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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;57(9):1123-1134. doi:10.1007/s40262-017-0616-3.
  • 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 Used for
Main paper (PDF) Methods, Results, Table 1, Table 2, Figure 5, Section 3.5 narrative on phase III regimen selection.

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