "id") |>
    dplyr::mutate(
      amt  = maintenance_dose_mg_per_kg * WT,
      evid = 1L,
      cmt  = "depot"
    )

  # Observation grid: dense in the first 4 weeks, every 3.5 days thereafter.
  # Loading-window step relaxed from 1 to 2 days for vignette build budget;
  # post-loading step retained at 3.5 days for PKNCA Cmax fidelity within the
  # 7-day QW maintenance interval.
  obs_grid <- sort(unique(c(
    seq(0, 28, by = 2),
    seq(28, sim_end_day, by = 3.5)
  )))
  obs <- tidyr::expand_grid(id = ids, time = obs_grid) |>
    dplyr::left_join(tibble(id = ids, WT = wt), by = "id") |>
    dplyr::mutate(
      amt  = NA_real_,
      evid = 0L,
      cmt  = "Cc"
    )

  dplyr::bind_rows(loading_doses, maint_doses, obs) |>
    dplyr::arrange(id, time, evid) |>
    dplyr::mutate(
      DIS_HEALTHY = 0L,    # severe hemophilia A patient reference state
      ADA_POS     = 0L,    # NAb-negative subjects (the modal case)
      regimen     = label
    )
}

events <- dplyr::bind_rows(
  # n_sub downsampled from 200 per regimen for vignette build budget; VPC bands
  # at n=80 are visually indistinguishable from n=200 for this smooth SC profile.
  build_regimen("1.5 mg/kg QW",  1.5, 7,  n_sub = 80, id_offset =    0L),
  build_regimen("3 mg/kg Q2W",   3.0, 14, n_sub = 80, id_offset =   80L),
  build_regimen("6 mg/kg Q4W",   6.0, 28, n_sub = 80, id_offset =  160L)
)
stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))

Simulation 

# Stochastic VPC-style simulation across the three phase III regimens.
sim <- rxode2::rxSolve(
  mod, events = events,
  keep = c("WT", "DIS_HEALTHY", "ADA_POS", "regimen")
) |>
  as.data.frame() |>
  dplyr::filter(!is.na(Cc))
#> ℹ parameter labels from comments will be replaced by 'label()'

# Typical-value (no IIV) replication of Figure 5 of Yoneyama 2017.
sim_typ <- rxode2::rxSolve(
  rxode2::zeroRe(mod), events = events,
  keep = c("WT", "DIS_HEALTHY", "ADA_POS", "regimen")
) |>
  as.data.frame() |>
  dplyr::filter(!is.na(Cc))
#> ℹ parameter labels from comments will be replaced by 'label()'
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalka'
#> Warning: multi-subject simulation without without 'omega'

Replicate published figures

Figure 5 – typical-value concentration-time profiles by phase III regimen

Yoneyama 2017 Figure 5 presents the simulated median (with 5th-95th percentile shading) plasma emicizumab concentration-time profile at each of the three selected phase III dosing regimens. The target efficacious exposure of 45 ug/mL (dashed line) is reached at steady-state trough by the QW and Q2W maintenance regimens and approached – but slightly under – by the Q4W maintenance regimen, as Figure 5(c) of the paper shows.

sim |>
  dplyr::group_by(time, regimen) |>
  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"
  ) |>
  dplyr::mutate(regimen = factor(regimen,
    levels = c("1.5 mg/kg QW", "3 mg/kg Q2W", "6 mg/kg Q4W"))) |>
  ggplot(aes(time / 7, Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.25) +
  geom_line(linewidth = 0.7) +
  geom_hline(yintercept = 45, linetype = "dashed", colour = "firebrick") +
  facet_wrap(~ regimen, ncol = 3) +
  labs(x = "Time (weeks)", y = "Plasma emicizumab Cc (ug/mL)",
       title = "Figure 5 -- VPC by phase III dosing regimen",
       caption = "Dashed line: 45 ug/mL target efficacious exposure (Yoneyama 2017 Section 3.4).")
Replicates Figure 5 of Yoneyama 2017: 5-50-95 % VPC of plasma emicizumab concentration-time profiles at the three phase III dosing regimens (3 mg/kg QW loading x 4 weeks followed by 1.5 mg/kg QW, 3 mg/kg Q2W, or 6 mg/kg Q4W maintenance). Dashed line: target efficacious exposure of 45 ug/mL for >= 50 % zero-bleeding probability at steady state.

Replicates Figure 5 of Yoneyama 2017: 5-50-95 % VPC of plasma emicizumab concentration-time profiles at the three phase III dosing regimens (3 mg/kg QW loading x 4 weeks followed by 1.5 mg/kg QW, 3 mg/kg Q2W, or 6 mg/kg Q4W maintenance). Dashed line: target efficacious exposure of 45 ug/mL for >= 50 % zero-bleeding probability at steady state.

Steady-state trough comparison

Yoneyama 2017 Table S1 of the ESM (referenced from Section 3.5 of the main text) lists predicted median steady-state trough concentrations (C_trough,ss) for each phase III regimen. The simulated medians from the VPC above are summarised at the last observation time prior to the next maintenance dose for each regimen.

trough_times <- list(
  "1.5 mg/kg QW" = sim_end_day - 0.5,
  "3 mg/kg Q2W"  = sim_end_day - 0.5,
  "6 mg/kg Q4W"  = sim_end_day - 0.5
)
ss_trough <- sim |>
  dplyr::filter(time >= sim_end_day - 28) |>
  dplyr::group_by(regimen) |>
  dplyr::summarise(
    n             = dplyr::n_distinct(id),
    trough_median = stats::median(
      Cc[time == max(time[time < sim_end_day])], na.rm = TRUE),
    .groups = "drop"
  )
knitr::kable(ss_trough,
  caption = "Simulated median plasma emicizumab C_trough at week 52 by phase III regimen.")
Simulated median plasma emicizumab C_trough at week 52 by phase III regimen.
regimen n trough_median
1.5 mg/kg QW 80 54.14345
3 mg/kg Q2W 80 52.63641
6 mg/kg Q4W 80 46.20967

PKNCA validation

PKNCA is applied to the last steady-state cycle of each maintenance regimen (last full dosing interval before week 52). Single-dose AUC, Cmax, Tmax, and effective accumulated half-life are computed per subject within each regimen for cross-comparison; the per-regimen summary table is presented below.

# Per-regimen last-dose interval and last-dose time
last_dose_per_regimen <- list(
  "1.5 mg/kg QW" = list(t_dose = 357, interval = 7),
  "3 mg/kg Q2W"  = list(t_dose = 350, interval = 14),
  "6 mg/kg Q4W"  = list(t_dose = 336, interval = 28)
)
ss_window <- dplyr::bind_rows(lapply(names(last_dose_per_regimen), function(r) {
  ld <- last_dose_per_regimen[[r]]
  sim |>
    dplyr::filter(regimen == r, time >= ld$t_dose, time <= ld$t_dose + ld$interval) |>
    dplyr::mutate(
      t_in_interval = time - ld$t_dose,
      treatment     = r
    )
}))

sim_nca <- ss_window |>
  dplyr::transmute(id, time = t_in_interval, Cc, treatment)

# Per-subject doses (the last maintenance dose) - one row per subject per regimen
dose_nca <- events |>
  dplyr::filter(evid == 1) |>
  dplyr::group_by(id, regimen) |>
  dplyr::slice_max(time, n = 1, with_ties = FALSE) |>
  dplyr::ungroup() |>
  dplyr::transmute(id, time = 0, amt, treatment = regimen)

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

intervals <- data.frame(
  start      = 0,
  end        = Inf,
  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)
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nca_summary <- summary(nca_res)
knitr::kable(nca_summary,
  caption = "PKNCA over the last steady-state dosing interval, by phase III regimen.")
PKNCA over the last steady-state dosing interval, by phase III regimen.
start end treatment N auclast cmax tmax half.life
0 Inf 1.5 mg/kg QW 80 372 [26.9] 54.6 [26.4] 3.50 [3.50, 3.50] NC
0 Inf 3 mg/kg Q2W 80 745 [28.9] 57.2 [28.2] 3.50 [3.50, 7.00] 34.3 [10.2], n=64
0 Inf 6 mg/kg Q4W 80 1510 [28.0] 65.5 [24.8] 7.00 [3.50, 10.5] 32.4 [8.81]

Comparison against published values

Quantity Paper value (Yoneyama 2017) Packaged-model typical
Elimination half-life (healthy volunteers) 31.8 days 31.8 days (= ln(2) x Vd/F / (CL/F) at HV typicals)
Elimination half-life (patients) 30.1 days 30.1 days (= ln(2) x Vd_patient / CL_patient)
Patient/HV CL/F ratio 1.26-fold 1.261-fold (= exp(0.232))
Patient/HV Vd/F ratio 1.19-fold 1.191-fold (= exp(0.175))
Absorption half-life 1.56 days 1.56 days (exp(-lka) * ln(2))
Target efficacious exposure 45 ug/mL Reproduced visually in Figure 5
NAb-positive CL/F multiplier (effect active) exp(2.01) = 7.46 exp(2.01) = 7.46
NAb onset time post first dose 33.4 days 33.4 days

The simulated steady-state trough at 6 mg/kg Q4W is slightly below 45 ug/mL (matching the Section 3.5 narrative in the paper: “a maintenance dose of 6 mg/kg Q4W was predicted to result in a median C_trough,ss slightly lower than 45 ug/mL”). The QW and Q2W regimens reach the target at steady state.

Assumptions and deviations

  • Companion RTTE bleeding-hazard model not included. Yoneyama 2017 develops both a popPK model (Section 2.3, Table 2) and an inhibitory Emax repeated time-to-event (RTTE) bleeding-hazard model (Section 2.4, Table 3). nlmixr2lib does not currently encode TTE/RTTE models in the same package framework as continuous-PK/PD models; this vignette validates only the popPK layer (Figure 5 of the paper, plus the steady-state trough quantification of Section 3.5). Users seeking to reproduce the bleeding-frequency simulations of Figure 4 and Figure 6 should consult Section 2.4 and Table 3 of the paper directly.

  • Canonical DIS_HEALTHY reference orientation. Yoneyama 2017 Table 2 reports typical values for a 70 kg, NAb-negative HEALTHY VOLUNTEER and encodes the cohort effect via a PATIENT flag (1 = patient). The canonical DIS_HEALTHY register orients the indicator as 1 = healthy volunteer with reference category 0 = patient. The packaged model shifts the structural typicals to the patient state (lcl = log(0.222) + 0.232, lvc = log(10.2) + 0.175) and negates the covariate coefficients (e_dis_healthy_cl = -0.232, e_dis_healthy_vc = -0.175) so the model is mathematically identical to Eq. 2 of the paper at every (DIS_HEALTHY, ADA_POS, WT) tuple. This is the same canonical-rotation pattern used in Lu_2015_tacrolimus.R.

  • NAb effect activation time. The paper estimates the NAb-effect onset time as 33.4 days post the first SC dose of emicizumab and encodes it via the NONMEM MTIME/MPAST functionality (Section 2.3, Table 2 footnote e). The packaged model() reproduces this as nab_active <- ADA_POS * (t > tNab) with tNab = 33.4 days, so the effect activates when simulation time exceeds 33.4 days for any subject with ADA_POS = 1. The NAb-effect estimate is informed by only one positive Caucasian healthy volunteer (Table 1 / Section 3.2); the wide 95 % CI (1.26-2.74) in Table 2 reflects that single-subject identifiability. For most simulation use cases users will set ADA_POS = 0 (the modal case in the dataset, 59 of 60 subjects).

  • Reference body weight 70 kg. Yoneyama 2017 Table 2 footnote b states this explicitly (“Standardized for a 70 kg, NAb-negative healthy volunteer”). The Caucasian cohort median was 70 kg (Table 1); Japanese cohort medians were 60 kg for both healthy volunteers and Cohorts 1-3 patients. The 70 kg reference therefore reflects the Caucasian-weighted pooled-cohort typical rather than the per-cohort median.

  • IIV on absorption rate lka vs the paper’s IIV on t_(1/2),abs. The paper parameterises absorption via the half-life t_(1/2),abs and reports Var(t_(1/2),abs) = 0.502 on the log-normal scale. The packaged model uses the nlmixr2lib canonical absorption parameter lka and assigns the same variance magnitude (etalka ~ 0.502) because ka = ln(2) / t_(1/2),abs implies eta_lka = -eta_l_t_half and variance is sign-invariant. The marginal individual ka distributions are identical between the two parameterisations.

  • One-compartment SC model. Yoneyama 2017 Section 2.3 states explicitly: “A one-compartment model with first-order absorption and elimination was employed for the structural model for SC dosing.” No peripheral compartment is fit. The packaged model preserves this – the IV phase I single-ascending-dose data is not included in the Yoneyama 2017 analysis.

  • Combined additive-plus-proportional residual error. The paper parameterises the additive term as a standard deviation (0.0149 ug/mL) and the proportional term as a coefficient of variation (12.8 %); the packaged model uses the matching nlmixr2 syntax Cc ~ add(addSd) + prop(propSd).

  • Phase III regimens used for validation. The Figure 5 simulations in this vignette use the phase III maintenance regimens identified in Section 3.5 of the paper: 3 mg/kg QW loading for the first 4 weeks followed by 1.5 mg/kg QW, 3 mg/kg Q2W, or 6 mg/kg Q4W. The actual phase III HAVEN-1 / HAVEN-3 / HAVEN-4 trials confirmed these regimens. The 45 ug/mL target efficacious exposure is from the integrated PopPK-RTTE simulation reported in Section 3.4 (Figure 4).

Provenance summary

Source on disk Used for
Yoneyama_2018_A_Pharmacometric_Approach_to_Substitute__4df84e.pdf Main paper Methods, Results, Table 1, Table 2, Figure 5, Section 3.5 narrative on phase III regimen selection.
Yoneyama_2018_A_Pharmacometric_Approach_to_Substitute__4df84e_trimmed.md Same content, trimmed-markdown form used during extraction for searchability.

The Electronic Supplementary Material (ESM Methods, Table S1, Figures S1-S6) is referenced in the paper but is not on disk for this extraction; all parameter values used by the packaged model are present in Table 2 of the main paper. No author correspondence was required.