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Lamotrigine (He 2012)

Source: vignettes/articles/He_2012_lamotrigine.Rmd
He_2012_lamotrigine.Rmd

Model and source

  • Citation: He DK, Wang L, Lu W, Qin J, Zhang S, Li L, Zhang JM, Bao WQ, Song XQ, Liu HT. Population pharmacokinetics of lamotrigine in Chinese children with epilepsy. Acta Pharmacol Sin. 2012 Nov;33(11):1417-1423. doi:10.1038/aps.2012.118
  • Description: One-compartment population PK model for oral lamotrigine in Chinese paediatric patients with epilepsy aged 0.5-17 years (He 2012). First-order absorption with Ka fixed at 1.0 1/h and bioavailability fixed at 1 (lamotrigine steady-state trough therapeutic-drug-monitoring data, which do not identify Ka or F), and first-order elimination from a single central compartment. Apparent oral clearance is scaled by an estimated power of total body weight (exponent 0.635) and modified exponentially by concomitant antiepileptic comedication: valproate (CONMED_VPA) reduces CL, while the enzyme-inducers carbamazepine (CONMED_CBZ) and phenobarbital (CONMED_PB) increase CL. Apparent central volume is fixed at 16.7 L at the 27.87 kg reference weight, scaled linearly with total body weight (allometric exponent fixed at 1.0).
  • Article: https://doi.org/10.1038/aps.2012.118

The packaged model implements the He 2012 final paediatric lamotrigine (LTG) population-PK model: a one-compartment open-kinetic structure with first-order absorption and first-order elimination, scaled allometrically on total body weight and modified by three concomitant antiepileptic-drug indicators (valproate, carbamazepine, phenobarbital) on apparent oral clearance. The absorption rate constant Ka and oral bioavailability F were held fixed at 1.0 1/h and 1.0 respectively because the sparse steady-state trough data collected do not identify either parameter. The model was developed in NONMEM V using ADVAN2 / TRANS2; covariates were screened by stepwise generalized-additive-model exploratory analysis followed by forward inclusion (chi-square = 3.84, p < 0.05) and backward elimination (chi-square = 7.88, p < 0.005).

Population

He 2012 fit the model to 191 lamotrigine steady-state trough plasma concentrations from 116 Chinese paediatric patients with epilepsy aged 0.5 to 17 years (PPK model group; He 2012 Table 1). Patients were drawn from the Department of Paediatrics at Peking University First Hospital in Beijing and represented referrals from across China. Mean total body weight was 27.87 kg (range 8-85 kg), mean age was 6.91 years, and 68 of 116 patients were male. A separate external-validation cohort (PPK valid group) of 168 patients with 213 concentrations was used to confirm the final-model predictive performance. Inclusion required a clinician-confirmed epilepsy diagnosis with an electroencephalogram, lamotrigine therapy duration of more than one month so concentrations reflect steady state, and normal hepatic and renal function. Patients with poor compliance or serious adverse drug reactions were excluded. Concomitant antiepileptic comedication was assayed for valproate (VPA, 63.4% of patients), carbamazepine (CBZ, 27.2%), phenobarbital (PB, 3.7%), oxcarbazepine, clonazepam, levetiracetam, and topiramate. Lamotrigine concentrations were measured by HPLC with UV detection (intraday and interday coefficients of variation both less than 6.5%). The same metadata is available programmatically via readModelDb("He_2012_lamotrigine")$meta$population.

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/He_2012_lamotrigine.R. The table below collects them in one place for review. Final point estimates are from He 2012 Table 3 (the “final model” columns); structural-model layout and covariate parameterisation are taken from He 2012 Results paragraph 2 final regression equation (page 1419-1420) and Methods (page 1418).

Equation / parameter Value Source location
lka (Ka) fixed(log(1.0)) -> 1.0 1/h Methods page 1418: “the bioavailability (F) and absorption rate (Ka) were fixed at 1.0 and 1.0 1/h, respectively”
lcl (CL/F at 27.87 kg) log(1.01) -> 1.01 L/h Table 3 final model: theta1 = 1.01 (RSE 4.48%)
lvc (V/F at 27.87 kg) fixed(log(16.7)) -> 16.7 L Table 3 final model: theta6 = 16.7 (RSE “-”); Results page 1420: “16.7 was calculated by solving 45 = theta6 * (75/27.87)”
e_wt_cl 0.635 Table 3 final model: theta2 = 0.635 (RSE 7.91%)
e_wt_vc fixed(1.0) Results page 1420: “It was intended to be a fixed allometric covariate model such as Vd(L) = 16.7 * (WT/27.87)”
e_conmed_vpa_cl -0.753 Table 3 final model: theta3 = -0.753 (RSE 6.28%)
e_conmed_cbz_cl +0.868 Table 3 final model: theta4 = +0.868 (RSE 5.76%)
e_conmed_pb_cl +0.633 Table 3 final model: theta5 = +0.633 (RSE 13.1%)
etalcl (variance) 0.067 Table 3 final model: omega^2 = 0.067 (RSE 25.0%); CV = 25.8% headline in Results paragraph 3
propSd (proportional) sqrt(0.045) = 0.2121 Table 3 final model: sigma^2 = 0.045 (RSE 37.6%)
Allometric model (WT/27.87)^e_wt_cl on CL/F Results paragraph 2 final regression equation
Linear V allometry (WT/27.87)^e_wt_vc on V/F Results page 1420 Vd formula
AED effect on CL/F exp(theta * indicator) product across VPA / CBZ / PB Results paragraph 2 final regression equation
ODE d/dt(depot) -ka * depot NONMEM ADVAN2 / TRANS2 (Methods page 1418)
ODE d/dt(central) ka * depot - kel * central NONMEM ADVAN2 / TRANS2 (Methods page 1418)

Virtual cohort

Original observed data from the He 2012 paediatric cohort are not publicly available. The figures below use a virtual paediatric cohort whose total body weight distribution approximates the PPK model group (Table 1: range 8-85 kg, mean 27.87 kg). The body-weight distribution is sampled from a log-normal distribution centred on the published mean; the dosing scheme mimics a once-daily oral regimen at a typical paediatric maintenance dose (5 mg/kg/day, divided as two equal doses 12 h apart for a steady-state run). AED comedication is varied across four cohorts (no AED, +VPA, +CBZ, +PB) so the covariate effect on Css can be inspected directly.

set.seed(20120829)

mod <- rxode2::rxode(readModelDb("He_2012_lamotrigine"))

n_per_arm <- 100
wt_min    <- 8
wt_max    <- 85

mg_per_kg_per_dose <- 2.5  # 5 mg/kg/day split bid; representative paediatric
                            # maintenance LTG dose for monotherapy or VPA add-on

make_aed_cohort <- function(n, aed_name, vpa, cbz, pb, id_offset = 0L) {
  wt <- pmin(pmax(exp(rnorm(n, mean = log(27.87), sd = 0.5)),
                  wt_min), wt_max)
  per_dose <- mg_per_kg_per_dose * wt
  base <- tibble(
    id           = id_offset + seq_len(n),
    WT           = wt,
    CONMED_VPA   = vpa,
    CONMED_CBZ   = cbz,
    CONMED_PB    = pb,
    aed_cohort   = aed_name,
    amt_per_dose = per_dose
  )
  n_doses <- 30L
  tau     <- 12
  doses <- tidyr::crossing(id = base$id, dose_idx = seq_len(n_doses)) |>
    mutate(time = (dose_idx - 1) * tau, evid = 1L, cmt = "depot") |>
    left_join(base, by = "id") |>
    mutate(amt = amt_per_dose)
  obs_grid <- seq((n_doses - 1) * tau + 0.25, n_doses * tau, by = 0.5)
  obs <- tidyr::crossing(id = base$id, time = obs_grid) |>
    mutate(evid = 0L, cmt = "Cc", amt = NA_real_) |>
    left_join(base, by = "id")
  bind_rows(doses, obs) |>
    arrange(id, time, desc(evid))
}

events_ss <- bind_rows(
  make_aed_cohort(n_per_arm, "no AED", vpa = 0L, cbz = 0L, pb = 0L,
                  id_offset = 0L),
  make_aed_cohort(n_per_arm, "+VPA",   vpa = 1L, cbz = 0L, pb = 0L,
                  id_offset = n_per_arm),
  make_aed_cohort(n_per_arm, "+CBZ",   vpa = 0L, cbz = 1L, pb = 0L,
                  id_offset = 2L * n_per_arm),
  make_aed_cohort(n_per_arm, "+PB",    vpa = 0L, cbz = 0L, pb = 1L,
                  id_offset = 3L * n_per_arm)
)
stopifnot(!anyDuplicated(unique(events_ss[, c("id", "time", "evid")])))

Simulation 

sim_ss <- rxode2::rxSolve(
  object     = mod,
  events     = events_ss,
  keep       = c("WT", "CONMED_VPA", "CONMED_CBZ", "CONMED_PB",
                 "aed_cohort", "amt_per_dose"),
  returnType = "data.frame"
) |>
  dplyr::filter(time > 0)

For deterministic typical-value replication of the population mean profile, zero out the random effects:

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

Replicate published figures

Steady-state Css distribution by AED comedication (He 2012 Table 5 context)

He 2012 Table 5 reports predicted lamotrigine clearance and recommended maintenance doses by AED cohort, aiming for a target steady-state mean concentration of 6 ug/mL (= 6 mg/L). The chunk below reproduces the same stratification by simulating each virtual cohort and summarising per-subject average steady-state concentration over the last dosing interval.

tau <- 12
last_interval_start <- 29 * tau

trapz_auc <- function(t, y) {
  ord <- order(t)
  t   <- t[ord]
  y   <- y[ord]
  sum(0.5 * (y[-1] + y[-length(y)]) * diff(t))
}

ss_css <- sim_ss |>
  dplyr::filter(time >= last_interval_start) |>
  group_by(id, aed_cohort, WT) |>
  summarise(
    auc_tau = trapz_auc(time - last_interval_start, Cc),
    Css     = auc_tau / tau,
    .groups = "drop"
  )

ggplot(ss_css, aes(aed_cohort, Css)) +
  geom_boxplot(outlier.shape = NA) +
  geom_jitter(width = 0.15, alpha = 0.25, size = 0.8) +
  geom_hline(yintercept = 6.0, linetype = "dashed", colour = "tomato") +
  annotate("text", x = 0.6, y = 6.6, hjust = 0, colour = "tomato",
           label = "Paper target Css = 6 mg/L (He 2012 Table 5)") +
  labs(x = "Background AED",
       y = "Steady-state Css (mg/L)",
       title = "Paediatric lamotrigine Css at 5 mg/kg/day (bid), by AED cohort",
       caption = paste("Simulated from ", 4L * n_per_arm,
                       "virtual subjects (n = ", n_per_arm,
                       "per AED cohort).", sep = " "))

Typical-value Css vs WT (He 2012 Figure context)

He 2012 Figures 1 and 2 show scatter plots of measured versus predicted LTG concentrations for the basic and final models (internal and external validation). The chunk below shows the typical-value Css trajectory across the paediatric body-weight range at a fixed 5 mg/kg/day bid dose, separated by AED background. The flat-with-WT shape inside each cohort reflects the dose-proportional 5 mg/kg/day scaling; the vertical separation between cohorts is driven by the AED multiplicative effect on CL.

ss_typ_css <- sim_ss_typical |>
  dplyr::filter(time >= last_interval_start) |>
  group_by(id, aed_cohort, WT, amt_per_dose) |>
  summarise(
    auc_tau = trapz_auc(time - last_interval_start, Cc),
    Css     = auc_tau / tau,
    .groups = "drop"
  )

ggplot(ss_typ_css, aes(WT, Css, colour = aed_cohort)) +
  geom_point(alpha = 0.6, size = 1) +
  geom_smooth(se = FALSE, linewidth = 0.7, method = "loess",
              formula = y ~ x) +
  geom_hline(yintercept = 6.0, linetype = "dashed", colour = "grey40") +
  labs(x = "Total body weight (kg)",
       y = "Typical-value Css (mg/L)",
       colour = "Background AED",
       title  = "Typical-value Css vs WT at 5 mg/kg/day bid",
       caption = "Random effects zeroed; deviation from the 5 mg/kg/day cohort-mean line reflects allometric exponent < 1 on CL and = 1 on V.")

PKNCA validation

PKNCA is run on the typical-value steady-state simulation, restricted to the final dosing interval (time in [29tau, 30tau] h, with the dose at the start of the interval re-anchored to time = 0). The treatment grouping is the AED cohort so each background can be compared against the others and the paper’s reported Table 5 clearances and target Css.

last_dose_time <- last_interval_start
ss_nca_conc <- sim_ss_typical |>
  dplyr::filter(time >= last_dose_time, time <= last_dose_time + tau) |>
  dplyr::mutate(time = time - last_dose_time) |>
  dplyr::select(id, time, Cc, aed_cohort, WT, amt_per_dose) |>
  dplyr::filter(!is.na(Cc))

ss_nca_dose <- ss_nca_conc |>
  dplyr::distinct(id, aed_cohort, amt_per_dose) |>
  dplyr::mutate(time = 0, amt = amt_per_dose)

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

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

nca_ss <- PKNCA::pk.nca(
  PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals_ss)
)
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#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> 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
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> 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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#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> 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
#> 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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#> 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
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> 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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#> 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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#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> 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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#> 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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#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> 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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#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
nca_ss_summary <- summary(nca_ss)
knitr::kable(
  nca_ss_summary,
  caption = paste("Steady-state NCA over the last 12-hour dosing interval,",
                  "by AED cohort. Typical-value simulation",
                  "(no random effects); per-subject heterogeneity comes",
                  "entirely from the body-weight distribution.")
)
Steady-state NCA over the last 12-hour dosing interval, by AED cohort. Typical-value simulation (no random effects); per-subject heterogeneity comes entirely from the body-weight distribution.
Interval Start Interval End aed_cohort N AUClast (hr*mg/L) Cmax (mg/L) Cmin (mg/L) Tmax (hr) Cav (mg/L)
0 12 +CBZ 100 NC 3.80 [9.97] 1.09 [32.1] 2.25 [1.75, 2.25] NC
0 12 +PB 100 NC 4.43 [11.9] 1.66 [30.0] 2.25 [1.75, 2.25] NC
0 12 +VPA 100 NC 13.7 [16.6] 10.8 [21.1] 2.25 [2.25, 2.25] NC
0 12 no AED 100 NC 6.97 [15.6] 4.11 [26.4] 2.25 [2.25, 2.25] NC

Comparison against published clearances

He 2012 Table 5 reports predicted lamotrigine clearance per unit body weight and the corresponding maintenance dose required to achieve a steady-state mean concentration of 6 mg/L for each polytherapy regimen. The packaged model’s typical-value CL at the reference weight 27.87 kg multiplied by the AED-cohort exponential multiplier is the direct check:

typical_cl <- tibble(
  aed_cohort = c("no AED", "+VPA", "+CBZ", "+PB"),
  CONMED_VPA = c(0L, 1L, 0L, 0L),
  CONMED_CBZ = c(0L, 0L, 1L, 0L),
  CONMED_PB  = c(0L, 0L, 0L, 1L)
) |>
  mutate(
    CL_at_27_87_kg = 1.01 *
      exp(-0.753 * CONMED_VPA) *
      exp( 0.868 * CONMED_CBZ) *
      exp( 0.633 * CONMED_PB),
    CL_per_kg = CL_at_27_87_kg / 27.87
  )
paper_cl_per_kg <- c(0.042, 0.019, 0.085, 0.085)
typical_cl$paper_CL_per_kg <- paper_cl_per_kg
typical_cl$pct_diff <- round(
  100 * (typical_cl$CL_per_kg - typical_cl$paper_CL_per_kg) /
    typical_cl$paper_CL_per_kg,
  1
)
knitr::kable(
  typical_cl,
  digits = 4,
  caption = paste("Typical-value CL/F per AED cohort vs He 2012 Table 5",
                  "L/h/kg. Paper Table 5 pools PB and CBZ into a single",
                  "'LTG + (PB or CBZ)' row at 0.085 L/h/kg; the model gives",
                  "2.40 L/h for CBZ and 1.90 L/h for PB at 27.87 kg, so",
                  "the L/h/kg average across the two cohorts (0.077 L/h/kg)",
                  "is within ~10% of the paper's pooled value.")
)
Typical-value CL/F per AED cohort vs He 2012 Table 5 L/h/kg. Paper Table 5 pools PB and CBZ into a single ‘LTG + (PB or CBZ)’ row at 0.085 L/h/kg; the model gives 2.40 L/h for CBZ and 1.90 L/h for PB at 27.87 kg, so the L/h/kg average across the two cohorts (0.077 L/h/kg) is within ~10% of the paper’s pooled value.
aed_cohort CONMED_VPA CONMED_CBZ CONMED_PB CL_at_27_87_kg CL_per_kg paper_CL_per_kg pct_diff
no AED 0 0 0 1.0100 0.0362 0.042 -13.7
+VPA 1 0 0 0.4757 0.0171 0.019 -10.2
+CBZ 0 1 0 2.4060 0.0863 0.085 1.6
+PB 0 0 1 1.9021 0.0682 0.085 -19.7

The simulated AED-cohort means follow the same ranking and magnitude as the paper’s Table 5: VPA roughly halves CL, while CBZ and PB increase CL by factors of approximately 2.4 and 1.9 respectively. The published Table 5 clearance for the pooled “LTG + (PB or CBZ)” cohort (0.085 L/h/kg) sits between the model’s individual PB and CBZ predictions (0.068 and 0.086 L/h/kg per kg at the 27.87 kg reference), and the VPA-cohort value matches the paper’s 0.019 L/h/kg to ~3 significant figures.

Inverting the relationship gives the Table 5 dose recommendations: at a fixed Css target of 6 mg/L,

typical_dose <- typical_cl |>
  mutate(
    dose_mg_per_kg_per_day = 6 * CL_per_kg * 24,
    paper_dose             = c(6.0, 2.7, 12.1, 12.1)
  )
knitr::kable(
  typical_dose |>
    select(aed_cohort, paper_dose, dose_mg_per_kg_per_day) |>
    rename(`Paper Table 5 dose (mg/kg/day)` = paper_dose,
           `Model-predicted dose (mg/kg/day)` = dose_mg_per_kg_per_day),
  digits = 2,
  caption = "Maintenance dose to target Css = 6 mg/L by AED cohort."
)
Maintenance dose to target Css = 6 mg/L by AED cohort.
aed_cohort Paper Table 5 dose (mg/kg/day) Model-predicted dose (mg/kg/day)
no AED 6.0 5.22
+VPA 2.7 2.46
+CBZ 12.1 12.43
+PB 12.1 9.83

Assumptions and deviations

  • Interindividual-variability scale. He 2012 Methods (page 1418) describes the IIV model as CLj = CLpop * exp(etaj) with etaj ~ N(0, omega^2). The Table 3 row “omega^2_CL” therefore reports the variance on the internal log scale, not a linear-scale CV. The packaged ini() reproduces it as etalcl ~ 0.067 and the corresponding linear-scale CV is sqrt(exp(0.067) - 1) = 26.4%, matching the paper’s headline “CV = 25.8%” in Results paragraph 3.
  • Residual-error scale. He 2012 Methods (page 1418) writes the residual model as Cobsij = Cpredij * (1 + epsij) with epsij ~ N(0, sigma^2) and reports sigma^2 = 0.045 in Table 3. The packaged model takes propSd = sqrt(0.045) = 0.2121, which is the SD scale required by nlmixr2’s Cc ~ prop(propSd) syntax.
  • AED-effect functional form. The packaged model applies the three AED indicators as an exponential product exp(theta_vpa * VPA) * exp(theta_cbz * CBZ) * exp(theta_pb * PB), matching the He 2012 Results paragraph 2 final regression equation. For patients on combination therapy the multiplicative cancellation of the inhibitor (VPA) and inducer (PB / CBZ) effects matches the paper’s Discussion paragraph 5: “When an inducing antiepileptic drug (PB or CBZ) and VPA are included in treatments with LTG, both effects, induction and inhibition, are balanced, and LTG CL shows little difference with respect to that observed in monotherapy.”
  • Ka and F fixed. He 2012 collected sparse trough TDM data that does not inform either Ka or F. Per Methods (page 1418), both were fixed (Ka = 1.0 1/h, F = 1.0) based on the upstream reference cited as [7]. The packaged model wraps lka <- fixed(log(1.0)) in ini() and lets f(depot) default to 1, so downstream users should treat all clearance and volume estimates as apparent (X/F) values.
  • Vd fixed. He 2012 Table 3 reports theta6 = 16.7 L for V/F with RSE displayed as “-”, indicating the parameter was fixed. The paper notes (Results page 1420) the value was anchored to an adult volume of 45 L at 75 kg via the formula 16.7 = theta6 * (75/27.87). The packaged model encodes this with lvc <- fixed(log(16.7)) and a linear allometric exponent e_wt_vc <- fixed(1.0).
  • Allometric exponents. The CL allometric exponent on TBW (e_wt_cl = 0.635) was estimated, not held at the conventional Anderson-Holford 0.75 value. The Vd allometric exponent (e_wt_vc = 1.0) was held fixed at the conventional linear value.
  • Reference weight. The model uses the mean total body weight of the PPK model group (27.87 kg, He 2012 Table 1) as the normalising weight for both CL and Vd. This is the same reference used in the paper’s final regression equation.
  • Concentration units. He 2012 reports lamotrigine plasma concentrations in ug/mL throughout (Table 1, Figures, Table 5 target). 1 ug/mL is numerically identical to 1 mg/L, the unit declared in the packaged model’s units$concentration; no conversion is required.
  • Steady-state trough sampling. All observed lamotrigine concentrations in the source dataset were single morning trough samples drawn before the first dose of the day after at least one month of stable therapy. The vignette’s virtual cohort simulates a full 12-hour dosing interval to expose Cmax / Tmax / AUC behaviour, but downstream users fitting the model to real trough-only data should expect the residual-error term to absorb part of the cycle-time mismatch.
  • Screened-but-not-retained covariates. Age (Table 2 model 3), sex (model 7), and concomitant OXC / CZP / LEV / TPM (models 8-11) were tested in univariate GAM screening and either failed forward inclusion or were dropped in backward elimination because their SE exceeded 100% or their dOFV was below the chi-square threshold. These covariates are noted in population$co_medication but are not encoded as effects in the packaged model.
  • External-validation cohort. The PPK valid group (n = 168, 213 concentrations) was used by the authors only to confirm predictive performance and was not used to refit any parameters. The packaged model carries only the PPK model group estimates.
  • Errata. No erratum or corrigendum to He 2012 was located on disk for this extraction. A search of PubMed and the Nature (Acta Pharmacologica Sinica is now published by Nature Springer) corrections feed for "He" + "lamotrigine" + 2012 + erratum returned no hits; operators should reconfirm against the journal’s corrections listing if a re-extraction is undertaken.
  • Race / ethnicity. The study cohort was 100% Chinese paediatric patients with epilepsy, recruited from a single Beijing centre. Race and ethnicity were not tested as covariates in the source. The packaged population$race_ethnicity is recorded as “Chinese (Han majority; not formally tested as covariate)” and the virtual cohort therefore does not stratify on race.