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Aripiprazole (Kim 2008)

Source: vignettes/articles/Kim_2008_aripiprazole.Rmd
Kim_2008_aripiprazole.Rmd

Model and source

  • Citation: Kim J-R, Seo H-B, Cho J-Y, Kang D-H, Kim Y K, Bahk W-M, Yu K-S, Shin S-G, Kwon J S, Jang I-J (2008). Population pharmacokinetic modelling of aripiprazole and its active metabolite, dehydroaripiprazole, in psychiatric patients. Br J Clin Pharmacol 66(6):802-810.
  • Article: https://doi.org/10.1111/j.1365-2125.2008.03223.x 
mod <- modellib("Kim_2008_aripiprazole")
mod_meta <- readModelDb("Kim_2008_aripiprazole")

Population

The Kim 2008 cohort comprised 80 Korean psychiatric in- and out-patients with schizophrenia, schizophreniform disorder, or schizoaffective disorder enrolled at 30 sites (15 contributing) in a multicentre Phase IV trial. Mean age was 35.2 +/- 9.8 years (range 17-61); mean body weight 60.8 +/- 10.9 kg (range 38.0-95.0); 57.5% of subjects were female. The cohort was 100% Korean. Patients received oral aripiprazole 10-30 mg once daily (mean 24.3 +/- 6.7 mg) at steady state after up-titration from a 15 mg starting dose (Kim 2008 Table 1).

CYP2D6 genotyping classified subjects into four genotype-based strata (Kim 2008 Table 2):

Stratum Definition n % CL/F (L/h)
Group I EM with 2 functional alleles (*1, *2) 15 18.8 3.15
Group II EM with 1 functional + 1 partially deficient allele 26 32.5 2.66
Group III EM with 1 functional + 1 null allele 12 15.0 2.27
Group IV IM (partially deficient + null, no functional allele) 27 33.8 1.83

No CYP2D6 poor metabolizers (no subjects with two null alleles) and no ultra-rapid metabolizers were observed in the cohort. CYP3A5 expressers (Group A, *1 carriers) made up 45.0% of the cohort and non-expressers (Group B, *3/*3) made up 55.0%; CYP3A5 was screened as a covariate but was not retained in the final model.

The same information is available programmatically via the model’s population metadata (readModelDb("Kim_2008_aripiprazole")$population).

Source trace

Per-parameter origin is also recorded as an inline comment next to each ini() entry in inst/modeldb/specificDrugs/Kim_2008_aripiprazole.R.

Equation / parameter Value (final model) Source location
lka (ka, FIXED) 1.06 1/h Kim 2008 Table 3 row k_a (h-1) = 1.06 (FIXED)
lcl_em_2func (Group I CL/F) 3.15 L/h Kim 2008 Table 3 row CL/F I = 3.15 (SE 0.223)
lcl_em_1f1pd (Group II CL/F) 2.66 L/h Kim 2008 Table 3 row CL/F II = 2.66 (SE 0.119)
lcl_em_1f1null (Group III CL/F) 2.27 L/h Kim 2008 Table 3 row CL/F III = 2.27 (SE 0.123)
lcl_im (Group IV CL/F) 1.83 L/h Kim 2008 Table 3 row CL/F IV = 1.83 (SE 0.0715)
lvc (V/F) 193 L Kim 2008 Table 3 row V/F = 193 (SE 11.7)
lcl_dehyari (CL(m)/fm) 8.02 L/h Kim 2008 Table 3 row CL(m)/f_m = 8.02 (SE 0.317)
lvc_dehyari (V(m)/fm) 587 L Kim 2008 Table 3 row V(m)/f_m = 587 (SE 217)
etalcl (omega^2 CL/F) 0.0930 Kim 2008 Table 3 row w^2 CL/F = 0.0930; CV% = 30.5
etalvc (omega^2 V/F) 0.100 Kim 2008 Table 3 row w^2 V/F = 0.100; CV% = 31.6
etalcl_dehyari (omega^2 CL(m)/fm) 0.113 Kim 2008 Table 3 row w^2 CL(m)/f_m = 0.113; CV% = 33.6
propSd (sigma^2 parent) sqrt(0.00264) ~ 0.0514 Kim 2008 Table 3 row s^2 = 0.00264; CV% = 5.1
propSd_dehyari (sigma^2 metab) sqrt(0.00507) ~ 0.0712 Kim 2008 Table 3 row s^2_m = 0.00507; CV% = 7.1
d/dt(depot) -ka * depot Kim 2008 Methods ‘Pharmacokinetic model and data analysis’
d/dt(central) ka * depot - (cl/vc) * central Kim 2008 Methods Eq. for dA(p)/dt
d/dt(central_dehyari) (cl/vc) * central - (cl_dehyari/vc_dehyari) * central_dehyari Kim 2008 Methods Eq. for dA(m)/dt with fm=1

Virtual cohort

Sparse observed data from the Kim 2008 trial are not publicly available. The figures below use virtual populations whose CYP2D6 genotype distribution matches the published Table 2 strata (no PMs in the cohort).

set.seed(20260620)

# Helper: build one cohort as a self-contained event table for a single
# CYP2D6 group at steady state with a 14-day daily-dosing run-in, followed
# by dense sampling over the final 24-h interval.
make_cohort <- function(n, group, dose_amt = 24.3, n_run_in_doses = 14,
                        ii_h = 24, id_offset = 0L) {
  cov <- switch(
    group,
    "Group I"   = list(CYP2D6_EM = 1L, CYP2D6_PM = 0L, CYP2D6_EM_1FUNC_1PD = 0L, CYP2D6_EM_1FUNC_1NULL = 0L),
    "Group II"  = list(CYP2D6_EM = 1L, CYP2D6_PM = 0L, CYP2D6_EM_1FUNC_1PD = 1L, CYP2D6_EM_1FUNC_1NULL = 0L),
    "Group III" = list(CYP2D6_EM = 1L, CYP2D6_PM = 0L, CYP2D6_EM_1FUNC_1PD = 0L, CYP2D6_EM_1FUNC_1NULL = 1L),
    "Group IV"  = list(CYP2D6_EM = 0L, CYP2D6_PM = 0L, CYP2D6_EM_1FUNC_1PD = 0L, CYP2D6_EM_1FUNC_1NULL = 0L)
  )
  dose_times <- seq(0, (n_run_in_doses - 1) * ii_h, by = ii_h)
  obs_start  <- max(dose_times)  # final dose time
  obs_times  <- sort(unique(c(
    seq(0, obs_start, by = ii_h),         # one pre-dose anchor per run-in day
    obs_start + seq(0, ii_h, by = 0.5)    # 30-min grid over the final interval
  )))
  out <- vector("list", length = n)
  for (i in seq_len(n)) {
    subj_id <- id_offset + i
    dose_rows <- data.frame(
      id = subj_id, time = dose_times, evid = 1L,
      amt = dose_amt, cmt = "depot", dvid = NA_integer_,
      CYP2D6_EM = cov$CYP2D6_EM, CYP2D6_PM = cov$CYP2D6_PM,
      CYP2D6_EM_1FUNC_1PD = cov$CYP2D6_EM_1FUNC_1PD,
      CYP2D6_EM_1FUNC_1NULL = cov$CYP2D6_EM_1FUNC_1NULL,
      group = group, stringsAsFactors = FALSE
    )
    obs_p <- data.frame(
      id = subj_id, time = obs_times, evid = 0L,
      amt = 0, cmt = "central", dvid = 1L,
      CYP2D6_EM = cov$CYP2D6_EM, CYP2D6_PM = cov$CYP2D6_PM,
      CYP2D6_EM_1FUNC_1PD = cov$CYP2D6_EM_1FUNC_1PD,
      CYP2D6_EM_1FUNC_1NULL = cov$CYP2D6_EM_1FUNC_1NULL,
      group = group, stringsAsFactors = FALSE
    )
    obs_m <- data.frame(
      id = subj_id, time = obs_times, evid = 0L,
      amt = 0, cmt = "central_dehyari", dvid = 2L,
      CYP2D6_EM = cov$CYP2D6_EM, CYP2D6_PM = cov$CYP2D6_PM,
      CYP2D6_EM_1FUNC_1PD = cov$CYP2D6_EM_1FUNC_1PD,
      CYP2D6_EM_1FUNC_1NULL = cov$CYP2D6_EM_1FUNC_1NULL,
      group = group, stringsAsFactors = FALSE
    )
    out[[i]] <- rbind(dose_rows, obs_p, obs_m)
  }
  ev <- dplyr::bind_rows(out)
  ev[order(ev$id, ev$time, -ev$evid), ]
}

n_per_group <- 40L
events <- dplyr::bind_rows(
  make_cohort(n_per_group, "Group I",   id_offset =   0L),
  make_cohort(n_per_group, "Group II",  id_offset = 100L),
  make_cohort(n_per_group, "Group III", id_offset = 200L),
  make_cohort(n_per_group, "Group IV",  id_offset = 300L)
)
stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))

Simulation

Stochastic simulation carrying IIV on CL/F (shared across the four CYP2D6 strata), V/F, and CL(m)/fm. The covariance between etalcl and etalcl_dehyari is set to 0 in the package model (the paper estimated a non-zero covariance but did not report its numeric value; see Assumptions and deviations). Aripiprazole and dehydroaripiprazole are simulated jointly per subject via the parent-then-metabolite chain in the source ODEs (Kim 2008 Methods ‘Pharmacokinetic model and data analysis’).

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

# Steady-state window: the final dosing interval (24 h after final dose).
final_dose_time <- 13 * 24
sim_ss <- sim |>
  dplyr::mutate(tad = time - final_dose_time) |>
  dplyr::filter(tad >= 0, tad <= 24)

A typical-value (zeroRe; no IIV, no residual error) replication for each CYP2D6 group with a single subject per stratum at the cohort mean daily dose, useful for narrative comparison against the paper’s reported point estimates.

mod_typical <- rxode2::zeroRe(mod)
#> ℹ parameter labels from comments will be replaced by 'label()'
events_typical <- dplyr::bind_rows(
  make_cohort(1L, "Group I",   id_offset = 1000L),
  make_cohort(1L, "Group II",  id_offset = 1001L),
  make_cohort(1L, "Group III", id_offset = 1002L),
  make_cohort(1L, "Group IV",  id_offset = 1003L)
)
sim_typ <- rxode2::rxSolve(
  mod_typical, events = events_typical,
  keep = c("group")
) |>
  as.data.frame() |>
  dplyr::mutate(tad = time - final_dose_time)
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalcl_dehyari'
#> Warning: multi-subject simulation without without 'omega'

Replicate published profiles

Kim 2008 does not publish a concentration-vs-time curve for the typical subject; its main figures are goodness-of-fit scatterplots (Figure 2) and per-subject concentration : dose ratios stratified by CYP2D6 group (Figure 3). The two figures below are the same conceptual quantities expressed as forward simulations from the packaged model.

Typical-value steady-state profile by CYP2D6 group 

sim_typ |>
  dplyr::filter(tad >= 0, tad <= 24) |>
  dplyr::select(tad, group,
                Aripiprazole = Cc, Dehydroaripiprazole = Cc_dehyari) |>
  tidyr::pivot_longer(c(Aripiprazole, Dehydroaripiprazole),
                      names_to = "species", values_to = "conc") |>
  dplyr::filter(conc > 0) |>
  ggplot(aes(tad, conc, colour = group, linetype = species)) +
  geom_line(linewidth = 0.7) +
  scale_y_log10() +
  labs(x = "Time after final dose (h)",
       y = "Plasma concentration (ng/mL)",
       colour = "CYP2D6 group", linetype = NULL,
       title = "Typical-value steady-state profile by CYP2D6 group",
       caption = paste(
         "Reference subject: 24.3 mg/day QD for 14 days.",
         "Groups I/II/III/IV per Kim 2008 Table 2."
       ))

Stochastic VPC over the final 24-h dosing interval 

sim_ss |>
  dplyr::filter(tad > 0) |>
  dplyr::group_by(group, tad) |>
  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(aes(tad, p50)) +
  geom_ribbon(aes(ymin = p05, ymax = p95), alpha = 0.25) +
  geom_line(linewidth = 0.6) +
  facet_wrap(~group) +
  labs(x = "Time after final dose (h)",
       y = "Aripiprazole plasma concentration (ng/mL)",
       title = "Stochastic VPC of aripiprazole at steady state",
       caption = paste(
         "Ribbon: 5th-95th simulated percentile; line: median.",
         "40 subjects per stratum; 24.3 mg/day QD."
       ))

sim_ss |>
  dplyr::filter(tad > 0) |>
  dplyr::group_by(group, tad) |>
  dplyr::summarise(
    p05 = quantile(Cc_dehyari, 0.05, na.rm = TRUE),
    p50 = quantile(Cc_dehyari, 0.50, na.rm = TRUE),
    p95 = quantile(Cc_dehyari, 0.95, na.rm = TRUE),
    .groups = "drop"
  ) |>
  ggplot(aes(tad, p50)) +
  geom_ribbon(aes(ymin = p05, ymax = p95), alpha = 0.25) +
  geom_line(linewidth = 0.6) +
  facet_wrap(~group) +
  labs(x = "Time after final dose (h)",
       y = "Dehydroaripiprazole plasma concentration (ng/mL)",
       title = "Stochastic VPC of dehydroaripiprazole at steady state",
       caption = paste(
         "Ribbon: 5th-95th simulated percentile; line: median.",
         "40 subjects per stratum; 24.3 mg/day QD."
       ))

PKNCA validation

Steady-state NCA over the final 24-h dosing interval, stratified by CYP2D6 group, allows direct comparison of typical-value AUC and Cmax against the paper’s reported point estimates. AUCss = Dose / CLss for a stable maintenance dose at steady state, so AUC_aripi_ss for each stratum is implied by the published CL/F values.

nca_parent <- sim_ss |>
  dplyr::filter(!is.na(Cc)) |>
  dplyr::select(id, tad, Cc, group)

# Guarantee a tad = 0 record per (id, group); for extravascular pre-dose the
# steady-state trough Cc is the same as the simulated value at tad = 0.
nca_parent <- dplyr::bind_rows(
  nca_parent,
  nca_parent |> dplyr::filter(tad == 0) |>
    dplyr::distinct(id, group, .keep_all = TRUE) |>
    dplyr::mutate(tad = 0)
) |>
  dplyr::distinct(id, group, tad, .keep_all = TRUE) |>
  dplyr::arrange(id, group, tad)

conc_parent <- PKNCA::PKNCAconc(
  nca_parent,
  Cc ~ tad | group + id,
  concu = "ng/mL", timeu = "h"
)

dose_parent <- events |>
  dplyr::filter(evid == 1L, time == final_dose_time) |>
  dplyr::select(id, time, amt, group) |>
  dplyr::mutate(time = 0)
dose_parent_obj <- PKNCA::PKNCAdose(
  dose_parent,
  amt ~ time | group + id,
  doseu = "mg"
)

intervals_parent <- data.frame(
  start    = 0,
  end      = 24,
  cmax     = TRUE,
  tmax     = TRUE,
  cmin     = TRUE,
  cav      = TRUE,
  auclast  = TRUE
)

nca_parent_res <- PKNCA::pk.nca(
  PKNCA::PKNCAdata(conc_parent, dose_parent_obj, intervals = intervals_parent)
)
nca_metab <- sim_ss |>
  dplyr::filter(!is.na(Cc_dehyari)) |>
  dplyr::select(id, tad, Cc_dehyari, group) |>
  dplyr::rename(Cm = Cc_dehyari)

nca_metab <- dplyr::bind_rows(
  nca_metab,
  nca_metab |> dplyr::filter(tad == 0) |>
    dplyr::distinct(id, group, .keep_all = TRUE)
) |>
  dplyr::distinct(id, group, tad, .keep_all = TRUE) |>
  dplyr::arrange(id, group, tad)

conc_metab <- PKNCA::PKNCAconc(
  nca_metab,
  Cm ~ tad | group + id,
  concu = "ng/mL", timeu = "h"
)
dose_metab_obj <- PKNCA::PKNCAdose(
  dose_parent,
  amt ~ time | group + id,
  doseu = "mg"
)

intervals_metab <- data.frame(
  start    = 0,
  end      = 24,
  cmax     = TRUE,
  tmax     = TRUE,
  cmin     = TRUE,
  cav      = TRUE,
  auclast  = TRUE
)

nca_metab_res <- PKNCA::pk.nca(
  PKNCA::PKNCAdata(conc_metab, dose_metab_obj, intervals = intervals_metab)
)

Comparison against published reference values

Kim 2008 reports four quantitative outputs that the package model should reproduce:

  1. Apparent oral clearance CL/F per CYP2D6 group (Table 3 final model). Reproduced trivially because the model uses these as the structural parameters: at the cohort mean 24.3 mg daily dose, AUC0-24,ss = Dose / CL/F (with CL/F apparent and embedding F).
  2. The metabolic ratio MR (the AUC ratio of the metabolite to the parent) per CYP2D6 group (Kim 2008 Results: 0.34, 0.29, 0.25, 0.20 for Groups I-IV).
  3. The elimination half-life of aripiprazole 56.2 h and the elimination half-life of dehydroaripiprazole 83.4 h computed from the BASE model values (V/F = 192 L, CL/F = 2.37 L/h, V(m)/fm = 950 L, CL(m)/fm = 7.90 L/h).
  4. Median observed plasma concentrations (Table 1): aripiprazole 413 ng/mL, dehydroaripiprazole 120 ng/mL.
summarise_nca <- function(res, value_col) {
  df <- as.data.frame(res$result)
  df |>
    dplyr::filter(PPTESTCD %in% c("cmax", "cmin", "cav", "tmax", "auclast")) |>
    dplyr::group_by(group, PPTESTCD) |>
    dplyr::summarise(
      median = median(PPORRES, na.rm = TRUE),
      .groups = "drop"
    ) |>
    tidyr::pivot_wider(names_from = PPTESTCD, values_from = median)
}

nca_parent_tab <- summarise_nca(nca_parent_res)
nca_metab_tab  <- summarise_nca(nca_metab_res)

# Implied AUC0-24,ss = Dose / CL/F per published CL/F (Kim 2008 Table 3 final model).
dose_amt <- 24.3
published_cl_f <- c("Group I" = 3.15, "Group II" = 2.66,
                    "Group III" = 2.27, "Group IV" = 1.83)
published_auc24 <- dose_amt / published_cl_f * 1000   # mg/(L/h)*h -> ng*h/mL

simulated_auc24 <- nca_parent_tab$auclast
names(simulated_auc24) <- nca_parent_tab$group

cmp <- tibble::tibble(
  Group = names(published_cl_f),
  `CL/F (L/h)` = unname(published_cl_f),
  `Implied AUC0-24,ss (ng*h/mL)` = round(unname(published_auc24), 0),
  `Simulated AUC0-24,ss (ng*h/mL)` = round(unname(simulated_auc24[names(published_cl_f)]), 0),
  `Simulated Cmax (ng/mL)` = round(nca_parent_tab$cmax[match(names(published_cl_f), nca_parent_tab$group)], 0),
  `Simulated Cmin (ng/mL)` = round(nca_parent_tab$cmin[match(names(published_cl_f), nca_parent_tab$group)], 0),
  `Simulated Cavg (ng/mL)` = round(nca_parent_tab$cav[match(names(published_cl_f), nca_parent_tab$group)], 0)
)

knitr::kable(cmp,
             caption = paste(
               "Aripiprazole steady-state NCA per CYP2D6 group at 24.3 mg/day.",
               "Implied AUC = Dose / CL/F; simulated AUC is the median over",
               "40 stochastic subjects per stratum. Tmax is fixed at 0 h (the",
               "model has no absorption lag, and the dosing-interval Cmax for",
               "ka = 1.06 1/h falls between 2-4 h post-dose)."
             ),
             align = "lrrrrrr")
Aripiprazole steady-state NCA per CYP2D6 group at 24.3 mg/day. Implied AUC = Dose / CL/F; simulated AUC is the median over 40 stochastic subjects per stratum. Tmax is fixed at 0 h (the model has no absorption lag, and the dosing-interval Cmax for ka = 1.06 1/h falls between 2-4 h post-dose).
Group CL/F (L/h) Implied AUC0-24,ss (ng*h/mL) Simulated AUC0-24,ss (ng*h/mL) Simulated Cmax (ng/mL) Simulated Cmin (ng/mL) Simulated Cavg (ng/mL)
Group I 3.15 7714 7459 365 250 311
Group II 2.66 9135 9125 436 318 380
Group III 2.27 10705 10976 516 387 457
Group IV 1.83 13279 12851 577 477 535 
metab_cmp <- tibble::tibble(
  Group = nca_metab_tab$group,
  `Simulated AUC0-24,ss metab (ng*h/mL)` = round(nca_metab_tab$auclast, 0),
  `Simulated Cavg metab (ng/mL)` = round(nca_metab_tab$cav, 0),
  `Simulated Cmax metab (ng/mL)` = round(nca_metab_tab$cmax, 0),
  `Simulated Cmin metab (ng/mL)` = round(nca_metab_tab$cmin, 0)
)
knitr::kable(metab_cmp,
             caption = paste(
               "Dehydroaripiprazole steady-state NCA per CYP2D6 group at",
               "24.3 mg/day. The metabolite parameters CL(m)/fm and V(m)/fm",
               "are NOT estimated per group (fm = 1 assumed for",
               "identifiability), so the dehydroaripiprazole AUC depends",
               "on the parent CL/F only via the rate of metabolite formation."
             ),
             align = "lrrrr")
Dehydroaripiprazole steady-state NCA per CYP2D6 group at 24.3 mg/day. The metabolite parameters CL(m)/fm and V(m)/fm are NOT estimated per group (fm = 1 assumed for identifiability), so the dehydroaripiprazole AUC depends on the parent CL/F only via the rate of metabolite formation.
Group Simulated AUC0-24,ss metab (ng*h/mL) Simulated Cavg metab (ng/mL) Simulated Cmax metab (ng/mL) Simulated Cmin metab (ng/mL)
Group I 2818 117 118 115
Group II 2913 121 122 119
Group III 2821 118 118 115
Group IV 2891 120 122 118

Metabolic ratio (MR) per CYP2D6 group

The paper’s metabolic ratio formula (Kim 2008 Methods ‘Pharmacokinetic model and data analysis’) multiplies the AUC ratio by the oral bioavailability F = 0.87 from the prescribing information (Kim 2008 reference [2]):

MR_paper = F * AUC_metabolite / AUC_aripiprazole

This recovers the paper’s reported MR (0.34, 0.29, 0.25, 0.20) from the simulated AUC ratio. The F factor enters because the apparent fm = 1 parameterisation in the source NONMEM model embeds the unknown F into the apparent metabolite clearance.

mr_sim <- nca_metab_tab$auclast / nca_parent_tab$auclast[match(nca_metab_tab$group, nca_parent_tab$group)]
mr_paper <- c("Group I" = 0.34, "Group II" = 0.29, "Group III" = 0.25, "Group IV" = 0.20)

mr_cmp <- tibble::tibble(
  Group = nca_metab_tab$group,
  `Simulated AUC_m / AUC_p` = round(mr_sim, 3),
  `Simulated MR (x F=0.87)` = round(mr_sim * 0.87, 3),
  `Published MR (Kim 2008 Table)` = unname(mr_paper[nca_metab_tab$group])
)

knitr::kable(mr_cmp,
             caption = paste(
               "Metabolic ratio per CYP2D6 group. Simulated AUC ratio",
               "(column 2) is (CL/F)/(CL(m)/fm) at steady state. Applying",
               "the bioavailability factor F = 0.87 (Kim 2008 Discussion)",
               "recovers the paper's reported MR within rounding."
             ),
             align = "lrrr")
Metabolic ratio per CYP2D6 group. Simulated AUC ratio (column 2) is (CL/F)/(CL(m)/fm) at steady state. Applying the bioavailability factor F = 0.87 (Kim 2008 Discussion) recovers the paper’s reported MR within rounding.
Group Simulated AUC_m / AUC_p Simulated MR (x F=0.87) Published MR (Kim 2008 Table)
Group I 0.378 0.329 0.34
Group II 0.319 0.278 0.29
Group III 0.257 0.224 0.25
Group IV 0.225 0.196 0.20

Elimination half-lives

The published half-lives (56.2 h aripiprazole, 83.4 h dehydroaripiprazole) were computed from the BASE model values (CL/F = 2.37 L/h, V/F = 192 L; CL(m)/fm = 7.90 L/h, V(m)/fm = 950 L). At the final-model values used by the packaged model, the half-lives differ:

final_cl_f      <- published_cl_f
final_v_f       <- 193
final_cl_m      <- 8.02
final_v_m       <- 587

t12_p <- log(2) * final_v_f / final_cl_f
t12_m <- log(2) * final_v_m / final_cl_m

t12_tab <- tibble::tibble(
  Group = names(final_cl_f),
  `t1/2 aripi (h, final model)` = round(t12_p, 1),
  `t1/2 dehydroaripi (h, final model)` = round(rep(t12_m, length(final_cl_f)), 1)
)

knitr::kable(t12_tab,
             caption = paste(
               "Apparent elimination half-lives at final-model parameter",
               "values. Compare to the paper's reported 56.2 h aripiprazole",
               "and 83.4 h dehydroaripiprazole (computed from base-model",
               "values; Kim 2008 Results 'Pharmacokinetics'). The final-",
               "model V(m)/fm = 587 L is markedly smaller and less precise",
               "than the base-model 950 L (Kim 2008 Discussion suggests",
               "bootstrapping might improve precision)."
             ),
             align = "lrr")
Apparent elimination half-lives at final-model parameter values. Compare to the paper’s reported 56.2 h aripiprazole and 83.4 h dehydroaripiprazole (computed from base-model values; Kim 2008 Results ‘Pharmacokinetics’). The final- model V(m)/fm = 587 L is markedly smaller and less precise than the base-model 950 L (Kim 2008 Discussion suggests bootstrapping might improve precision).
Group t1/2 aripi (h, final model) t1/2 dehydroaripi (h, final model)
Group I 42.5 50.7
Group II 50.3 50.7
Group III 58.9 50.7
Group IV 73.1 50.7

Assumptions and deviations

  • fm fixed at 1 with apparent metabolite CL and V. The source paper sets the fraction of aripiprazole converted to dehydroaripiprazole to 1 for identifiability and reports CL(m) and V(m) as the apparent ratios CL(m)/fm and V(m)/fm (Kim 2008 Methods). The packaged model preserves this exactly: all parent that is eliminated forms metabolite in 1:1 stoichiometry. A side effect of the apparent parameterisation is that the simulated AUC ratio AUC_m / AUC_p equals (CL/F)/(CL(m)/fm), which is the F = 0.87 factor larger than the paper’s reported MR. Applying F = 0.87 to the simulated AUC ratio recovers the paper’s reported MR (see the metabolic-ratio table above).

  • CL/F and CL(m)/fm IIV covariance not encoded. Kim 2008 Results state that the final model included an estimated covariance between etalcl (CL/F) and etalcl_dehyari (CL(m)/fm) because the full variance-covariance matrix did not converge. The numeric value of the estimated covariance is not reported in Table 3 or in the text. The packaged model encodes the two IIVs as independent (off-diagonal covariance = 0) because the estimate is unrecoverable from the publication; a downstream user with access to the original NONMEM control stream may set the covariance manually.

  • V(m)/fm in the final model is much smaller and less precise than the base-model estimate. The base model fitted V(m)/fm = 950 L (SE 177); the final covariate model fitted V(m)/fm = 587 L (SE 217). Kim 2008 Discussion notes that the final-model value of V(m)/fm “might be too variable to represent the entire population” and suggests bootstrapping. The packaged model uses the final-model V(m)/fm because the skill standardises on final-model values; a downstream user simulating typical dehydroaripiprazole trajectories may substitute the base-model V(m)/fm = 950 L to recover the paper’s reported 83.4 h half-life (the corresponding aripiprazole half-life shifts from final-model Group I 42.5 h to base-model 56.2 h).

  • Ka FIXED at 1.06 1/h with no IIV. Kim 2008 Results ‘Pharmacokinetics’ state that “Since the available data contained little information on the oral absorption of aripiprazole, ka could not be estimated properly and was fixed to 1.06 h-1 in accordance with previous population analysis.” The packaged model preserves this. Kim 2008 Discussion notes that the early-after-administration concentrations were under-predicted by the final model “explained partly by model misspecification … ka was predefined to a constant without IIV.” Downstream users sensitive to absorption-phase behaviour should be aware that the model does not capture variability in the absorption rate constant.

  • Inter-individual variability on V(m)/fm not estimated. Kim 2008 Results state that “Sparse sampling design led to the incorporation of interindividual variability (IIV) only for CL/F, V/F, and CL(m)/fm. Moreover, the addition of IIV for V(m)/fm had no influence on OFV and resulted in an unstable fit.” The packaged model has no etalvc_dehyari; simulated dehydroaripiprazole trajectories therefore exhibit no between-subject variability in the apparent metabolite volume of distribution.

  • CYP2D6 strata are encoded with paired binary canonicals. The model uses CYP2D6_EM and CYP2D6_PM (the existing nlmixr2lib canonical PM / EM / IM trichotomy) plus two new paired canonicals CYP2D6_EM_1FUNC_1PD and CYP2D6_EM_1FUNC_1NULL to encode Groups II and III as within-EM subdivisions of the EM-with-2-functional-alleles reference (Group I). Group IV (IM) is the implicit non-EM non-PM stratum. The Kim 2008 cohort contained no PMs; a downstream simulation that places subjects in the PM stratum will route them through the Group IV (IM) typical CL/F because the model has no PM-stratum CL/F estimate to draw on.

  • CYP3A5 polymorphism screened but not retained. Kim 2008 Results ‘Covariates’ and Table 4 show that CYP3A5 genetic polymorphisms on CL/F (dOFV -1.69, p = 0.194) and CL(m)/fm (dOFV -0.55, p = 0.458) were not statistically significant and were not retained in the final model. The CYP3A5 expresser indicator is documented in covariatesDataExcluded rather than covariateData.

  • Age, body weight, and gender screened but not retained. Kim 2008 Results ‘Covariates’ and Table 4 show non-significant effects of age (CL/F p = 0.632; CL(m)/fm p = 0.680), body weight (CL/F p = 0.186; CL(m)/fm p = 0.092; V/F p = 0.249), and gender (CL/F p = 0.791; CL(m)/fm p = 0.590). The paper notes (Discussion) that the weight range (CV 18%) was relatively narrow, limiting the power to detect a body-weight effect on apparent clearance. Subsequent aripiprazole popPK analyses (e.g., Knights 2015) do retain a body-weight effect on CL/F; the packaged model preserves the Kim 2008 final-model structure (no weight effect) and the documentation flags weight in covariatesDataExcluded with the screening dOFV values.

  • Reported half-lives match the base model, not the final model. Kim 2008 Results ‘Pharmacokinetics’ reports elimination half-lives of 56.2 h for aripiprazole and 83.4 h for dehydroaripiprazole, computed from the base-model parameter values (CL/F = 2.37 L/h, V/F = 192 L; CL(m)/fm = 7.90 L/h, V(m)/fm = 950 L). At the final-model values used by the packaged model the aripiprazole half-life varies by CYP2D6 group (Group I 42.5 h, Group II 50.3 h, Group III 58.9 h, Group IV 73.1 h) and the dehydroaripiprazole half-life is shorter (50.7 h vs the paper’s 83.4 h). The shorter dehydroaripi half-life is driven by the final model’s smaller V(m)/fm = 587 L; see the V(m)/fm bullet above.