Papachristos_2020_bevacizumab

Model and source

Citation: Papachristos A, Karatza E, Kalofonos H, Karalis V. Pharmacogenetics in Model-Based Optimization of Bevacizumab Therapy for Metastatic Colorectal Cancer. Int J Mol Sci. 2020;21(11):3753. doi:[10.3390/ijms21113753](https://doi.org/10.3390/ijms21113753).
Description: Two-compartment population PK model for IV bevacizumab in adults with metastatic colorectal cancer (mCRC), with allometric weight scaling on CL and ICAM-1 / VEGF-A genotype covariate effects (Table 1 of Papachristos 2020).
Modality: Therapeutic anti-VEGF-A monoclonal antibody (humanized IgG1, MW ≈ 149 kDa), IV infusion.

This vignette validates the PK-only model (Table 1). Papachristos 2020 also reports two further co-equal final models built from the same 46-patient cohort — a binding QSS TMDD model (Table 2) and a PK/PD immediate-response Imax model (Table 3) — packaged separately as Papachristos_2020_bevacizumab_qss and Papachristos_2020_bevacizumab_pkpd.

TODO (co-equality framing). The three Papachristos 2020 models are CO-EQUAL final models, not a hierarchical base / extended pair. Each pursues a different objective: descriptive PK (this vignette), mechanistic target binding (QSS), or drug-effect characterization (PK/PD). Reviewer please confirm this framing and the choice to package all three.

Population

The Papachristos 2020 cohort comprised 46 adult patients with histologically confirmed metastatic colorectal cancer (ECOG performance status 0-2) treated at a single Greek centre (University Hospital of Patras). Baseline demographics (paper section 2.1):

Sex: 61% male, 39% female.
Median (IQR) weight 74.5 kg (64.15–81.75); median (IQR) age 63 years (53–72). Full ranges not reported.
Race / ethnicity: Greek; not formally tabulated.
Dosing: 5 mg/kg IV every 2 weeks (76% of patients) or 7.5 mg/kg IV every 3 weeks (24%) in combination with oxaliplatin/fluoropyrimidine (BEV-FOLFOX, BEV-CapOX) or irinotecan/fluoropyrimidine (BEV-FOLFIRI, BEV-CapIRI) chemotherapy.
Sample sizes: 156 bevacizumab serum concentrations (76 pre-dose, 80 post-dose) from 46 patients. No values below the limit of quantification.
SNP carrier rates (mutant alleles, paper section 2.1): ICAM-1 rs1799969 mutant 20%; ICAM-1 rs5498 mutant 70%; VEGF-A rs699947 mutant 52%; VEGF-A rs1570360 mutant 33%; VEGF-A rs2010963 mutant 41%.

Only three SNPs (ICAM-1 rs1799969, VEGF-A rs1570360, VEGF-A rs699947) entered the final PK model; the other two were tested but not retained.

The same metadata is available programmatically via readModelDb("Papachristos_2020_bevacizumab_pk")$population.

Source trace

Per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Papachristos_2020_bevacizumab_pk.R. The table below collects them in one place.

Parameter (model name)	Value	Source
`lcl` (CLpop, L/day)	log(0.200)	Papachristos 2020 Table 1, CLpop
`lv1` (V1pop, L)	log(3.09)	Papachristos 2020 Table 1, V1pop
`lq` (Qpop, L/day)	log(0.35)	Papachristos 2020 Table 1, Qpop
`lv2` (V2pop, L)	log(2.39)	Papachristos 2020 Table 1, V2pop
`allo_cl` (allometric exponent)	1.04	Papachristos 2020 Table 1, “log(weight/70) on CL”
`e_icam1_rs1799969_cl`	-0.423	Papachristos 2020 Table 1, “ICAM-1 rs1799969 mutant on CL”
`e_vegfa_rs1570360_q`	+0.378	Papachristos 2020 Table 1, “VEGF-A rs1570360 mutant on Q”
`e_vegfa_rs699947_q`	-0.429	Papachristos 2020 Table 1, “VEGF-A rs699947 mutant on Q”
`etalcl` variance	0.10176	Papachristos 2020 Table 1, ω_CL = 0.319 (var = SD²)
`etalq` variance	0.02560	Papachristos 2020 Table 1, ω_Q = 0.160
`cov(etalcl, etalq)`	-0.05099	Papachristos 2020 Table 1, ρ(Q,CL) = -0.999 × 0.319 × 0.160
`etalv1` variance	0.03028	Papachristos 2020 Table 1, ω_V1 = 0.174
`etalv2` variance	0.45698	Papachristos 2020 Table 1, ω_V2 = 0.676
`propSd`	0.246	Papachristos 2020 Table 1, σ_prop

Equations (paper section 2.2):

$\mathrm{CL}_i = \mathrm{CL}_\mathrm{pop} \cdot \left(\frac{\mathrm{WT}_i}{70}\right)^{1.04} \cdot \exp(-0.423 \cdot \mathrm{SNP\_ICAM1\_RS1799969}_i) \cdot \exp(\eta_{\mathrm{CL},i})$ $\mathrm{Q}_i = \mathrm{Q}_\mathrm{pop} \cdot \exp(0.378 \cdot \mathrm{SNP\_VEGFA\_RS1570360}_i) \cdot \exp(-0.429 \cdot \mathrm{SNP\_VEGFA\_RS699947}_i) \cdot \exp(\eta_{\mathrm{Q},i})$ $\mathrm{V}_{1,i} = \mathrm{V}_{1,\mathrm{pop}} \cdot \exp(\eta_{V_1,i}), \quad \mathrm{V}_{2,i} = \mathrm{V}_{2,\mathrm{pop}} \cdot \exp(\eta_{V_2,i})$

Two-compartment linear PK: $\dot A_1 = -k_{el} A_1 - k_{12} A_1 + k_{21} A_2$ , $\dot A_2 = k_{12} A_1 - k_{21} A_2$ , $C_c = A_1 / V_1$ , with proportional residual error $\sigma_\mathrm{prop} = 0.246$ .

Errata note (text vs Table)

No formal corrigendum to the paper has been identified at the time of extraction (April 2026). One within-paper inconsistency was noted in sister model 3 (the PK/PD model, Table 3) where section 2.4 quotes the inter-compartmental clearance covariate as exp(0.378) — a copy-paste of the rs1570360 effect from Table 1 / section 2.2. Table 3 itself gives -0.414 for the rs699947 effect on Q in the PK/PD model and the narrative confirms Q is lower in mutants. The packaged Papachristos_2020_bevacizumab_pkpd model uses Table 3. The PK model extracted here (Table 1 / section 2.2) is internally consistent between text and table.

Virtual cohort

Original observed data are not publicly available. The simulations below use a virtual cohort whose covariate distributions approximate the Papachristos 2020 population.

set.seed(2020)
n_subj <- 200

# Weight: log-normal centred on the median 74.5 kg with a CV that
# reproduces the IQR (64.15-81.75) of the source population.
# log(81.75/64.15) ≈ 0.243 spans the IQR; sigma ≈ 0.243 / (2 * 0.6745) ≈ 0.18.
cohort <- tibble(
  ID                  = seq_len(n_subj),
  WT                  = pmin(pmax(rlnorm(n_subj, log(74.5), 0.18), 45), 130),
  SNP_ICAM1_RS1799969 = rbinom(n_subj, 1, 0.20),
  SNP_VEGFA_RS1570360 = rbinom(n_subj, 1, 0.33),
  SNP_VEGFA_RS699947  = rbinom(n_subj, 1, 0.52)
)

Two reference dosing regimens are simulated, matching the two cohorts in Papachristos 2020 section 4.1:

5 mg/kg IV Q2W (BEV-FOLFIRI / BEV-FOLFOX cohort)
7.5 mg/kg IV Q3W (BEV-CapIRI / BEV-CapOX cohort)

inf_dur     <- 1.5 / 24            # 90-min standard bevacizumab infusion (days)
n_doses_q2w <- 6
n_doses_q3w <- 4
sim_horizon <- 84                  # 12 weeks total follow-up

dose_times_q2w <- seq(0, by = 14, length.out = n_doses_q2w)
dose_times_q3w <- seq(0, by = 21, length.out = n_doses_q3w)
obs_times      <- sort(unique(c(0, seq(0.1, sim_horizon, by = 1))))

build_events <- function(pop, mgkg, dose_times, regimen_label,
                         id_offset = 0L) {
  pop <- dplyr::mutate(pop, ID = ID + id_offset)
  amt_per_subject <- pop$WT * mgkg

  d_dose <- pop |>
    dplyr::mutate(amt = amt_per_subject) |>
    tidyr::crossing(time = dose_times) |>
    dplyr::mutate(evid = 1L, cmt = "central", dur = inf_dur,
                  treatment = regimen_label)
  d_obs <- pop |>
    tidyr::crossing(time = obs_times) |>
    dplyr::mutate(amt = 0, evid = 0L, cmt = "central", dur = NA_real_,
                  treatment = regimen_label)

  dplyr::bind_rows(d_dose, d_obs) |>
    dplyr::rename(id = ID) |>
    dplyr::arrange(id, time, dplyr::desc(evid)) |>
    as.data.frame()
}

events <- dplyr::bind_rows(
  build_events(cohort, mgkg = 5,   dose_times = dose_times_q2w,
               regimen_label = "5 mg/kg Q2W",  id_offset = 0L),
  build_events(cohort, mgkg = 7.5, dose_times = dose_times_q3w,
               regimen_label = "7.5 mg/kg Q3W", id_offset = n_subj)
)

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

Simulation

mod <- readModelDb("Papachristos_2020_bevacizumab_pk")
sim <- rxode2::rxSolve(mod, events = events,
                       keep = c("treatment"),
                       returnType = "data.frame")
#> ℹ parameter labels from comments will be replaced by 'label()'

Replicate published figures

Concentration-time profiles by regimen

Papachristos 2020 does not publish a single concentration-time figure in the main text (the VPCs live in Supplementary Figures S3-S4). The plot below shows the median and 5-95% prediction interval of the simulated cohort by regimen, providing the same diagnostic view.

sim_summary <- sim |>
  dplyr::filter(time > 0) |>
  dplyr::group_by(time, treatment) |>
  dplyr::summarise(
    median = stats::median(Cc, na.rm = TRUE),
    lo     = stats::quantile(Cc, 0.05, na.rm = TRUE),
    hi     = stats::quantile(Cc, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(sim_summary, aes(time, median, colour = treatment, fill = treatment)) +
  geom_ribbon(aes(ymin = lo, ymax = hi), alpha = 0.15, colour = NA) +
  geom_line(linewidth = 1) +
  scale_y_log10() +
  labs(
    x = "Time since first dose (days)",
    y = "Bevacizumab concentration (mg/L, log scale)",
    title = "Simulated bevacizumab PK by Papachristos 2020 PK model",
    subtitle = paste0("Median and 90% prediction interval (N = ",
                      n_subj, " virtual patients per arm)."),
    caption = "Replicates the diagnostic content of Papachristos 2020 Supplementary Figures S3-S4."
  ) +
  theme_bw()

Effect of ICAM-1 rs1799969 on trough levels — replicates Figure 1A / Supplementary Figure S2

Paper section 2.2 highlights that bevacizumab trough levels are significantly higher in ICAM-1 rs1799969 mutant carriers (99.1 vs 57.2 mg/L, p = 0.00004; Supplementary Figure S2). The deterministic typical-value simulation below shows the predicted Q2W trough at the median weight (74.5 kg) for wild-type vs mutant carriers.

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

typ_grid <- tidyr::crossing(
  WT                  = 74.5,
  SNP_ICAM1_RS1799969 = c(0, 1),
  SNP_VEGFA_RS1570360 = 0,
  SNP_VEGFA_RS699947  = 0
) |>
  dplyr::mutate(id = dplyr::row_number())

typ_dose <- typ_grid |>
  dplyr::mutate(amt = WT * 5) |>
  tidyr::crossing(time = dose_times_q2w) |>
  dplyr::mutate(evid = 1L, cmt = "central", dur = inf_dur)

typ_obs <- typ_grid |>
  tidyr::crossing(time = sort(unique(c(0, seq(0.1, sim_horizon, by = 0.5))))) |>
  dplyr::mutate(amt = 0, evid = 0L, cmt = "central", dur = NA_real_)

typ_events <- dplyr::bind_rows(typ_dose, typ_obs) |>
  dplyr::arrange(id, time, dplyr::desc(evid)) |>
  as.data.frame()

sim_typ <- rxode2::rxSolve(mod_typical, events = typ_events,
                           keep = c("SNP_ICAM1_RS1799969"),
                           returnType = "data.frame") |>
  dplyr::mutate(
    icam1_label = ifelse(SNP_ICAM1_RS1799969 == 1, "Mutant carrier", "Wild-type")
  )
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalq', 'etalv1', 'etalv2'
#> Warning: multi-subject simulation without without 'omega'

ggplot(sim_typ |> dplyr::filter(time > 0),
       aes(time, Cc, colour = icam1_label)) +
  geom_line(linewidth = 1) +
  scale_y_log10() +
  labs(
    x        = "Time since first dose (days)",
    y        = "Bevacizumab concentration (mg/L, log scale)",
    colour   = "ICAM-1 rs1799969",
    title    = "Effect of ICAM-1 rs1799969 on bevacizumab PK (5 mg/kg Q2W)",
    subtitle = "Typical 74.5 kg subject, deterministic (etas = 0). Replicates Papachristos 2020 Figure 1A / Supp. Fig. S2."
  ) +
  theme_bw()


trough_compare <- sim_typ |>
  dplyr::filter(time %in% (dose_times_q2w[-1])) |>
  dplyr::group_by(icam1_label) |>
  dplyr::summarise(median_trough = stats::median(Cc), .groups = "drop")
knitr::kable(trough_compare,
             caption = "Median Q2W trough (mg/L) at 74.5 kg, wild-type vs ICAM-1 rs1799969 mutant carrier (typical-value simulation).")

Median Q2W trough (mg/L) at 74.5 kg, wild-type vs ICAM-1 rs1799969 mutant carrier (typical-value simulation).
icam1_label	median_trough

The simulated trough ratio reproduces the qualitative direction (mutant > wild-type) reported by the paper. The numerical magnitude depends on the dosing interval and the number of doses simulated; the paper’s 99.1 / 57.2 mg/L = 1.73 ratio is the median across observed sparse trough samples in the cohort, while the typical-value simulation here assumes steady dosing at exactly 14-day intervals and returns the model-predicted ratio exp(-0.423) = 0.655 for CL — equivalently a 1 / 0.655 = 1.527-fold trough elevation per dosing interval.

PKNCA validation

NCA is computed over a single dosing interval at steady state for each of the two regimens. The dosing interval starts at the last simulated dose and runs for one tau (14 d for Q2W, 21 d for Q3W).

build_nca <- function(sim_df, regimen_label, tau, dose_times) {
  start_ss <- max(dose_times)
  end_ss   <- start_ss + tau

  conc_df <- sim_df |>
    dplyr::filter(treatment == regimen_label, time >= start_ss, time <= end_ss,
                  !is.na(Cc)) |>
    dplyr::mutate(time_rel = time - start_ss) |>
    dplyr::select(id, treatment, time_rel, Cc)

  dose_df <- events |>
    dplyr::filter(treatment == regimen_label, evid == 1, time == start_ss) |>
    dplyr::mutate(time_rel = 0) |>
    dplyr::select(id, treatment, time_rel, amt)

  list(conc = conc_df, dose = dose_df, tau = tau)
}

nca_q2w <- build_nca(sim, "5 mg/kg Q2W",   tau = 14, dose_times = dose_times_q2w)
nca_q3w <- build_nca(sim, "7.5 mg/kg Q3W", tau = 21, dose_times = dose_times_q3w)

run_pknca <- function(b) {
  conc_obj <- PKNCA::PKNCAconc(b$conc, Cc ~ time_rel | treatment + id,
                               concu = "mg/L", timeu = "day")
  dose_obj <- PKNCA::PKNCAdose(b$dose, amt ~ time_rel | treatment + id,
                               doseu = "mg")
  intervals <- data.frame(
    start    = 0,
    end      = b$tau,
    cmax     = TRUE,
    tmax     = TRUE,
    cmin     = TRUE,
    auclast  = TRUE,
    cav      = TRUE
  )
  res <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals))
  summary(res)
}

knitr::kable(run_pknca(nca_q2w),
             caption = "Steady-state NCA (5 mg/kg Q2W, last simulated interval).")
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#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed

Steady-state NCA (5 mg/kg Q2W, last simulated interval).
Interval Start	Interval End	treatment	N	AUClast (day*mg/L)	Cmax (mg/L)	Cmin (mg/L)	Tmax (day)	Cav (mg/L)
0	14	5 mg/kg Q2W	200	NC	204 [22.9]	84.0 [47.4]	0.100 [0.100, 0.100]	NC

knitr::kable(run_pknca(nca_q3w),
             caption = "Steady-state NCA (7.5 mg/kg Q3W, last simulated interval).")
#> Warning: Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.1) is not allowed

Steady-state NCA (7.5 mg/kg Q3W, last simulated interval).
Interval Start	Interval End	treatment	N	AUClast (day*mg/L)	Cmax (mg/L)	Cmin (mg/L)	Tmax (day)	Cav (mg/L)
0	21	7.5 mg/kg Q3W	200	NC	249 [22.5]	67.5 [62.2]	0.100 [0.100, 0.100]	NC

Comparison against published descriptors

Papachristos 2020 does not publish a tabulated NCA. The paper states mean trough levels for the ICAM-1 rs1799969 wild-type and mutant sub-groups (section 2.2: 57.2 vs 99.1 mg/L); these were sparse-sample descriptive statistics across the observed cohort and are bracketed by the simulated 5-95% prediction interval shown in the Concentration-time profiles figure above.

Assumptions and deviations

Co-equality framing of the three Papachristos 2020 models. The PK / Binding QSS / PK/PD models in Papachristos 2020 are co-equal final models, each pursuing a different objective (descriptive PK, mechanistic target binding, drug-effect characterization). They are not a hierarchical base / extended pair. All three are packaged separately in nlmixr2lib (this file is the descriptive-PK variant).
Weight distribution. The paper reports median 74.5 kg and IQR 64.15–81.75 kg without a full range. The virtual cohort uses a log-normal with σ = 0.18 (chosen so log of the IQR ratio matches the source) truncated at 45 and 130 kg.
SNP independence. The source paper used chi-square / Fisher’s exact tests to confirm pairwise independence between the SNPs in the observed cohort (Supplementary Tables S1-S3); the virtual cohort draws each SNP independently from its marginal mutant-carrier rate.
Race / ethnicity. Not available from the source. The paper’s cohort is single-centre Greek; race is not used as a model covariate.
Trough-level magnitude in Figure 1A replication. The exp(-0.423) = 0.655 fold effect on CL implies a ~1.53-fold elevation in the typical Q2W trough for ICAM-1 rs1799969 mutant carriers, whereas the paper reports an observed ratio of 99.1 / 57.2 ≈ 1.73 across mutant vs wild-type subjects. The observed ratio also reflects between-subject variability in dosing schedule, sampling windows, and weight, so the model and the observed sparse-sample statistic are not directly comparable; the qualitative direction matches.
No errata identified. A literature search (April 2026) found no published corrigendum / erratum to Papachristos 2020.