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TAS-114 (Araki 2022)

Source: vignettes/articles/Araki_2022_TAS114.Rmd
Araki_2022_TAS114.Rmd

Model and source

  • Citation: Araki H, Takenaka T, Takahashi K, Yamashita F, Matsuoka K, Yoshisue K, Ieiri I. A semimechanistic population pharmacokinetic and pharmacodynamic model incorporating autoinduction for the dose justification of TAS-114. CPT Pharmacometrics Syst Pharmacol. 2022;11(5):604-615. doi:10.1002/psp4.12747
  • Description: Semimechanistic population PK/PD model of oral TAS-114 (dual dUTPase / dihydropyrimidine dehydrogenase inhibitor) in healthy adult men and adults with advanced solid tumours (Araki 2022). TAS-114 follows a two-compartment model with first-order absorption and an absorption lag; clearance is scaled by the relative amount of a metabolising enzyme (CYP3A) whose zero-order synthesis is stimulated by the central TAS-114 concentration through an Emax function (enzyme-turnover autoinduction). Age (power) and AST (exponential) act on CL/F and body surface area (exponential) on Vc/F. Plasma uracil, the endogenous DPD substrate, follows an indirect-response model in which TAS-114 inhibits the first-order uracil elimination (Imax model) with the elimination rate fixed from the literature uracil half-life.
  • Article: https://doi.org/10.1002/psp4.12747 (open access; the supporting information holds the NONMEM code of the final PK model, Text S1, and of the PK/PD model, Text S2, plus the simulated dose-exposure summary, Table S1)

TAS-114 is an oral dual inhibitor of deoxyuridine triphosphatase (dUTPase) and dihydropyrimidine dehydrogenase (DPD), developed to widen the therapeutic index of capecitabine. It is metabolised mainly by CYP3A4 and induces CYP3A, so its exposure falls over repeated dosing. Araki et al. described this autoinduction with an enzyme-turnover model and linked TAS-114 to the plasma concentration of uracil, the endogenous DPD substrate, through an indirect-response model.

Population

The PK model was fit to 2661 plasma TAS-114 concentrations from 185 subjects in four studies (Table 1): healthy Japanese men given single doses or 14 days of twice-daily dosing (study 10057010, n = 28), and adults with advanced solid tumours given TAS-114 twice daily for 14 days of a 21-day cycle with S-1 (10057020, n = 68; TPU-TAS-114-102, n = 48) or capecitabine (TPU-TAS-114-101, n = 41). Doses ranged from 6 to 800 mg (median 270 mg). Table 2 gives the demographics: median age 59 years (20-81), weight 62 kg (36-119), body surface area 1.70 m^2 (1.25-2.35), AST 24 U/L (7-140); 106 men and 79 women; 96 Japanese, 77 Caucasian, 7 African American and 5 other. The uracil PD model was fit to 240 plasma uracil concentrations from the 24 healthy men of study 10057010 who had uracil sampled.

The same information is available programmatically via readModelDb("Araki_2022_TAS114")()$population.

Source trace

Equation / parameter Value Source location
lka log(0.508) 1/h Table 3
lvc log(17.0) L Table 3
lvp log(10.5) L Table 3
lq log(4.02) L/h Table 3
lcl log(8.74) L/h Table 3
ltlag log(0.217) h Table 3
lemax log(4.69) Table 3
lec50 log(5870) ng/mL Table 3
lkenz log(0.0230) 1/h Table 3
e_bsa_vc 1.52 Table 3; exponential form EXP(THETA(1)*(BSA - 1.7)) from Text S1
e_ast_cl -0.00753 Table 3; exponential form EXP(THETA(2)*(AST - 24)) from Text S1
e_age_cl -0.983 Table 3; power form (AGE/59)**THETA(3) from Text S1
etalka, etalvc, etalcl 0.04316, 0.39692, 0.35882 Table 3 CV% 21.0 / 69.8 / 65.7 as log(1 + CV^2); match Text S1 $OMEGA
propSd 0.37177 Text S1 $THETA 13 (see Assumptions)
lkout log(2.67) 1/h, not estimated Table 4
lic50 log(1046) ng/mL Table 4
limax log(0.888) Table 4
lrbase log(9.27) ng/mL Table 4
etalrbase 0.02344 Table 4 CV% 15.4 as log(1 + CV^2)
propSd_uracil 0.159 Table 4, 0.399^2 (see Assumptions)
d/dt(enzyme) = kenz * (1 + Emax*Cc/(EC50 + Cc)) - kenz * enzyme n/a Methods enzyme-turnover equations; Text S1 $DES
d/dt(central): elimination kel * enzyme * central n/a Text S1 $DES (K20*A(2)*A(4)); Results (“linear relationship”)
d/dt(uracil) = kin - kout * (1 - Imax*Cc/(IC50 + Cc)) * uracil n/a Text S2 $DES; Figure 1
enzyme(0) = 1, uracil(0) = rbase, kin = kout * rbase n/a Text S1 / S2 A_0(4), A_0(5), KIN

Typical-value reproduction of Table S1 (relative CL/F)

The relative CL/F (CL/F divided by its pre-dose value) equals the relative enzyme amount, which depends only on the TAS-114 concentration through the induction parameters. Table S1 reports its median minimum and maximum over Day 14 after 14 days of twice-daily dosing at 13 doses. A typical subject at the covariate medians reproduces them closely.

mod <- readModelDb("Araki_2022_TAS114")

doses <- c(6, 10, 25, 50, 100, 150, 200, 300, 400, 500, 600, 700, 800)
cov_median <- c(AGE = 59, AST = 24, BSA = 1.7)

# Observation rows go on the `uracil` state: it is both an ODE state and a
# declared endpoint, so the two-endpoint model accepts it, and Cc and
# `enzyme` come back at every row.
make_bid_events <- function(dose, obs_times) {
  rxode2::et(amt = dose, ii = 12, addl = 27, cmt = "depot") |>
    rxode2::et(obs_times, cmt = "uracil")
}

typ <- lapply(doses, function(d) {
  s <- rxode2::rxSolve(
    mod, make_bid_events(d, seq(0, 336, by = 0.25)),
    params = cov_median, omega = NA, sigma = NA, useLinCmt = FALSE,
    returnType = "data.frame"
  )
  s$dose <- d
  s
}) |>
  dplyr::bind_rows()
#> ℹ parameter labels from comments will be replaced by 'label()'

table_s1 <- tibble::tribble(
  ~dose, ~rel_min, ~rel_max, ~cmax, ~auclast, ~inh_min, ~inh_max,
  6, 1.041, 1.044, 132, 627, 0.7, 11.0,
  10, 1.066, 1.071, 216, 1018, 1.1, 16.7,
  25, 1.148, 1.159, 513, 2361, 2.4, 31.6,
  50, 1.258, 1.278, 962, 4301, 3.9, 45.2,
  100, 1.423, 1.457, 1763, 7534, 5.8, 58.2,
  150, 1.552, 1.593, 2494, 10353, 7.2, 65.0,
  200, 1.654, 1.705, 3175, 12919, 8.2, 69.1,
  300, 1.816, 1.883, 4454, 17577, 9.9, 73.9,
  400, 1.944, 2.020, 5663, 21854, 11.3, 76.7,
  500, 2.051, 2.137, 6805, 25820, 12.4, 78.5,
  600, 2.144, 2.234, 7942, 29649, 13.5, 79.9,
  700, 2.226, 2.319, 9087, 33367, 14.4, 80.8,
  800, 2.297, 2.394, 10146, 36848, 15.2, 81.6
)

rel_cl <- typ |>
  dplyr::filter(time >= 312, time <= 324) |>
  dplyr::group_by(dose) |>
  dplyr::summarise(sim_min = min(enzyme), sim_max = max(enzyme), .groups = "drop") |>
  dplyr::left_join(table_s1 |> dplyr::select(dose, rel_min, rel_max), by = "dose") |>
  dplyr::mutate(
    pct_min = 100 * (sim_min / rel_min - 1),
    pct_max = 100 * (sim_max / rel_max - 1)
  )

rel_cl |>
  dplyr::rename(
    "Dose (mg)" = dose,
    "Simulated min" = sim_min, "Simulated max" = sim_max,
    "Table S1 min" = rel_min, "Table S1 max" = rel_max,
    "Diff min (%)" = pct_min, "Diff max (%)" = pct_max
  ) |>
  knitr::kable(digits = 3, caption = "Relative CL/F on Day 14: typical subject vs. Table S1 medians.")
Relative CL/F on Day 14: typical subject vs. Table S1 medians.
Dose (mg) Simulated min Simulated max Table S1 min Table S1 max Diff min (%) Diff max (%)
6 1.041 1.045 1.041 1.044 0.020 0.051
10 1.066 1.072 1.066 1.071 0.037 0.077
25 1.149 1.162 1.148 1.159 0.087 0.224
50 1.259 1.282 1.258 1.278 0.107 0.316
100 1.425 1.463 1.423 1.457 0.128 0.432
150 1.550 1.601 1.552 1.593 -0.107 0.499
200 1.653 1.713 1.654 1.705 -0.084 0.469
300 1.815 1.890 1.816 1.883 -0.076 0.391
400 1.942 2.029 1.944 2.020 -0.126 0.443
500 2.046 2.143 2.051 2.137 -0.226 0.279
600 2.136 2.240 2.144 2.234 -0.380 0.265
700 2.214 2.324 2.226 2.319 -0.539 0.228
800 2.283 2.399 2.297 2.394 -0.591 0.207 

# Deterministic solve, so a tight bound is appropriate. Measured maximum
# absolute difference is about 0.7%; a mis-transcribed Emax, EC50 or kenz,deg
# moves these values by several percent.
stopifnot(nrow(rel_cl) == length(doses))
stopifnot(max(abs(c(rel_cl$pct_min, rel_cl$pct_max))) < 2)

Figure 3a: relative CL/F over 14 days 

typ |>
  dplyr::filter(time <= 336) |>
  ggplot(aes(time / 24, enzyme, group = dose, colour = factor(dose))) +
  geom_line() +
  labs(
    x = "Days after first dose", y = "Relative CL/F (CL/F / baseline CL/F)",
    colour = "Dose (mg BID)",
    title = "Relative CL/F of TAS-114, typical subject",
    caption = "Replicates Figure 3a of Araki 2022 (typical-value prediction)."
  ) +
  theme_bw()

Virtual cohort

Observed data are not public. The stochastic simulations use 200 virtual subjects per dose, with age, AST and body surface area drawn to approximate Table 2 (median and range); the covariates are independent of one another, which the paper does not report.

Table S1 was generated the way NONMEM’s $SIMULATION generates data: as simulated observations, residual error included, at the planned sampling times. The Day 14 grid below is the clinical one of Table 1 (pre-dose, 0.5, 1, 2, 4, 6, 8 and 12 h). Cmax taken from noisy samples sits above the Cmax of the noise-free profile and the minimum inhibition sits below it, while AUClast is almost unaffected; with that design the model reproduces all of Table S1 (the noise-free comparison underestimates Cmax by about 12% and overestimates the minimum inhibition by about 3 percentage points).

rxode2::rxSetSeed(20220511)
set.seed(20220511)
n_per_dose <- 200

draw_trunc <- function(n, draw, lo, hi) {
  x <- draw(n)
  while (any(bad <- x < lo | x > hi)) x[bad] <- draw(sum(bad))
  x
}

covs <- tibble::tibble(
  id = seq_len(n_per_dose * length(doses)),
  dose_mg = rep(doses, each = n_per_dose),
  AGE = draw_trunc(length(id), function(n) rnorm(n, 59, 11), 20, 81),
  AST = draw_trunc(length(id), function(n) rlnorm(n, log(24), 0.4), 7, 140),
  BSA = draw_trunc(length(id), function(n) rnorm(n, 1.70, 0.20), 1.25, 2.35)
)

day14_grid <- 312 + c(0, 0.5, 1, 2, 4, 6, 8, 12)
obs_times <- c(seq(0, 12, by = 0.5), day14_grid)
dose_rows <- covs |>
  tidyr::crossing(time = seq(0, 324, by = 12)) |>
  dplyr::mutate(evid = 1L, amt = dose_mg, cmt = "depot")
obs_rows <- covs |>
  tidyr::crossing(time = obs_times) |>
  dplyr::mutate(evid = 0L, amt = NA_real_, cmt = "uracil")
events <- dplyr::bind_rows(dose_rows, obs_rows) |>
  dplyr::arrange(id, time, dplyr::desc(evid))

stopifnot(!anyDuplicated(events[, c("id", "time", "evid")]))
stopifnot(all(table(covs$dose_mg) == n_per_dose))

Simulation 

sim <- rxode2::rxSolve(
  mod, events = events, keep = c("dose_mg"), useLinCmt = FALSE,
  returnType = "data.frame"
) |>
  dplyr::mutate(treatment = paste(dose_mg, "mg"))

# Simulated TAS-114 observations: proportional residual error added in base R
# (seeded above), so the same draws serve both residual-error readings
# compared later. An error draw below -1/SD would give a negative
# concentration; such values are floored at zero.
prop_sd <- rxode2::rxode(mod)$iniDf
#> ℹ parameter labels from comments will be replaced by 'label()'
prop_sd <- prop_sd$est[prop_sd$name == "propSd"]
eps <- rnorm(nrow(sim))
sim <- sim |>
  dplyr::mutate(
    dv = pmax(Cc * (1 + prop_sd * eps), 0),
    dv_table = pmax(Cc * (1 + 0.610 * eps), 0)
  )

PKNCA validation (Day 14, Figure 3b)

Table S1 reports the median Cmax and AUClast over the Day 14 dosing interval (Days 14 to 14.5) after twice-daily dosing.

sim_nca <- sim |>
  dplyr::filter(!is.na(dv), time >= 312) |>
  dplyr::select(id, time, dv, treatment)

dose_df <- events |>
  dplyr::filter(evid == 1) |>
  dplyr::mutate(treatment = paste(dose_mg, "mg")) |>
  dplyr::select(id, time, amt, treatment)

conc_obj <- PKNCA::PKNCAconc(sim_nca, dv ~ time | treatment + id)
dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | treatment + id)
intervals <- data.frame(start = 312, end = 324, cmax = TRUE, auclast = TRUE)
nca_res <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals))

published <- table_s1 |>
  dplyr::transmute(treatment = paste(dose, "mg"), cmax, auclast)

cmp <- nlmixr2lib::ncaComparisonTable(
  simulated = nca_res,
  reference = published,
  by = "treatment",
  units = c(cmax = "ng/mL", auclast = "ng*h/mL"),
  tolerance_pct = 20
)
knitr::kable(
  cmp,
  caption = "Day 14 simulated median vs. Table S1 median. * differs by >20%."
)
Day 14 simulated median vs. Table S1 median. * differs by >20%.
NCA parameter treatment Reference Simulated % diff
Cmax (ng/mL) 6 mg 132 126 -4.3%
Cmax (ng/mL) 10 mg 216 212 -1.8%
Cmax (ng/mL) 25 mg 513 484 -5.6%
Cmax (ng/mL) 50 mg 962 950 -1.2%
Cmax (ng/mL) 100 mg 1760 1770 +0.3%
Cmax (ng/mL) 150 mg 2490 2520 +1.1%
Cmax (ng/mL) 200 mg 3180 3120 -1.7%
Cmax (ng/mL) 300 mg 4450 4270 -4.1%
Cmax (ng/mL) 400 mg 5660 5590 -1.3%
Cmax (ng/mL) 500 mg 6800 7220 +6.1%
Cmax (ng/mL) 600 mg 7940 8100 +2.0%
Cmax (ng/mL) 700 mg 9090 9540 +5.0%
Cmax (ng/mL) 800 mg 10100 10800 +6.3%
AUClast (ng*h/mL) 6 mg 627 614 -2.0%
AUClast (ng*h/mL) 10 mg 1020 981 -3.6%
AUClast (ng*h/mL) 25 mg 2360 2290 -3.1%
AUClast (ng*h/mL) 50 mg 4300 4220 -1.8%
AUClast (ng*h/mL) 100 mg 7530 7570 +0.5%
AUClast (ng*h/mL) 150 mg 10400 10000 -3.1%
AUClast (ng*h/mL) 200 mg 12900 12900 +0.2%
AUClast (ng*h/mL) 300 mg 17600 18200 +3.6%
AUClast (ng*h/mL) 400 mg 21900 20900 -4.2%
AUClast (ng*h/mL) 500 mg 25800 27800 +7.7%
AUClast (ng*h/mL) 600 mg 29600 29700 +0.0%
AUClast (ng*h/mL) 700 mg 33400 34400 +3.1%
AUClast (ng*h/mL) 800 mg 36800 36600 -0.8% 
nca_med <- as.data.frame(nca_res) |>
  dplyr::filter(PPTESTCD %in% c("cmax", "auclast")) |>
  dplyr::group_by(treatment, PPTESTCD) |>
  dplyr::summarise(sim = median(PPORRES), .groups = "drop") |>
  tidyr::pivot_wider(names_from = PPTESTCD, values_from = sim) |>
  dplyr::left_join(published, by = "treatment", suffix = c("_sim", "_pub")) |>
  dplyr::mutate(
    pct_cmax = 100 * (cmax_sim / cmax_pub - 1),
    pct_auc = 100 * (auclast_sim / auclast_pub - 1)
  )
stopifnot(nrow(nca_med) == length(doses))
# Medians of 200 subjects with ~66% CV on CL/F carry a ~6% standard error.
# Centre: a mis-transcribed CL/F, volume or the mg -> ng/mL factor moves every
# dose by tens of percent. Envelope: robust to which dose lands in the tail.
stopifnot(
  abs(median(c(nca_med$pct_cmax, nca_med$pct_auc))) < 10,
  quantile(abs(c(nca_med$pct_cmax, nca_med$pct_auc)), 0.9) < 20
)
as.data.frame(nca_res) |>
  dplyr::filter(PPTESTCD %in% c("cmax", "auclast")) |>
  dplyr::mutate(dose = as.numeric(sub(" mg", "", treatment))) |>
  dplyr::group_by(dose, PPTESTCD) |>
  dplyr::summarise(
    Q50 = median(PPORRES), Q025 = quantile(PPORRES, 0.025),
    Q975 = quantile(PPORRES, 0.975), .groups = "drop"
  ) |>
  ggplot(aes(dose, Q50, colour = PPTESTCD)) +
  geom_pointrange(aes(ymin = Q025, ymax = Q975), position = position_dodge(width = 15)) +
  geom_point(
    data = table_s1 |>
      tidyr::pivot_longer(c(cmax, auclast), names_to = "PPTESTCD", values_to = "Q50"),
    shape = 4, size = 3, colour = "black"
  ) +
  labs(
    x = "TAS-114 dose (mg BID)", y = "Cmax (ng/mL) or AUClast (ng*h/mL)",
    colour = NULL,
    title = "Day 14 exposure (median and 95% prediction interval)",
    caption = "Replicates Figure 3b of Araki 2022; crosses are the Table S1 medians."
  ) +
  theme_bw()
#> Warning: `position_dodge()` requires non-overlapping x intervals.

DPD inhibition on Day 14 (Figure 3c)

The inhibition percentage of TAS-114-mediated uracil metabolism is 100 * Imax * C / (IC50 + C), the fractional reduction of the uracil elimination rate, here evaluated at the simulated Day 14 TAS-114 observations. Its minimum and maximum per subject are summarised by dose.

inhib_pct <- function(conc, imax, ic50) 100 * imax * conc / (ic50 + conc)
day14 <- sim |> dplyr::filter(time %in% day14_grid)

inh <- day14 |>
  dplyr::mutate(inh = inhib_pct(dv, imax, ic50)) |>
  dplyr::group_by(id, dose_mg) |>
  dplyr::summarise(inh_min = min(inh), inh_max = max(inh), .groups = "drop")

inh_sum <- inh |>
  tidyr::pivot_longer(c(inh_min, inh_max), names_to = "stat", values_to = "inh") |>
  dplyr::group_by(dose_mg, stat) |>
  dplyr::summarise(
    Q50 = median(inh), Q025 = quantile(inh, 0.025), Q975 = quantile(inh, 0.975),
    .groups = "drop"
  )

inh_cmp <- inh_sum |>
  dplyr::select(dose = dose_mg, stat, Q50) |>
  tidyr::pivot_wider(names_from = stat, values_from = Q50) |>
  dplyr::left_join(table_s1 |> dplyr::select(dose, pub_min = inh_min, pub_max = inh_max), by = "dose")

inh_cmp |>
  dplyr::select(dose, inh_min, inh_max, pub_min, pub_max) |>
  dplyr::rename(
    "Dose (mg)" = dose, "Simulated min (%)" = inh_min, "Simulated max (%)" = inh_max,
    "Table S1 min (%)" = pub_min, "Table S1 max (%)" = pub_max
  ) |>
  knitr::kable(digits = 1, caption = "Median Day 14 inhibition of uracil metabolism vs. Table S1.")
Median Day 14 inhibition of uracil metabolism vs. Table S1.
Dose (mg) Simulated min (%) Simulated max (%) Table S1 min (%) Table S1 max (%)
6 0.6 9.6 0.7 11.0
10 1.2 15.0 1.1 16.7
25 2.1 28.1 2.4 31.6
50 4.1 42.3 3.9 45.2
100 6.0 55.8 5.8 58.2
150 7.4 62.8 7.2 65.0
200 7.7 66.5 8.2 69.1
300 10.1 71.3 9.9 73.9
400 10.9 74.8 11.3 76.7
500 13.0 77.6 12.4 78.5
600 11.9 78.6 13.5 79.9
700 14.3 80.0 14.4 80.8
800 16.6 81.0 15.2 81.6 

# Absolute percentage-point differences (the minimum is small at low doses,
# where a relative difference would be meaningless). A mis-transcribed IC50
# or Imax shifts every dose by many points.
stopifnot(
  nrow(inh_cmp) == length(doses),
  abs(median(inh_cmp$inh_max - inh_cmp$pub_max)) < 4,
  abs(median(inh_cmp$inh_min - inh_cmp$pub_min)) < 2.5,
  quantile(abs(c(inh_cmp$inh_max - inh_cmp$pub_max, inh_cmp$inh_min - inh_cmp$pub_min)), 0.9) < 6
)

ggplot(inh_sum, aes(dose_mg, Q50, colour = stat)) +
  geom_pointrange(aes(ymin = Q025, ymax = Q975), position = position_dodge(width = 15)) +
  labs(
    x = "TAS-114 dose (mg BID)", y = "Inhibition of uracil metabolism (%)", colour = NULL,
    title = "Day 14 inhibition (median and 95% prediction interval)",
    caption = "Replicates Figure 3c of Araki 2022."
  ) +
  theme_bw()
#> Warning: `position_dodge()` requires non-overlapping x intervals.

The simulated maximum inhibition flattens near 80% from about 600 mg, the maximum tolerated dose, while Cmax and AUClast keep rising, which is the dose justification the paper draws.

Residual-error scale (Figure 2)

Tables 3 and 4 print the proportional residual errors as “CV%” values of 61.0 and 39.9. The NONMEM code in Text S1 and S2 writes the error as W = THETA*IPRED with $SIGMA 1 FIX, so the THETA is itself the standard deviation, and the Text S1 value of that THETA, 0.37177, is the square of 0.610. The tables therefore report the square root of the THETA. The prediction-corrected VPCs of Figure 2 and the simulated summary of Table S1 decide between the two readings. The Figure 2 rows below use a 200-subject single-dose solve with IIV, with the residual error added in base R under each candidate SD; the Table S1 rows reuse the Day 14 cohort above.

rxode2::rxSetSeed(7)
set.seed(7)
tt <- c(1, 2, 4, 48)
ev1 <- rxode2::et(amt = 300, cmt = "depot") |>
  rxode2::et(tt, cmt = "uracil") |>
  rxode2::et(id = 1:200)
s1 <- rxode2::rxSolve(mod, ev1, params = cov_median, sigma = NA, useLinCmt = FALSE,
                      returnType = "data.frame")
p1 <- rxode2::rxSolve(mod, rxode2::et(amt = 300, cmt = "depot") |> rxode2::et(tt, cmt = "uracil"),
                      params = cov_median, omega = NA, sigma = NA, useLinCmt = FALSE,
                      returnType = "data.frame")
s1$pred <- p1$Cc[match(s1$time, p1$time)]

# 50 residual draws per subject and time point.
ruv_quant <- function(x, sd, p) {
  y <- rep(x, each = 50) * (1 + sd * rnorm(50 * length(x)))
  unname(quantile(y, p))
}
pk <- s1 |> dplyr::filter(time <= 4)
base <- s1 |> dplyr::filter(time == 48)

# Table S1: median over the 13 doses of the difference between the simulated
# and published Day 14 medians, from the noisy observations of the cohort above.
table_s1_check <- function(col) {
  d <- day14 |>
    dplyr::mutate(y = .data[[col]], inh = inhib_pct(y, imax, ic50)) |>
    dplyr::group_by(id, dose_mg) |>
    dplyr::summarise(sim_cmax = max(y), sim_imin = min(inh), .groups = "drop") |>
    dplyr::group_by(dose_mg) |>
    dplyr::summarise(sim_cmax = median(sim_cmax), sim_imin = median(sim_imin), .groups = "drop") |>
    dplyr::left_join(table_s1, by = c(dose_mg = "dose"))
  stopifnot(nrow(d) == length(doses))
  c(median(100 * (d$sim_cmax / d$cmax - 1)), median(d$sim_imin - d$inh_min))
}
ts_ctrl <- table_s1_check("dv")
ts_tab <- table_s1_check("dv_table")

ruv_tab <- tibble::tibble(
  Quantity = c(
    "TAS-114 pcVPC 5th percentile / median, 1-4 h",
    "Uracil baseline 5th percentile (ng/mL), 48 h",
    "Uracil baseline 95th percentile (ng/mL), 48 h",
    "Table S1 Cmax: median difference over doses (%)",
    "Table S1 minimum inhibition: median difference (points)"
  ),
  `Published (Figure 2 read by eye; Table S1)` = c("about 0.15-0.2", "about 5.8", "about 13.9", "0", "0"),
  `Control-stream SD (0.372 / 0.159)` = c(
    ruv_quant(pk$Cc / pk$pred, 0.37177, 0.05) / ruv_quant(pk$Cc / pk$pred, 0.37177, 0.5),
    ruv_quant(base$uracil, 0.159, 0.05), ruv_quant(base$uracil, 0.159, 0.95),
    ts_ctrl
  ),
  `Table CV% as SD (0.610 / 0.399)` = c(
    ruv_quant(pk$Cc / pk$pred, 0.610, 0.05) / ruv_quant(pk$Cc / pk$pred, 0.610, 0.5),
    ruv_quant(base$uracil, 0.399, 0.05), ruv_quant(base$uracil, 0.399, 0.95),
    ts_tab
  )
)
knitr::kable(ruv_tab, digits = 2, caption = "Residual-error readings against Figure 2 and Table S1.")
Residual-error readings against Figure 2 and Table S1.
Quantity Published (Figure 2 read by eye; Table S1) Control-stream SD (0.372 / 0.159) Table CV% as SD (0.610 / 0.399)
TAS-114 pcVPC 5th percentile / median, 1-4 h about 0.15-0.2 0.26 -0.01
Uracil baseline 5th percentile (ng/mL), 48 h about 5.8 6.32 3.05
Uracil baseline 95th percentile (ng/mL), 48 h about 13.9 13.52 16.99
Table S1 Cmax: median difference over doses (%) 0 -1.24 13.05
Table S1 minimum inhibition: median difference (points) 0 0.08 -6.32 

# The two readings are far apart: the table-as-SD reading drives the TAS-114
# lower band to about zero (Figure 2a stays well above it), the uracil
# baseline 5th percentile to about 3 ng/mL (Figure 2e: about 5.8), and the
# Table S1 Cmax about 15% too high. The Table S1 rows share their IIV and
# error draws, so the gap between the readings is systematic, not noise.
stopifnot(
  ruv_tab[[3]][1] > 0.12, ruv_tab[[4]][1] < 0.08,
  abs(ruv_tab[[3]][2] - 5.8) < 1, ruv_tab[[4]][2] < 4.2,
  abs(ts_ctrl[1]) < 7, ts_tab[1] - ts_ctrl[1] > 7,
  abs(ts_ctrl[2]) < 2.5, ts_ctrl[2] - ts_tab[2] > 3
)

Assumptions and deviations

  • Residual-error scale. The proportional residual SDs are the control-stream values: 0.37177 for TAS-114 (Text S1 $THETA 13) and 0.399^2 = 0.159 for uracil. Tables 3 and 4 print the square roots of these THETAs (61.0% and 39.9%) as if they were CVs. Text S2 lists only initial estimates, so the uracil value assumes the same convention as the PK table, and the Figure 2e baseline band supports it. The Figure 2a lower band and the Table S1 Cmax and minimum inhibition support the TAS-114 value (see the check above). Users who prefer the tables as printed can set propSd = 0.610 and propSd_uracil = 0.399 in ini().
  • Values from Table 3 rather than Text S1. The Text S1 $THETA block mixes final and initial estimates (for example Vc/F 18 vs. the final 17.0). All structural and covariate values come from Tables 3 and 4. The IIV variances are log(1 + CV^2) of the Table 3 CVs, which agree with the Text S1 $OMEGA values to the printed precision.
  • Units. The NONMEM data set dosed in micrograms, so A(2)/V2 was already in ng/mL. The packaged model doses in mg and computes Cc = 1000 * central / vc.
  • Imax cap. Text S2 caps Imax at 1. The estimate is 0.888 with no IIV, so the cap never applies and is omitted.
  • Sequential PK/PD fit. The uracil model was fit with the individual PK parameters fixed at their posterior estimates; the packaged model carries the PK IIV through to the PD, which is the usual way to simulate such a model.
  • Virtual cohort. Covariates were drawn independently from truncated normal (age, BSA) and log-normal (AST) distributions matched to the Table 2 median and range; the paper’s simulations used its own data set. The paper does not state the body surface area formula.
  • No IIV on induction or PD parameters other than baseline uracil. The paper reports that these could not be estimated.
  • Errata. No correction notice was found for this article as of 2026-10-01.