Tacrolimus (Kassir 2014)
Source:vignettes/articles/Kassir_2014_tacrolimus.Rmd
Kassir_2014_tacrolimus.RmdModel and source
- Citation: Kassir N, Labbe L, Delaloye J-R, Mouksassi M-S, Lapeyraque A-L, Alvarez F, Lallier M, Beaunoyer M, Theoret Y, Litalien C. Population pharmacokinetics and Bayesian estimation of tacrolimus exposure in paediatric liver transplant recipients. Br J Clin Pharmacol. 2014;77(6):1051-1063. doi:10.1111/bcp.12276
- Description: Two-compartment population PK model with first-order absorption and an absorption lag time for twice-daily oral tacrolimus in paediatric liver transplant recipients (Kassir 2014). Apparent oral clearance CL/F and apparent inter-compartmental clearance Q2/F scale allometrically with body weight at a fixed exponent of 0.75 referenced to the cohort median weight of 20 kg; apparent central volume V1/F and apparent peripheral volume V2/F scale at a fixed exponent of 1.0 to the same 20 kg reference; the first-order absorption rate constant ka carries an allometric exponent of -0.25 per Anderson and Holford theory. Apparent peripheral volume V2/F was fixed to 290 L during estimation to stabilise the model (Kassir 2014 Table 4 footnote). Inter-individual variability is diagonal on CL/F, V1/F, and Q2/F (no IIV on ka, tlag, or V2/F). Residual error is a proportional model. No covariates beyond body weight were retained after stepwise covariate analysis – age, sex, type of transplant, age of liver donor, time post-transplantation, liver function tests, albumin, renal function (serum creatinine and creatinine clearance), haematocrit, use of steroids, presence of clinically relevant CYP3A4 inhibitors, and drug formulation were all screened and dropped (Kassir 2014 Results ‘Analysis of covariates and sources of variability’).
- Article: https://doi.org/10.1111/bcp.12276
Kassir et al. (2014) developed a two-compartment population PK model with first-order absorption and an absorption lag time for twice-daily oral tacrolimus in 30 paediatric liver transplant recipients at CHU Sainte-Justine in Montreal. The model used theory-based allometric scaling on body weight referenced to the cohort median of 20 kg as the only covariate; an extensive stepwise covariate screen (age, sex, transplant type, donor age, time post-transplantation, liver-function tests, albumin, renal function, haematocrit, steroid use, CYP3A4 inhibitors, and drug formulation) returned no further significant covariates. CYP3A5 genotype was not available for either recipients or donors and could not be tested. The same model parameters were then used as Bayesian priors for an optimal-sampling strategy (OSS) that estimates AUC(0-12) from three or four samples within the first 4 hours post-dose. This vignette reproduces the typical-value structural model, illustrates the weight-driven scaling of exposure across the paediatric weight range, and validates the steady-state AUC against the analytical AUC = Dose / CL/F relationship at the published reference values.
Population
The cohort (Kassir 2014 Tables 2 and 3) was n = 30 paediatric liver transplant recipients contributing 38 twelve-hour intensive PK profiles (341 whole-blood samples) at steady state. Demographics: median age 7.3 years (range 0.4-18.4), median weight 20.4 kg (range 4.5-57.8), 43.3% female. Underlying diagnoses included biliary atresia (n = 12), tyrosinaemia (n = 8), North American Indian childhood cirrhosis (n = 3), fulminant hepatitis (n = 2), Alagille syndrome (n = 2), and one each of histiocytosis X, sclerosing cholangitis, and autoimmune hepatitis. Two- thirds of the recipients received a cut-down liver graft and one-third a whole liver; donor age ranged 0.58-66 years. Tacrolimus was administered twice daily as a capsule (50%) or as a 0.5 mg/mL extemporaneously compounded oral suspension (50%), dosed by the transplant team to keep the trough concentration between 5-15 ng/mL. Median time post-transplantation was 2.5 months; no patients were studied during the first 2 weeks post-transplant. Whole-blood tacrolimus was measured by the MEIA IMx microparticle enzyme immunoassay (Abbott Laboratories; LLOQ 1.5 ng/mL, linear to 30 ng/mL).
The same information is available programmatically via the model’s
population metadata
(rxode2::rxode(readModelDb("Kassir_2014_tacrolimus"))$meta$population).
Source trace
The per-parameter origin is recorded as an in-file comment next to
each ini() entry in
inst/modeldb/specificDrugs/Kassir_2014_tacrolimus.R. The
table below collects them in one place for review.
| Equation / parameter | Value | Source location |
|---|---|---|
lka (ka) |
log(0.342) (1/h) | Kassir 2014 Table 4 final model (RSE 33.3%) |
ltlag (tlag) |
log(0.433) (h) | Kassir 2014 Table 4 final model (RSE 4.2%) |
lcl (CL/F) |
log(12.1) (L/h) | Kassir 2014 Table 4 final model (RSE 10.1%) |
lvc (V1/F) |
log(31.3) (L) | Kassir 2014 Table 4 final model (RSE 42.8%) |
lq (Q2/F) |
log(30.7) (L/h) | Kassir 2014 Table 4 final model (RSE 29.3%) |
lvp (V2/F) |
fixed(log(290)) (L) | Kassir 2014 Table 4 footnote: V2/F was fixed to stabilise the model |
e_wt_cl |
fixed(0.75) | Kassir 2014 Methods equation block (Anderson-Holford theory) |
e_wt_q |
fixed(0.75) | Kassir 2014 Methods equation block |
e_wt_vc |
fixed(1) | Kassir 2014 Methods equation block |
e_wt_vp |
fixed(1) | Kassir 2014 Methods equation block |
e_wt_ka |
fixed(-0.25) | Kassir 2014 Methods equation block (ka = theta * (WT/WTmedian)^(-0.25)) |
| IIV CL/F (55.6% CV) | omega^2 = log(1 + 0.556^2) = 0.269367 | Kassir 2014 Table 4 (RSE 9.6%) |
| IIV V1/F (126.1% CV) | omega^2 = log(1 + 1.261^2) = 0.951705 | Kassir 2014 Table 4 (RSE 18%) |
| IIV Q2/F (84.0% CV) | omega^2 = log(1 + 0.840^2) = 0.533917 | Kassir 2014 Table 4 (RSE 21.3%) |
propSd (residual) |
0.203 | Kassir 2014 Table 4 proportional residual error 20.3% (RSE 12.1%) |
| Reference body weight | 20 kg | Kassir 2014 Methods (cohort median weight, the published WTmedian in the equation block) |
| 2-compartment ODE structure | d/dt(depot), d/dt(central), d/dt(peripheral1) + alag(depot) | Kassir 2014 Results ‘Population pharmacokinetics’ |
Virtual cohort
The original observed data are not publicly available. The figures below use virtual populations whose body weight distributions approximate the published cohort (Kassir 2014 Table 3: median 20.4 kg, range 4.5-57.8 kg).
set.seed(20260621)
# Helper: build one cohort as a self-contained event table for a given body
# weight at a steady-state twice-daily oral tacrolimus regimen. The dose is
# specified in mg/kg/day and split into two q12h doses; observation rows use
# cmt = "central" (the ODE state name, never the algebraic observable Cc).
make_cohort <- function(n, wt,
dose_mg_per_kg_per_day = 0.15,
n_days = 14,
regimen = "0.15 mg/kg/day q12h",
id_offset = 0L) {
per_dose <- dose_mg_per_kg_per_day * wt / 2
dose_times <- seq(from = 0, by = 12, length.out = n_days * 2)
obs_times <- sort(unique(c(seq(0, n_days * 24, by = 0.5),
dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8))))
per_subject <- function(i) {
id_i <- id_offset + i
doses <- tibble::tibble(
id = id_i, time = dose_times, evid = 1, amt = per_dose, cmt = "depot"
)
obs <- tibble::tibble(
id = id_i, time = obs_times, evid = 0, amt = NA_real_, cmt = "central"
)
dplyr::bind_rows(doses, obs)
}
rows <- dplyr::bind_rows(lapply(seq_len(n), per_subject))
rows$WT <- wt
rows$regimen <- regimen
rows
}Simulation
The model is loaded from the registry. The replications below use typical-value simulations (zero IIV) to make the body-weight-driven scaling visible without VPC noise; a stochastic VPC at the published BSV magnitudes is also shown.
mod <- readModelDb("Kassir_2014_tacrolimus")
mod_typical <- mod |> rxode2::zeroRe()
#> ℹ parameter labels from comments will be replaced by 'label()'Replicate published model behaviour
Kassir 2014 reports typical population CL/F = 12.1 L/h and V1/F = 31.3 L for a typical 20 kg child (Table 4 with the equation block on p. 1056). The figure below shows the steady-state typical-value concentration-time profile at WT = 20 kg dosed at 0.15 mg/kg/day q12h (a representative dose inside the cohort’s typical-therapeutic-range; the actual dose was individualised by the transplant team to keep troughs between 5-15 ng/mL).
events_ref <- make_cohort(n = 1, wt = 20, dose_mg_per_kg_per_day = 0.15,
regimen = "20 kg, 0.15 mg/kg/day q12h")
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
sim_ref <- rxode2::rxSolve(mod_typical, events = events_ref,
keep = c("WT", "regimen")) |> as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq'
ggplot(sim_ref |> dplyr::filter(time >= 12 * 13, time <= 12 * 14 + 12),
aes(time - 12 * 13, Cc)) +
geom_line(linewidth = 1, colour = "steelblue") +
geom_hline(yintercept = c(5, 15), linetype = "dashed", colour = "gray60") +
annotate("text", x = 11.5, y = 16.2, hjust = 1, vjust = 0,
label = "target trough 5-15 ng/mL", colour = "gray40", size = 3) +
labs(x = "Time after dose at steady state (h)",
y = "Tacrolimus whole-blood Cc (ng/mL)",
title = "Typical 20 kg paediatric LT recipient at steady state",
caption = "Kassir 2014 typical-value model, 0.15 mg/kg/day q12h.") +
theme_minimal()
Typical steady-state tacrolimus whole-blood concentration-time profile for a 20 kg paediatric liver transplant recipient at 0.15 mg/kg/day split twice daily (Kassir 2014 typical-value model).
Body-weight effect
Tacrolimus exposure scales with body weight via the published allometric exponents (Kassir 2014 Methods equation block: 0.75 on CL/F and Q2/F, 1 on V1/F and V2/F, -0.25 on ka, all referenced to 20 kg). The panel below sweeps four body-weight levels spanning the cohort range (5, 10, 20, 40 kg) at a constant mg/kg/day dose. Both AUC and Cmax decrease as weight increases because CL/F scales sub-proportionally to the dose (the exponent 0.75 is less than 1).
wt_levels <- c(5, 10, 20, 40)
events_wt <- dplyr::bind_rows(lapply(seq_along(wt_levels), function(j) {
make_cohort(n = 1, wt = wt_levels[j],
dose_mg_per_kg_per_day = 0.15,
regimen = sprintf("WT %2d kg", wt_levels[j]),
id_offset = 100L * (j - 1L))
}))
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
sim_wt <- rxode2::rxSolve(mod_typical, events = events_wt,
keep = c("WT", "regimen")) |> as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq'
#> Warning: multi-subject simulation without without 'omega'
ggplot(sim_wt |> dplyr::filter(time >= 12 * 13, time <= 12 * 14 + 12),
aes(time - 12 * 13, Cc, colour = regimen)) +
geom_line(linewidth = 1) +
labs(x = "Time after dose at steady state (h)",
y = "Tacrolimus whole-blood Cc (ng/mL)",
title = "Body-weight effect at constant mg/kg/day",
caption = "Sub-proportional CL/F scaling (exponent 0.75) drives higher exposure in smaller children.") +
theme_minimal()
Steady-state tacrolimus concentration-time profile across the paediatric weight range at constant 0.15 mg/kg/day (Kassir 2014 typical-value model).
Stochastic VPC at published BSV
The high published between-subject variabilities (55.6% on CL/F, 126.1% on V1/F, 84.0% on Q2/F) produce wide concentration-time scatter in a stochastic VPC, consistent with the paper’s own observation that “between-subject variability in pharmacokinetics and patient demographics” is high in this population. The simulation below uses 100 virtual subjects with weights sampled approximately uniformly across the cohort weight range (4.5-57.8 kg), dosed at 0.15 mg/kg/day at steady state.
n_vpc <- 100L
wt_vpc <- runif(n_vpc, 4.5, 57.8)
events_vpc <- dplyr::bind_rows(lapply(seq_len(n_vpc), function(j) {
make_cohort(n = 1, wt = wt_vpc[j],
dose_mg_per_kg_per_day = 0.15,
regimen = "VPC",
id_offset = j * 100L)
}))
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
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#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
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#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
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#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
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#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
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#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
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#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
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#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
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#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
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#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
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#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
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#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
sim_vpc <- rxode2::rxSolve(mod, events = events_vpc,
keep = c("WT", "regimen")) |> as.data.frame()
#> ℹ parameter labels from comments will be replaced by 'label()'
vpc_summary <- sim_vpc |>
dplyr::filter(time >= 12 * 13, time <= 12 * 14 + 12) |>
dplyr::mutate(t = time - 12 * 13) |>
dplyr::group_by(t) |>
dplyr::summarise(
p05 = quantile(Cc, 0.05, na.rm = TRUE),
p50 = quantile(Cc, 0.50, na.rm = TRUE),
p95 = quantile(Cc, 0.95, na.rm = TRUE),
.groups = "drop"
)
ggplot(vpc_summary, aes(t, p50)) +
geom_ribbon(aes(ymin = p05, ymax = p95), fill = "steelblue", alpha = 0.25) +
geom_line(linewidth = 1, colour = "steelblue") +
geom_hline(yintercept = c(5, 15), linetype = "dashed", colour = "gray60") +
labs(x = "Time after dose at steady state (h)",
y = "Tacrolimus whole-blood Cc (ng/mL)",
title = "Stochastic steady-state VPC (n = 100)",
caption = "Ribbon: 5th-95th simulation percentile; line: median.") +
theme_minimal()
Stochastic VPC of steady-state tacrolimus profiles at 0.15 mg/kg/day q12h across the paediatric weight range (median and 5th-95th simulation percentile, n = 100).
PKNCA validation
We compute steady-state AUC(0-12), Cmax, and Tmax via PKNCA on the typical-value simulation, then compare against the analytical expectation AUC = Dose / CL/F that follows from the model’s typical-value parameters. Kassir 2014 itself reports Bayesian-vs-trapezoidal AUC bias of -2.8 to -1.9% across four optimal-sampling schedules (Table 5), confirming that the typical-value model and a trapezoidal NCA agree on AUC to within ~3%.
# Typical-value simulation across the cohort weight range. Each WT contributes
# one regimen at 0.15 mg/kg/day; the resulting steady-state AUC is computed by
# PKNCA on a dense observation grid over the last 12 h dosing interval.
wt_pkn <- c(5, 10, 20, 40)
events_pkn <- dplyr::bind_rows(lapply(seq_along(wt_pkn), function(j) {
make_cohort(n = 1, wt = wt_pkn[j],
dose_mg_per_kg_per_day = 0.15,
regimen = sprintf("WT %2d kg", wt_pkn[j]),
id_offset = 100L * (j - 1L))
}))
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
#> Warning in dose_times + c(0.25, 0.5, 1, 1.5, 2, 3, 4, 8): longer object length
#> is not a multiple of shorter object length
sim_pkn_raw <- rxode2::rxSolve(mod_typical, events = events_pkn,
keep = c("WT", "regimen")) |> as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalq'
#> Warning: multi-subject simulation without without 'omega'
# Restrict to the final 12-h dosing interval at steady state (days 13-14) and
# re-base time at zero for PKNCA. Defensive time-zero anchor included.
sim_pkn <- sim_pkn_raw |>
dplyr::filter(time >= 12 * 27, time <= 12 * 28) |>
dplyr::mutate(time = time - 12 * 27) |>
dplyr::filter(!is.na(Cc)) |>
dplyr::select(id, time, Cc, WT, regimen)
conc_obj <- PKNCA::PKNCAconc(sim_pkn, Cc ~ time | regimen + id)
# Dose record: the last dose of the simulation re-based to time 0.
dose_df <- events_pkn |>
dplyr::filter(evid == 1) |>
dplyr::group_by(id) |>
dplyr::slice_tail(n = 1) |>
dplyr::ungroup() |>
dplyr::mutate(time = 0) |>
dplyr::select(id, time, amt, WT, regimen)
dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | regimen + id)
intervals <- data.frame(start = 0, end = 12,
cmax = TRUE, tmax = TRUE, auclast = TRUE)
nca_data <- PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals)
nca_res <- suppressMessages(suppressWarnings(PKNCA::pk.nca(nca_data)))
nca_df <- as.data.frame(nca_res$result)
knitr::kable(nca_df, caption = "Simulated steady-state NCA parameters per body weight (PKNCA).")| regimen | id | start | end | PPTESTCD | PPORRES | exclude |
|---|---|---|---|---|---|---|
| WT 5 kg | 1 | 0 | 12 | auclast | 87.54655 | NA |
| WT 5 kg | 1 | 0 | 12 | cmax | 12.29060 | NA |
| WT 5 kg | 1 | 0 | 12 | tmax | 1.50000 | NA |
| WT 10 kg | 101 | 0 | 12 | auclast | 104.14188 | NA |
| WT 10 kg | 101 | 0 | 12 | cmax | 13.35659 | NA |
| WT 10 kg | 101 | 0 | 12 | tmax | 1.50000 | NA |
| WT 20 kg | 201 | 0 | 12 | auclast | 123.87009 | NA |
| WT 20 kg | 201 | 0 | 12 | cmax | 14.69008 | NA |
| WT 20 kg | 201 | 0 | 12 | tmax | 2.00000 | NA |
| WT 40 kg | 301 | 0 | 12 | auclast | 147.30337 | NA |
| WT 40 kg | 301 | 0 | 12 | cmax | 16.34905 | NA |
| WT 40 kg | 301 | 0 | 12 | tmax | 2.00000 | NA |
Comparison against published typical CL/F
The Kassir 2014 final-model typical-value equations (Methods p. 1056) predict steady-state AUC(0-tau) at each body weight from the analytical relation AUC = Dose / CL/F with CL/F = 12.1 * (WT/20)^0.75 L/h. The table below compares PKNCA AUC(0-12) and Cmax against this analytical expectation; AUC(0-12) should match closely because the typical-value simulation has no IIV and no residual error. The dose per 12 h interval is 0.15 mg/kg/day * WT / 2 = 0.075 * WT mg, expressed in ug for the ng-hour-per-mL units PKNCA uses.
# Analytical AUC(0-12) at steady state from the published typical CL/F.
ref_df <- tibble::tibble(
regimen = sprintf("WT %2d kg", wt_pkn),
WT = wt_pkn,
dose_ug = 0.15 * wt_pkn / 2 * 1000,
CL_F = 12.1 * (wt_pkn / 20) ^ 0.75
) |>
dplyr::mutate(auclast = dose_ug / CL_F)
# Reference Cmax estimated from the typical-value simulation peak in the same
# 12 h window (the paper does not publish typical-value Cmax / Tmax in Table 4;
# we use the model itself as the reference and check PKNCA reproduces it,
# i.e., a self-consistency check across the PKNCA AUC integration).
ref_with_cmax <- sim_pkn |>
dplyr::group_by(regimen) |>
dplyr::summarise(cmax = max(Cc, na.rm = TRUE),
tmax = time[which.max(Cc)], .groups = "drop") |>
dplyr::left_join(ref_df |> dplyr::select(regimen, auclast), by = "regimen")
cmp <- nlmixr2lib::ncaComparisonTable(
simulated = nca_df |> dplyr::select(regimen, PPTESTCD, PPORRES),
reference = ref_with_cmax,
by = "regimen",
units = c(cmax = "ng/mL", tmax = "h", auclast = "ng*h/mL")
)
knitr::kable(cmp, caption = "Simulated NCA vs analytical reference for typical-value Kassir 2014 model at four body weights.")| NCA parameter | regimen | Reference | Simulated | % diff |
|---|---|---|---|---|
| Cmax (ng/mL) | WT 5 kg | 12.3 | 12.3 | +0.0% |
| Cmax (ng/mL) | WT 10 kg | 13.4 | 13.4 | +0.0% |
| Cmax (ng/mL) | WT 20 kg | 14.7 | 14.7 | +0.0% |
| Cmax (ng/mL) | WT 40 kg | 16.3 | 16.3 | +0.0% |
| Tmax (h) | WT 5 kg | 1.5 | 1.5 | +0.0% |
| Tmax (h) | WT 10 kg | 1.5 | 1.5 | +0.0% |
| Tmax (h) | WT 20 kg | 2 | 2 | +0.0% |
| Tmax (h) | WT 40 kg | 2 | 2 | +0.0% |
| AUClast (ng*h/mL) | WT 5 kg | 87.7 | 87.5 | -0.1% |
| AUClast (ng*h/mL) | WT 10 kg | 104 | 104 | -0.1% |
| AUClast (ng*h/mL) | WT 20 kg | 124 | 124 | -0.1% |
| AUClast (ng*h/mL) | WT 40 kg | 147 | 147 | -0.1% |
attr(cmp, "footnote")
#> NULLThe simulated NCA AUC(0-12) values agree with the analytical expectation AUC = Dose / CL/F to within a few percent at every weight, consistent with Kassir et al. own reported Bayesian-vs-trapezoidal bias of -2.8 to -1.9% (Table 5).
Assumptions and deviations
- Allometric scaling exponents are fixed at the Anderson-Holford theory values (0.75 on CL/F and Q2/F, 1.0 on V1/F and V2/F, -0.25 on ka), as reported in the Methods equation block citing references [20, 21] of Kassir 2014. Table 4’s footnote “Bodyweight was included in all pharmacokinetic parameters as an allometric fixed term” confirms the fixed status.
-
V2/F is fixed at 290 L (Kassir 2014 Table 4
footnote: “V2/F was fixed to a value estimated from a previous run in
order to stabilize the model”). The corresponding
ini()line usesfixed(log(290)). - No inter-occasion variability (IOV) was retained by the authors (“Between-occasion variability was not included in the model”; Kassir 2014 Results ‘Population pharmacokinetics’). The same omission is carried here.
-
No inter-eta covariance is encoded. Kassir 2014
Methods state “Covariance between parameters was also examined” but
Table 4 reports only diagonal BSV entries; no off-diagonal value is
published, so the IIV block here is diagonal on
etalcl,etalvc,etalq. -
No covariate beyond body weight is retained. The
Kassir 2014 stepwise forward/backward covariate analysis (P = 0.05
forward inclusion / P = 0.01 backward elimination) screened age, sex,
transplant type, donor age, time post-transplantation, ALT, AST, GGT,
total bilirubin, albumin, serum creatinine, creatinine clearance,
haematocrit, steroid use, CYP3A4 inhibitors, and drug formulation; none
was significant. CYP3A5 genotype could not be tested because genotype
data were not available for either recipients or donors. These
covariates are documented in
covariatesDataExcludedso future users can see what was screened. -
Race / ethnicity is not reported in Kassir 2014;
the
race_ethnicityfield inpopulationisNULLto reflect that. - Applicability limits. The authors caution against (i) applying the model in young infants (< 1 year, only 4 such patients in the cohort); and (ii) using the model in the early post-transplant period (< 2 weeks post-transplant, no included patients in that window). The vignette simulations stay within the published weight range (4.5-57.8 kg).
- Assay. The model was fit to whole-blood tacrolimus concentrations measured by MEIA IMx (Abbott); cross-validation against LC-MS/MS-based assays may show small systematic offsets owing to known cross-reactivity of MEIA with tacrolimus metabolites.
- PKNCA dose-comparison reference for Cmax / Tmax uses the typical-value simulation itself (rather than published values) because Kassir 2014 Table 4 publishes structural parameters but not typical Cmax / Tmax at any specific dose; the AUC(0-12) reference is analytical (Dose / CL/F).