Budha_2023_tislelizumab
Source:vignettes/articles/Budha_2023_tislelizumab.Rmd
Budha_2023_tislelizumab.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':
#>
#> filterTislelizumab population PK simulation
Simulate tislelizumab (anti-PD-1 IgG4) concentration-time profiles using the final three-compartment population PK model from Budha et al. (2023). The pooled analysis included 2596 patients with advanced tumors from 12 studies (14,473 serum concentration observations).
The structural model is a three-compartment IV model with linear elimination. Final covariates: body weight, albumin, baseline tumor size, ADA status, and tumor-type indicators for classical Hodgkin lymphoma and gastric cancer on CL; and body weight, age, and sex on Vc. Tislelizumab PK were linear across the 0.5–10 mg/kg dose range, and the approved dose is 200 mg IV every 3 weeks.
Source trace
| Element | Source location | Value / form |
|---|---|---|
| CL, Vc, Q2, V2, Q3, V3 | Budha 2023 Table 3 | 0.153 L/day, 3.05 L, 0.740 L/day, 1.27 L, 0.092 L/day, 2.10 L |
| WT on CL | Budha 2023 Eq. 5 / Table 3 (theta7) | Power: (WT/65)^0.565 |
| ALB on CL | Budha 2023 Eq. 5 / Table 3 (theta10) | Power: (ALB/41)^-0.457 |
| TUMSZ on CL | Budha 2023 Eq. 5 / Table 3 (theta11) | Power: (TUMSZ/63)^0.0735 |
| ADA on CL | Budha 2023 Eq. 5 / Table 3 (theta13) | Exponential: exp(0.111 * ADA_POS) |
| TUMTP=GC on CL | Budha 2023 Eq. 5 / Table 3 (theta14) | Exponential: exp(0.069 * TUMTP_GC) |
| TUMTP=cHL on CL | Budha 2023 Eq. 5 / Table 3 (theta15) | Exponential: exp(-0.216 * TUMTP_CHL) |
| WT on Vc | Budha 2023 Eq. 6 / Table 3 (theta8) | Power: (WT/65)^0.397 |
| SEX on Vc | Budha 2023 Eq. 6 / Table 3 (theta9) | Exponential: exp(-0.116 * SEXF) |
| AGE on Vc | Budha 2023 Eq. 6 / Table 3 (theta12) | Power: (AGE/60)^0.0966 |
| IIV CL / Vc | Budha 2023 Table 3 | 26.3% / 16.7% CV, covariance 0.020 (log-scale) |
| IIV V2, V3 | Budha 2023 Table 3 | 74.7% CV (shrinkage 55.8%), 99.9% CV (shrinkage 44.4%) |
| Residual error | Budha 2023 Table 3 | Proportional 12.6%, additive 2.09 μg/mL |
| Reference dose | Budha 2023 Methods; label | 200 mg IV q3w (flat) |
Covariate column naming
| Source column | Canonical column used here |
|---|---|
SEX (character “Female” / “Male”) |
SEXF (1 = female, 0 = male) |
ADA (Positive / Negative) |
ADA_POS (1 = ADA-positive, 0 = negative) |
TUMTP (categorical: cHL, GC, NSCLC, …) |
split into TUMTP_CHL and TUMTP_GC
indicators; reference = all other tumor types |
TUMSZ |
TUMSZ (baseline tumor size, mm) |
See inst/references/covariate-columns.md for the
canonical register.
Virtual population
Approximate the Budha 2023 Table 2 distributions for the pooled 2596-patient cohort (medians and ranges only — the paper does not publish individual covariates or covariate correlations).
set.seed(2023)
n_subj <- 500
# Weight and age: log-normal / normal fits to reported medians and ranges
WT <- pmin(pmax(rlnorm(n_subj, log(65), 0.20), 31.9), 130)
AGE <- pmin(pmax(rnorm(n_subj, 60, 12), 18), 90)
# Albumin (g/L): normal around median, clipped to observed range
ALB <- pmin(pmax(rnorm(n_subj, 41, 5), 17), 61.3)
# Tumor size (mm): log-normal around median 63.3, clipped to observed range
TUMSZ <- pmin(pmax(rlnorm(n_subj, log(63), 0.75), 10), 408)
# Sex: 26.0% female
SEXF <- rbinom(n_subj, 1, 0.26)
# ADA: 16.6% positive (of the 98.9% non-missing; treat missing as negative here)
ADA_POS <- rbinom(n_subj, 1, 0.166)
# Tumor type: sample from Table 2 proportions; only cHL and GC get indicators
tumtp_p <- c(
cHL = 0.027,
CRC = 0.031,
EC = 0.144,
GC = 0.039,
HCC = 0.122,
NPC = 0.008,
NSCLC = 0.443,
OC = 0.020,
UC = 0.058,
Other = 0.108
)
TUMTP <- sample(names(tumtp_p), n_subj, replace = TRUE, prob = tumtp_p)
TUMTP_CHL <- as.integer(TUMTP == "cHL")
TUMTP_GC <- as.integer(TUMTP == "GC")
pop <- data.frame(
ID = seq_len(n_subj),
WT, AGE, ALB, TUMSZ,
SEXF, ADA_POS,
TUMTP, TUMTP_CHL, TUMTP_GC
)Dosing dataset
Approved flat regimen: 200 mg IV q3w. Simulate 10 cycles (≈ 30 weeks) followed by an observation tail to capture terminal disposition.
cycle_days <- 21
n_cycles <- 10
dose_times <- seq(0, (n_cycles - 1) * cycle_days, by = cycle_days)
obs_times <- sort(unique(c(
seq(0, 21, by = 0.5), # intensive profile through cycle 1
seq(21, n_cycles * cycle_days, by = 3), # pre/post dose through multi-dose
seq(n_cycles * cycle_days, 365, by = 7) # washout tail
)))
d_dose <- pop |>
tidyr::crossing(TIME = dose_times) |>
dplyr::mutate(
AMT = 200, # flat 200 mg
EVID = 1,
CMT = "central",
DUR = 30 / (60 * 24), # 30-minute IV infusion in days
DV = NA_real_
)
d_obs <- pop |>
tidyr::crossing(TIME = obs_times) |>
dplyr::mutate(
AMT = NA_real_,
EVID = 0,
CMT = "central",
DUR = NA_real_,
DV = NA_real_
)
d_sim <- dplyr::bind_rows(d_dose, d_obs) |>
dplyr::arrange(ID, TIME, dplyr::desc(EVID)) |>
as.data.frame()Simulate
mod <- readModelDb("Budha_2023_tislelizumab")
set.seed(20230331)
sim <- rxSolve(mod, d_sim, returnType = "data.frame")
#> ℹ parameter labels from comments will be replaced by 'label()'Concentration-time profile
sim_summary <- sim |>
dplyr::filter(time > 0) |>
dplyr::group_by(time) |>
dplyr::summarise(
median = median(Cc, na.rm = TRUE),
lo = quantile(Cc, 0.05, na.rm = TRUE),
hi = quantile(Cc, 0.95, na.rm = TRUE),
.groups = "drop"
)
ggplot(sim_summary, aes(x = time / 7)) +
geom_ribbon(aes(ymin = lo, ymax = hi), alpha = 0.2, fill = "steelblue") +
geom_line(aes(y = median), color = "steelblue", linewidth = 1) +
scale_y_log10() +
labs(
x = "Time (weeks)",
y = "Tislelizumab concentration (\u03bcg/mL)",
title = "Simulated tislelizumab PK, 200 mg IV q3w x 10 cycles",
subtitle = "Median and 90% prediction interval (N = 500 virtual patients)",
caption = "Model: Budha et al. (2023) CPT Pharmacometrics Syst Pharmacol"
) +
theme_bw()
Effect of ADA status on PK
sim_ada <- sim |>
dplyr::filter(time > 0) |>
dplyr::mutate(ADA_label = ifelse(ADA_POS == 1, "ADA-positive", "ADA-negative")) |>
dplyr::group_by(time, ADA_label) |>
dplyr::summarise(median = median(Cc, na.rm = TRUE), .groups = "drop")
ggplot(sim_ada, aes(x = time / 7, y = median, color = ADA_label)) +
geom_line(linewidth = 1) +
scale_y_log10() +
scale_color_manual(values = c("ADA-negative" = "steelblue", "ADA-positive" = "tomato")) +
labs(
x = "Time (weeks)",
y = "Tislelizumab concentration (\u03bcg/mL)",
title = "Tislelizumab median concentrations by ADA status",
subtitle = "ADA-positive patients have ~11.7% higher CL (exp(0.111) - 1)",
color = "Immunogenicity",
caption = "Model: Budha et al. (2023)"
) +
theme_bw()
NCA validation
Run PKNCA on the first dosing interval (day 0–21) and a pseudo-steady-state interval (cycle 10, days 189–210), stratified by ADA status. Terminal half-life is expected to approximate the paper’s reported ≈ 23.8 days (Budha 2023 Methods) in the ADA-negative arm.
# Per-subject treatment grouping for PKNCA
pop$treatment <- ifelse(pop$ADA_POS == 1, "ADA-positive", "ADA-negative")
# Cycle 1 interval
conc1 <- sim |>
dplyr::filter(time >= 0, time <= 21, Cc > 0) |>
dplyr::rename(ID = id) |>
dplyr::left_join(dplyr::select(pop, ID, treatment), by = "ID") |>
dplyr::transmute(ID, time_rel = time, Cc, treatment, interval = "Cycle 1")
dose1 <- pop |>
dplyr::transmute(ID, time_rel = 0, AMT = 200, treatment, interval = "Cycle 1")
conc_obj <- PKNCAconc(conc1, Cc ~ time_rel | treatment + ID)
dose_obj <- PKNCAdose(dose1, AMT ~ time_rel | treatment + ID)
nca_data <- PKNCAdata(
conc_obj, dose_obj,
intervals = data.frame(
start = 0,
end = 21,
cmax = TRUE,
tmax = TRUE,
auclast = TRUE,
half.life = TRUE
)
)
nca_results <- pk.nca(nca_data)
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#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> ■■■■■■■■■■■■■■■■■ 54% | ETA: 9s
#> Warning: Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> ■■■■■■■■■■■■■■■■■■■■■■ 71% | ETA: 6s
#> Warning: Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> ■■■■■■■■■■■■■■■■■■■■■■■■■■■ 87% | ETA: 2s
#> Warning: Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.5) is not allowed
knitr::kable(
summary(nca_results),
digits = 2,
caption = "Cycle 1 NCA summary (days 0-21), stratified by ADA status"
)| start | end | treatment | N | auclast | cmax | tmax | half.life |
|---|---|---|---|---|---|---|---|
| 0 | 21 | ADA-negative | 410 | NC | 58.5 [17.4] | 0.500 [0.500, 0.500] | 20.4 [8.17] |
| 0 | 21 | ADA-positive | 90 | NC | 59.4 [18.0] | 0.500 [0.500, 0.500] | 18.5 [7.65] |
# Steady-state-ish interval at cycle 10 (day 189-210)
conc_ss <- sim |>
dplyr::filter(time >= 189, time <= 210, Cc > 0) |>
dplyr::rename(ID = id) |>
dplyr::left_join(dplyr::select(pop, ID, treatment), by = "ID") |>
dplyr::transmute(ID, time_rel = time - 189, Cc, treatment)
dose_ss <- pop |>
dplyr::transmute(ID, time_rel = 0, AMT = 200, treatment)
conc_obj_ss <- PKNCAconc(conc_ss, Cc ~ time_rel | treatment + ID)
dose_obj_ss <- PKNCAdose(dose_ss, AMT ~ time_rel | treatment + ID)
nca_data_ss <- PKNCAdata(
conc_obj_ss, dose_obj_ss,
intervals = data.frame(
start = 0,
end = 21,
cmax = TRUE,
cmin = TRUE,
auclast = TRUE
)
)
nca_results_ss <- pk.nca(nca_data_ss)
#> ■■■■■■■■■■■■■■■■■■■■■■■■■■■■■ 93% | ETA: 0s
knitr::kable(
summary(nca_results_ss),
digits = 2,
caption = "Cycle 10 NCA summary (days 189-210, pseudo-steady state), stratified by ADA status"
)| start | end | treatment | N | auclast | cmax | cmin |
|---|---|---|---|---|---|---|
| 0 | 21 | ADA-negative | 410 | 1170 [30.1] | 77.3 [24.0] | 40.2 [38.5] |
| 0 | 21 | ADA-positive | 90 | 1050 [34.3] | 72.2 [26.3] | 34.7 [45.6] |
Volume of distribution at steady state
The paper reports Vss = 6.42 L (Budha 2023 Results). With the nlmixr2 model, Vss is simply the sum of the central and peripheral volumes at typical covariates:
Assumptions and deviations
Budha 2023 does not publish individual PK or covariate tables, so the virtual population approximates Table 2 medians and ranges:
- Weight: log-normal, median 65 kg, clipped to 31.9–130 kg.
- Age: normal, median 60 y, clipped to 18–90 y.
- Albumin: normal, median 41 g/L, clipped to 17–61.3 g/L. The paper uses g/L (SI), not g/dL.
- Tumor size: log-normal, median 63.3 mm (matched to Budha 2023 Table 2 median 63.3 mm), clipped to 10–408 mm.
- Sex: 26% female (Budha 2023 Table 2).
- ADA status: 16.6% positive (Budha 2023 Table 2; 1.1% missing re-coded as negative for simulation).
- Tumor-type mix: sampled independently from Table 2 proportions; only cHL (2.7%) and GC (3.9%) get indicator columns — all other types are reference.
- No covariate correlations are imposed (paper does not report them).
- Dose regimen uses the approved 200 mg q3w flat dose (Budha 2023 Methods and label); the model is also valid over 0.5–10 mg/kg per the PopPK dataset.
- Infusion duration is set to 30 min (clinical administration); the final PopPK model treats infusions as bolus after deriving concentration-time profiles from study EDC.
Notes on the model
- Structure: three-compartment IV with linear elimination.
- Reference covariates: WT 65 kg, AGE 60 y, ALB 41 g/L, TUMSZ 63 mm, male, ADA-negative, non-cHL / non-GC tumor.
- Strongest covariates on CL (Budha 2023 Figures 6–7, not clinically meaningful): ±20% range of WT (0.565 exponent) and ALB (-0.457 exponent).
-
cHL patients have ~19% lower CL
(
exp(-0.216) = 0.806) than the reference tumor mix. - Shrinkage on V2 and V3 IIV is high (55.8%, 44.4%). The paper retains these etas; this implementation follows the paper.
Reference
- Budha N, Wu CY, Tang Z, et al. Model-based population pharmacokinetic analysis of tislelizumab in patients with advanced tumors. CPT Pharmacometrics Syst Pharmacol. 2023;12(1):95-109. doi:10.1002/psp4.12880