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Oxaliplatin in rats with acute kidney injury (Kobuchi 2021)

Source: vignettes/articles/Kobuchi_2021_oxaliplatin_rat.Rmd
Kobuchi_2021_oxaliplatin_rat.Rmd

Model and source

  • Citation: Kobuchi S, Kai M, Ito Y. Population Pharmacokinetic Model-Based Evaluation of Intact Oxaliplatin in Rats with Acute Kidney Injury. Cancers (Basel). 2021;13(24):6382. doi:10.3390/cancers13246382 (PMCID PMC8699120).
  • Description: Preclinical (rat). Two-compartment population PK model with linear elimination for intact (unbiotransformed) oxaliplatin in plasma after a single intravenous bolus of 3 or 8 mg/kg to male Wistar rats with normal renal function or mild / severe acute kidney injury induced by 30 / 60 min renal ischemia-reperfusion (Kobuchi 2021). Parameters are per kg body weight (dose in mg/kg), exponential IIV on the central volume, clearance and intercompartmental clearance, proportional residual error. The final model carries no covariates: the paper’s renal-function simulation (Figure 5) substituted a post hoc clearance-versus-plasma-creatinine regression whose coefficients are not printed (see the vignette).
  • Article: https://doi.org/10.3390/cancers13246382 (open access, PMC8699120)
  • Supplement: https://www.mdpi.com/article/10.3390/cancers13246382/s1 (Figure S1, goodness-of-fit plots only; no parameter values)

Kobuchi 2021 measured intact oxaliplatin (L-OHP, not total platinum) by LC-MS/MS in rat plasma and fitted a two-compartment population PK model in Phoenix NLME 8.2 (FOCE-ELS). The model was then used to simulate exposure over a range of plasma creatinine values to ask whether oxaliplatin needs a dose reduction in acute kidney injury (AKI).

Population

Thirty 10-week-old male Wistar rats (about 300 g) were split into normal, mild-AKI and severe-AKI groups. AKI was induced by clamping both renal arteries for 30 min (mild) or 60 min (severe) followed by 24 h of reperfusion; controls had sham surgery. Each renal-function group received a single intravenous bolus of oxaliplatin (Elplat) at 3 or 8 mg/kg into the jugular vein (n = 5 per dose group). Plasma was sampled at 3, 5, 10, 20, 30 and 45 min and 1, 1.5 and 2 h. Table 1 of the paper gives mean (SD) plasma creatinine of 0.27 (0.02), 0.54 (0.21) and 0.95 (0.17) mg/dL and creatinine clearance of 4.2 (1.3), 2.2 (0.7) and 1.6 (0.7) mL/min/kg in the normal, mild and severe groups.

The same information is available programmatically via readModelDb("Kobuchi_2021_oxaliplatin_rat")()$population.

Source trace

Every ini() value carries an in-file comment in inst/modeldb/specificDrugs/Kobuchi_2021_oxaliplatin_rat.R. They are collected here.

Equation / parameter Value Source location
Two-compartment, linear elimination, IV bolus n/a Section 2.4 and Section 3.3 (“A two-compartment model with a linear elimination”)
lvc (V) log(0.44) L/kg Table 3, fixed effects
lvp (V2) log(2.26) L/kg Table 3, fixed effects
lcl (CL) log(1.76) L/h/kg Table 3, fixed effects
lq (CL2) log(1.0) L/h/kg Table 3, fixed effects
etalvc 0.375^2 = 0.140625 Table 3, IIV on V = 37.5%
etalcl 0.305^2 = 0.093025 Table 3, IIV on CL = 30.5%
etalq 0.315^2 = 0.099225 Table 3, IIV on CL2 = 31.5%
Exponential IIV n/a Section 2.4 (“assumed by the exponential error model”)
propSd 0.149 Table 3, residual variability C = 14.9%; proportional per Section 2.4
Cc <- central / vc n/a Plasma concentration in the central compartment (Table 3 footnote, C)

The text of Section 3.3 restates the estimates: V and V2 of 0.44 and 2.26 L/kg (sum 2.70 L/kg), CL of 1.76 and CL2 of 1.0 L/h/kg. The paper’s “CLtot: 2.76 L/h/kg” is the arithmetic sum CL + CL2; it is not a model quantity (total clearance of the model is CL alone).

mod <- readModelDb("Kobuchi_2021_oxaliplatin_rat")
ui <- rxode2::rxode(mod)
#> ℹ parameter labels from comments will be replaced by 'label()'
th <- ui$theta
stopifnot(
  abs(exp(th[["lvc"]]) + exp(th[["lvp"]]) - 2.70) < 1e-8, # Section 3.3 'Vd: 2.70 L/kg'
  abs(exp(th[["lcl"]]) + exp(th[["lq"]]) - 2.76) < 1e-8 #   Section 3.3 'CLtot: 2.76 L/h/kg'
)

Typical-value check

For a linear model after an IV bolus, AUC(0-inf) = Dose / CL exactly, so the typical rat must give 3 / 1.76 = 1.705 and 8 / 1.76 = 4.545 ug*h/mL. The solve below uses a log-spaced grid out to 72 h, which leaves a negligible extrapolated tail.

mod_typ <- rxode2::zeroRe(mod)
#> ℹ parameter labels from comments will be replaced by 'label()'
tgrid <- sort(unique(c(0, exp(seq(log(0.005), log(72), length.out = 400)))))
ev_typ <- dplyr::bind_rows(
  data.frame(id = 1L, time = 0, amt = 3, evid = 1L, cmt = "central", dose = 3),
  data.frame(id = 1L, time = tgrid, amt = 0, evid = 0L, cmt = "central", dose = 3),
  data.frame(id = 2L, time = 0, amt = 8, evid = 1L, cmt = "central", dose = 8),
  data.frame(id = 2L, time = tgrid, amt = 0, evid = 0L, cmt = "central", dose = 8)
)
sim_typ <- rxode2::rxSolve(mod_typ, events = ev_typ, keep = "dose") |>
  as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalvc', 'etalcl', 'etalq'
#> Warning: multi-subject simulation without without 'omega'

typ_nca <- sim_typ |>
  dplyr::group_by(dose) |>
  dplyr::summarise(
    auc = sum(diff(time) * (head(Cc, -1) + tail(Cc, -1)) / 2) +
      dplyr::last(Cc) / (log(Cc[n() - 1] / Cc[n()]) / (time[n()] - time[n() - 1])),
    cl = dplyr::first(cl),
    .groups = "drop"
  ) |>
  dplyr::mutate(expected = dose / cl, pct_diff = 100 * (auc / expected - 1))
knitr::kable(typ_nca, digits = 3, caption = "Typical-value AUC(0-inf) against Dose / CL.")
Typical-value AUC(0-inf) against Dose / CL.
dose auc cl expected pct_diff
3 1.705 1.76 1.705 0.01
8 4.546 1.76 4.545 0.01 
# Same drawn (typical) parameters on both sides: the only difference is
# trapezoidal error on the log-spaced grid.
stopifnot(all(abs(typ_nca$pct_diff) < 1))

Virtual cohort and simulation

Two dose arms of 200 virtual rats each, sampled at the paper’s nine plasma times plus a time-zero row (the IV-bolus initial concentration).

rxode2::rxSetSeed(20211220)
paper_times <- c(3, 5, 10, 20, 30, 45, 60, 90, 120) / 60
make_arm <- function(n, dose, id_offset) {
  ids <- id_offset + seq_len(n)
  dplyr::bind_rows(
    data.frame(id = ids, time = 0, amt = dose, evid = 1L, cmt = "central"),
    tidyr::expand_grid(id = ids, time = c(0, paper_times)) |>
      dplyr::mutate(amt = 0, evid = 0L, cmt = "central")
  ) |>
    dplyr::mutate(treatment = paste(dose, "mg/kg")) |>
    dplyr::arrange(id, time, dplyr::desc(evid))
}
events <- dplyr::bind_rows(
  make_arm(200, 3, 0L),
  make_arm(200, 8, 200L)
)
stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))

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

Replicate Figure 1 

# Replicates Figure 1 of Kobuchi 2021: plasma intact oxaliplatin after 3 or
# 8 mg/kg IV. The paper plots mean +/- SD per renal-function group; the model
# has no renal-function covariate, so one pooled band is shown per dose.
sim |>
  dplyr::filter(time > 0) |>
  dplyr::group_by(treatment, time) |>
  dplyr::summarise(
    Q05 = quantile(Cc, 0.05), Q50 = median(Cc), Q95 = quantile(Cc, 0.95),
    .groups = "drop"
  ) |>
  ggplot(aes(time, Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.25) +
  geom_line() +
  geom_point() +
  facet_wrap(~treatment) +
  scale_y_log10() +
  labs(
    x = "Time (h)", y = "Intact oxaliplatin (ug/mL)",
    caption = "Median and 5th-95th percentiles of 200 simulated rats per dose. Replicates Figure 1 of Kobuchi 2021."
  )

PKNCA validation

Kobuchi 2021 ran NCA in Phoenix WinNonlin with the linear trapezoidal rule on the 0-2 h profiles; PKNCA is set to the same rule. The published Table 2 means are per renal-function group, so the reference below is the unweighted mean of the three group means at each dose (all groups had n = 4-5).

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

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

conc_obj <- PKNCA::PKNCAconc(sim_nca, Cc ~ time | treatment + id)
dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | treatment + id, route = "intravascular")
intervals <- data.frame(
  start = 0, end = Inf,
  aucinf.obs = TRUE, half.life = TRUE, cl.obs = TRUE, vz.obs = TRUE
)
nca_res <- PKNCA::pk.nca(PKNCA::PKNCAdata(
  conc_obj, dose_obj,
  intervals = intervals,
  options = list(auc.method = "linear")
))

# Table 2 of Kobuchi 2021, mean over the normal / mild / severe group means.
published <- tibble::tribble(
  ~treatment, ~aucinf.obs, ~half.life, ~cl.obs, ~vz.obs,
  "3 mg/kg", mean(c(2.0, 2.2, 2.4)), mean(c(2.6, 2.8, 2.3)), mean(c(1.6, 1.4, 1.3)), mean(c(5.8, 5.7, 3.8)),
  "8 mg/kg", mean(c(3.4, 3.3, 4.4)), mean(c(0.7, 0.7, 0.9)), mean(c(2.5, 2.2, 1.9)), mean(c(2.4, 2.9, 2.2))
)

cmp <- nlmixr2lib::ncaComparisonTable(
  simulated = nca_res,
  reference = published,
  by = "treatment",
  units = c(aucinf.obs = "ug*h/mL", half.life = "h", cl.obs = "L/h/kg", vz.obs = "L/kg"),
  tolerance_pct = 20
)
knitr::kable(
  cmp,
  caption = "Simulated (median) vs. published NCA (Table 2, mean of the three renal-function groups). * differs by >20%."
)
Simulated (median) vs. published NCA (Table 2, mean of the three renal-function groups). * differs by >20%.
NCA parameter treatment Reference Simulated % diff
AUC0-∞ (obs) (ug*h/mL) 3 mg/kg 2.2 1.58 -28.4%*
AUC0-∞ (obs) (ug*h/mL) 8 mg/kg 3.7 4.18 +12.9%
t½ (h) 3 mg/kg 2.57 1.86 -27.5%*
t½ (h) 8 mg/kg 0.767 1.94 +152.5%*
CL/F (L/h/kg) 3 mg/kg 1.43 1.9 +32.8%*
CL/F (L/h/kg) 8 mg/kg 2.2 1.91 -13.0%
Vz/F (L/kg) 3 mg/kg 5.1 4.63 -9.2%
Vz/F (L/kg) 8 mg/kg 2.5 4.96 +98.6%*

The model is one pooled fit across both doses and all three renal-function groups, and Table 2 itself is not dose-proportional: dose-normalised AUC is 0.67-0.80 at 3 mg/kg and 0.41-0.55 at 8 mg/kg (h*kg/L), while the linear model gives a single 1 / CL = 0.57 for both. The simulated AUC therefore falls below the 3 mg/kg groups and inside the range of the 8 mg/kg groups, with clearance mirroring it. (NCA on the 0-2 h window also puts the simulated median AUC a little under Dose / CL, because the terminal slope fitted inside 2 h is steeper than the model’s true terminal phase, whose half-life is about 2.5 h.) The half-life and volume differ most at 8 mg/kg, where the published half-life of 0.7-0.9 h is far shorter than at 3 mg/kg on the same sampling schedule; the authors attribute the difference to sampling, and the pooled linear model cannot reproduce it. ncaComparisonTable() labels the clearance and volume rows “CL/F” and “Vz/F”; after an IV bolus they are CL and Vz. The paper states only that its model values are “comparable with” / “similar to” the NCA values, which is what the check below asserts.

# Structural checks the paper itself states (Section 3.3): the model CL lies
# within the NCA CLtot range 1.3-2.5 L/h/kg, the model V + V2 lies within the
# NCA Vd range 2.2-5.8 L/kg, and the typical dose-normalised AUC lies between
# the published 3 mg/kg and 8 mg/kg group means.
cl_typ <- exp(th[["lcl"]])
dn_auc_pub <- c(c(2.0, 2.2, 2.4) / 3, c(3.4, 3.3, 4.4) / 8)
stopifnot(
  cl_typ > 1.3, cl_typ < 2.5,
  exp(th[["lvc"]]) + exp(th[["lvp"]]) > 2.2,
  exp(th[["lvc"]]) + exp(th[["lvp"]]) < 5.8,
  1 / cl_typ > min(dn_auc_pub), 1 / cl_typ < max(dn_auc_pub)
)

Replicate Figure 5: exposure against plasma creatinine

Section 2.5 simulates 8 mg/kg IV with CL “determined by the regression equations of Cr level and post hoc CL” over plasma creatinine 0.3-2.5 mg/dL, and Section 3.4 prints the median (5th-95th percentile) AUC(0-inf) at five creatinine values. The regression coefficients themselves are not printed. Because AUC(0-inf) = Dose / CL for this model, each published median fixes the typical clearance at that creatinine: CL(Cr) = 8 / median AUC. The five back-solved clearances fall on a straight line, so the maintainers take the paper’s regression to be linear, CL = a + b * Cr, and fit it here.

fig5 <- tibble::tribble(
  ~CREAT, ~auc_med, ~auc_p05, ~auc_p95,
  0.3, 3.4, 2.2, 5.3,
  0.5, 3.7, 2.4, 5.7,
  1.0, 4.6, 3.0, 7.2,
  1.5, 6.3, 4.1, 9.8,
  2.5, 21.7, 13.8, 42.5
) |>
  dplyr::mutate(cl_backsolved = 8 / auc_med)

fit5 <- lm(cl_backsolved ~ CREAT, data = fig5)
fit4 <- lm(cl_backsolved ~ CREAT, data = fig5[fig5$CREAT < 2.5, ])
fig5 <- fig5 |>
  dplyr::mutate(
    cl_fit = unname(predict(fit5, newdata = fig5)),
    pct_resid = 100 * (cl_fit / cl_backsolved - 1)
  )
auc25_from_fit4 <- 8 / unname(predict(fit4, newdata = data.frame(CREAT = 2.5)))
knitr::kable(
  fig5 |> dplyr::select(CREAT, auc_med, cl_backsolved, cl_fit, pct_resid),
  digits = 3,
  caption = "Clearance back-solved from each published median AUC and the linear fit."
)
Clearance back-solved from each published median AUC and the linear fit.
CREAT auc_med cl_backsolved cl_fit pct_resid
0.3 3.4 2.353 2.353 0.010
0.5 3.7 2.162 2.173 0.503
1.0 4.6 1.739 1.723 -0.947
1.5 6.3 1.270 1.272 0.194
2.5 21.7 0.369 0.372 0.789 
coef(fit5)
#> (Intercept)       CREAT 
#>   2.6233909  -0.9007269
auc25_from_fit4
#> [1] 20.95816
# A straight line in Cr must reproduce all five back-solved clearances; this
# is what licenses the linear form. Held-out check: the line through the four
# Cr <= 1.5 points predicts the Cr = 2.5 median (21.7 ug*h/mL) to within 5%
# (it is the most leveraged point: CL falls to about 0.37 L/h/kg there).
stopifnot(
  all(abs(fig5$pct_resid) < 2),
  abs(auc25_from_fit4 / 21.7 - 1) < 0.05
)

The fitted line gives CL = 2.623 + (-0.901) x Cr L/h/kg. At the normal-group creatinine of 0.27 mg/dL this is about 2.38 L/h/kg, higher than the population estimate of 1.76 L/h/kg in Table 3, as expected for a regression on post hoc clearances rather than on the population typical value.

The simulation below keeps every Table 3 parameter except the typical CL, which is replaced by the fitted CL(Cr); the Table 3 IIV on CL is applied on top.

cr_levels <- fig5$CREAT
ev5 <- dplyr::bind_rows(lapply(seq_along(cr_levels), function(i) {
  make_arm(200, 8, (i - 1L) * 200L) |>
    dplyr::mutate(CREAT = cr_levels[i])
})) |>
  dplyr::select(-treatment)
# Replace the dense 0-2 h grid for the plot.
ev5 <- dplyr::bind_rows(
  ev5 |> dplyr::filter(evid == 1),
  tidyr::expand_grid(
    ev5 |> dplyr::distinct(id, CREAT),
    time = seq(0, 2, by = 0.05)
  ) |>
    dplyr::mutate(amt = 0, evid = 0L, cmt = "central")
) |>
  dplyr::arrange(id, time, dplyr::desc(evid))
stopifnot(!anyDuplicated(unique(ev5[, c("id", "time", "evid")])))

sim5 <- dplyr::bind_rows(lapply(cr_levels, function(cr) {
  cl_cr <- unname(predict(fit5, newdata = data.frame(CREAT = cr)))
  rxode2::rxSolve(
    mod,
    events = ev5[ev5$CREAT == cr, ],
    params = c(lcl = log(cl_cr)),
    keep = "CREAT"
  ) |>
    as.data.frame()
}))

sim5 |>
  dplyr::group_by(CREAT, time) |>
  dplyr::summarise(
    Q05 = quantile(Cc, 0.05), Q50 = median(Cc), Q95 = quantile(Cc, 0.95),
    .groups = "drop"
  ) |>
  dplyr::mutate(panel = paste("Cr =", CREAT, "mg/dL")) |>
  ggplot(aes(time, Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.25) +
  geom_line() +
  facet_wrap(~panel, nrow = 1) +
  scale_y_log10(limits = c(0.01, 100)) +
  labs(
    x = "Time (h)", y = "Intact oxaliplatin (ug/mL)",
    caption = "8 mg/kg IV; median and 5th-95th percentiles, 200 rats per panel. Replicates Figure 5A of Kobuchi 2021."
  )

# AUC(0-inf) per rat is exactly Dose / individual CL for this linear model.
auc5 <- sim5 |>
  dplyr::distinct(id, CREAT, cl) |>
  dplyr::mutate(auc = 8 / cl) |>
  dplyr::group_by(CREAT) |>
  dplyr::summarise(
    sim_med = median(auc), sim_p05 = quantile(auc, 0.05), sim_p95 = quantile(auc, 0.95),
    .groups = "drop"
  ) |>
  dplyr::left_join(fig5 |> dplyr::select(CREAT, auc_med, auc_p05, auc_p95), by = "CREAT") |>
  dplyr::mutate(pct_diff_med = 100 * (sim_med / auc_med - 1))

auc5 |>
  dplyr::rename(
    "Cr (mg/dL)" = CREAT,
    "Simulated median" = sim_med, "Simulated 5th" = sim_p05, "Simulated 95th" = sim_p95,
    "Published median" = auc_med, "Published 5th" = auc_p05, "Published 95th" = auc_p95,
    "Median % diff" = pct_diff_med
  ) |>
  knitr::kable(digits = 2, caption = "AUC(0-inf) (ug*h/mL) after 8 mg/kg by plasma creatinine; published values from Section 3.4 (Figure 5B).")
AUC(0-inf) (ug*h/mL) after 8 mg/kg by plasma creatinine; published values from Section 3.4 (Figure 5B).
Cr (mg/dL) Simulated median Simulated 5th Simulated 95th Published median Published 5th Published 95th Median % diff
0.3 3.47 2.04 5.28 3.4 2.2 5.3 1.98
0.5 3.73 2.40 6.07 3.7 2.4 5.7 0.72
1.0 4.62 2.76 7.49 4.6 3.0 7.2 0.36
1.5 6.24 3.54 9.94 6.3 4.1 9.8 -0.98
2.5 20.68 13.05 34.34 21.7 13.8 42.5 -4.69 

# The medians are close to the published values by construction (the line was
# fitted to them); with 200 rats the sampling SE of a median is about 2.7% in
# log terms, so a 10% bound fails only if the CL(Cr) override did not reach
# the solve (every panel would then sit at 8 / 1.76 = 4.5 ug*h/mL, 79% off at
# Cr = 2.5) or the IIV is centred wrongly.
stopifnot(all(abs(auc5$pct_diff_med) < 10))
# Replicates Figure 5B of Kobuchi 2021 (AUC by creatinine), with the published
# median and 5th-95th percentiles overlaid in red.
sim5 |>
  dplyr::distinct(id, CREAT, cl) |>
  dplyr::mutate(auc = 8 / cl) |>
  ggplot(aes(factor(CREAT), auc)) +
  geom_boxplot(outlier.size = 0.5) +
  geom_pointrange(
    data = fig5,
    aes(x = factor(CREAT), y = auc_med, ymin = auc_p05, ymax = auc_p95),
    colour = "red", position = position_nudge(x = 0.3), inherit.aes = FALSE
  ) +
  scale_y_log10() +
  labs(
    x = "Plasma creatinine (mg/dL)", y = "AUC(0-inf) (ug*h/mL)",
    caption = "Simulated (boxes) vs. published median and 5th-95th percentiles (red). Replicates Figure 5B of Kobuchi 2021."
  )

For Cr of 0.3-1.5 mg/dL each published 5th-95th percentile band spans a factor of about 2.4, a log-scale SD of about 0.27. The Table 3 IIV on CL of 30.5% gives 0.305 under the omega x 100 reading used here and 0.298 under the lognormal-CV reading. Both are a little wider than the published band, and they differ from each other by far less than the sampling noise in a 5th or 95th percentile, so the band cannot choose between the two readings. At Cr = 2.5 mg/dL the published band is wider and skewed upward (upper limit 42.5 against a median of 21.7), which suggests the paper computed AUC(0-inf) by NCA on the simulated 0-2 h profiles, where the extrapolated tail dominates once CL is this low. The percentile bands are recorded as a known deviation and are not asserted.

Assumptions and deviations

  • IIV scale. Table 3 gives the IIV as a bare percentage under the heading “Inter-individual variability (omega)”. The maintainers read the percentages as omega x 100 (omega^2 = 0.375^2, 0.305^2 and 0.315^2), the convention the same group’s Phoenix NLME tables were shown to use for dapagliflozin (Kobuchi_2025_dapagliflozin, where a published simulated percentile band separated the two readings). The lognormal-CV reading, omega^2 = log(1 + CV^2), gives 0.1316, 0.0889 and 0.0945: under 7% less variance and not distinguishable with the data printed in this paper (see the Figure 5 band discussion above). The IIV rows’ “CV%” column (19.3, 26.0, 18.7) is the precision of the estimate, not the IIV.
  • No renal-function covariate in the packaged model. Table 3 is the final estimated model and has no covariate. The creatinine dependence shown in Figure 5 comes from a separate regression of post hoc CL on creatinine whose coefficients are not printed. The maintainers back-solved a linear CL(Cr) from the five published median AUC values in the Figure 5 chunk above; it lives only in this vignette, and plasma creatinine is documented in the model’s covariatesDataExcluded.
  • Per-kg parameterisation. The model is in L/kg and L/h/kg, as published; supply the dose in mg/kg and read Cc in ug/mL (mg/L).
  • Pooled NCA reference. The model has no dose or renal-function effect, so the Table 2 comparison uses the mean of the three renal-function group means at each dose.
  • Urinary excretion not modelled. Cumulative urinary excretion of intact oxaliplatin (Figure 2) was below 0.1% of the dose and was not part of the population model.
  • Figure 4 (pcVPC) not reproduced. Individual observed data are not published; Figure 1 is reproduced instead as the simulated profile check.
  • No erratum or correction notice for this article was found on the publisher page or in Europe PMC as of 2026-09-30.