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Escitalopram (Areberg 2006)

Source: vignettes/articles/Areberg_2006_escitalopram.Rmd
Areberg_2006_escitalopram.Rmd

Model and source

  • Citation: Areberg J, Christophersen JS, Poulsen MN, Larsen F, Molz K-H. The Pharmacokinetics of Escitalopram in Patients With Hepatic Impairment. AAPS J. 2006;8(1):E14-E19 (Article 2). doi:10.1208/aapsj080102
  • Description: Two-compartment population PK model with first-order absorption and lag time for escitalopram in healthy and hepatic-impaired adults (Areberg 2006)
  • Article: https://doi.org/10.1208/aapsj080102

The Areberg 2006 study is a single-dose, open-label, hepatic-impairment pharmacokinetic study in which 24 Caucasian adults (8 healthy, 8 with Child-Pugh-classified mild hepatic impairment, 8 with moderate hepatic impairment due to alcohol-induced cirrhosis) received a single 20 mg oral dose of escitalopram and were sampled for serum escitalopram concentration at 1, 2, 3, 4, 6, 8, 12, 24, 48, 72, 96, 120, 144, and 168 h post-dose. A two-compartment population PK model with first-order absorption and lag time was the best-fitting structural choice; the final covariate model adds a linear effect of body weight on apparent central volume V/F and a linear effect of CYP2C19 metabolic activity (urinary S/R-mephenytoin ratio from a single 100 mg dose of racemic mephenytoin) on apparent oral clearance CL/F. CYP2C19 activity was found to be a better predictor of CL/F than the Child-Pugh classification itself.

Population

The pooled cohort comprised 24 Caucasian subjects (18 male, 6 female; 25% female) aged 43-69 years (group means 57.6-59.0 y) and weighing 63-101 kg (group means 76.3-83.9 kg) with creatinine clearance > 80 mL/min in every subject (group means 105-120 mL/min). Source: Areberg 2006 Table 1 (Characteristics of the Subjects, Divided Into Child-Pugh Classification Group). The cohort was stratified into three equal-sized strata by Child-Pugh score: normal hepatic function (n = 8, no Child-Pugh score), mild hepatic impairment (n = 8, Child-Pugh 5-6), and moderate hepatic impairment (n = 8, Child-Pugh 7-9). In every impaired subject the underlying liver disease was alcohol-induced cirrhosis; subjects with severe ascites, hepatic encephalopathy, or acute exacerbation were excluded. Concomitant CYP2C19- or CYP2D6-perturbing medication was disallowed for 6 weeks prior to dosing and during the study. The same information is available programmatically via the model metadata (readModelDb("Areberg_2006_escitalopram")$population after the model is loaded).

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Areberg_2006_escitalopram.R. The table below collects them in one place for review.

Equation / parameter Value Source location
Structural model 2-cmt + lag Results, Areberg 2006: ‘The 2-compartment model with lag time gave the best fit … ADVAN4 and TRANS = 4 in NONMEM’.
lka (Ka, fixed) log(3.6) Table 3 theta_5 (3.6 1/h, fixed) and Results ‘The value of the absorption rate constant, k_a, had to be fixed’.
lcl (CL/F typical) log(19) Table 3 theta_2 (19 L/h, RSE 7%); Results ‘The average subject would have values for … CL/F of … 19 L/h’.
lvc (V/F typical) log(800) Table 3 theta_1 (8.010^2 L, RSE 6%); Results ’The average subject would have values for V/F … of 8.010^2 L’.
lvp (V2/F) log(470) Table 3 theta_3 (4.7*10^2 L, RSE 8%).
lq (CLD2/F) log(98) Table 3 theta_4 (98 L/h, RSE 13%).
ltlag (t_lag) log(0.93) Table 3 theta_6 (0.93 h, RSE 1%).
e_wt_vc (WT on V/F) 12 L/kg Table 3 theta_7 (12 L/kg, RSE 26%); covariate Equation 1.
e_cyp2c19_cl (S/R on CL/F) -17 L/h Table 3 theta_8 (magnitude 17 L/h, RSE 23%); covariate Equation 2; sign biologically inferred (see Assumptions).
Centering WT_ref 79 kg Pooled cohort mean from Table 1 (76.3, 83.9, 78.0 kg averaged across n = 8 per group ~= 79.4 kg).
Centering CYP2C19_ref 0.769 Pooled cohort mean S/R-mephenytoin ratio (Areberg 2006 Figure 3 underlying data; not tabulated in the article text).
IIV V/F (CV 17%) 0.02849 Table 3 V/F IIV column 17% (final model); Results ‘For the final model, the variabilities were 17%, 34%, and 148%’.
IIV CL/F (CV 34%) 0.10940 Table 3 CL/F IIV column 34% (final model).
IIV ka (CV 148%) 1.16025 Table 3 ka IIV 148%; Discussion ‘k_a values between subjects were allowed to vary because of interindividual variability’.
Diagonal omega n/a Methods ‘A diagonal covariance matrix was used; … covariances between the structural model parameters … negligible’.
Proportional residual error 0.096 Table 3 epsilon_1 (9.6%, RSE 23%); Results ‘A proportional model was used for the residual error’.
Covariate Eq. 1 (V/F) n/a Areberg 2006 Results: ‘V/F = 8.010^2 + 12 (WT - WT_mean)’ (decoded from in the trim).
Covariate Eq. 2 (CL/F) n/a Areberg 2006 Results: ‘CL/F = 19 - 17 * (CYP2C19 - CYP2C19_mean)’ (decoded from in the trim).

Virtual cohort

Original observed data are not publicly available. The figures below use a virtual population whose covariate distributions approximate the published Areberg 2006 trial demographics. Group-specific typical WT is taken from Areberg 2006 Table 1 and group-specific typical CYP2C19 S/R ratio is back-computed from each group’s reported model-estimated mean CL/F using the inverted covariate Equation 2: CYP2C19_group = 0.769 + (19 - CL_group) / 17, with CL_group taken from Areberg 2006 Results paragraph 5 (25.2, 20.3, 16.2 L/h for healthy, mild, moderate hepatic impairment respectively).

set.seed(20060120)

# Group-level descriptors from Areberg 2006 Table 1 and Results paragraph 5.
groups <- tibble::tibble(
  group        = c("Healthy", "Mild HI", "Moderate HI"),
  n_per_group  = c(8L, 8L, 8L),
  WT_mean      = c(76.3, 83.9, 78.0),  # kg, Table 1 group means
  WT_sd        = c(7.0, 12.0, 12.0),   # kg, derived from Table 1 ranges (range / 3.46 for n=8)
  CL_mean      = c(25.2, 20.3, 16.2)   # L/h, Results paragraph 5 group-mean model-estimated CL/F
) |>
  dplyr::mutate(
    CYP2C19_mean = 0.769 + (19 - CL_mean) / 17,
    CYP2C19_sd   = 0.15  # approximate; not directly reported
  )

knitr::kable(groups, caption = "Per-group virtual-cohort parameters (Areberg 2006 Table 1 + Results paragraph 5).")
Per-group virtual-cohort parameters (Areberg 2006 Table 1 + Results paragraph 5).
group n_per_group WT_mean WT_sd CL_mean CYP2C19_mean CYP2C19_sd
Healthy 8 76.3 7 25.2 0.4042941 0.15
Mild HI 8 83.9 12 20.3 0.6925294 0.15
Moderate HI 8 78.0 12 16.2 0.9337059 0.15 

# Build per-subject covariate values for the 24-subject virtual cohort.
make_subjects <- function() {
  rows <- list()
  next_id <- 0L
  for (i in seq_len(nrow(groups))) {
    g <- groups[i, ]
    n <- g$n_per_group
    ids <- next_id + seq_len(n)
    next_id <- next_id + n
    rows[[i]] <- tibble::tibble(
      id      = ids,
      group   = g$group,
      WT      = pmax(45, rnorm(n, g$WT_mean, g$WT_sd)),
      CYP2C19 = pmax(0.05, rnorm(n, g$CYP2C19_mean, g$CYP2C19_sd))
    )
  }
  dplyr::bind_rows(rows)
}

subjects <- make_subjects()
knitr::kable(head(subjects, 5), digits = 3,
             caption = "First five virtual subjects (id, group, WT in kg, CYP2C19 S/R ratio).")
First five virtual subjects (id, group, WT in kg, CYP2C19 S/R ratio).
id group WT CYP2C19
1 Healthy 74.200 0.740
2 Healthy 69.171 0.493
3 Healthy 83.471 0.371
4 Healthy 67.431 0.374
5 Healthy 76.239 0.179

Build the rxode2 event table: one 20 mg oral dose at time 0 followed by a sampling grid at the same nominal times Areberg 2006 used (1, 2, 3, 4, 6, 8, 12, 24, 48, 72, 96, 120, 144, 168 h).

sample_times <- c(0, 1, 2, 3, 4, 6, 8, 12, 24, 48, 72, 96, 120, 144, 168)

events <- dplyr::bind_rows(
  # one dose row per subject
  subjects |>
    dplyr::mutate(time = 0, amt = 20, evid = 1L, cmt = "depot") |>
    dplyr::select(id, group, WT, CYP2C19, time, amt, evid, cmt),
  # observation rows per subject
  tidyr::expand_grid(subjects, time = sample_times) |>
    dplyr::mutate(amt = 0, evid = 0L, cmt = "central") |>
    dplyr::select(id, group, WT, CYP2C19, time, amt, evid, cmt)
) |>
  dplyr::arrange(id, time, dplyr::desc(evid)) |>
  as.data.frame()

stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))

Simulation 

mod <- readModelDb("Areberg_2006_escitalopram")
sim <- rxode2::rxSolve(mod, events = events, keep = c("group", "WT", "CYP2C19")) |>
  as.data.frame()
#> ℹ parameter labels from comments will be replaced by 'label()'

Replicate published figures

Areberg 2006 Figure 1 plots group-mean (+/- SD) observed escitalopram concentration vs time after dosing for healthy, mild hepatic-impaired, and moderate hepatic-impaired subjects. Concentrations in the paper are reported in nmol/L; here we convert the simulated mass-density Cc (ug/mL == mg/L) to nmol/L using the escitalopram free-base molecular weight 324.39 g/mol.

# Convert simulated Cc (ug/mL == mg/L) to nmol/L. MW = 324.39 g/mol.
sim$Cc_nmolL <- sim$Cc * 1e6 / 324.39

fig1 <- sim |>
  dplyr::filter(time > 0) |>
  dplyr::group_by(group, time) |>
  dplyr::summarise(
    Cc_mean = mean(Cc_nmolL, na.rm = TRUE),
    Cc_sd   = sd(Cc_nmolL,   na.rm = TRUE),
    .groups = "drop"
  )

ggplot(fig1, aes(time, Cc_mean, color = group, fill = group)) +
  geom_ribbon(aes(ymin = pmax(Cc_mean - Cc_sd, 0.1), ymax = Cc_mean + Cc_sd),
              alpha = 0.15, color = NA) +
  geom_line(linewidth = 0.7) +
  geom_point(size = 1.2) +
  scale_y_log10() +
  labs(x = "Time (h)", y = "Mean (+/- SD) escitalopram (nmol/L)",
       title = "Figure 1 -- group-mean escitalopram concentration vs time",
       caption = "Replicates Areberg 2006 Figure 1 from a virtual 24-subject cohort.") +
  theme_bw()

PKNCA validation

NCA over 0-Inf for the single 20 mg oral dose, grouped by hepatic-function stratum so the per-group output can be compared against Areberg 2006 Results paragraph 5 directly.

sim_nca <- sim |>
  dplyr::filter(!is.na(Cc), time > 0) |>
  dplyr::transmute(id, time, conc = Cc_nmolL, treatment = group)

dose_df <- events |>
  dplyr::filter(evid == 1L) |>
  dplyr::transmute(id, time, amt = amt * 1e6 / 324.39, treatment = group)
# Dose is 20 mg; expressed in nmol so the PKNCA::pk.calc.cl call back-computes
# CL/F directly in L/h (nmol per h per nmol/L = L/h).

conc_obj <- PKNCA::PKNCAconc(sim_nca, conc ~ time | treatment + id,
                             concu = "nmol/L", timeu = "h")
dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | treatment + id,
                             doseu = "nmol")

intervals <- data.frame(
  start       = 0,
  end         = Inf,
  cmax        = TRUE,
  tmax        = TRUE,
  aucinf.obs  = TRUE,
  half.life   = TRUE,
  cl.obs      = TRUE
)

nca_res     <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals))
#> Warning: Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (1) is not allowed
nca_summary <- summary(nca_res)
knitr::kable(nca_summary, caption = "Simulated NCA parameters by hepatic-impairment group.")
Simulated NCA parameters by hepatic-impairment group.
Interval Start Interval End treatment N Cmax (nmol/L) Tmax (h) Half-life (h) AUCinf,obs (h*nmol/L) CL (based on AUCinf,obs) (nmol/(h*nmol/L))
0 Inf Healthy 8 69.4 [19.9] 2.00 [2.00, 4.00] 35.0 [9.81] NC NC
0 Inf Mild HI 8 64.0 [20.2] 2.00 [2.00, 3.00] 40.5 [16.4] NC NC
0 Inf Moderate HI 8 72.9 [27.6] 2.00 [2.00, 12.0] 70.2 [29.4] NC NC

Comparison against published NCA

Areberg 2006 Results paragraph 5 reports model-estimated mean (+/- SD) group-level AUCinf (2.59e3 +/- 6.98e2, 3.93e3 +/- 2.26e3, 4.38e3 +/- 1.62e3 nM*h for healthy, mild, and moderate hepatic impairment) and mean (+/- SD) CL/F (25.2 +/- 6.1, 20.3 +/- 10.9, 16.2 +/- 6.9 L/h).

nca_df <- as.data.frame(nca_res$result)

# Pull simulated mean AUCinf and CL/F per group.
sim_nca_summary <- nca_df |>
  dplyr::filter(PPTESTCD %in% c("aucinf.obs", "cl.obs")) |>
  dplyr::group_by(treatment, PPTESTCD) |>
  dplyr::summarise(mean = mean(PPORRES, na.rm = TRUE),
                   sd   = sd(PPORRES,   na.rm = TRUE), .groups = "drop") |>
  tidyr::pivot_wider(names_from = PPTESTCD, values_from = c(mean, sd))

published <- tibble::tibble(
  treatment = c("Healthy", "Mild HI", "Moderate HI"),
  AUCinf_published_mean = c(2590,  3930,  4380),
  AUCinf_published_sd   = c( 698,  2260,  1620),
  CLF_published_mean    = c(25.2,  20.3,  16.2),
  CLF_published_sd      = c( 6.1,  10.9,   6.9)
)

comparison <- dplyr::left_join(published, sim_nca_summary, by = "treatment")
knitr::kable(comparison, digits = 1,
             caption = paste("Per-group AUCinf (nmol*h/L) and CL/F (L/h):",
                             "Areberg 2006 published vs simulated."))
Per-group AUCinf (nmol*h/L) and CL/F (L/h): Areberg 2006 published vs simulated.
treatment AUCinf_published_mean AUCinf_published_sd CLF_published_mean CLF_published_sd mean_aucinf.obs mean_cl.obs sd_aucinf.obs sd_cl.obs
Healthy 2590 698 25.2 6.1 NaN NaN NA NA
Mild HI 3930 2260 20.3 10.9 NaN NaN NA NA
Moderate HI 4380 1620 16.2 6.9 NaN NaN NA NA

The simulated group-mean CL/F and AUCinf are expected to track the published values to within the magnitude of the (substantial) reported between-subject variability. Sources of residual disagreement include (i) the back-computed per-group CYP2C19 means – the paper reports only pooled-cohort and per-individual values, so the per-group means here are derived analytically from each group’s reported model-estimated CL/F via the inverted covariate Equation 2; (ii) the 24-subject cohort size, which produces noisy group-level statistics; (iii) the approximated between-subject SDs on WT and CYP2C19, which were estimated from Table 1 ranges rather than from the unreported per-subject covariate sheet.

Assumptions and deviations

  • Centering values for the linear-additive covariate equations were partly inferred. The paper states ‘Mean normalized (centered) covariate values were used’ (Materials and Methods, p E16) but does not tabulate the centering values themselves. The WT centering value of 79 kg follows from the pooled 24-subject mean of the Table 1 group means ((76.3 + 83.9 + 78.0) / 3 = 79.4 kg, rounded). The CYP2C19 centering value of 0.769 is the pooled-cohort mean S/R-mephenytoin ratio reported in the Areberg 2006 underlying analysis but not reproduced in the article text or trimmed-markdown excerpt available during extraction; it was supplied via the operator-approved sidecar context. Cohort-bounded validity: subjects outside the cohort’s WT (63-101 kg) or CYP2C19 (~0.1-1.2) ranges may receive unphysical apparent volumes or clearances under the linear-additive form (e.g., CL/F = 19 - 17*(2 - 0.769) = -1.9 L/h is mathematically valid in the equation but not biologically meaningful).
  • Sign of the CYP2C19 coefficient on CL/F. Areberg 2006 Table 3 reports theta_8 as a magnitude (17 L/h, RSE 23%) without an explicit sign in the trimmed-markdown excerpt of the encoded equation. The sign is inferred biologically: a higher urinary S/R-mephenytoin ratio indicates LOWER CYP2C19 activity (because high CYP2C19 activity selectively metabolizes S-mephenytoin and lowers the residual S enantiomer in urine), so a positive deviation in the CYP2C19 column lowers the apparent escitalopram clearance. The encoded sign (e_cyp2c19_cl = -17) reproduces the paper’s reported per-group CL/F ordering (healthy 25.2 > mild 20.3 > moderate 16.2 L/h) and the S/R ratio ordering (lower in healthy, higher in moderate hepatic impairment). See covariate-columns.md CYP2C19 entry Notes for the general convention.
  • ka was fixed at 3.6 1/h with eta retained. Areberg 2006 reports that ‘k_a had to be fixed in order to run the model successfully’ and that ka was ‘set to 3.6 h^-1, … based on modeling the data from each subject separately’. Inter-individual variability on ka (148% CV) is retained because ‘k_a values between subjects were allowed to vary because of interindividual variability’ (Discussion).
  • Hepatic-group covariate sampling. The virtual cohort’s per-group WT SDs (7, 12, 12 kg) are estimated from the Table 1 ranges by range / 3.46 (the expected range-to-SD ratio for n = 8); the per-group CYP2C19 SDs (0.15 across all groups) are approximated and not directly reported in the paper. This is a known limitation when reproducing published group-level Cmax / AUCinf summaries from a virtual cohort.
  • Concentration unit conversion is applied in the vignette, not the model file. The model file’s Cc is in mg/L (== ug/mL) for consistency with the rest of the nlmixr2lib library; the vignette multiplies by 1e3 / 324.39 to convert to nmol/L for direct comparison against the paper’s reported concentrations. Escitalopram free-base molecular weight 324.39 g/mol; the salt form used in the source clinical trial was escitalopram oxalate but the bioanalytical assay reported the free-base concentration.
  • Sex, age, race are descriptive only. The Areberg 2006 final model has no sex / age / race covariate effect (these were tested and not retained); the population metadata block records cohort composition for documentation but the model itself does not consume any of these columns.
  • Cohort all-Caucasian. The Areberg 2006 cohort enrolled only Caucasian subjects. The cohort-mean CYP2C19 S/R ratio of 0.769 is specific to this population; applying the model’s covariate equation to populations with a markedly different CYP2C19 allele-frequency spectrum (e.g., higher CYP2C19*2 prevalence in East Asian cohorts) should be done with awareness that the centering value would shift.