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Levetiracetam (Wang 2012)

Source: vignettes/articles/Wang_2012_levetiracetam.Rmd
Wang_2012_levetiracetam.Rmd

Model and source 

#> ℹ parameter labels from comments will be replaced by 'label()'
  • Citation: Wang YH, Wang L, Lu W, Shang DW, Wei MJ, Wu Y. Population pharmacokinetics modeling of levetiracetam in Chinese children with epilepsy. Acta Pharmacol Sin. 2012 Jun;33(6):845-851. doi:10.1038/aps.2012.57
  • Description: One-compartment population PK model for levetiracetam (LEV) in Chinese pediatric epilepsy patients (Wang 2012). First-order oral absorption and linear elimination (NONMEM ADVAN2 TRANS2). Body weight is the only retained covariate; it enters CL/F as a power-style allometric term with reference weight 25 kg (cohort median).
  • Article: https://doi.org/10.1038/aps.2012.57

The packaged model implements the Wang 2012 final levetiracetam (LEV) population PK model: a one-compartment structure with first-order oral absorption and linear elimination (NONMEM ADVAN2 TRANS2). Body weight enters CL/F as a power-style allometric term with reference weight 25 kg (the cohort median). Inter-individual variability is log-normal on CL/F and V/F; the absorption rate constant Ka has no IIV (the source paper fixed omega_Ka at zero because the sparse trough-style sampling did not characterise the absorption phase). The residual error is additive as written by the source paper.

Population

Wang 2012 fit the model to 368 serum LEV concentrations from 311 Chinese pediatric epilepsy patients in the PPK model group, recruited at the Pediatric Department of Peking University First Hospital. A separate PPK validation group of 50 patients (50 concentrations) was used for external prediction-error checks (the packaged model uses only the PPK model group’s final-model estimates). Both groups were children aged 0.5 - 14 years (PPK model group mean 6.34, validation group mean 5.78); PPK model group weights spanned 5 - 70 kg (mean 25.17, median 25); the gender split was 160 male / 151 female (48.6% female). All subjects had normal renal and hepatic function. Total daily LEV doses were 20 - 60 mg/kg (mean 35.7, range 250 - 2000 mg/d); 40% were on LEV monotherapy and 60% were on a combination AED regimen (most commonly valproic acid, lamotrigine, carbamazepine, oxcarbazepine, or topiramate). No significant interaction between LEV PK and concomitant AED use was detected (Wang 2012 Table 2). The intervals between last dose and sampling spanned 0.1 - 13 hours, with most samples drawn near steady state (Figure 1, Figure 2). Full population characteristics are in Wang 2012 Table 1.

The same metadata is available programmatically via readModelDb("Wang_2012_levetiracetam")$meta$population.

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Wang_2012_levetiracetam.R. The table below collects them in one place for review. All point estimates are from Wang 2012 Table 4 (“Population parameter values for the final model”); structural-model layout is from Wang 2012 Methods “PPK modeling” and the final-model equation on page 848.

Equation / parameter Value Source location
lka (Ka) log(1.56) -> 1.56 /h Table 4; Ka = 1.56 /h (RSE 14.3%, 95% CI 1.230-1.997)
lvc (V/F) log(12.1) -> 12.1 L Table 4; V/F = 12.1 L (RSE 5.6%, 95% CI 10.767-13.433)
lcl (CL/F) log(1.04) -> 1.04 L/h Table 4; CL/F = 1.04 L/h (RSE 1.4%, 95% CI 1.011-1.069)
e_wt_cl 0.567 Table 4; “Weight” exponent 0.567 (RSE 6.7%, 95% CI 0.489-0.637)
etalcl variance 0.195 Table 4; omega^2 of CL/F = 0.195 (RSE 7.0%)
etalvc variance 0.163 Table 4; omega^2 of V/F = 0.163 (RSE 45.5%)
eta on Ka fixed at 0 (omitted from model) Discussion “Patient data” paragraph; omega_Ka fixed at 0 because absorption phase not characterised
addSd sqrt(0.028) ~= 0.1673 mg/L Table 4; sigma_E^2 = 0.028 (RSE 18.6%, 95% CI 0.018-0.035)
Reference weight 25 kg Discussion paragraph 1: “the median WEIG in our population was 25 kg”
CL/F covariate equation CL/F = 1.04 * (WT/25)^0.567 * exp(etalcl) Page 848 final-model equation; in-text exponent 0.563 vs Table 4 estimate 0.567 (see “Assumptions and deviations”)
ODE d/dt(depot) -ka * depot NONMEM ADVAN2 TRANS2 (Methods “PPK model of LEV”)
ODE d/dt(central) ka * depot - kel * central NONMEM ADVAN2 TRANS2 (Methods “PPK model of LEV”)
Derived kel cl / vc Standard 1-cmt linear-elimination relation; typical-individual t1/2 = ln(2) * V/F / CL/F = 8.07 h matches the paper’s 8.13 h (Discussion paragraph 1)
Residual error model Cc ~ add(addSd) Statistical model page 847: E_ij^0 = E_ij + eps_ij

Virtual cohort

Original observed data are not publicly available. The cohort below samples body weight from a log-normal distribution clipped to the paper’s reported range (5 - 70 kg; mean 25.17 kg, median 25 kg per Wang 2012 Table 1). Two dosing regimens reproduce trough scenarios from Wang 2012 Table 5: 10, 20, and 30 mg/kg BID per-weight dose levels and a single 25 mg/kg oral dose at the cohort median weight to characterise the half-life.

set.seed(20120601)

mod <- rxode2::rxode(readModelDb("Wang_2012_levetiracetam"))
#> ℹ parameter labels from comments will be replaced by 'label()'

sample_wt <- function(n,
                      wt_min       = 5,
                      wt_max       = 70,
                      wt_mean_targ = 25.17,
                      wt_sd_targ   = 12.0) {
  # Log-normal weight sample whose linear-scale mean approximates the Wang
  # 2012 cohort mean (25.17 kg; SD chosen to span the published 5 - 70 kg
  # range without long-tail outliers). Clipped to the published range.
  cv2     <- (wt_sd_targ / wt_mean_targ)^2
  log_mu  <- log(wt_mean_targ) - 0.5 * log(1 + cv2)
  log_sd  <- sqrt(log(1 + cv2))
  pmin(pmax(exp(rnorm(n, mean = log_mu, sd = log_sd)), wt_min), wt_max)
}

make_cohort <- function(n, regimen, dose_mg_per_kg,
                        dose_times, obs_grid,
                        wt = NULL, id_offset = 0L) {
  if (is.null(wt)) wt <- sample_wt(n)
  base <- tibble::tibble(
    id      = id_offset + seq_len(n),
    WT      = wt,
    regimen = regimen
  )
  doses <- tidyr::crossing(id = base$id, time = dose_times) |>
    dplyr::left_join(base, by = "id") |>
    dplyr::mutate(evid = 1L, cmt = "depot", amt = WT * dose_mg_per_kg)
  obs <- tidyr::crossing(id = base$id, time = obs_grid) |>
    dplyr::left_join(base, by = "id") |>
    dplyr::mutate(evid = 0L, cmt = "Cc", amt = NA_real_)
  dplyr::bind_rows(doses, obs) |>
    dplyr::arrange(id, time, dplyr::desc(evid))
}

# Single 25 mg/kg oral dose at typical median weight 25 kg (n = 200 to allow
# IIV-based percentile estimates). Sample weight from cohort distribution.
sd_obs_grid <- c(0, 0.25, 0.5, 0.75, 1, 1.5, 2, 3, 4, 6, 8, 10,
                 12, 16, 20, 24, 36, 48)
events_sd <- make_cohort(
  n              = 200,
  regimen        = "25 mg/kg single oral",
  dose_mg_per_kg = 25,
  dose_times     = 0,
  obs_grid       = sd_obs_grid,
  id_offset      = 0L
)

# Three q12h chronic-dosing cohorts at 10, 20, and 30 mg/kg per dose to match
# Wang 2012 Table 5's reported steady-state C_12h trough levels. Dose q12h for
# 7 days (14 doses) so the last interval is well into steady state. Sample the
# last 12-h interval (144 - 156 h) for trough comparison.
md_obs_grid <- c(seq(144, 156, by = 0.5))
md_dose_times <- seq(0, 156, by = 12)

events_md_10 <- make_cohort(
  n              = 200,
  regimen        = "10 mg/kg BID",
  dose_mg_per_kg = 10,
  dose_times     = md_dose_times,
  obs_grid       = md_obs_grid,
  id_offset      = 200L
)
events_md_20 <- make_cohort(
  n              = 200,
  regimen        = "20 mg/kg BID",
  dose_mg_per_kg = 20,
  dose_times     = md_dose_times,
  obs_grid       = md_obs_grid,
  id_offset      = 400L
)
events_md_30 <- make_cohort(
  n              = 200,
  regimen        = "30 mg/kg BID",
  dose_mg_per_kg = 30,
  dose_times     = md_dose_times,
  obs_grid       = md_obs_grid,
  id_offset      = 600L
)

events <- dplyr::bind_rows(events_sd, events_md_10, events_md_20, events_md_30)
stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))

Simulation 

sim <- rxode2::rxSolve(
  object     = mod,
  events     = events,
  keep       = c("WT", "regimen"),
  returnType = "data.frame"
) |>
  dplyr::filter(time >= 0)

For deterministic typical-value replication (random effects zeroed), use rxode2::zeroRe():

sim_typical <- rxode2::rxSolve(
  object     = rxode2::zeroRe(mod),
  events     = events,
  keep       = c("WT", "regimen"),
  returnType = "data.frame"
) |>
  dplyr::filter(time >= 0)
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc'
#> Warning: multi-subject simulation without without 'omega'

Replicate published profiles

Single-dose concentration vs time (typical values)

Wang 2012 does not publish a concentration-vs-time plot for an isolated single dose, but the final-model typical values predict a terminal half-life of 8.06 hours (Discussion paragraph 1 reports 8.13 h). The chunk below traces the typical-value concentration over 48 hours after a single 25 mg/kg dose across the cohort weight distribution.

sd_typical <- sim_typical |> dplyr::filter(regimen == "25 mg/kg single oral")

ggplot(sd_typical, aes(time, Cc, group = id, colour = WT)) +
  geom_line(alpha = 0.4, linewidth = 0.3) +
  scale_y_log10() +
  scale_colour_viridis_c(name = "WT (kg)") +
  labs(x = "Time after dose (hours)",
       y = "Serum LEV (mg/L, log scale)",
       title = "Single 25 mg/kg oral dose -- typical-value profile",
       caption = "Random effects zeroed; weight sampled from the Wang 2012 cohort distribution. Heavier subjects have higher CL/F via (WT/25)^0.567 and therefore lower exposures.")
#> Warning in scale_y_log10(): log-10 transformation introduced infinite values.

Steady-state trough vs published Table 5

Wang 2012 Table 5 reports steady-state pre-dose (C_12h) concentrations for three dose levels in the “Our study” column: 11.25 +/- 3.10 mg/L at 10 mg/kg BID, 17.5 +/- 2.63 mg/L at 20 mg/kg BID, and 31.25 +/- 3.8 mg/L at 30 mg/kg BID. The chunk below renders the simulated last- interval trough distribution under each regimen.

ss_trough <- sim |>
  dplyr::filter(regimen %in% c("10 mg/kg BID", "20 mg/kg BID", "30 mg/kg BID"),
                time == 156)

published_troughs <- tibble::tibble(
  regimen        = c("10 mg/kg BID", "20 mg/kg BID", "30 mg/kg BID"),
  published_mean = c(11.25, 17.50, 31.25),
  published_sd   = c( 3.10,  2.63,  3.80)
)

ggplot(ss_trough, aes(Cc)) +
  geom_histogram(bins = 25, fill = "grey75", colour = "white") +
  geom_vline(data = published_troughs, aes(xintercept = published_mean),
             colour = "tomato", linetype = "dashed", linewidth = 0.6) +
  geom_vline(data = published_troughs,
             aes(xintercept = published_mean - published_sd),
             colour = "tomato", linetype = "dotted", linewidth = 0.4) +
  geom_vline(data = published_troughs,
             aes(xintercept = published_mean + published_sd),
             colour = "tomato", linetype = "dotted", linewidth = 0.4) +
  facet_wrap(~ regimen, ncol = 1, scales = "free_y") +
  labs(x = "Simulated C_12h (mg/L)",
       y = "Number of virtual subjects",
       title = "Steady-state trough distribution after q12h dosing for 7 days",
       caption = "Dashed red line = Wang 2012 Table 5 'Our study' published mean; dotted lines = +/- 1 SD.")

PKNCA validation

PKNCA is run on the single-dose typical-value simulation, with the regimen label as the treatment grouping variable. Cmax, Tmax, AUCinf and half-life are computed and compared against Wang 2012’s reported half-life.

sd_nca_conc <- sim_typical |>
  dplyr::filter(regimen == "25 mg/kg single oral", !is.na(Cc), time > 0) |>
  dplyr::select(id, time, Cc, regimen, WT)

sd_nca_dose <- events_sd |>
  dplyr::filter(evid == 1) |>
  dplyr::select(id, time, amt, regimen)

conc_obj <- PKNCA::PKNCAconc(
  sd_nca_conc, Cc ~ time | regimen + id,
  concu = "mg/L", timeu = "hr"
)
dose_obj <- PKNCA::PKNCAdose(
  sd_nca_dose, amt ~ time | regimen + id,
  doseu = "mg"
)

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

nca <- PKNCA::pk.nca(
  PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals)
)
#> Warning: Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
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#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
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nca_summary <- summary(nca)
knitr::kable(
  nca_summary,
  caption = paste("Single-dose NCA after 25 mg/kg oral dose,",
                  "typical-value simulation across the Wang 2012 cohort",
                  "weight distribution.")
)
Single-dose NCA after 25 mg/kg oral dose, typical-value simulation across the Wang 2012 cohort weight distribution.
Interval Start Interval End regimen N Cmax (mg/L) Tmax (hr) Clast (mg/L) Half-life (hr) λz\lambda_z (1/hr) AUCinf,obs (hr*mg/L) AUCinf,pred (hr*mg/L)
0 Inf 25 mg/kg single oral 200 40.7 [42.6] 2.00 [1.50, 2.00] 0.857 [61.1] 8.67 [2.20] 0.0824 [25.3] NC NC

Comparison against the published half-life

Wang 2012 Discussion paragraph 1 reports a terminal half-life of 8.13 hours. The chunk below extracts the simulated half-life and compares it to the published value.

hl_sim <- as.data.frame(nca$result) |>
  dplyr::filter(PPTESTCD == "half.life") |>
  dplyr::summarise(
    median_hl = median(PPORRES, na.rm = TRUE),
    q05_hl    = stats::quantile(PPORRES, 0.05, na.rm = TRUE),
    q95_hl    = stats::quantile(PPORRES, 0.95, na.rm = TRUE)
  )

comparison <- tibble::tibble(
  metric          = "Terminal half-life (hours)",
  published       = 8.13,
  simulated_med   = hl_sim$median_hl,
  simulated_q05   = hl_sim$q05_hl,
  simulated_q95   = hl_sim$q95_hl,
  pct_diff_median = round(100 * (hl_sim$median_hl / 8.13 - 1), 1)
)

knitr::kable(
  comparison,
  digits  = 2,
  caption = paste("Simulated half-life vs Wang 2012 Discussion paragraph 1",
                  "reported value. Per-individual half-life varies with",
                  "WT because CL/F scales as (WT/25)^0.567 while V/F is",
                  "weight-independent.")
)
Simulated half-life vs Wang 2012 Discussion paragraph 1 reported value. Per-individual half-life varies with WT because CL/F scales as (WT/25)^0.567 while V/F is weight-independent.
metric published simulated_med simulated_q05 simulated_q95 pct_diff_median
Terminal half-life (hours) 8.13 8.43 5.66 12.39 3.7

Comparison against published steady-state troughs

The simulated median C_12h trough for each regimen is tabulated alongside the Wang 2012 Table 5 “Our study” values.

trough_comparison <- ss_trough |>
  dplyr::group_by(regimen) |>
  dplyr::summarise(
    sim_median = stats::median(Cc),
    sim_q05    = stats::quantile(Cc, 0.05),
    sim_q95    = stats::quantile(Cc, 0.95),
    .groups    = "drop"
  ) |>
  dplyr::left_join(published_troughs, by = "regimen") |>
  dplyr::mutate(
    pct_diff_median = round(100 * (sim_median / published_mean - 1), 1)
  ) |>
  dplyr::select(regimen, published_mean, published_sd,
                sim_median, sim_q05, sim_q95, pct_diff_median)

knitr::kable(
  trough_comparison,
  digits  = 2,
  caption = paste("Simulated steady-state C_12h trough vs Wang 2012 Table 5",
                  "'Our study' column. The 30 mg/kg BID trough is",
                  "approximately three times the 10 mg/kg trough,",
                  "consistent with linear kinetics.")
)
Simulated steady-state C_12h trough vs Wang 2012 Table 5 ‘Our study’ column. The 30 mg/kg BID trough is approximately three times the 10 mg/kg trough, consistent with linear kinetics.
regimen published_mean published_sd sim_median sim_q05 sim_q95 pct_diff_median
10 mg/kg BID 11.25 3.10 11.20 2.98 33.26 -0.4
20 mg/kg BID 17.50 2.63 24.20 6.26 57.46 38.3
30 mg/kg BID 31.25 3.80 35.19 9.40 92.90 12.6

Assumptions and deviations

  • Final-model equation vs Table 4 estimate (exponent typo). The paper’s narrative on page 848 reports the final-model CL/F equation with weight exponent 0.563: CL/F = 1.04 * (WEIG/25)^0.563. Table 4 reports the formal estimate as 0.567 (RSE 6.7%, 95% CI 0.489-0.637). The packaged model uses 0.567 as the formal point estimate; the in-text 0.563 appears to be a rounding or typo of the same quantity and is documented in the model file comment so a downstream user is not surprised by the discrepancy.
  • Residual-error magnitude is unusually small. Wang 2012 writes the residual model as additive on the linear concentration scale (E_ij^0 = E_ij + eps_ij, Statistical model paragraph page 847), with Table 4 reporting sigma_E^2 = 0.028. The packaged model encodes this literally as addSd = sqrt(0.028) ~= 0.167 mg/L. On a 4.85 - 116.11 mg/L observed concentration range that is implausibly tight (~0.15 - 3.4% relative magnitude); two possible explanations are (a) the paper meant a proportional error model with sigma^2 = 0.028 interpreted as a CV variance (giving 16.7% CV, which is typical for chromatography assays at this concentration range and matches the LEV popPK references the paper cites) or (b) the structural and IIV terms absorbed most of the residual variability (the V/F shrinkage of 44.9% in Table 4 is consistent with weak identifiability of the residual term). The literal additive form is kept here because that is what the paper’s equation states; users who want to refit on their own data should consider testing a proportional residual model as an alternative.
  • No IIV on Ka. The packaged model has no etalka term because the paper fixed omega_Ka at zero (Discussion “Patient data” paragraph page 848). Simulations therefore use the typical Ka = 1.56 /h for every individual.
  • No covariate effect on V/F or Ka. The covariate-screening table (Table 2) shows that age, weight, dose, sex, and concomitant AED use were tested against CL/F, V/F, and Ka, but only weight on CL/F reached the pre-specified significance threshold (delta-OFV < -7.88). These screened-but-not-retained covariates are documented in the model file’s vignette text rather than in covariateData – adding them as covariateData entries would trigger a “declared but not referenced” convention warning.
  • Cohort weight distribution. The simulation samples body weight log-normally with mean 25.17 kg and clipped to 5 - 70 kg (Wang 2012 Table 1). The published cohort weight SD is not reported beyond the mean and range, so a working SD of 12 kg was chosen to span the range without long tails; the typical individual at the median weight 25 kg still recovers the paper’s published typical-value CL/F (1.04 L/h) exactly.
  • No race / ethnicity heterogeneity. All 311 subjects were Chinese pediatric epilepsy patients at Peking University First Hospital. The Discussion observes that the typical CL/F in this Chinese pediatric cohort (0.69 mL/min/kg) is approximately 50% lower than that of Western pediatric cohorts (1.21 - 1.46 mL/min/kg, Toublanc 2008 and Chhun 2009), but this between-cohort gap is reported descriptively and is not modelled as a covariate. The packaged model therefore applies only to Chinese pediatric populations or to ratiometric comparisons against the published typical individual.
  • No upstream PK dependency. Wang 2012 did not fix any parameter from a prior publication; all final-model estimates are from the paper’s own NONMEM run on the PPK model group. The cited prior studies (Pigeole 2007, Toublanc 2008, Chhun 2009, Glauser 2007, Merhar 2011, Pellock 2001) appear only in the Discussion as comparison points.
  • Errata. No erratum or corrigendum to Wang 2012 was located on disk for this extraction. A search of PubMed and the Acta Pharmacologica Sinica corrections feed for "Wang 2012" + levetiracetam + Chinese pediatric + erratum returned no hits as of the extraction date (2026-06-03); operators should reconfirm against the journal’s corrections listing if a re-extraction is undertaken.