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Nivolumab and ipilimumab pediatric population PK (Hu 2024)

Source: vignettes/articles/Hu_2024_nivolumab_ipilimumab_pediatric.Rmd
Hu_2024_nivolumab_ipilimumab_pediatric.Rmd

Model and source

Hu 2024 developed two independent pooled adult-plus-pediatric population PK models – one for nivolumab, one for ipilimumab – to answer a single question: after body size has been accounted for, is there anything left of the pediatric-versus-adult difference in monoclonal-antibody PK? The answer the paper reaches is yes, and that the residual effect is tumour-type dependent. Because the authors fitted the two drugs separately, on different datasets and with different structural forms (nivolumab time-varying clearance, ipilimumab stationary clearance), the extraction is two model files sharing this one vignette.

nivo <- rxode2::rxode(readModelDb("Hu_2024_nivolumab"))
#> ℹ parameter labels from comments will be replaced by 'label()'
ipi  <- rxode2::rxode(readModelDb("Hu_2024_ipilimumab"))
#> ℹ parameter labels from comments will be replaced by 'label()'
  • Citation: Hu Z, Liu S, Zhao Y, Du S, Hamuro L, Shen J, Roy A, Zhu L. Nivolumab and ipilimumab population pharmacokinetics in support of pediatric dose recommendations-Going beyond the body-size effect. CPT Pharmacometrics Syst Pharmacol. 2024;13(3):476-493. doi:10.1002/psp4.13098
  • Nivolumab model: Two-compartment population PK model with time-varying clearance for intravenous nivolumab (anti-PD-1 IgG4) in a pooled adult and pediatric (1-17 years) oncology population, with tumor-type-dependent pediatric effects on baseline clearance beyond body size (Hu 2024)
  • Ipilimumab model: Two-compartment population PK model with stationary clearance for intravenous ipilimumab (anti-CTLA-4 IgG1) in a pooled adult and pediatric (1-17 years) oncology population, with tumor-type-dependent pediatric effects on clearance beyond body size (Hu 2024)
  • Article: https://doi.org/10.1002/psp4.13098
  • Supplement (Appendix S1 supplementary results and tables, Appendix File S2 and S3 NONMEM control streams): https://www.ebi.ac.uk/europepmc/webservices/rest/PMC10941504/supplementaryFiles

Population

Nivolumab (Table 1). 13,104 concentrations from 2,325 patients across 13 studies, of whom 275 were pediatric. The analysis populations are adult melanoma (n = 993, the reference), adult lymphoma (n = 274), adult glioblastoma (n = 556), adult other solid tumours (n = 227), pediatric solid tumours (n = 79), pediatric lymphoma (n = 46), and pediatric CNS tumours (n = 150). Overall age median 55 years (range 1-90), baseline body weight median 76.2 kg (range 9.3-168), 36.5% female, 90.3% White. The pediatric cohorts are markedly smaller in both weight and lean body mass than the adults: pediatric CNS-tumour median weight 33 kg with mean lean body mass 30.2 kg, against an adult-melanoma mean weight of 82.3 kg and mean lean body mass of 57.7 kg.

Ipilimumab (Table 2). 6,020 concentrations from 1,427 patients across 10 studies, of whom 138 were pediatric: adult melanoma (n = 1261, the reference), adult CNS tumours (n = 6), adult other solid tumours (n = 22), pediatric solid tumours (n = 43), pediatric CNS tumours (n = 72), and pediatric melanoma (n = 23). Overall age median 58 years (range 1-89), weight median 78.1 kg (range 10.2-160), 36.9% female, 94.8% White.

Both analyses estimated lean body mass by the Boer equation in adults and the Peter equation in children (Table 1 Note).

The same information is available programmatically from each model’s population metadata:

str(nivo$population, max.level = 1, give.attr = FALSE)
#> List of 18
#>  $ species           : chr "human"
#>  $ n_subjects        : int 2325
#>  $ n_studies         : int 13
#>  $ n_observations    : int 13104
#>  $ n_pediatric       : int 275
#>  $ age_range         : chr "1-90 years (pediatric 1-17 years; adult >= 18 years)"
#>  $ age_median        : chr "55 years overall; pediatric solid tumors 12 y, pediatric lymphoma 15 y, pediatric CNS tumors 10 y"
#>  $ weight_range      : chr "9.3-168 kg"
#>  $ weight_median     : chr "76.2 kg overall; pediatric solid tumors 43.2 kg, pediatric lymphoma 58.2 kg, pediatric CNS tumors 33 kg"
#>  $ sex_female_pct    : num 36.5
#>  $ race_ethnicity    : Named num [1:4] 90.3 2.8 3.7 3.2
#>  $ disease_state     : chr "Advanced melanoma (n = 994), Hodgkin / non-Hodgkin lymphoma (n = 320), central nervous system tumors including "| __truncated__
#>  $ dose_range        : chr "Nivolumab 0.1-20 mg/kg or 240/480 mg flat intravenous infusion q2w, q3w, or q4w, alone or combined with ipilimu"| __truncated__
#>  $ regions           : chr "Pooled global phase I, I/II, II, and III studies (13 trials; Table S1)"
#>  $ performance_status: chr "ECOG PS 0 50.5%, PS 1 45.1%, PS 2 4.3%, PS 3 0.04%"
#>  $ renal_function    : chr "Baseline eGFR mean 93.8 (SD 22.8) mL/min/1.73 m^2, median 92.9"
#>  $ body_composition  : chr "Baseline lean body mass mean 54.5 (SD 13.8) kg, median 55.8 kg; estimated by the Boer equation (adults) and the"| __truncated__
#>  $ notes             : chr "Baseline demographics per Hu 2024 Table 1 (N = 2325 across 13 nivolumab studies, of whom 275 were pediatric). T"| __truncated__

Source trace

Every ini() entry in both model files carries an in-file comment naming its source location. The table below collects them.

Equation / parameter Value Source location
CL_i(t) = CL0TV_i * exp(Emax_i * t^HILL / (T50^HILL + t^HILL)) * exp(eta_CL) n/a Hu 2024 Results, first nivolumab equation
CL0TV_i = CL0REF * (WTB/75)^CLWTB * (eGFR/90)^CLeGFR * exp(...) n/a Hu 2024 Results, nivolumab CL0TV,i equation
EMAX_i = EMAXREF + EMAXPS + EMAXCOMBO + EMAXHL + EMAXOTH + EMAXpedCNST + eta_EMAX n/a Hu 2024 Results, nivolumab EMAX_i equation
VC_i = VCREF * (LBM/55)^VCLBM * exp(VCSEX) * exp(VCado) * exp(VCped) * exp(eta_VC) n/a Hu 2024 Results, nivolumab VC_i equation
Q_i = QREF * (WTB/75)^QWTB * exp(eta_Q); VP_i = VPREF * (LBM/55)^VPLBM * exp(eta_VP) n/a Hu 2024 Results, nivolumab Q_i and VP_i equations
nivolumab CL0REF 9.66 mL/h Table 4
nivolumab VCREF, QREF, VPREF 4.01 L, 35.9 mL/h, 2.77 L Table 4
nivolumab CLWTB, CLeGFR, VCLBM 0.630, 0.0982, 0.932 Table 4
nivolumab CLSEX, CLPS, CLRAAA, CLRAAS -0.0998, 0.166, 0.0693, 0.00333 Table 4
nivolumab EMAXREF, T50, HILL -0.298, 2670 h, 2.32 Table 4
nivolumab CLHL, CLGBM, CLOTH -0.382, -0.578, 0.00699 Table 4
nivolumab CLPEDST, CLADOST, CLPEDHL, CLPEDCNST -0.580, -0.223, -0.411, -0.801 Table 4
nivolumab CLI1Q3, CLI3Q3, CLBVCO 0.0973, 0.349, 0.132 Table 4
nivolumab EMAXPS, EMAXIPICO, EMAXHL, EMAXOTH, EMAXPEDCNST -0.157, -0.124, 0.132, 0.118, 0.696 Table 4
nivolumab VCSEX, VCPED, VCADO 0.0195, -0.277, -0.273 Table 4
nivolumab omega^2 CL / VC / covariance / Emax 0.108, 0.0751, 0.0220, 0.160 Table 4
nivolumab omega^2 Q / VP / covariance constrained equal to the CL / VC block Appendix File S2, $OMEGA BLOCK(2) SAME
nivolumab proportional residual error 0.199 Table 4
QWTB = CLWTB, VPLBM = VCLBM 0.630, 0.932 Figure 1 caption (“fixed to be similar to those of CL and VC”)
adult-CNS-tumour Emax = 0 (stationary CL) n/a Appendix File S2, IF (POP_I .EQ. 4) EMAX = 0
pediatric ST / HL Emax offsets = 0 n/a Methods; Appendix File S2 THETA(38) and THETA(39) = 0 FIX
CL_i = CL0TV_i * exp(eta_CL) (ipilimumab, stationary) n/a Hu 2024 Results, first ipilimumab equation
CL0TV_i = CL0REF * (LBM/55)^CLLBM * exp(...) n/a Hu 2024 Results, ipilimumab CL0TV,i equation (see Errata on the printed subscript)
VC_i = VCREF * (LBM/55)^VCLBM * exp(VCado) * exp(VCped) * exp(eta_VC) n/a Hu 2024 Results, ipilimumab VC_i equation
ipilimumab CLREF, VCREF, QREF, VPREF 13.5 mL/h, 3.90 L, 35.8 mL/h, 3.47 L Table 5
ipilimumab CLLBM, VCLBM 0.789, 0.874 Table 5
ipilimumab CLCNST, CLOTH, CLPEDOTH, CLPEDCNST, CLPEDMEL -0.661, -0.698, -0.462, -0.668, -0.347 Table 5
ipilimumab CLN1Q3, CLN3Q3 0.0417, 0.316 Table 5
ipilimumab VCPED, VCADO -0.296, -0.217 Table 5
ipilimumab omega^2 CL / VC / covariance 0.147, 0.0531, 0.0258 Table 5
ipilimumab residual error (proportional, additive) 0.185, 1.14 ug/mL Table 5
age bands < 12, 12-17, >= 18 years n/a Methods; Appendix Files S2 and S3 (AGE <= 11, 12 <= AGE <= 17)

Structural verification of the covariate wiring

The paper reports every patient-population effect twice: once as a coefficient in Table 4 / Table 5, and once as a percentage change in the Results narrative. Because those percentages are exactly exp(theta), reproducing them from a typical-value solve is a direct check that each coefficient reaches the correct (tumour type x age band) cell of the model – the one thing a transcription of this model can most easily get wrong.

# Reference covariates from Hu 2024 Table 4 Note / Results: 75 kg, LBM 55 kg,
# eGFR 90 mL/min/1.73 m^2, male, White/Other, performance status 0, monotherapy.
nivo_cells <- tibble::tribble(
  ~cell,                                   ~AGE, ~TUMTP_LYMPH, ~TUMTP_CNS_PRIM, ~TUMTP_OTHER,
  "Adult melanoma (reference)",              55,            0,               0,            0,
  "Adult lymphoma",                          36,            1,               0,            0,
  "Adult CNS tumour (glioblastoma)",         57,            0,               1,            0,
  "Adult other solid tumour",                62,            0,               0,            1,
  "Adolescent (12-17 y) solid tumour",       15,            0,               0,            1,
  "Young pediatric (<12 y) solid tumour",     8,            0,               0,            1,
  "Pediatric (<18 y) lymphoma",              15,            1,               0,            0,
  "Pediatric (<18 y) CNS tumour",            10,            0,               1,            0
) |>
  mutate(
    id = row_number(), WT = 75, LBM = 55, CRCL = 90, SEXF = 0,
    ECOG_GE1 = 0, RACE_BLACK = 0, RACE_ASIAN = 0,
    CONMED_IPI_1Q3W = 0, CONMED_IPI_3Q3W = 0,
    CONMED_BRENTUXIMAB = 0, CONMED_IPI_ANY = 0
  )

# One dose plus a t = 0 observation. At t = 0 the sigmoid time term is exactly
# zero, so the returned `cl` is the baseline CL0 the paper tabulates.
nivo_cell_ev <- bind_rows(
  nivo_cells |> mutate(time = 0, amt = 240, evid = 1L, cmt = "central"),
  nivo_cells |> mutate(time = 0, amt = NA_real_, evid = 0L, cmt = "central")
) |>
  arrange(id, desc(evid))

nivo_cell_sim <- rxode2::rxSolve(
  rxode2::zeroRe(nivo), events = nivo_cell_ev, keep = "cell"
) |>
  as.data.frame() |>
  group_by(cell) |>
  summarise(cl = first(cl), vc = first(vc), .groups = "drop")
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp', 'etacl_time_max'
#> Warning: multi-subject simulation without without 'omega'

nivo_ref <- nivo_cell_sim$cl[nivo_cell_sim$cell == "Adult melanoma (reference)"]
nivo_ref_vc <- nivo_cell_sim$vc[nivo_cell_sim$cell == "Adult melanoma (reference)"]
nivo_expected <- tibble::tribble(
  ~cell,                                   ~theta,   ~published_pct_lower,
  "Adult melanoma (reference)",             0,       0,
  "Adult lymphoma",                        -0.382,  32,
  "Adult CNS tumour (glioblastoma)",       -0.578,  44,
  "Adult other solid tumour",               0.00699, 0,
  "Adolescent (12-17 y) solid tumour",     -0.223,  20,
  "Young pediatric (<12 y) solid tumour",  -0.580,  44,
  "Pediatric (<18 y) lymphoma",            -0.411,  34,
  "Pediatric (<18 y) CNS tumour",          -0.801,  55
)

nivo_chk <- nivo_cell_sim |>
  left_join(nivo_expected, by = "cell") |>
  mutate(
    ratio_model    = cl / nivo_ref,
    ratio_expected = exp(theta),
    pct_lower      = 100 * (1 - ratio_model),
    abs_err        = abs(ratio_model - ratio_expected)
  )

# Deterministic (zeroRe) solve of a closed-form algebraic expression: the only
# error here is floating point, so the bound is tight on purpose.
stopifnot(max(nivo_chk$abs_err) < 1e-8)
# The narrative percentages in Hu 2024 Results are rounded to whole percent.
stopifnot(max(abs(nivo_chk$pct_lower - nivo_chk$published_pct_lower)) < 1)

nivo_chk |>
  select(cell, ratio_model, pct_lower, published_pct_lower) |>
  mutate(across(c(ratio_model, pct_lower), \(x) round(x, 3))) |>
  rename(
    "Patient population"                = cell,
    "CL0 / CL0 (adult MEL)"             = ratio_model,
    "% lower (model)"                   = pct_lower,
    "% lower (Hu 2024 Results)"         = published_pct_lower
  ) |>
  knitr::kable(
    caption = paste(
      "Nivolumab baseline-clearance covariate effects reproduced from the",
      "packaged model at the paper's reference covariates. Compare with the",
      "Hu 2024 Results narrative and Figure 1a."
    )
  )
Nivolumab baseline-clearance covariate effects reproduced from the packaged model at the paper’s reference covariates. Compare with the Hu 2024 Results narrative and Figure 1a.
Patient population CL0 / CL0 (adult MEL) % lower (model) % lower (Hu 2024 Results)
Adolescent (12-17 y) solid tumour 0.800 19.989 20
Adult CNS tumour (glioblastoma) 0.561 43.898 44
Adult lymphoma 0.682 31.750 32
Adult melanoma (reference) 1.000 0.000 0
Adult other solid tumour 1.007 -0.701 0
Pediatric (<18 y) CNS tumour 0.449 55.112 55
Pediatric (<18 y) lymphoma 0.663 33.701 34
Young pediatric (<12 y) solid tumour 0.560 44.010 44

The central-volume age effects are gated the same way. Hu 2024 reports both pediatric bands at 24% lower VC than adults.

nivo_vc_chk <- nivo_cell_sim |>
  mutate(
    band = case_when(
      cell %in% c("Adolescent (12-17 y) solid tumour",
                  "Pediatric (<18 y) lymphoma")        ~ "Adolescent (12-17 y)",
      cell %in% c("Young pediatric (<12 y) solid tumour",
                  "Pediatric (<18 y) CNS tumour")      ~ "Young pediatric (<12 y)",
      TRUE                                              ~ "Adult"
    ),
    ratio_vc = vc / nivo_ref_vc
  ) |>
  group_by(band) |>
  summarise(ratio_vc = mean(ratio_vc), .groups = "drop")

vc_expected <- c(
  "Adult"                   = 1,
  "Adolescent (12-17 y)"    = exp(-0.273),
  "Young pediatric (<12 y)" = exp(-0.277)
)
stopifnot(max(abs(nivo_vc_chk$ratio_vc - vc_expected[nivo_vc_chk$band])) < 1e-8)
# Hu 2024 Results: "adolescent (12-17 years) and pediatric (<12 years) patients
# had 24% lower VC than adult patients".
stopifnot(all(abs(100 * (1 - nivo_vc_chk$ratio_vc[nivo_vc_chk$band != "Adult"]) - 24) < 1))

nivo_vc_chk |>
  mutate(`% lower than adult` = round(100 * (1 - ratio_vc), 1),
         ratio_vc = round(ratio_vc, 3)) |>
  rename("Age band" = band, "VC / VC (adult)" = ratio_vc) |>
  knitr::kable(caption = "Nivolumab central-volume age effects (Hu 2024 Figure 1b).")
Nivolumab central-volume age effects (Hu 2024 Figure 1b).
Age band VC / VC (adult) % lower than adult
Adolescent (12-17 y) 0.761 23.9
Adult 1.000 0.0
Young pediatric (<12 y) 0.758 24.2

The same check for the ipilimumab model, whose patient-population factor pools the whole under-18 range on CL (no 12-year split) but does split VC at 12 years.

ipi_cells <- tibble::tribble(
  ~cell,                                 ~AGE, ~TUMTP_MEL, ~TUMTP_CNS_PRIM, ~TUMTP_OTHER, ~theta, ~published_pct_lower,
  "Adult melanoma (reference)",            55,          1,               0,            0,  0,      0,
  "Adult CNS tumour",                      19,          0,               1,            0, -0.661, 48,
  "Adult other solid tumour",              21,          0,               0,            1, -0.698, 50,
  "Pediatric (<18 y) other solid tumour",  13,          0,               0,            1, -0.462, 37,
  "Pediatric (<18 y) CNS tumour",          10,          0,               1,            0, -0.668, 49,
  "Pediatric (<18 y) melanoma",            13,          1,               0,            0, -0.347, 29
) |>
  mutate(id = row_number(), LBM = 55, CONMED_NIVO_1Q3W = 0, CONMED_NIVO_3Q3W = 0)

ipi_cell_ev <- bind_rows(
  ipi_cells |> mutate(time = 0, amt = 200, evid = 1L, cmt = "central"),
  ipi_cells |> mutate(time = 0, amt = NA_real_, evid = 0L, cmt = "central")
) |>
  select(-theta, -published_pct_lower) |>
  arrange(id, desc(evid))

ipi_cell_sim <- rxode2::rxSolve(
  rxode2::zeroRe(ipi), events = ipi_cell_ev, keep = "cell"
) |>
  as.data.frame() |>
  group_by(cell) |>
  summarise(cl = first(cl), vc = first(vc), .groups = "drop")
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc'
#> Warning: multi-subject simulation without without 'omega'

ipi_ref <- ipi_cell_sim$cl[ipi_cell_sim$cell == "Adult melanoma (reference)"]

ipi_chk <- ipi_cell_sim |>
  left_join(ipi_cells |> select(cell, theta, published_pct_lower), by = "cell") |>
  mutate(ratio_model = cl / ipi_ref,
         pct_lower   = 100 * (1 - ratio_model),
         abs_err     = abs(ratio_model - exp(theta)))

stopifnot(max(ipi_chk$abs_err) < 1e-8)
stopifnot(max(abs(ipi_chk$pct_lower - ipi_chk$published_pct_lower)) < 1)

ipi_chk |>
  select(cell, ratio_model, pct_lower, published_pct_lower) |>
  mutate(across(c(ratio_model, pct_lower), \(x) round(x, 3))) |>
  rename(
    "Patient population"        = cell,
    "CL / CL (adult MEL)"       = ratio_model,
    "% lower (model)"           = pct_lower,
    "% lower (Hu 2024 Results)" = published_pct_lower
  ) |>
  knitr::kable(
    caption = paste(
      "Ipilimumab clearance covariate effects reproduced from the packaged",
      "model at LBM = 55 kg. Compare with the Hu 2024 Results narrative and",
      "Figure 2."
    )
  )
Ipilimumab clearance covariate effects reproduced from the packaged model at LBM = 55 kg. Compare with the Hu 2024 Results narrative and Figure 2.
Patient population CL / CL (adult MEL) % lower (model) % lower (Hu 2024 Results)
Adult CNS tumour 0.516 48.367 48
Adult melanoma (reference) 1.000 0.000 0
Adult other solid tumour 0.498 50.242 50
Pediatric (<18 y) CNS tumour 0.513 48.727 49
Pediatric (<18 y) melanoma 0.707 29.319 29
Pediatric (<18 y) other solid tumour 0.630 36.998 37

The time-varying-clearance arm

Figure 1b of Hu 2024 reports the steady-state-to-baseline clearance ratio and states the identity used to compute it: CLss / CL0 = exp(EMAX). Simulating a typical subject far past T50 recovers that ratio, and does so per covariate cell – including the adult CNS-tumour cell, where the source control stream sets EMAX to exactly zero so clearance is stationary. That last row is not visible anywhere in the printed equations; it comes from Appendix File S2.

emax_cells <- tibble::tribble(
  ~cell,                              ~AGE, ~TUMTP_LYMPH, ~TUMTP_CNS_PRIM, ~TUMTP_OTHER, ~ECOG_GE1, ~CONMED_IPI_ANY, ~emax_expected,
  "Adult MEL, mono, PS 0",              55,            0,               0,            0,         0,               0, -0.298,
  "Adult MEL, mono, PS > 0",            55,            0,               0,            0,         1,               0, -0.298 - 0.157,
  "Adult MEL + ipilimumab, PS 0",       55,            0,               0,            0,         0,               1, -0.298 - 0.124,
  "Adult lymphoma, mono, PS 0",         36,            1,               0,            0,         0,               0, -0.298 + 0.132,
  "Adult other ST, mono, PS 0",         62,            0,               0,            1,         0,               0, -0.298 + 0.118,
  "Pediatric CNS tumour, mono, PS 0",   10,            0,               1,            0,         0,               0, -0.298 + 0.696,
  "Adult CNS tumour (GBM), mono, PS 0", 57,            0,               1,            0,         0,               0,  0
) |>
  mutate(
    id = row_number(), WT = 75, LBM = 55, CRCL = 90, SEXF = 0,
    RACE_BLACK = 0, RACE_ASIAN = 0, CONMED_IPI_1Q3W = 0,
    CONMED_IPI_3Q3W = 0, CONMED_BRENTUXIMAB = 0
  )

# t = 0 gives CL0; t = 2000 days is ~18 x T50, so the sigmoid has reached
# 99.88% of its plateau. The residual approach error is < 0.1% and is the
# reason the tolerance below is 0.5% rather than machine epsilon.
emax_ev <- bind_rows(
  emax_cells |> mutate(time = 0, amt = 240, evid = 1L, cmt = "central"),
  tidyr::crossing(emax_cells, time = c(0, 2000)) |>
    mutate(amt = NA_real_, evid = 0L, cmt = "central")
) |>
  select(-emax_expected) |>
  arrange(id, time, desc(evid))

emax_sim <- rxode2::rxSolve(
  rxode2::zeroRe(nivo), events = emax_ev, keep = "cell"
) |>
  as.data.frame() |>
  group_by(cell) |>
  summarise(cl0 = cl[which.min(time)], clss = cl[which.max(time)], .groups = "drop") |>
  left_join(emax_cells |> select(cell, emax_expected), by = "cell") |>
  mutate(ratio_model = clss / cl0, ratio_expected = exp(emax_expected))
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp', 'etacl_time_max'
#> Warning: multi-subject simulation without without 'omega'

stopifnot(max(abs(emax_sim$ratio_model / emax_sim$ratio_expected - 1)) < 0.005)
# The stationary-CL cell must be exactly flat, not merely close.
stopifnot(abs(emax_sim$ratio_model[emax_sim$cell == "Adult CNS tumour (GBM), mono, PS 0"] - 1) < 1e-10)

emax_sim |>
  mutate(across(c(ratio_model, ratio_expected), \(x) round(x, 3))) |>
  select(cell, ratio_model, ratio_expected) |>
  rename(
    "Covariate cell"            = cell,
    "CLss / CL0 (model)"        = ratio_model,
    "exp(EMAX) (Hu 2024)"       = ratio_expected
  ) |>
  knitr::kable(
    caption = paste(
      "Nivolumab steady-state-to-baseline clearance ratio, reproducing the",
      "CLss/CL0 = exp(EMAX) identity of Hu 2024 Figure 1b. The last row is the",
      "stationary-clearance adult CNS-tumour cell defined only in Appendix",
      "File S2."
    )
  )
Nivolumab steady-state-to-baseline clearance ratio, reproducing the CLss/CL0 = exp(EMAX) identity of Hu 2024 Figure 1b. The last row is the stationary-clearance adult CNS-tumour cell defined only in Appendix File S2.
Covariate cell CLss / CL0 (model) exp(EMAX) (Hu 2024)
Adult CNS tumour (GBM), mono, PS 0 1.000 1.000
Adult MEL + ipilimumab, PS 0 0.656 0.656
Adult MEL, mono, PS 0 0.743 0.742
Adult MEL, mono, PS > 0 0.635 0.634
Adult lymphoma, mono, PS 0 0.847 0.847
Adult other ST, mono, PS 0 0.835 0.835
Pediatric CNS tumour, mono, PS 0 1.488 1.489 
prof_ev <- bind_rows(
  emax_cells |> mutate(time = 0, amt = 240, evid = 1L, cmt = "central"),
  tidyr::crossing(emax_cells, time = seq(0, 700, by = 7)) |>
    mutate(amt = NA_real_, evid = 0L, cmt = "central")
) |>
  select(-emax_expected) |>
  arrange(id, time, desc(evid))

rxode2::rxSolve(rxode2::zeroRe(nivo), events = prof_ev, keep = "cell") |>
  as.data.frame() |>
  group_by(cell) |>
  mutate(rel_cl = cl / first(cl)) |>
  ungroup() |>
  ggplot(aes(time, rel_cl, colour = cell)) +
  geom_line(linewidth = 0.7) +
  labs(x = "Time since first dose (days)", y = expression(CL(t)/CL[0]),
       colour = NULL,
       title = "Time-varying nivolumab clearance by patient population") +
  theme(legend.position = "bottom") +
  guides(colour = guide_legend(ncol = 2))
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq', 'etalvp', 'etacl_time_max'
#> Warning: multi-subject simulation without without 'omega'
Time course of typical nivolumab clearance by patient population, reproducing the direction and magnitude of the CLss/CL0 effects in Hu 2024 Figure 1b.

Time course of typical nivolumab clearance by patient population, reproducing the direction and magnitude of the CLss/CL0 effects in Hu 2024 Figure 1b.

Virtual cohort

Individual patient data are not public. The cohorts below approximate the covariate distributions of Hu 2024 Tables 1 and 2. Body weight is drawn from the published per-population mean and SD, truncated to the published range; lean body mass is then set to the published population mean LBM/WT ratio times the drawn weight, with a small lognormal residual. Hu 2024 computed lean body mass by the Boer and Peter equations, which require height – a variable the paper does not tabulate – so this ratio construction is the closest paper-sourced substitute (see Assumptions).

# set.seed() seeds R's RNG, not rxode2's; rxode2 partitions its streams per
# solver thread, so the cohort below differs between a 2-core CI runner and a
# 16-thread workstation. Every assertion downstream is written to hold for any
# cohort this model can produce.
set.seed(20240301)

n_arm <- 150L

draw_subjects <- function(n, wt_mean, wt_sd, wt_lo, wt_hi, lbm_ratio, id_offset) {
  wt <- pmin(pmax(rnorm(n, wt_mean, wt_sd), wt_lo), wt_hi)
  tibble(
    id  = id_offset + seq_len(n),
    WT  = wt,
    LBM = wt * lbm_ratio * exp(rnorm(n, 0, 0.06))
  )
}

# Hu 2024 Table 1: adult MEL weight 82.3 (18.1) kg, LBM 57.7 (10.8) kg;
# pediatric ST weight 44.1 (23.6) kg, LBM 35.4 (16.1) kg (median age 12 y).
adult_mel  <- \(n, off) draw_subjects(n, 82.3, 18.1, 40, 160, 57.7 / 82.3, off)
adol_st    <- \(n, off) draw_subjects(n, 55.0, 15.0, 30, 100, 35.4 / 44.1, off)

The adolescent-solid-tumour weight distribution is centred at 55 kg rather than the whole pediatric-cohort mean of 44.1 kg, because the pediatric solid-tumour row of Table 1 pools 1-17 year olds while the dosing question in Hu 2024 concerns 12-17 year olds specifically (Figure S2 shows the adolescent weight-age relationship the authors sampled from NHANES).

# 30-minute IV infusions (see Assumptions).
INF_DUR <- 0.5 / 24

make_arm <- function(subjects, arm, dose_fun, dose_times, obs_times,
                     covariates) {
  subj <- subjects |> mutate(arm = arm) |> bind_cols(covariates)
  doses <- tidyr::crossing(subj, time = dose_times) |>
    mutate(amt = dose_fun(WT), evid = 1L, cmt = "central",
           rate = amt / INF_DUR)
  obs <- tidyr::crossing(subj, time = obs_times) |>
    mutate(amt = NA_real_, evid = 0L, cmt = "central", rate = 0)
  bind_rows(doses, obs) |> arrange(id, time, desc(evid))
}

nivo_cov_adult <- tibble(
  AGE = 55, CRCL = 90, SEXF = 0, ECOG_GE1 = 0, RACE_BLACK = 0, RACE_ASIAN = 0,
  TUMTP_LYMPH = 0, TUMTP_CNS_PRIM = 0, TUMTP_OTHER = 0,
  CONMED_IPI_1Q3W = 0, CONMED_IPI_3Q3W = 0, CONMED_BRENTUXIMAB = 0,
  CONMED_IPI_ANY = 0
)
nivo_cov_adol <- nivo_cov_adult |> mutate(AGE = 15, TUMTP_OTHER = 1)

# Twelve q2w doses reaches steady state for a mAb with a ~3-week half-life;
# NCA is taken over the last (twelfth) dosing interval.
nivo_dose_times <- seq(0, by = 14, length.out = 12)
nivo_obs_times  <- sort(unique(c(seq(0, 154, by = 14), seq(154, 168, by = 0.5))))

nivo_events <- bind_rows(
  make_arm(adult_mel(n_arm, 0L),      "Adult MEL, 240 mg q2w",
           \(wt) 240,                  nivo_dose_times, nivo_obs_times, nivo_cov_adult),
  make_arm(adol_st(n_arm, 1000L),     "Adolescent ST, 240 mg q2w",
           \(wt) 240,                  nivo_dose_times, nivo_obs_times, nivo_cov_adol),
  make_arm(adol_st(n_arm, 2000L),     "Adolescent ST, 3 mg/kg q2w (cap 240 mg)",
           \(wt) pmin(3 * wt, 240),    nivo_dose_times, nivo_obs_times, nivo_cov_adol)
)
stopifnot(!anyDuplicated(unique(nivo_events[, c("id", "time", "evid")])))

ipi_cov_adult <- tibble(
  AGE = 55, TUMTP_MEL = 1, TUMTP_CNS_PRIM = 0, TUMTP_OTHER = 0,
  CONMED_NIVO_1Q3W = 0, CONMED_NIVO_3Q3W = 0
)
ipi_cov_adol <- ipi_cov_adult |> mutate(AGE = 15)

# Approved adult ipilimumab melanoma regimen: 3 mg/kg q3w for four doses.
ipi_dose_times <- c(0, 21, 42, 63)
ipi_obs_times  <- sort(unique(c(seq(0, 63, by = 7), seq(63, 84, by = 0.5))))

ipi_events <- bind_rows(
  make_arm(adult_mel(n_arm, 0L),  "Adult MEL, 3 mg/kg q3w",
           \(wt) 3 * wt, ipi_dose_times, ipi_obs_times, ipi_cov_adult),
  make_arm(adol_st(n_arm, 1000L), "Adolescent MEL, 3 mg/kg q3w",
           \(wt) 3 * wt, ipi_dose_times, ipi_obs_times, ipi_cov_adol)
)
stopifnot(!anyDuplicated(unique(ipi_events[, c("id", "time", "evid")])))

Simulation 

nivo_sim <- rxode2::rxSolve(
  nivo, events = as.data.frame(nivo_events), keep = "arm"
) |>
  as.data.frame()

ipi_sim <- rxode2::rxSolve(
  ipi, events = as.data.frame(ipi_events), keep = "arm"
) |>
  as.data.frame()

stopifnot(nrow(nivo_sim) > 0, nrow(ipi_sim) > 0)
nivo_sim |>
  filter(time >= 154) |>
  group_by(arm, time) |>
  summarise(
    Q05 = quantile(Cc, 0.05, na.rm = TRUE),
    Q50 = quantile(Cc, 0.50, na.rm = TRUE),
    Q95 = quantile(Cc, 0.95, na.rm = TRUE),
    .groups = "drop"
  ) |>
  ggplot(aes(time - 154, Q50, colour = arm, fill = arm)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.15, colour = NA) +
  geom_line(linewidth = 0.7) +
  labs(x = "Time since twelfth dose (days)", y = "Nivolumab (ug/mL)",
       colour = NULL, fill = NULL,
       title = "Nivolumab at steady state: adolescents vs adults") +
  theme(legend.position = "bottom") +
  guides(colour = guide_legend(ncol = 1), fill = guide_legend(ncol = 1))
Steady-state nivolumab concentration-time profiles over the twelfth dosing interval. Adolescents on the adult flat dose sit above adults; weight-based dosing with a 240 mg cap brings them back into the adult range. Reproduces the qualitative finding of Hu 2024 Figures S9 and S10.

Steady-state nivolumab concentration-time profiles over the twelfth dosing interval. Adolescents on the adult flat dose sit above adults; weight-based dosing with a 240 mg cap brings them back into the adult range. Reproduces the qualitative finding of Hu 2024 Figures S9 and S10.

PKNCA validation

Hu 2024 publishes no NCA table, so the NCA below serves two purposes: an internal numerical check that the model’s units are self-consistent, and a quantitative statement of the exposure comparisons the paper makes only in figures.

Nivolumab: steady-state exposure over the last dosing interval 

nivo_nca_conc <- nivo_sim |>
  filter(!is.na(Cc)) |>
  select(id, time, Cc, arm)

nivo_nca_conc <- bind_rows(
  nivo_nca_conc,
  nivo_nca_conc |> distinct(id, arm) |> mutate(time = 0, Cc = 0)
) |>
  distinct(id, arm, time, .keep_all = TRUE) |>
  arrange(id, arm, time)

nivo_conc_obj <- PKNCA::PKNCAconc(nivo_nca_conc, Cc ~ time | arm + id)

nivo_dose_obj <- PKNCA::PKNCAdose(
  nivo_events |> filter(evid == 1L) |> select(id, time, amt, arm),
  amt ~ time | arm + id
)

nivo_intervals <- data.frame(
  start = 154, end = 168,
  cmax = TRUE, tmax = TRUE, auclast = TRUE, cav = TRUE, ctrough = TRUE
)

nivo_nca <- PKNCA::pk.nca(
  PKNCA::PKNCAdata(nivo_conc_obj, nivo_dose_obj, intervals = nivo_intervals)
)

nivo_nca_tab <- as.data.frame(nivo_nca) |>
  filter(PPTESTCD %in% c("cmax", "cav", "auclast", "ctrough")) |>
  group_by(arm, PPTESTCD) |>
  summarise(gm = exp(mean(log(PPORRES))), .groups = "drop") |>
  tidyr::pivot_wider(names_from = PPTESTCD, values_from = gm)

nivo_nca_tab |>
  mutate(across(where(is.numeric), \(x) signif(x, 3))) |>
  rename(
    "Arm"                          = arm,
    "Cavg,ss (ug/mL)"              = cav,
    "Cmax,ss (ug/mL)"              = cmax,
    "Ctrough,ss (ug/mL)"           = ctrough,
    "AUCtau,ss (ug*day/mL)"        = auclast
  ) |>
  knitr::kable(
    caption = paste(
      "Geometric-mean steady-state nivolumab exposure over the twelfth q2w",
      "dosing interval (n = 150 per arm)."
    )
  )
Geometric-mean steady-state nivolumab exposure over the twelfth q2w dosing interval (n = 150 per arm).
Arm AUCtau,ss (ug*day/mL) Cavg,ss (ug/mL) Cmax,ss (ug/mL) Ctrough,ss (ug/mL)
Adolescent ST, 240 mg q2w 1800 128.0 187 NA
Adolescent ST, 3 mg/kg q2w (cap 240 mg) 1220 87.0 126 NA
Adult MEL, 240 mg q2w 1120 79.8 113 NA 
gm <- \(a, p) nivo_nca_tab[[p]][nivo_nca_tab$arm == a]

flat_adult <- gm("Adult MEL, 240 mg q2w", "cav")
flat_adol  <- gm("Adolescent ST, 240 mg q2w", "cav")
wt_adol    <- gm("Adolescent ST, 3 mg/kg q2w (cap 240 mg)", "cav")

flat_ratio <- 100 * flat_adol / flat_adult
wt_ratio   <- 100 * wt_adol   / flat_adult

# Hu 2024: "Steady-state nivolumab exposures in adolescent patients with STs
# ... who received the approved adult flat dose of nivolumab monotherapy
# (240 mg q2w) were predicted to exceed those of adults" (Figure S9), whereas
# "With body-weight-based dosing at 3 mg/kg q2w (up to a maximum dose of
# 240 mg), nivolumab steady-state exposures in adolescents ... were predicted
# to be similar to those of adults" (Figure S10).
#
# These are large, structurally driven effects: the flat-dose arm is elevated
# by BOTH the ~20% lower adolescent solid-tumour CL and the smaller body size,
# while weight-based dosing removes the size component. The bounds below are
# deliberately wide of any single cohort draw -- an exceedance of "at least
# 20%" and a similarity window of "within 35%" -- while still going red on a
# mis-transcribed clearance coefficient or dose, which move these ratios by
# tens of percent.
stopifnot(flat_ratio > 120)
stopifnot(abs(wt_ratio - 100) < 35)
# Weight-based dosing must be the closer of the two to the adult reference.
stopifnot(abs(wt_ratio - 100) < abs(flat_ratio - 100) - 10)

tibble::tibble(
  Claim = c(
    "Adolescent ST on adult flat 240 mg q2w exceeds adult MEL exposure",
    "Adolescent ST on 3 mg/kg q2w (cap 240 mg) is similar to adult MEL"
  ),
  `Hu 2024 source` = c("Figure S9", "Figure S10"),
  `Cavg,ss vs adult (%)` = round(c(flat_ratio, wt_ratio), 1)
) |>
  knitr::kable(caption = "Nivolumab dosing claims reproduced from the packaged model.")
Nivolumab dosing claims reproduced from the packaged model.
Claim Hu 2024 source Cavg,ss vs adult (%)
Adolescent ST on adult flat 240 mg q2w exceeds adult MEL exposure Figure S9 160.7
Adolescent ST on 3 mg/kg q2w (cap 240 mg) is similar to adult MEL Figure S10 109.0

Ipilimumab: fourth-dose exposure, and a closed-form clearance identity

Ipilimumab clearance is stationary in this model, so a single-dose AUCinf must equal Dose / CL exactly. Because the typical-value solve and the closed form use the same parameters, the only difference between them is numerical integration error, and the bound below is correspondingly tight. This is the check that catches a units slip in the mL/h to L/day conversion.

ident_subj <- tibble(
  id = 1L, LBM = 55, AGE = 55, TUMTP_MEL = 1, TUMTP_CNS_PRIM = 0,
  TUMTP_OTHER = 0, CONMED_NIVO_1Q3W = 0, CONMED_NIVO_3Q3W = 0
)
ident_dose <- 200

ident_ev <- bind_rows(
  ident_subj |> mutate(time = 0, amt = ident_dose, evid = 1L, cmt = "central",
                       rate = ident_dose / INF_DUR),
  tidyr::crossing(ident_subj, time = c(seq(0, 5, by = 0.05), seq(5, 400, by = 0.25))) |>
    mutate(amt = NA_real_, evid = 0L, cmt = "central", rate = NA_real_)
) |>
  arrange(time, desc(evid)) |>
  distinct(time, evid, .keep_all = TRUE)

ident_sim <- rxode2::rxSolve(rxode2::zeroRe(ipi), events = as.data.frame(ident_ev)) |>
  as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc'
ident_cl <- ident_sim$cl[1]

ident_nca <- PKNCA::pk.nca(PKNCA::PKNCAdata(
  PKNCA::PKNCAconc(
    ident_sim |> filter(!is.na(Cc)) |> select(time, Cc) |> mutate(id = 1L),
    Cc ~ time | id
  ),
  PKNCA::PKNCAdose(
    data.frame(id = 1L, time = 0, amt = ident_dose), amt ~ time | id
  ),
  intervals = data.frame(start = 0, end = Inf, aucinf.obs = TRUE, half.life = TRUE)
))

ident_res  <- as.data.frame(ident_nca)
auc_nca    <- ident_res$PPORRES[ident_res$PPTESTCD == "aucinf.obs"]
auc_closed <- ident_dose / ident_cl   # mg / (L/day) = mg*day/L = ug*day/mL

stopifnot(abs(auc_nca / auc_closed - 1) < 0.01)

tibble::tibble(
  Quantity = c("CL (L/day)", "AUCinf from PKNCA (ug*day/mL)",
               "Dose / CL closed form (ug*day/mL)", "Relative difference (%)"),
  Value = signif(c(ident_cl, auc_nca, auc_closed,
                   100 * (auc_nca / auc_closed - 1)), 4)
) |>
  knitr::kable(
    caption = paste(
      "Ipilimumab single-dose mass-balance identity for a reference adult",
      "(LBM 55 kg, melanoma, monotherapy; 200 mg IV). Stationary clearance",
      "makes AUCinf = Dose/CL exact up to integration error."
    )
  )
Ipilimumab single-dose mass-balance identity for a reference adult (LBM 55 kg, melanoma, monotherapy; 200 mg IV). Stationary clearance makes AUCinf = Dose/CL exact up to integration error.
Quantity Value
CL (L/day) 0.3240
AUCinf from PKNCA (ug*day/mL) 616.5000
Dose / CL closed form (ug*day/mL) 617.3000
Relative difference (%) -0.1206

Hu 2024 states that at the approved 3 mg/kg q3w regimen, adolescent ipilimumab exposure after the fourth dose exceeds adult exposure (Figure S13). The check below makes that comparison on typical subjects with zeroRe(), so it is a deterministic function of the parameters: the only thing that can move it is a mis-transcribed coefficient, not which subjects a cohort happened to draw. This is the load-bearing gate on the claim; the stochastic cohort that follows is for display.

# Typical adult MEL (Table 2: WT 82.3 kg, LBM 57.7 kg) versus a typical
# adolescent MEL subject on the same mg/kg dose.
ipi_typ <- tibble::tribble(
  ~cell,                          ~AGE, ~WT,  ~LBM,
  "Adult MEL, 3 mg/kg q3w",         55, 82.3, 57.7,
  "Adolescent MEL, 3 mg/kg q3w",    15, 55.0, 55.0 * 35.4 / 44.1
) |>
  mutate(id = row_number(), TUMTP_MEL = 1, TUMTP_CNS_PRIM = 0, TUMTP_OTHER = 0,
         CONMED_NIVO_1Q3W = 0, CONMED_NIVO_3Q3W = 0)

ipi_typ_ev <- bind_rows(
  tidyr::crossing(ipi_typ, time = ipi_dose_times) |>
    mutate(amt = 3 * WT, evid = 1L, cmt = "central", rate = amt / INF_DUR),
  tidyr::crossing(ipi_typ, time = ipi_obs_times) |>
    mutate(amt = NA_real_, evid = 0L, cmt = "central", rate = 0)
) |>
  arrange(id, time, desc(evid))

ipi_typ_sim <- rxode2::rxSolve(
  rxode2::zeroRe(ipi), events = as.data.frame(ipi_typ_ev), keep = "cell"
) |>
  as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc'
#> Warning: multi-subject simulation without without 'omega'

ipi_typ_conc <- ipi_typ_sim |> filter(!is.na(Cc)) |> select(id, time, Cc, cell)
ipi_typ_conc <- bind_rows(
  ipi_typ_conc,
  ipi_typ_conc |> distinct(id, cell) |> mutate(time = 0, Cc = 0)
) |>
  distinct(id, cell, time, .keep_all = TRUE) |>
  arrange(id, time)

ipi_typ_nca <- PKNCA::pk.nca(PKNCA::PKNCAdata(
  PKNCA::PKNCAconc(ipi_typ_conc, Cc ~ time | cell + id),
  PKNCA::PKNCAdose(
    ipi_typ_ev |> filter(evid == 1L) |> select(id, time, amt, cell),
    amt ~ time | cell + id
  ),
  intervals = data.frame(start = 63, end = 84, cav = TRUE)
))

ipi_typ_tab <- as.data.frame(ipi_typ_nca) |> filter(PPTESTCD == "cav")
ipi_typ_ratio <- 100 *
  ipi_typ_tab$PPORRES[ipi_typ_tab$cell == "Adolescent MEL, 3 mg/kg q3w"] /
  ipi_typ_tab$PPORRES[ipi_typ_tab$cell == "Adult MEL, 3 mg/kg q3w"]

# Deterministic, so this is bounded tightly. The value is driven by the 29%
# lower pediatric-melanoma CL (exp(-0.347)) partly offset by the smaller
# mg/kg dose that a lighter subject receives; a sign error on CL_PEDMEL or a
# mis-wired LBM exponent moves it by tens of percent.
stopifnot(ipi_typ_ratio > 100)
stopifnot(abs(ipi_typ_ratio - 113.6) < 3)

tibble::tibble(
  Quantity = c("Typical adult Cavg (ug/mL)", "Typical adolescent Cavg (ug/mL)",
               "Adolescent / adult (%)"),
  Value = signif(c(
    ipi_typ_tab$PPORRES[ipi_typ_tab$cell == "Adult MEL, 3 mg/kg q3w"],
    ipi_typ_tab$PPORRES[ipi_typ_tab$cell == "Adolescent MEL, 3 mg/kg q3w"],
    ipi_typ_ratio
  ), 4)
) |>
  knitr::kable(
    caption = paste(
      "Typical-value ipilimumab exposure over the fourth q3w dosing interval.",
      "Adolescent exposure exceeds adult, reproducing Hu 2024 Figure S13."
    )
  )
Typical-value ipilimumab exposure over the fourth q3w dosing interval. Adolescent exposure exceeds adult, reproducing Hu 2024 Figure S13.
Quantity Value
Typical adult Cavg (ug/mL) 33.17
Typical adolescent Cavg (ug/mL) 37.68
Adolescent / adult (%) 113.60 
ipi_nca_conc <- ipi_sim |>
  filter(!is.na(Cc)) |>
  select(id, time, Cc, arm)

ipi_nca_conc <- bind_rows(
  ipi_nca_conc,
  ipi_nca_conc |> distinct(id, arm) |> mutate(time = 0, Cc = 0)
) |>
  distinct(id, arm, time, .keep_all = TRUE) |>
  arrange(id, arm, time)

ipi_nca <- PKNCA::pk.nca(PKNCA::PKNCAdata(
  PKNCA::PKNCAconc(ipi_nca_conc, Cc ~ time | arm + id),
  PKNCA::PKNCAdose(
    ipi_events |> filter(evid == 1L) |> select(id, time, amt, arm),
    amt ~ time | arm + id
  ),
  intervals = data.frame(
    start = 63, end = 84,
    cmax = TRUE, cav = TRUE, auclast = TRUE, ctrough = TRUE
  )
))

ipi_nca_tab <- as.data.frame(ipi_nca) |>
  filter(PPTESTCD %in% c("cmax", "cav", "auclast", "ctrough")) |>
  group_by(arm, PPTESTCD) |>
  summarise(gm = exp(mean(log(PPORRES))), .groups = "drop") |>
  tidyr::pivot_wider(names_from = PPTESTCD, values_from = gm)

ipi_ratio <- 100 *
  ipi_nca_tab$cav[ipi_nca_tab$arm == "Adolescent MEL, 3 mg/kg q3w"] /
  ipi_nca_tab$cav[ipi_nca_tab$arm == "Adult MEL, 3 mg/kg q3w"]

# This is the SAME comparison as the typical-value check above, but taken over
# a random cohort, and it is deliberately gated far more loosely. The
# geometric-mean ratio of a 150-per-arm draw moves over roughly 106-123% purely
# with the eta draw (omega^2_CL = 0.147 is large, and rxSetSeed() fixes
# rxode2's stream per solver thread, so CI draws a different cohort than a
# workstation does). Gating this near its own central value is exactly the
# assertion shape that passes locally and then fails CI. The transcription
# check lives in `ipi-typical-exposure`; this one only confirms the cohort
# lands on the same side of parity.
stopifnot(ipi_ratio > 100)

ipi_nca_tab |>
  mutate(across(where(is.numeric), \(x) signif(x, 3))) |>
  rename(
    "Arm"                        = arm,
    "Cavg (ug/mL)"               = cav,
    "Cmax (ug/mL)"               = cmax,
    "Ctrough (ug/mL)"            = ctrough,
    "AUCtau (ug*day/mL)"         = auclast
  ) |>
  knitr::kable(
    caption = paste(
      "Geometric-mean ipilimumab exposure over the fourth q3w dosing interval",
      "(n = 150 per arm). Adolescent exposure is",
      paste0(round(ipi_ratio), "%"), "of adult, reproducing Hu 2024 Figure S13."
    )
  )
Geometric-mean ipilimumab exposure over the fourth q3w dosing interval (n = 150 per arm). Adolescent exposure is 108% of adult, reproducing Hu 2024 Figure S13.
Arm AUCtau (ug*day/mL) Cavg (ug/mL) Cmax (ug/mL) Ctrough (ug/mL)
Adolescent MEL, 3 mg/kg q3w 760 36.2 75.4 NA
Adult MEL, 3 mg/kg q3w 704 33.5 72.9 NA

Assumptions and deviations

  • Time units. Hu 2024 reports CL and Q in mL/h and T50 in hours. Both model files convert to L/day and days (x 24 / 1000 and / 24) so the time axis matches the sibling nivolumab and ipilimumab models in nlmixr2lib (Bajaj_2017_nivolumab, Zhang_2019_nivolumab, Feng_2019_ipilimumab). No value is otherwise altered.

  • cl_time_max is not log-transformed. checkModelConventions() suggests renaming the Emax parameter to lcl_time_max and back-transforming. That is not possible here: EMAXREF = -0.298 is negative by construction (it is the log-scale maximal decrease in clearance), and Hu 2024 places a normally distributed additive eta on it. The model therefore keeps the linear-scale name cl_time_max, matching Bajaj_2017_nivolumab and Zhang_2019_nivolumab.

  • Patient population is encoded as tumour-type indicators crossed with age bands. Hu 2024 uses a single multi-level POPN column. Its levels are a cross of tumour type and age band (adult MEL, adult HL, adult GBM, adult other ST, pediatric ST, pediatric HL, pediatric CNST), so the model files reconstruct them from the canonical TUMTP_MEL / TUMTP_LYMPH / TUMTP_CNS_PRIM / TUMTP_OTHER indicators and AGE. One consequence is worth noting: the analysis dataset assigns its single pediatric melanoma subject to the pediatric solid-tumour group (Table 1 footnote d), so a pediatric TUMTP_MEL = 1 record does not occur in the nivolumab source data even though the encoding admits one. The companion ipilimumab model does estimate a pediatric-melanoma effect.

  • Structural details taken from the supplement, not the printed equations. Three facts that materially change the model are in the NONMEM control streams (Appendix Files S2 and S3) and nowhere in the article body:

    1. adult CNS-tumour subjects have EMAX set to exactly zero, so their clearance is stationary; (ii) the nivolumab Q / VP random effects are declared $OMEGA BLOCK(2) SAME, i.e. constrained to the same variances and covariance as the CL / VC block – which is why Table 4 lists no omega^2 for them; (iii) the ipilimumab model has no Q or VP random effects at all. Without the supplement, (i) would be missed entirely and (ii) would have had to be guessed at.

  • A printed-equation subscript in the ipilimumab model is a typo. The ipilimumab CL0TV,i equation prints the lean-body-mass power as CLWTB, but the base of the power is LBM_i / LBM_REF, Table 5 has no CLWTB row (only CL_LBM = 0.789), the surrounding prose says “the typical CL value at the reference value of LBM (55 kg)”, and Appendix File S3 codes CL_LBM = (LBM_I/LBM_R)**THETA(7). The model uses CL_LBM = 0.789. The label appears to be carried over from the body-weight-based base model.

  • Zero-fixed covariate coefficients are recorded, not modelled. The nivolumab dataset contains ipilimumab 1 mg/kg q6w, radiotherapy, and radiotherapy-plus-temozolomide arms, and the ipilimumab dataset an oral budesonide arm, whose clearance coefficients were declared 0 FIX in the control streams and do not appear in Tables 4 or 5. They are documented in each model file’s covariatesDataExcluded list rather than given a fixed(0) parameter, since a coefficient held at zero contributes no term to the equations. The numeric power effects of age on CL (both models) and on VC (ipilimumab) were likewise 0 FIX; age enters both models only through the categorical bands.

  • Lean body mass in the virtual cohort. Hu 2024 computed lean body mass by the Boer equation (adults) and the Peter equation (children), both of which need height. The paper tabulates weight and lean body mass but not height, so the cohort sets LBM = (published LBM mean / published WT mean) x WT with a 6% lognormal residual. This reproduces the published per-population mean LBM/WT ratio exactly and is used only for the exposure-comparison figures; the covariate-wiring and clearance-identity checks above all run at the paper’s own reference covariates and do not depend on it.

  • Infusion duration. The analysis datasets carry a DOSEDUR column but the paper does not report infusion durations. The simulations use 30-minute IV infusions. This affects Cmax but not AUC, Cavg, or Ctrough, and none of the gated comparisons depend on it.

  • Adolescent weight distribution. Hu 2024 simulated adolescents by sampling the 2017-2018 NHANES database (Figure S2), which is not redistributed here. The adolescent arm draws weight from a normal distribution centred at 55 kg (SD 15, truncated to 30-100 kg), chosen to sit inside the published adolescent range rather than the 1-17 year pooled pediatric mean of 44.1 kg.

  • The third model in the paper is not extracted. Appendix S1 reports a separate nivolumab population PK model (Full5) for adolescents receiving adjuvant melanoma treatment, fitted to a different dataset (24,546 concentrations, 3,965 patients, 11 studies). Its covariate effects are given as percentages in Figure S17, but none of its structural parameters – CL0REF, VCREF, QREF, VPREF, EMAXREF, T50, HILL, the random effects, or the residual error – is reported anywhere in the article, the supplement text, or the figure panels. Figure S17 panels A and B were both inspected directly at publisher resolution and carry only covariate ratios. The model is therefore not reconstructable and is omitted; the two models in the article body (Full1c for nivolumab, Full1 for ipilimumab) are fully specified and are what this vignette validates.

  • No published NCA to compare against. Hu 2024 reports no Cmax / AUC / half-life table, so there is no ncaComparisonTable() block here. The NCA section instead gates on the closed-form AUCinf = Dose/CL identity for the stationary ipilimumab model and on the three exposure comparisons the paper states in prose for Figures S9, S10, and S13.