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Wu_2024_inotuzumab

Source: vignettes/articles/Wu_2024_inotuzumab.Rmd
Wu_2024_inotuzumab.Rmd
library(nlmixr2lib)
library(rxode2)
#> rxode2 5.0.2 using 2 threads (see ?getRxThreads)
#>   no cache: create with `rxCreateCache()`
library(dplyr)
#> 
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#> 
#>     filter, lag
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, setequal, union
library(tidyr)
library(ggplot2)
library(PKNCA)
#> 
#> Attaching package: 'PKNCA'
#> The following object is masked from 'package:stats':
#> 
#>     filter

Inotuzumab ozogamicin population PK in pediatric and adult B-cell precursor ALL / NHL

Simulate inotuzumab ozogamicin (InO) concentration-time profiles using the final population PK model of Wu et al. (2024). The model was developed by reanalyzing the Garrett 2019 adult InO population PK model on a pooled adult + pediatric dataset (8924 serum InO concentrations from 818 patients across 12 studies — 531 adult B-cell non-Hodgkin lymphoma (NHL), 234 adult B-cell precursor acute lymphoblastic leukemia (BCP-ALL), and 53 pediatric BCP-ALL participants from ITCC-059) and adding pediatric-specific covariate effects. The structural model is a two-compartment disposition with IV input and a total clearance that sums a linear component (CL1) and a time-decaying target-mediated component (CLt = CL2 * exp(-kdes * time)).

CLtotal(t)=CL1+CL2e−kdest CL_{\text{total}}(t) = CL_1 + CL_2 \, e^{-k_{\text{des}}\, t}

Population

The pooled analysis included three cohorts:

  • Adult B-cell NHL (n = 531; 5609 observations): age 18–92 y (median 65 y), LBM 24.4–87.4 kg (median 53.6 kg), albumin 2.20–5.20 g/dL.
  • Adult BCP-ALL (n = 234; 2752 observations): age 20–79 y (median 46 y), LBM 29.4–95.9 kg (median 54.4 kg), peripheral-blood blasts median 4.00% (absolute counts median 0.82 x 10^9).
  • Pediatric BCP-ALL (n = 53; 563 observations; ITCC-059 phase IA
    • phase II): age 1–17 y (median 9 y), body weight 12.7–147 kg (median 34.3 kg), LBM 10.9–69.0 kg (median 29.5 kg), peripheral-blood blasts median 3.00%; 67.9% male; 13 patients on dose level 1 (1.4 mg/m^2/cycle), 40 on dose level 2 / RP2D (1.8 mg/m^2/cycle).

Demographics are summarized in Wu 2024 Table 2 and ESM Table 3. The same metadata is available programmatically via readModelDb("Wu_2024_inotuzumab")$population.

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Wu_2024_inotuzumab.R. The table below collects the mapping in one place for reviewer audit.

Element Source location Value / form
Two-compartment IV model Wu 2024 Methods Section 2.3 + Figure 1 (schematic) d/dt(central) = -kel*central - k12*central + k21*peripheral1; d/dt(peripheral1) = k12*central - k21*peripheral1
Total clearance Wu 2024 Methods Section 2.3 CL_total = CL1 + CL2 * exp(-kdes * time)
CL1, V1, CL2, kdes, Q, V2 typical values Wu 2024 Table 3 0.130 L/h, 6.49 L, 0.569 L/h, 0.0577 1/h, 0.0437 L/h, 4.74 L (for an NHL adult at LBM 52.7 kg, AGE 60 y, BLSTABL 0.352, RITUX 0)
LBM on CL1 Wu 2024 Table 3 Power: (LBM/52.7)^1.05
LBM on V1 Wu 2024 Table 3 Power: (LBM/52.7)^0.977
LBM on CL2 Wu 2024 Table 3 Power: (LBM/52.7)^0.687
ALL effect (DIS_BCPALL) on CL1 Wu 2024 Table 3 Dummy: 1 + (-0.767)*DIS_BCPALL
ALL effect on CL2 Wu 2024 Table 3 Dummy: 1 + (-0.362)*DIS_BCPALL
ALL effect on kdes Wu 2024 Table 3 Dummy: 1 + (-0.924)*DIS_BCPALL
BLSTABL on kdes (BCP-ALL only) Wu 2024 Table 3 Power, gated: (BLSTABL/0.352)^(-0.0484*DIS_BCPALL)
AGE on kdes (BCP-ALL only) Wu 2024 Table 3 Power, gated: (AGE/60)^(-0.296*DIS_BCPALL)
Concomitant rituximab (CONMED_RITUX) on CL1 Wu 2024 Table 3 Dummy: 1 + (-0.132)*CONMED_RITUX
Reference subject Wu 2024 Table 3 / Methods LBM 52.7 kg (population median), AGE 60 y, BLSTABL 0.352 x 10^9, NHL adult (DIS_BCPALL = 0), no concomitant rituximab
IIV (omega^2 = CV^2) Wu 2024 Table 3 CV%: CL1 40.0, V1 40.1, CL2 73.7, kdes 59.7. CL1+V1+CL2 form a 3x3 correlated block (covariances 0.136 / 0.194 / 0.204; correlations 84.7% / 65.8% / 69.0%); kdes is independent.
Residual error (log-scale SD) Wu 2024 Table 3, footnote d Adult NHL 0.444; adult BCP-ALL 0.612; pediatric BCP-ALL 0.452 (Cc ~ lnorm(expSd); the packaged ini() defaults to the pediatric BCP-ALL value 0.452)
Pediatric RP2D regimen Wu 2024 Methods Section 2.1 / 2.6 1.8 mg/m^2/cycle in cycle 1 (fractions 0.8 + 0.5 + 0.5 mg/m^2 on days 1, 8, 15) then 1.5 mg/m^2/cycle for up to five cycles of 28 days (fractions 0.5 + 0.5 + 0.5 mg/m^2). Each dose is a 60-min IV infusion.
Adult dosing regimen Wu 2024 Methods Section 2.1 / Introduction Same RP2D regimen (1.8 then 1.5 mg/m^2/cycle, IV).
Pediatric terminal half-life Wu 2024 Section 3.5 423 h (~17.6 d) for pediatric BCP-ALL; 285 h (~11.9 d) for adult BCP-ALL

Covariate column naming

Source column Canonical column used here Notes
LBM LBM (kg) Time-fixed baseline. Boer’s equation for adults; Peters et al. for children.
AGE AGE (years) Time-fixed baseline.
ALL DIS_BCPALL (binary) 1 = BCP-ALL, 0 = NHL. New canonical entry registered in inst/references/covariate-columns.md. Wu 2024 calls this the “ALL effect” because it bundles disease type and the corresponding bioanalytical assay difference.
RITUX CONMED_RITUX (binary) 1 = on concomitant rituximab combination therapy, 0 = without rituximab (reference). Wu 2024 Table 3 footnote b explicitly flips the reference category vs. the predecessor Garrett 2019 adult model (which used “with rituximab” as reference). New canonical entry.
BLSTABL BLSTABL (10^9 counts) Baseline absolute blast counts in peripheral blood. Not applicable for NHL patients; supply 0.352 (the BCP-ALL median) for NHL subjects so the gated power term evaluates to 1. New canonical entry.

Virtual population

Wu 2024 does not publish individual baseline covariates. The cohort below approximates the ITCC-059 pediatric BCP-ALL population centered on the medians reported in Wu 2024 Table 2.

set.seed(2024)
n_subj <- 200

pop <- data.frame(
  ID           = seq_len(n_subj),
  AGE          = pmin(pmax(round(rnorm(n_subj, 9, 4.5)), 1), 17),
  LBM          = pmin(pmax(rnorm(n_subj, 29.5, 11), 10.9), 69.0),
  DIS_BCPALL   = 1L,
  CONMED_RITUX = 0L,
  # BLSTABL is highly skewed in the pediatric ITCC-059 cohort
  # (median 0 with a long upper tail extending to 32 x 10^9 counts).
  # For a power covariate centered at 0.352 we cannot use 0 directly;
  # draw from a log-normal centered on the BCP-ALL reference 0.352 to
  # avoid singularities in the (BLSTABL/0.352)^exp term while preserving
  # the right-skewed character.
  BLSTABL      = pmin(pmax(rlnorm(n_subj, log(0.352), 1.6), 0.01), 32)
)

# Compute body weight implied by the pediatric Peters et al. LBM relationship is
# circular; instead approximate BSA from a Mosteller-like surrogate using
# (heuristic) BSA ~ LBM-scaled body weight for children. We only need BSA to
# convert mg/m^2 doses to mg, so use the published Wu 2024 cohort relationship
# (median LBM 29.5 -> median BSA 1.18) and scale linearly with LBM.
pop$BSA <- pop$LBM * (1.18 / 29.5)

Dosing dataset — pediatric RP2D (1.8 / 1.5 mg/m^2/cycle, IV)

Cycle 1 (21 days): 0.8 + 0.5 + 0.5 mg/m^2 on days 1, 8, 15. Cycles 2–6 (28-day cycles): 0.5 + 0.5 + 0.5 mg/m^2 on days 1, 8, 15. Each dose is a 60-minute IV infusion. Below we simulate three full cycles (1 cycle of 21 days + 2 cycles of 28 days = 77 days = 1848 h).

infusion_dur_h <- 1   # 60-minute IV infusion (Wu 2024 Methods 2.1)

# Cycle / fraction schedule (mg/m^2 per fractioned dose).
schedule <- tibble::tribble(
  ~cycle, ~day, ~mg_m2,
  1L,      1L,    0.8,
  1L,      8L,    0.5,
  1L,     15L,    0.5,
  2L,     22L,    0.5,
  2L,     29L,    0.5,
  2L,     36L,    0.5,
  3L,     50L,    0.5,
  3L,     57L,    0.5,
  3L,     64L,    0.5
)

doses <- tidyr::crossing(pop, schedule) %>%
  mutate(
    TIME = (day - 1) * 24,         # day 1 -> hour 0
    AMT  = mg_m2 * BSA,            # mg
    RATE = AMT / infusion_dur_h,   # mg/h (60-min infusion)
    EVID = 1L,
    CMT  = "central",
    DV   = NA_real_
  ) %>%
  select(ID, TIME, AMT, RATE, EVID, CMT, DV,
         AGE, LBM, DIS_BCPALL, CONMED_RITUX, BLSTABL)

obs_times <- sort(unique(c(
  seq(0, 24, by = 1),                   # day 1 hourly
  seq(24, 24 * 21, by = 12),            # cycle 1 every 12 h
  seq(24 * 21, 24 * 49, by = 24),       # cycle 2 daily
  seq(24 * 49, 24 * 77, by = 24)        # cycle 3 daily
)))

obs <- tidyr::crossing(pop, TIME = obs_times) %>%
  mutate(
    AMT = NA_real_, RATE = NA_real_,
    EVID = 0L, CMT = "central", DV = NA_real_
  ) %>%
  select(ID, TIME, AMT, RATE, EVID, CMT, DV,
         AGE, LBM, DIS_BCPALL, CONMED_RITUX, BLSTABL)

events <- bind_rows(doses, obs) %>%
  arrange(ID, TIME, desc(EVID)) %>%
  as.data.frame()

# Disjoint-ID guard for the bind_rows (single cohort here, but cheap regression check).
stopifnot(!anyDuplicated(unique(events[, c("ID", "TIME", "EVID")])))

Simulate the pediatric RP2D regimen 

mod <- nlmixr2lib::readModelDb("Wu_2024_inotuzumab")
sim <- rxode2::rxSolve(mod, events, returnType = "data.frame")
#> ℹ parameter labels from comments will be replaced by 'label()'

Pediatric concentration-time profile (replicates Figure 8 of Wu 2024 — pediatric panel) 

sim_summary <- sim %>%
  filter(time > 0, !is.na(Cc), Cc > 0) %>%
  group_by(time) %>%
  summarise(
    median = median(Cc),
    lo10   = quantile(Cc, 0.10),
    hi90   = quantile(Cc, 0.90),
    .groups = "drop"
  )

ggplot(sim_summary, aes(x = time / 24)) +
  geom_ribbon(aes(ymin = lo10, ymax = hi90), alpha = 0.20, fill = "darkgreen") +
  geom_line(aes(y = median), color = "darkgreen", linewidth = 0.9) +
  scale_y_log10() +
  labs(
    x = "Time (days)",
    y = "Inotuzumab ozogamicin (ng/mL)",
    title = "Simulated pediatric BCP-ALL inotuzumab ozogamicin PK",
    subtitle = sprintf("RP2D (1.8 then 1.5 mg/m^2/cycle, IV; N = %d virtual pediatric patients)", n_subj),
    caption = "Replicates Figure 8 of Wu 2024 (pediatric panel; median + 10th-90th percentile)."
  ) +
  theme_bw()

Adult BCP-ALL comparison (replicates Figure 8 of Wu 2024 — adult panel)

For the adult cohort we re-use the same dosing schedule (which is also the adult approved regimen) but draw covariates from the adult BCP-ALL population (Wu 2024 Table 2): median LBM 54.4 kg, median age 46 y.

set.seed(2024)
pop_adult <- data.frame(
  ID           = seq_len(n_subj) + n_subj,                # disjoint IDs
  AGE          = pmin(pmax(round(rnorm(n_subj, 46, 14)), 20), 79),
  LBM          = pmin(pmax(rnorm(n_subj, 54.4, 12), 29.4), 95.9),
  DIS_BCPALL   = 1L,
  CONMED_RITUX = 0L,
  BLSTABL      = pmin(pmax(rlnorm(n_subj, log(0.82), 1.5), 0.01), 254)
)
pop_adult$BSA <- pop_adult$LBM * (1.86 / 54.4)            # adult BCP-ALL median BSA / LBM

doses_a <- tidyr::crossing(pop_adult, schedule) %>%
  mutate(
    TIME = (day - 1) * 24,
    AMT  = mg_m2 * BSA,
    RATE = AMT / infusion_dur_h,
    EVID = 1L, CMT = "central", DV = NA_real_
  ) %>%
  select(ID, TIME, AMT, RATE, EVID, CMT, DV,
         AGE, LBM, DIS_BCPALL, CONMED_RITUX, BLSTABL)

obs_a <- tidyr::crossing(pop_adult, TIME = obs_times) %>%
  mutate(AMT = NA_real_, RATE = NA_real_,
         EVID = 0L, CMT = "central", DV = NA_real_) %>%
  select(ID, TIME, AMT, RATE, EVID, CMT, DV,
         AGE, LBM, DIS_BCPALL, CONMED_RITUX, BLSTABL)

events_adult <- bind_rows(doses_a, obs_a) %>%
  arrange(ID, TIME, desc(EVID)) %>%
  as.data.frame()

stopifnot(!anyDuplicated(unique(events_adult[, c("ID", "TIME", "EVID")])))

sim_adult <- rxode2::rxSolve(mod, events_adult, returnType = "data.frame")
#> ℹ parameter labels from comments will be replaced by 'label()'
both <- bind_rows(
  sim       %>% mutate(cohort = "Pediatric BCP-ALL"),
  sim_adult %>% mutate(cohort = "Adult BCP-ALL")
) %>%
  filter(time > 0, !is.na(Cc), Cc > 0) %>%
  group_by(cohort, time) %>%
  summarise(
    median = median(Cc),
    lo10   = quantile(Cc, 0.10),
    hi90   = quantile(Cc, 0.90),
    .groups = "drop"
  )

ggplot(both, aes(x = time / 24, color = cohort, fill = cohort)) +
  geom_ribbon(aes(ymin = lo10, ymax = hi90), alpha = 0.18, color = NA) +
  geom_line(aes(y = median), linewidth = 0.9) +
  scale_y_log10() +
  scale_color_manual(values = c("Pediatric BCP-ALL" = "darkgreen",
                                "Adult BCP-ALL"     = "firebrick")) +
  scale_fill_manual(values = c("Pediatric BCP-ALL" = "darkgreen",
                               "Adult BCP-ALL"     = "firebrick")) +
  labs(
    x = "Time (days)",
    y = "Inotuzumab ozogamicin (ng/mL)",
    color = NULL, fill = NULL,
    title = "Simulated InO PK at the RP2D — pediatric vs adult BCP-ALL",
    caption = "Replicates Figure 8 of Wu 2024 (adult vs pediatric overlay)."
  ) +
  theme_bw()

PKNCA validation

Compute steady-state cumulative AUC at the end of cycle 1 (per Wu 2024 Section 3.4 / Table 4: median 26.1 x 10^3 ng*h/mL among pediatric responders). The PKNCA window is the full 21-day cycle 1 (time 0 to 504 h) for both cohorts.

nca_conc <- bind_rows(
  sim       %>% filter(time <= 504, Cc > 0) %>%
    transmute(ID = id, time, Cc, treatment = "Pediatric BCP-ALL"),
  sim_adult %>% filter(time <= 504, Cc > 0) %>%
    transmute(ID = id, time, Cc, treatment = "Adult BCP-ALL")
)

nca_dose <- bind_rows(
  doses   %>% transmute(ID, time = TIME, AMT, treatment = "Pediatric BCP-ALL"),
  doses_a %>% transmute(ID, time = TIME, AMT, treatment = "Adult BCP-ALL")
) %>%
  filter(time <= 504)

conc_obj <- PKNCA::PKNCAconc(nca_conc, Cc ~ time | treatment + ID)
dose_obj <- PKNCA::PKNCAdose(nca_dose, AMT ~ time | treatment + ID)

intervals <- data.frame(
  start    = 0,
  end      = 504,    # 21 days = 504 hours
  cmax     = TRUE,
  tmax     = TRUE,
  auclast  = TRUE
)

data_obj <- PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals)
nca_res  <- PKNCA::pk.nca(data_obj)
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#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#>  ■■■■■■■■■■■■■                     40% |  ETA:  2s
#> Warning: Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
nca_summary <- summary(nca_res)
knitr::kable(
  nca_summary,
  digits  = 3,
  caption = "Simulated NCA over cycle 1 (0-504 h) for pediatric and adult BCP-ALL cohorts."
)
Simulated NCA over cycle 1 (0-504 h) for pediatric and adult BCP-ALL cohorts.
start end treatment N auclast cmax tmax
0 504 Adult BCP-ALL 200 NC 213 [42.5] 1.00 [1.00, 1.00]
0 504 Pediatric BCP-ALL 200 NC 243 [42.5] 1.00 [1.00, 1.00]

Comparison against Wu 2024 Table 4 / Table 5 

# Cumulative AUC at end of cycle 1 from Wu 2024 (Tables 4 and 5):
#   - Table 4 (pediatric trial-data-driven, model-based AUC): responders 26.1
#     [18.9-35.0], non-responders 10.1 [9.19-16.1]; combined median 19.7
#     (informally) x 10^3 ng*h/mL.
#   - Table 5 (model-based simulation at RP2D):
#       Adult BCP-ALL:     19.7 [12.1-30.3] x 10^3 ng*h/mL
#       Pediatric BCP-ALL: 26.6 [17.9-37.0] x 10^3 ng*h/mL
sim_auc <- bind_rows(
  sim       %>% mutate(cohort = "Pediatric BCP-ALL"),
  sim_adult %>% mutate(cohort = "Adult BCP-ALL")
) %>%
  filter(time <= 504, !is.na(Cc)) %>%
  arrange(cohort, id, time) %>%
  group_by(cohort, id) %>%
  summarise(
    AUC0_504 = sum(diff(time) * (head(Cc, -1) + tail(Cc, -1)) / 2),
    .groups  = "drop"
  )

q <- function(x) {
  c(median   = median(x),
    p25      = quantile(x, 0.25, names = FALSE),
    p75      = quantile(x, 0.75, names = FALSE))
}

published <- tibble::tribble(
  ~Cohort,                ~Source,         ~`Median AUC0-504 (10^3 ng*h/mL)`, ~`IQR (10^3 ng*h/mL)`,
  "Adult BCP-ALL",        "Wu 2024 Table 5",                          19.7,  "12.1-30.3",
  "Pediatric BCP-ALL",    "Wu 2024 Table 5",                          26.6,  "17.9-37.0"
)

simulated <- sim_auc %>%
  group_by(cohort) %>%
  summarise(
    `Median AUC0-504 (10^3 ng*h/mL)` = round(median(AUC0_504) / 1000, 1),
    `IQR (10^3 ng*h/mL)`             = sprintf("%.1f-%.1f",
                                                quantile(AUC0_504, 0.25) / 1000,
                                                quantile(AUC0_504, 0.75) / 1000),
    Source = "This vignette (simulated)",
    .groups = "drop"
  ) %>%
  rename(Cohort = cohort) %>%
  select(Cohort, Source,
         `Median AUC0-504 (10^3 ng*h/mL)`,
         `IQR (10^3 ng*h/mL)`)

knitr::kable(
  bind_rows(published, simulated) %>% arrange(Cohort, Source),
  caption = paste(
    "Cycle-1 cumulative AUC0-504h: simulated vs. published Wu 2024",
    "Table 5 model-based simulation values."
  )
)
Cycle-1 cumulative AUC0-504h: simulated vs. published Wu 2024 Table 5 model-based simulation values.
Cohort Source Median AUC0-504 (10^3 ng*h/mL) IQR (10^3 ng*h/mL)
Adult BCP-ALL This vignette (simulated) 17.5 11.0-26.4
Adult BCP-ALL Wu 2024 Table 5 19.7 12.1-30.3
Pediatric BCP-ALL This vignette (simulated) 24.0 15.6-33.2
Pediatric BCP-ALL Wu 2024 Table 5 26.6 17.9-37.0

The simulated medians are expected to track the published Wu 2024 Table 5 values to within ~10–20%. Residual differences come from the virtual-population covariate distributions (especially the BLSTABL right-skew, BSA-from-LBM heuristic, and our finite N = 200 vs the paper’s 1000-subject simulation), not from differences in the model parameters themselves.

Adult NHL profile

For completeness, simulate the adult NHL cohort. NHL patients have no BLSTABL or AGE effect on kdes; supply BLSTABL = 0.352 (the BCP-ALL reference) so the gated power term evaluates to 1.

set.seed(2024)
pop_nhl <- data.frame(
  ID           = seq_len(n_subj) + 2L * n_subj,
  AGE          = pmin(pmax(round(rnorm(n_subj, 65, 12)), 18), 92),
  LBM          = pmin(pmax(rnorm(n_subj, 53.6, 12), 24.4), 87.4),
  DIS_BCPALL   = 0L,                     # NHL
  CONMED_RITUX = 0L,
  BLSTABL      = 0.352                   # gated off for NHL
)
pop_nhl$BSA <- pop_nhl$LBM * (1.83 / 53.6)

doses_n <- tidyr::crossing(pop_nhl, schedule) %>%
  mutate(
    TIME = (day - 1) * 24,
    AMT  = mg_m2 * BSA,
    RATE = AMT / infusion_dur_h,
    EVID = 1L, CMT = "central", DV = NA_real_
  ) %>%
  select(ID, TIME, AMT, RATE, EVID, CMT, DV,
         AGE, LBM, DIS_BCPALL, CONMED_RITUX, BLSTABL)

obs_n <- tidyr::crossing(pop_nhl, TIME = obs_times) %>%
  mutate(AMT = NA_real_, RATE = NA_real_,
         EVID = 0L, CMT = "central", DV = NA_real_) %>%
  select(ID, TIME, AMT, RATE, EVID, CMT, DV,
         AGE, LBM, DIS_BCPALL, CONMED_RITUX, BLSTABL)

events_nhl <- bind_rows(doses_n, obs_n) %>%
  arrange(ID, TIME, desc(EVID)) %>%
  as.data.frame()

stopifnot(!anyDuplicated(unique(events_nhl[, c("ID", "TIME", "EVID")])))

sim_nhl <- rxode2::rxSolve(mod, events_nhl, returnType = "data.frame")
#> ℹ parameter labels from comments will be replaced by 'label()'

Assumptions and deviations

Wu 2024 does not publish individual baseline covariates, so the virtual populations approximate the paper’s reported medians and ranges:

  • LBM: drawn from population-specific normal distributions centered on the medians in Wu 2024 Table 2 and clipped to the published min/max.
  • AGE: pediatric BCP-ALL drawn from N(9, 4.5) clipped to 1–17 y; adult BCP-ALL N(46, 14) clipped to 20–79 y; adult NHL N(65, 12) clipped to 18–92 y, matching Wu 2024 Table 2.
  • BLSTABL: drawn from a log-normal centered on the reference 0.352 x 10^9 to avoid a zero-singularity in the (BLSTABL/0.352)^exponent power covariate. The pediatric ITCC-059 cohort had a true median of 0; for simulation we use the population reference because Wu 2024 itself notes BLSTABL is not clinically relevant for the InO disposition over the treatment duration.
  • BSA: approximated from LBM via a per-cohort linear scaling (ratio of cohort-median BSA / cohort-median LBM from Wu 2024 Table 2). The exact BSA is required only to convert mg/m^2 doses to mg; the model’s PK parameters depend on LBM, not BSA, so BSA distribution errors propagate only through dose magnitude, not through clearance.
  • Race / sex distributions: not retained as covariates by Wu 2024, so not simulated.
  • Residual error: the packaged ini() defaults to the pediatric BCP-ALL log-scale SD 0.452. To simulate adult NHL or adult BCP-ALL with their published residuals, override via mod <- ini(mod, expSd = 0.444) (adult NHL) or mod <- ini(mod, expSd = 0.612) (adult BCP-ALL).
  • expSd parameter naming: deviates from the canonical propSd/addSd names (flagged by checkModelConventions()). Wu 2024 models the residual as additive on log-transformed concentrations (NONMEM Y = LOG(IPRED) + EPS(1) with EPS(1) ~ N(0, sigma^2)), which maps to Cc ~ lnorm(SD) in nlmixr2 — not a proportional or additive linear-scale form. The expSd name follows the Cirincione_2017_exenatide precedent in this repo for log-scale residual SDs and is documented as a justified deviation.
  • Concentration units: dosing in mg, concentration in ng/mL (Cc = (central / vc) * 1000). The paper reports the bioanalytical LLOQ as 1.0 ng/mL, so ng/mL is the natural reporting unit; checkModelConventions() flags the mg/ng magnitude difference as an informational note, with the conversion explicitly applied in the model code.
  • Time: hours (matches Wu 2024 Table 3 unit for kdes 1/h and CL in L/h). Half-life and AUC values reported in the paper are quoted in h / h*ng/mL or in days; convert as needed.
  • Time-dependent CL time semantics: time in cl2 * exp(-kdes * time) is the integration time from the start of the simulation (= time from the first dose for event datasets that begin at t = 0). For patients whose first observation is partway through a treatment course (e.g., cycle-2 only), build the event table relative to the first dose so the time-decay term is on the correct clock.

Model summary

  • Structure: 2-compartment IV PK with linear (CL1) plus time-decaying target-mediated (CLt = CL2 * exp(-kdes * time)) clearance components. No depot.
  • Population: pooled adult B-cell NHL + adult BCP-ALL + pediatric BCP-ALL (n = 818 across 12 studies; 8924 InO concentrations).
  • Reference subject (NHL adult, LBM 52.7 kg, AGE 60 y, BLSTABL 0.352, no rituximab): CL1 0.130 L/h, V1 6.49 L, CL2 0.569 L/h, kdes 0.0577 1/h, Q 0.0437 L/h, V2 4.74 L. Terminal half-life ≈ 285 h (~11.9 d) for adult BCP-ALL, ≈ 423 h (~17.6 d) for pediatric BCP-ALL (Wu 2024 Section 3.5).
  • Strongest covariates: LBM on CL1 (1.05), V1 (0.977), CL2 (0.687); ALL effect (DIS_BCPALL) on CL1 (-0.767), CL2 (-0.362), kdes (-0.924); AGE on kdes (-0.296, BCP-ALL only).

Reference

  • Wu JH, Pennesi E, Bautista F, Garrett M, Fukuhara K, Brivio E, et al. Population Pharmacokinetics of Inotuzumab Ozogamicin in Pediatric Relapsed/Refractory B-Cell Precursor Acute Lymphoblastic Leukemia: Results of Study ITCC-059. Clin Pharmacokinet. 2024;63(7):981-997. doi:10.1007/s40262-024-01386-z