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Marzeptacog alfa (activated) (Faraj 2022)

Source: vignettes/articles/Faraj_2022_marzeptacogAlfa.Rmd
Faraj_2022_marzeptacogAlfa.Rmd

Model and source

  • Citation: Faraj A, Knudsen T, Desai S, Neuman L, Blouse GE, Simonsson USH. Phase III dose selection of marzeptacog alfa (activated) informed by population pharmacokinetic modeling: A novel hemostatic drug. CPT Pharmacometrics Syst Pharmacol. 2022;11(12):1628-1637. doi:[10.1002/psp4.12872](https://doi.org/10.1002/psp4.12872)
  • Description: Two-compartment population PK model for marzeptacog alfa (activated) (MarzAA), an activated recombinant human factor VII (rFVIIa) variant, after intravenous and subcutaneous dosing in adult males with haemophilia A or B.
  • Article: https://doi.org/10.1002/psp4.12872
  • Modality: recombinant protein (activated FVII variant), intravenous and subcutaneous.

Faraj 2022 pooled MarzAA concentrations from three trials and built the model in sequential steps: intravenous data first (two-compartment disposition), then subcutaneous absorption, then a joint re-estimation. The final model (Results “Model development”; parameters in supplementary Table S1; NONMEM control stream in supplementary Data S1) has

  • two-compartment disposition with linear elimination (Michaelis-Menten elimination was dropped in the last step, dOFV = +4.3, with no change in the VPCs);
  • subcutaneous input as a zero-order release of duration D1 into an absorption depot followed by first-order absorption (ka) into the central compartment, with a logit-transformed bioavailability F;
  • allometric body-weight scaling, fixed exponents 0.75 (CL, Q) and 1 (Vc, Vp), reference 70 kg;
  • an estimated endogenous FVIIa baseline added to the drug concentration, because the clotting-activity assay measures endogenous FVIIa as well as MarzAA;
  • IIV on CL and Vc (correlated), baseline, F and ka; inter-occasion variability (IOV) on D1, F and Vc; proportional residual error.

The model was then used to simulate candidate phase III regimens (Table 2, Figure 2) against a target of 24 ng/mL.

Population

46 adult males with haemophilia A or B, with or without inhibitors, from three trials (NCT01439971, NCT04072237, NCT03407651), contributing 1225 observations (Methods “Study design and patients”, Table 1). Median body weight 75 kg (10th-90th percentile 60-94 kg; range 43-120 kg); median age 32 years (10th-90th percentile 23-52 years; range 18-62 years). Doses: single i.v. 4.5-30 ug/kg; single s.c. 30-120 ug/kg; 60 ug/kg s.c. two or three times 3 h apart; and daily s.c. 30 ug/kg (escalated to 60 ug/kg on breakthrough bleeding) for 50 days. Race and region were not reported. The same information is in the model’s population metadata.

Source trace

Element Value Source
Structure: 2-cmt, zero-order into depot then first-order ka – Results “Model development” final paragraph; Data S1 $DES
Baseline added to drug concentration IPRED = BASE + A(2)/Vc Methods “Model building”; Data S1 $ERROR
Allometry, reference 70 kg CL, Q: 0.75; Vc, Vp: 1 Methods “Model building”; Data S1 $PK
lcl 1085 mL/h Table S1
lvc 3393 mL Table S1
lvp 619 mL Table S1
lq 213 mL/h Table S1
lrbase 0.96 ng/mL Table S1
lka 0.05 1/h Table S1
logitfdepot logit(0.26) Table S1; Data S1 PHI = LOG(TVF1/(1-TVF1))
ld1 0.875 h Table S1
etalcl, etalvc 28%, 26%, correlation 0.92 Table S1
etalrbase 56% Table S1
etalogitfdepot 54% (logit scale) Table S1
etalka 30% Table S1
etaiov_ld1_* 61% Table S1; Data S1 IOV block
etaiov_logitfdepot_* 21% (logit scale) Table S1; Data S1 IOV block
etaiov_lvc_* 45% Table S1; Data S1 IOV block
propSd 29% Table S1; Data S1 Y = IPRED*EXP(EPS(1))

Virtual cohort and simulation

Faraj 2022 simulated 1000 subjects per regimen with body weight drawn from a truncated normal distribution (bounds 40-105 kg) using the mean and SD of the analysis data set. The mean and SD are not printed; they are approximated here from the median (75 kg) and 10th-90th percentiles (60-94 kg) as mean 76 kg, SD 13.3 kg. Each arm uses 200 subjects. Subcutaneous doses go to the depot compartment with rate = -2 so that the modelled zero-order duration D1 applies.

All simulated subjects take OCC = 2, i.e. one subcutaneous occasion with its IOV draw. The paper does not say whether its simulations included IOV; with IOV the simulated Tmax 80% interval matches Table 2 (5.3-11.1 h for a single dose), while without IOV it is about half as wide, so IOV is kept.

rxode2::rxSetSeed(20221216)
set.seed(20221216)
n_per_arm <- 200

draw_wt <- function(n) {
  x <- rnorm(5 * n, mean = 76, sd = 13.3)
  x[x >= 40 & x <= 105][seq_len(n)]
}

regimens <- tibble::tribble(
  ~treatment,             ~dose, ~times,
  "60 ug/kg single",      60,    list(0),
  "90 ug/kg single",      90,    list(0),
  "120 ug/kg single",     120,   list(0),
  "60 ug/kg x2 (0, 3 h)", 60,    list(c(0, 3)),
  "60 ug/kg x3 (0, 3, 6 h)", 60, list(c(0, 3, 6))
)

obs_times <- sort(unique(c(seq(0, 24, by = 0.25))))

make_arm <- function(k) {
  r <- regimens[k, ]
  wt <- draw_wt(n_per_arm)
  ids <- (k - 1) * n_per_arm + seq_len(n_per_arm)
  dose_times <- r$times[[1]][[1]]
  doses <- expand.grid(i = seq_len(n_per_arm), time = dose_times)
  doses <- data.frame(
    id = ids[doses$i], time = doses$time, evid = 1L,
    amt = r$dose * wt[doses$i], cmt = "depot", rate = -2,
    WT = wt[doses$i]
  )
  obs <- expand.grid(i = seq_len(n_per_arm), time = obs_times)
  obs <- data.frame(
    id = ids[obs$i], time = obs$time, evid = 0L,
    amt = 0, cmt = "central", rate = 0,
    WT = wt[obs$i]
  )
  out <- rbind(doses, obs)
  out$OCC <- 2L
  out$treatment <- r$treatment
  out
}

events <- do.call(rbind, lapply(seq_len(nrow(regimens)), make_arm))
events <- events[order(events$id, events$time, -events$evid), ]
mod <- readModelDb("Faraj_2022_marzeptacogAlfa")
sim <- rxode2::rxSolve(
  mod, events,
  keep = c("treatment", "WT"),
  returnType = "data.frame"
)
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_ld1_2, etaiov_ld1_3, etaiov_ld1_4, etaiov_ld1_5, etaiov_ld1_6, etaiov_ld1_7, etaiov_ld1_8, etaiov_ld1_9, etaiov_logitfdepot_2, etaiov_logitfdepot_3, etaiov_logitfdepot_4, etaiov_logitfdepot_5, etaiov_logitfdepot_6, etaiov_logitfdepot_7, etaiov_logitfdepot_8, etaiov_logitfdepot_9, etaiov_lvc_2, etaiov_lvc_3, etaiov_lvc_4, etaiov_lvc_5, etaiov_lvc_6, etaiov_lvc_7, etaiov_lvc_8, etaiov_lvc_9
#> as a work-around try putting the mu-referenced expression on a simple line
sim <- sim |>
  mutate(treatment = factor(treatment, levels = regimens$treatment))
stopifnot(!anyNA(sim$Cc))

Cc is the individual prediction without residual error and, like the paper’s predictions, includes the endogenous FVIIa baseline.

Concentration-time profiles 

sim |>
  group_by(treatment, time) |>
  summarise(
    med = median(Cc), lo = quantile(Cc, 0.1), hi = quantile(Cc, 0.9),
    .groups = "drop"
  ) |>
  ggplot(aes(time, med)) +
  geom_ribbon(aes(ymin = lo, ymax = hi), alpha = 0.25) +
  geom_line() +
  geom_hline(yintercept = c(24, 120), linetype = "dashed") +
  facet_wrap(~treatment) +
  scale_y_log10() +
  labs(
    x = "Time after first dose (h)", y = "FVIIa activity (ng/mL)",
    caption = "Median and 80% prediction interval; dashed lines: 24-120 ng/mL target range."
  )

Percentage of the population above target (Figure 2) 

above <- sim |>
  group_by(treatment, time) |>
  summarise(pct = 100 * mean(Cc >= 24), .groups = "drop")

ggplot(above, aes(time, pct, colour = treatment)) +
  geom_line() +
  geom_hline(yintercept = 90, linetype = "dashed") +
  labs(
    x = "Time after first dose (h)", y = "Population above 24 ng/mL (%)",
    colour = NULL,
    caption = "Replicates Figure 2 of Faraj 2022."
  )

The paper reports the percentages at selected times in Results “Clinical trial simulations” and the Discussion.

ref_above <- tibble::tribble(
  ~treatment,              ~time, ~paper,
  "60 ug/kg single",       3,     51,
  "90 ug/kg single",       3,     74,
  "120 ug/kg single",      3,     86,
  "60 ug/kg single",       6,     70,
  "90 ug/kg single",       6,     87,
  "120 ug/kg single",      6,     94,
  "60 ug/kg single",       24,    33,
  "90 ug/kg single",       24,    63,
  "120 ug/kg single",      24,    78,
  "60 ug/kg x2 (0, 3 h)",  6,     90,
  "60 ug/kg x2 (0, 3 h)",  24,    81,
  "60 ug/kg x3 (0, 3, 6 h)", 9,   96
)
cmp_above <- ref_above |>
  left_join(above |> mutate(treatment = as.character(treatment)),
            by = c("treatment", "time")) |>
  mutate(diff = pct - paper)
cmp_above |>
  dplyr::rename(
    Regimen = treatment, "Time (h)" = time, "Paper (%)" = paper,
    "Simulated (%)" = pct, "Difference (points)" = diff
  ) |>
  knitr::kable(digits = 0)
Regimen Time (h) Paper (%) Simulated (%) Difference (points)
60 ug/kg single 3 51 58 7
90 ug/kg single 3 74 74 0
120 ug/kg single 3 86 86 0
60 ug/kg single 6 70 77 7
90 ug/kg single 6 87 86 0
120 ug/kg single 6 94 96 2
60 ug/kg single 24 33 34 2
90 ug/kg single 24 63 64 2
120 ug/kg single 24 78 80 2
60 ug/kg x2 (0, 3 h) 6 90 91 1
60 ug/kg x2 (0, 3 h) 24 81 86 6
60 ug/kg x3 (0, 3, 6 h) 9 96 99 3

The simulated percentages agree with the paper within a few points. With 200 subjects per arm the binomial standard error is up to 3.5 points, so differences of 5-7 points at a single time point are within sampling noise.

# 200 subjects per arm gives a binomial SE of up to 3.5 points per time point;
# a transcription error in F, ka, CL or a volume moves these by tens of points.
stopifnot(
  abs(median(cmp_above$diff)) < 5,
  quantile(abs(cmp_above$diff), 0.9) < 12
)

NCA (PKNCA) and comparison with Table 2

Table 2 reports the median and 80% prediction interval of Cmax, Tmax, Cmin and AUC over 0-24 h. After the subcutaneous doses the concentration rises until Tmax and then declines, so the paper’s Cmin over 24 h is the concentration at 24 h; it is compared with PKNCA’s clast.obs (last observation, at 24 h). The 0-24 h minimum including the pre-dose time point would be the endogenous baseline instead.

conc <- sim |>
  dplyr::filter(!is.na(Cc)) |>
  select(id, time, Cc, treatment)
dose <- events |>
  dplyr::filter(evid == 1) |>
  select(id, time, amt, treatment) |>
  mutate(treatment = factor(treatment, levels = regimens$treatment))

conc_obj <- PKNCA::PKNCAconc(conc, Cc ~ time | treatment + id)
dose_obj <- PKNCA::PKNCAdose(dose, amt ~ time | treatment + id)
intervals <- data.frame(
  start = 0, end = 24,
  cmax = TRUE, tmax = TRUE, clast.obs = TRUE, auclast = TRUE
)
nca <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals))
reference <- tibble::tribble(
  ~treatment,                ~cmax, ~tmax, ~clast.obs, ~auclast,
  "60 ug/kg single",         34.5,  7.8,   19.3,       604,
  "90 ug/kg single",         51.1,  7.8,   28.3,       905.3,
  "120 ug/kg single",        67.7,  7.8,   37.4,       1207.1,
  "60 ug/kg x2 (0, 3 h)",    68.7,  9.5,   40.4,       1166,
  "60 ug/kg x3 (0, 3, 6 h)", 106.1, 11.6,  66.7,       1715
)
tbl <- nlmixr2lib::ncaComparisonTable(
  simulated = nca,
  reference = reference,
  by = "treatment",
  units = c(cmax = "ng/mL", tmax = "h", clast.obs = "ng/mL", auclast = "h*ng/mL")
)
knitr::kable(tbl)
NCA parameter treatment Reference Simulated % diff
Cmax (ng/mL) 60 ug/kg single 34.5 35.4 +2.5%
Cmax (ng/mL) 90 ug/kg single 51.1 50.1 -2.1%
Cmax (ng/mL) 120 ug/kg single 67.7 68.9 +1.8%
Cmax (ng/mL) 60 ug/kg x2 (0, 3 h) 68.7 62.7 -8.8%
Cmax (ng/mL) 60 ug/kg x3 (0, 3, 6 h) 106 97.2 -8.4%
Tmax (h) 60 ug/kg single 7.8 7.5 -3.8%
Tmax (h) 90 ug/kg single 7.8 8 +2.6%
Tmax (h) 120 ug/kg single 7.8 8 +2.6%
Tmax (h) 60 ug/kg x2 (0, 3 h) 9.5 9.5 +0.0%
Tmax (h) 60 ug/kg x3 (0, 3, 6 h) 11.6 11.8 +1.3%
Clast (ng/mL) 60 ug/kg single 19.3 19.8 +2.7%
Clast (ng/mL) 90 ug/kg single 28.3 30.6 +8.1%
Clast (ng/mL) 120 ug/kg single 37.4 38.8 +3.8%
Clast (ng/mL) 60 ug/kg x2 (0, 3 h) 40.4 39.1 -3.3%
Clast (ng/mL) 60 ug/kg x3 (0, 3, 6 h) 66.7 64.2 -3.7%
AUClast (h*ng/mL) 60 ug/kg single 604 659 +9.1%
AUClast (h*ng/mL) 90 ug/kg single 905 936 +3.4%
AUClast (h*ng/mL) 120 ug/kg single 1210 1260 +4.7%
AUClast (h*ng/mL) 60 ug/kg x2 (0, 3 h) 1170 1120 -3.9%
AUClast (h*ng/mL) 60 ug/kg x3 (0, 3, 6 h) 1720 1690 -1.6% 
if (!is.null(attr(tbl, "footnote"))) cat(attr(tbl, "footnote"))
pct <- as.numeric(gsub("[^0-9.-]", "", tbl[["% diff"]]))
stopifnot(!anyNA(pct))
# Medians of 200 subjects; a mis-transcribed F, ka, CL or volume moves the
# whole distribution by tens of percent.
stopifnot(
  abs(median(pct)) < 7,
  quantile(abs(pct), 0.9) < 15
)

All simulated medians are within 10% of Table 2. The two repeated-dose Cmax rows run about 8% below the paper; Tmax, the 24 h concentration and AUC0-24 for the same regimens agree within 4%.

The 80% prediction intervals are compared for the single 60 ug/kg dose, where Table 2 prints Cmax 17.6-68.5 ng/mL, Tmax 5.3-11.1 h and AUC0-24 310-1190 h*ng/mL.

nca$result |>
  dplyr::filter(treatment == "60 ug/kg single",
                PPTESTCD %in% c("cmax", "tmax", "clast.obs", "auclast")) |>
  group_by(PPTESTCD) |>
  summarise(
    median = median(PPORRES), p10 = quantile(PPORRES, 0.1),
    p90 = quantile(PPORRES, 0.9), .groups = "drop"
  ) |>
  dplyr::rename(Parameter = PPTESTCD, Median = median, "10th pct" = p10, "90th pct" = p90) |>
  knitr::kable(digits = 1)
Parameter Median 10th pct 90th pct
auclast 659.2 338.4 1306.0
clast.obs 19.8 10.3 40.6
cmax 35.4 17.6 72.9
tmax 7.5 5.2 11.0

Intravenous dosing

A typical-value profile after the 18 ug/kg i.v. dose used in two of the trials, beside the 60 ug/kg subcutaneous dose, for a 70 kg subject. The subcutaneous profile is absorption-limited (ka = 0.05 1/h is well below the elimination rate constant CL/Vc = 0.32 1/h).

typ_ev <- rbind(
  data.frame(id = 1L, time = 0, evid = 1L, amt = 18 * 70, cmt = "central", rate = 0),
  data.frame(id = 1L, time = seq(0, 48, by = 0.25), evid = 0L, amt = 0, cmt = "central", rate = 0),
  data.frame(id = 2L, time = 0, evid = 1L, amt = 60 * 70, cmt = "depot", rate = -2),
  data.frame(id = 2L, time = seq(0, 48, by = 0.25), evid = 0L, amt = 0, cmt = "central", rate = 0)
)
typ_ev$WT <- 70
typ_ev$OCC <- 1L
typ <- rxode2::rxSolve(rxode2::zeroRe(mod), typ_ev, returnType = "data.frame") |>
  mutate(route = ifelse(id == 1, "18 ug/kg i.v.", "60 ug/kg s.c."))
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_ld1_2, etaiov_ld1_3, etaiov_ld1_4, etaiov_ld1_5, etaiov_ld1_6, etaiov_ld1_7, etaiov_ld1_8, etaiov_ld1_9, etaiov_logitfdepot_2, etaiov_logitfdepot_3, etaiov_logitfdepot_4, etaiov_logitfdepot_5, etaiov_logitfdepot_6, etaiov_logitfdepot_7, etaiov_logitfdepot_8, etaiov_logitfdepot_9, etaiov_lvc_2, etaiov_lvc_3, etaiov_lvc_4, etaiov_lvc_5, etaiov_lvc_6, etaiov_lvc_7, etaiov_lvc_8, etaiov_lvc_9
#> as a work-around try putting the mu-referenced expression on a simple line
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_ld1_2, etaiov_ld1_3, etaiov_ld1_4, etaiov_ld1_5, etaiov_ld1_6, etaiov_ld1_7, etaiov_ld1_8, etaiov_ld1_9, etaiov_logitfdepot_2, etaiov_logitfdepot_3, etaiov_logitfdepot_4, etaiov_logitfdepot_5, etaiov_logitfdepot_6, etaiov_logitfdepot_7, etaiov_logitfdepot_8, etaiov_logitfdepot_9, etaiov_lvc_2, etaiov_lvc_3, etaiov_lvc_4, etaiov_lvc_5, etaiov_lvc_6, etaiov_lvc_7, etaiov_lvc_8, etaiov_lvc_9
#> as a work-around try putting the mu-referenced expression on a simple line
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalrbase', 'etalogitfdepot', 'etalka', 'etaiov_ld1_2', 'etaiov_ld1_3', 'etaiov_ld1_4', 'etaiov_ld1_5', 'etaiov_ld1_6', 'etaiov_ld1_7', 'etaiov_ld1_8', 'etaiov_ld1_9', 'etaiov_logitfdepot_2', 'etaiov_logitfdepot_3', 'etaiov_logitfdepot_4', 'etaiov_logitfdepot_5', 'etaiov_logitfdepot_6', 'etaiov_logitfdepot_7', 'etaiov_logitfdepot_8', 'etaiov_logitfdepot_9', 'etaiov_lvc_2', 'etaiov_lvc_3', 'etaiov_lvc_4', 'etaiov_lvc_5', 'etaiov_lvc_6', 'etaiov_lvc_7', 'etaiov_lvc_8', 'etaiov_lvc_9'
#> Warning: multi-subject simulation without without 'omega'
stopifnot(!anyNA(typ$Cc))
ggplot(typ, aes(time, Cc, colour = route)) +
  geom_line() +
  scale_y_log10() +
  labs(x = "Time (h)", y = "FVIIa activity (ng/mL)", colour = NULL)

Assumptions and deviations

  • Random-effect scale. Table S1 prints all random effects as percentages. They are read as 100 x the SD of the eta, so each variance is (value/100)^2. This is the only reading available for the logit-scale F etas, whose percentages cannot be log-normal CVs; for the log-normal parameters the difference from the log-normal CV conversion is small (for example 0.314 vs 0.272 for the 56% baseline IIV).
  • CL-Vc correlation. Table S1 “Covariance between CL and V (%)” = 92 is read as a correlation of 0.92 (covariance 0.92 x 0.28 x 0.26 = 0.0670).
  • Initial versus final estimates. The $THETA and $OMEGA values in Data S1 are initial estimates (for example CL 1300 mL/h, Vp 988 mL) and differ from the final values in Table S1, which are used here. Data S1 is used only for the model structure.
  • Fixed-to-zero terms omitted. Data S1 carries an absorption lag time fixed at 0 and IIV on Vp and D1 fixed at 0; these are left out. Q and Vp have no IIV.
  • Occasions. Data S1 indexes the IOV on the data column REGI: REGI = 1 has no IOV, and REGI = 2-9 each have their own IOV eta with a shared variance. The model’s OCC column takes the REGI value. The paper does not define REGI beyond describing IOV for subcutaneous data obtained on more than one occasion per subject. Use OCC = 1 for no IOV, or 2-9 for separate occasions.
  • Simulation cohort. The paper simulated 1000 subjects per regimen with weights from a truncated normal distribution using the data-set mean and SD, which are not printed; this vignette uses 200 per regimen with mean 76 kg and SD 13.3 kg, approximated from the printed median and 10th-90th percentiles. Whether the paper’s simulations included IOV is not stated; including it reproduces the Table 2 Tmax interval.
  • Age. Age on ka was statistically significant but not clinically relevant and was not retained in the final model; no coefficient is printed, so it is recorded only in covariatesDataExcluded.
  • Endogenous baseline. Cc includes the endogenous FVIIa baseline (typical 0.96 ng/mL). To get the MarzAA contribution alone, subtract rbase or set lrbase to a very small value.