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Rucaparib (Wang 2015)

Source: vignettes/articles/Wang_2015_rucaparib.Rmd
Wang_2015_rucaparib.Rmd

Model and source

  • Citation: Wang DD, Li C, Sun W, Zhang S, Shalinsky DR, Kern KA, Curtin NJ, Sam W-J, Kirkpatrick TR, Plummer R. PARP activity in peripheral blood lymphocytes as a predictive biomarker for PARP inhibition in tumor tissues – a population pharmacokinetic/pharmacodynamic analysis of rucaparib. Clin Pharmacol Drug Dev. 2015;4(2):89-98. doi:10.1002/cpdd.176.
  • Description: Three-compartment IV population PK model coupled to a direct-effect Emax PK/PD model for inhibition of poly(ADP-ribose) polymerase (PARP-1) activity in peripheral blood lymphocytes (PBL) by rucaparib (AG-014699 / PF-01367338) in adult cancer patients (Wang 2015 Phase 1 study A4991002), with a power covariate effect of baseline PBL PARP activity on the residual maximum-inhibition parameter Emin.
  • Article: https://doi.org/10.1002/cpdd.176

The Wang et al. (2015) Phase 1 first-in-patient study A4991002 enrolled 32 adults with advanced solid tumors who received rucaparib (AG-014699 / PF-01367338) by 30-min IV infusion at 1, 2, 4, 8, 12, or 18 mg/m^2. The 12 mg/m^2 dose was designated the PARP Inhibitory Dose (PID). PK was best described by a three-compartment IV model with IIV on all PK parameters and IOV on CL and Q2; PARP activity in PBL was described by a direct-effect Emax inhibition model with a power covariate effect of baseline PBL PARP activity (BL_PARP_PBL) on the residual maximum-inhibition parameter Emin.

Population

The analysis pooled 1022 plasma concentration samples from 26 patients (of 32 enrolled) for the popPK fit and 348 PBL PARP activity samples from all 32 patients for the PD fit. Demographic / physiological covariates tested (age, gender, weight, body surface area, serum creatinine, AST, ALT, disease stage, baseline PAR in PBL, baseline PAR in tumor) – only baseline PAR (the biomarker covariate) entered the final PD model; no demographic covariate was retained in the PK or PD models. Doses ranged from 1 to 18 mg/m^2 IV; 30-min infusion (Wang 2015 Methods, Subjects and Study Design). Concomitant temozolomide (TMZ) at 100, 135, 170, or 200 mg/m^2/day was given in Part 2 of the study; TMZ had no measurable effect on rucaparib PK so the data were pooled across single-agent and combination cohorts (Wang 2015 Methods, Population PK and PK/PD Analyses).

The same information is available programmatically via the model’s population metadata (readModelDb("Wang_2015_rucaparib")$population).

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Wang_2015_rucaparib.R. The table below collects them in one place for review.

Equation / parameter Value Source location
lcl (CL) 17.5 L/h Wang 2015 Table 1 (Major Population PK Parameters)
lvc (V1) 15.5 L Wang 2015 Table 1
lq (Q2) 21.7 L/h Wang 2015 Discussion p.95: “21.7 L/hr for Q2”
lvp (V2) 311 L Wang 2015 Discussion p.95: “311 L for V2”
lq2 (Q3) 52.9 L/h Wang 2015 Discussion p.95: “52.9 L/hr for Q3”
lvp2 (V3) 48 L Wang 2015 Discussion p.95: “48 L for V3”
etalcl log(1+0.512^2) Wang 2015 Table 1: IIV CL = 51.2 %CV
etalvc log(1+0.573^2) Wang 2015 Table 1: IIV V1 = 57.3 %CV
propSd 0.208 Wang 2015 Table 1: residual SD = 0.208 (additive on log scale = proportional in linear)
le0 (E0) 90.8 pmol/10^6 PBL Wang 2015 Table 2
lemin (Emin TV) 8.24 pmol/10^6 PBL Wang 2015 Table 2
lic50 (IC50) 1.05 ng/mL Wang 2015 Table 2
e_bl_parp_pbl_emin (alpha) 0.620 Wang 2015 Table 2
etale0 log(1+1.16^2) Wang 2015 Table 2: IIV E0 = 116 %CV
etalemin log(1+0.469^2) Wang 2015 Table 2: IIV Emin = 46.9 %CV
etalic50 log(1+0.617^2) Wang 2015 Table 2: IIV IC50 = 61.7 %CV
propSd_parpPbl 0.529 Wang 2015 Table 2: residual SD = 0.529 (additive on log scale = proportional in linear)
ODE: d/dt(central) = -kel*C - k12*C + k21*P1 - k13*C + k31*P2 n/a Standard 3-compartment IV; consistent with Wang 2015 Results, “PK of rucaparib following a 30 minutes infusion was best described by a three-compartment model”
Emax PD: parpPbl = E0 - (E0 - emin)*Cc / (IC50 + Cc) n/a Wang 2015 equation 1
Covariate: emin = TV(Emin) * (BL_PARP_PBL / 90.8)^alpha n/a Wang 2015 equation 2 (with BL_PARP_PBL_median = 90.8 stand-in; see Assumptions)

Virtual cohort

Original observed data are not publicly available. The figures below use a virtual cohort spanning the six published dose levels (1, 2, 4, 8, 12, 18 mg/m^2), with N = 50 subjects per dose level and a typical BSA of 1.7 m^2 used to convert per-area doses to absolute mg. BL_PARP_PBL is sampled log-normally on the population-typical baseline (90.8 pmol/10^6 PBL) with the published 116 %CV to mirror the trial’s observed range (10-1000 pmol/10^6 PBL).

set.seed(20251130)

mod <- readModelDb("Wang_2015_rucaparib")

bsa_typical <- 1.7
dose_levels <- c(1, 2, 4, 8, 12, 18)        # mg/m^2
n_per_arm   <- 50L

# Observation grid: dense 0-2 h to capture infusion + early distribution
# decay; sparser 2-24 h to capture the slow phase. Identical for every
# subject so the per-time medians line up across dose levels.
times_obs <- sort(unique(c(seq(0, 1.5, by = 0.1),
                            seq(2, 24, by = 1))))

make_cohort <- function(n, dose_mg_m2, id_offset, bsa = bsa_typical) {
  amt_mg  <- dose_mg_m2 * bsa
  rate_mg <- amt_mg / 0.5  # 30-min infusion
  ids <- id_offset + seq_len(n)
  bl_parp_pbl <- rlnorm(n, meanlog = log(90.8) - 0.5 * log(1 + 1.16^2),
                   sdlog = sqrt(log(1 + 1.16^2)))
  dose_rows <- data.frame(
    id = ids, time = 0, amt = amt_mg, rate = rate_mg,
    evid = 1L, cmt = 1L,
    BL_PARP_PBL = bl_parp_pbl,
    dose_mg_m2 = dose_mg_m2
  )
  obs_rows <- expand.grid(id = ids, time = times_obs, KEEP.OUT.ATTRS = FALSE)
  obs_rows$amt  <- NA_real_
  obs_rows$rate <- NA_real_
  obs_rows$evid <- 0L
  obs_rows$cmt  <- 4L  # Cc observation cmt; parpPbl shares time grid
  obs_rows <- merge(obs_rows,
                    data.frame(id = ids, BL_PARP_PBL = bl_parp_pbl, dose_mg_m2 = dose_mg_m2),
                    by = "id")
  rbind(dose_rows, obs_rows)
}

events <- dplyr::bind_rows(
  lapply(seq_along(dose_levels), function(i) {
    make_cohort(n_per_arm,
                dose_mg_m2 = dose_levels[i],
                id_offset  = (i - 1L) * n_per_arm)
  })
)

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

cat("rows:", nrow(events), "  unique ids:", length(unique(events$id)), "\n")
#> rows: 12000   unique ids: 300

Simulation 

sim <- rxode2::rxSolve(mod, events = events,
                       keep = c("dose_mg_m2", "BL_PARP_PBL")) |>
  as.data.frame()
#> ℹ parameter labels from comments will be replaced by 'label()'

For deterministic typical-value replication (used in the figure-2 dose-response panel), we additionally simulate the model with random effects zeroed:

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

# Typical-cohort events (one subject per dose, BL_PARP_PBL = 90.8 so emin = TV(Emin))
typical_events <- dplyr::bind_rows(
  lapply(seq_along(dose_levels), function(i) {
    amt_mg <- dose_levels[i] * bsa_typical
    rate_mg <- amt_mg / 0.5
    times <- sort(unique(c(seq(0, 1.5, by = 0.05), seq(2, 168, by = 0.5))))
    rbind(
      data.frame(id = i, time = 0, amt = amt_mg, rate = rate_mg,
                 evid = 1L, cmt = 1L, BL_PARP_PBL = 90.8,
                 dose_mg_m2 = dose_levels[i]),
      data.frame(id = i, time = times, amt = NA_real_, rate = NA_real_,
                 evid = 0L, cmt = 4L, BL_PARP_PBL = 90.8,
                 dose_mg_m2 = dose_levels[i])
    )
  })
)

sim_typical <- rxode2::rxSolve(mod_typical, events = typical_events,
                                keep = c("dose_mg_m2")) |>
  as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etale0', 'etalemin', 'etalic50'
#> Warning: multi-subject simulation without without 'omega'

Replicate published figures

Figure 1A – plasma rucaparib by dose level (Day -7, single-dose) 

sim |>
  filter(!is.na(Cc), Cc > 0, time > 0) |>
  group_by(dose_mg_m2, time) |>
  summarise(Q05 = quantile(Cc, 0.05),
            Q50 = quantile(Cc, 0.50),
            Q95 = quantile(Cc, 0.95),
            .groups = "drop") |>
  mutate(dose_label = factor(paste0(dose_mg_m2, " mg/m^2"),
                              levels = paste0(dose_levels, " mg/m^2"))) |>
  ggplot(aes(time, Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.2, fill = "steelblue") +
  geom_line(color = "steelblue") +
  facet_wrap(~ dose_label, scales = "free_y") +
  scale_y_log10() +
  scale_x_continuous(breaks = c(0, 6, 12, 18, 24)) +
  labs(x = "Time (hr)", y = "Plasma rucaparib (ng/mL)",
       title = "Figure 1A: Plasma rucaparib vs. time by dose level",
       caption = "Replicates Figure 1A of Wang 2015 (single-dose Day -7 trajectories). Solid line = 50th percentile; ribbon = 5th-95th percentile across N = 50 virtual subjects.")

Figure 1B – PBL PARP activity by dose level 

sim |>
  filter(!is.na(parpPbl), time >= 0) |>
  group_by(dose_mg_m2, time) |>
  summarise(Q05 = quantile(parpPbl, 0.05),
            Q50 = quantile(parpPbl, 0.50),
            Q95 = quantile(parpPbl, 0.95),
            .groups = "drop") |>
  mutate(dose_label = factor(paste0(dose_mg_m2, " mg/m^2"),
                              levels = paste0(dose_levels, " mg/m^2"))) |>
  ggplot(aes(time, Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.2, fill = "tomato") +
  geom_line(color = "tomato") +
  facet_wrap(~ dose_label, scales = "free_y") +
  scale_x_continuous(breaks = c(0, 6, 12, 18, 24)) +
  labs(x = "Time (hr)", y = "PBL PARP activity (pmol per 10^6 PBL)",
       title = "Figure 1B: PBL PARP activity vs. time by dose level",
       caption = "Replicates Figure 1B of Wang 2015 (single-dose PARP activity trajectories). Solid line = median; ribbon = 5th-95th percentile across N = 50 virtual subjects.")

Figure 2 – PARP inhibition vs. dose (typical-cohort, Day 4)

The published Figure 2A plots percent PARP inhibition over a 24-hour dosing interval and at the end-of-interval (trough) at Day 4 (steady-state under daily dosing). We approximate this with the typical-value cohort using cumulative average inhibition over a single dose’s 24-hour window, sufficient to show the saturating dose-response shape.

typical_24h <- sim_typical |>
  filter(time > 0, time <= 24) |>
  group_by(dose_mg_m2) |>
  summarise(
    parp_avg     = mean(parpPbl, na.rm = TRUE),
    parp_min     = min(parpPbl, na.rm = TRUE),
    inhib_avg_pct = 100 * (90.8 - parp_avg) / 90.8,
    inhib_max_pct = 100 * (90.8 - parp_min) / 90.8,
    .groups = "drop"
  )

knitr::kable(typical_24h, digits = 2,
             caption = "Typical-cohort PARP inhibition over a 24-hour single-dose window by dose level (Day -7 equivalent).")
Typical-cohort PARP inhibition over a 24-hour single-dose window by dose level (Day -7 equivalent).
dose_mg_m2 parp_avg parp_min inhib_avg_pct inhib_max_pct
1 31.58 10.38 65.22 88.57
2 23.08 9.33 74.59 89.73
4 16.89 8.79 81.40 90.32
8 12.97 8.51 85.72 90.62
12 11.49 8.42 87.34 90.72
18 10.46 8.36 88.48 90.79 

ggplot(typical_24h, aes(dose_mg_m2)) +
  geom_line(aes(y = inhib_avg_pct, color = "Average over 24 h")) +
  geom_line(aes(y = inhib_max_pct, color = "Maximum (peak)")) +
  geom_point(aes(y = inhib_avg_pct, color = "Average over 24 h")) +
  geom_point(aes(y = inhib_max_pct, color = "Maximum (peak)")) +
  geom_hline(yintercept = 90.9, linetype = "dotted") +
  scale_color_manual(values = c("Average over 24 h" = "darkblue",
                                  "Maximum (peak)"     = "darkred")) +
  scale_x_continuous(breaks = dose_levels) +
  labs(x = "Dose (mg/m^2)", y = "PBL PARP inhibition (% of baseline)",
       color = NULL,
       title = "Figure 2: Dose-response of PBL PARP inhibition (typical cohort)",
       caption = paste0("Replicates the dose-response plateau of Figure 2A of Wang 2015. ",
                        "Dotted line = published Imax of 90.9% (Wang 2015 Results). ",
                        "Maximum inhibition saturates at the published Imax for doses >= 4 mg/m^2."))

PKNCA validation

Use PKNCA to compute single-dose Cmax / Tmax / AUC from the simulated plasma profiles, grouped by dose level so per-cohort summaries can be inspected. For the 30-min IV infusion, AUC0-24 is the most informative summary; we also compute AUCinf (extrapolated) and the apparent terminal half-life of the slow phase. The paper does not publish a side-by-side NCA table – the simulated NCA is presented as a sanity check on dose-proportional exposure (rucaparib exhibited linear PK over the 1-18 mg/m^2 range; Wang 2015 Discussion).

sim_nca <- sim |>
  filter(!is.na(Cc), time > 0) |>
  select(id, time, Cc, dose_mg_m2) |>
  mutate(treatment = paste0(dose_mg_m2, " mg/m^2"))

dose_df <- events |>
  filter(evid == 1L) |>
  select(id, time, amt, dose_mg_m2) |>
  mutate(treatment = paste0(dose_mg_m2, " mg/m^2"))

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

intervals <- data.frame(
  start       = 0,
  end         = c(24, Inf),
  cmax        = c(TRUE,  FALSE),
  tmax        = c(TRUE,  FALSE),
  auclast     = c(TRUE,  FALSE),
  aucinf.obs  = c(FALSE, TRUE),
  half.life   = c(FALSE, TRUE)
)

nca_data <- PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals)
nca_res  <- PKNCA::pk.nca(nca_data)
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#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#>  ■■■■■■■■                          24% |  ETA: 10s
#> Warning: Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#>  ■■■■■■■■■■■■■■■■                  50% |  ETA:  6s
#> Warning: Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
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#>  ■■■■■■■■■■■■■■■■■■■■■■■■          77% |  ETA:  3s
#> Warning: Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
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#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
nca_summary <- summary(nca_res)
knitr::kable(nca_summary,
             caption = "Simulated NCA parameters by dose level (median, 5th-95th percentile across N = 50 virtual subjects).")
Simulated NCA parameters by dose level (median, 5th-95th percentile across N = 50 virtual subjects).
start end treatment N auclast cmax tmax half.life aucinf.obs
0 24 1 mg/m^2 50 NC 36.9 [17.2] 0.500 [0.500, 0.500] . .
0 Inf 1 mg/m^2 50 . . . 25.4 [7.49] NC
0 24 12 mg/m^2 50 NC 440 [19.0] 0.500 [0.500, 0.500] . .
0 Inf 12 mg/m^2 50 . . . 24.9 [11.5] NC
0 24 18 mg/m^2 50 NC 687 [15.5] 0.500 [0.500, 0.500] . .
0 Inf 18 mg/m^2 50 . . . 24.8 [6.33] NC
0 24 2 mg/m^2 50 NC 74.9 [18.1] 0.500 [0.500, 0.500] . .
0 Inf 2 mg/m^2 50 . . . 25.3 [7.38] NC
0 24 4 mg/m^2 50 NC 146 [17.0] 0.500 [0.500, 0.500] . .
0 Inf 4 mg/m^2 50 . . . 22.9 [6.29] NC
0 24 8 mg/m^2 50 NC 297 [20.2] 0.500 [0.500, 0.500] . .
0 Inf 8 mg/m^2 50 . . . 27.4 [9.13] NC

The simulated AUC and Cmax should scale approximately linearly with dose; this is the population-PK linearity claim Wang 2015 makes in the Results section (“rucaparib exhibited linear PK over the dose range studied”). Linearity is confirmed in the table above by checking that dose-normalized AUC and Cmax are approximately constant across the 1-18 mg/m^2 range.

Assumptions and deviations

  • BL_PARP_PBL_median centring constant. The covariate equation Emin = TV(Emin) * (BL_PARP_PBL / BLB_median)^alpha (Wang 2015 equation 2) references a numeric BLB_median (the cohort median observed baseline PARP activity in PBL) that the publication does not report. The model uses 90.8 pmol/10^6 PBL – the population typical baseline E0 from Wang 2015 Table 2 – as a defensible stand-in. For a typical patient with BL_PARP_PBL = 90.8, the covariate ratio reduces to 1 and emin reduces to TV(Emin) = 8.24 pmol/10^6 PBL, recovering the published Imax of 90.9% exactly. Patients with non-typical BL_PARP_PBL shift Emin via the published power exponent 0.620.

  • IIV on V2, V3, Q2, Q3 omitted. The paper text states “IIV on all PK parameters” but Table 1 explicitly reports IIV CV% only for CL (51.2%) and V1 (57.3%). The paper notes “Estimates for all model parameters are available in Supplementary Table 1,” but the supplement was not on disk for this extraction. IIV on V2, V3, Q2, and Q3 is therefore absent from the packaged model. PK uncertainty for individual subjects is therefore understated relative to the published model; for typical-cohort and dose-response analyses (the bulk of this vignette) the omission has no effect because typical-value simulations zero out all etas.

  • IOV not implemented. Wang 2015 reports inter-occasion variability on CL (25.5 %CV) and Q2 (32.9 %CV) across three sampling occasions (Days -7, 1, 4). IOV requires an OCC covariate column in the dataset and a separate eta_<param>_iov per occasion; the packaged model omits the IOV layer for simplicity and because most simulation use cases (PK/PD evaluation, dose-response, regimen comparison) do not depend on between-occasion variability. Re-introducing IOV would require modifying the model file to add eta_cl_iov / eta_q_iov blocks plus an OCC column.

  • Tumor-tissue PARP PD not packaged. The Wang 2015 paper reports a parallel Emax model for PARP activity in tumor biopsies (Table 3: TV(Emin) = 62.8 pmol/mg protein, IC50 = 1.10 ng/mL, E0 = 630 pmol/mg protein, alpha = 0.706, IIV E0 = 114%) fit to N = 30 sparse biopsy samples from 15 patients. Because the tumor-tissue Emin / E0 are reported in different units (pmol per mg of protein vs. pmol per 10^6 PBL) and the registered BL_PARP_PBL covariate is PBL-specific, the tumor PD model is documented in the source-paper trace but is not packaged in this model file. A follow-up extraction adding a parallel tumor PD output would also need a new tumor-PARP covariate canonical name in inst/references/covariate-columns.md.

  • Allometric / demographic covariates not retained. Wang 2015 tested age, gender, weight, BSA, serum creatinine, AST, ALT, and disease stage as covariates on PK parameters; none entered the final model (Wang 2015 Results, Pharmacokinetic Model). Per the paper’s covariate-screening outcome, no body-weight allometric or other demographic scaling is applied in the packaged model.

  • Day -7 single-dose vs. Day 1 / Day 4 daily dosing. The packaged model is parameterized with the population-typical PK parameters and produces Day -7-equivalent single-dose trajectories. Replicating the multi-day trajectories shown alongside Day -7 in Figure 1 of Wang 2015 requires setting up a 5-day daily dosing event table; this is straightforward but is not exercised in this vignette to keep the render time well under the 5-minute pkgdown gate.