Efavirenz (Robarge 2017) • nlmixr2lib

Model and source

Citation: Robarge JD, Metzger IF, Lu J, Thong N, Skaar TC, Desta Z, Bies RR (2017). Population pharmacokinetic modeling to estimate the contributions of genetic and nongenetic factors to efavirenz disposition. Antimicrob Agents Chemother 61(1):e01813-16.
Article: https://doi.org/10.1128/AAC.01813-16
ClinicalTrials.gov: https://clinicaltrials.gov/ct2/show/NCT00668395

Two-compartment population PK model fit to 1,132 plasma efavirenz concentrations from 73 HIV-seronegative adult volunteers (1 of 73 had a single 145 h sample, 3 of 73 withdrew early, the rest contributed 14-16 samples) after a single 600 mg oral dose. Absorption is parallel zero-order (fraction F2 = 0.586 of the dose, lag t_lag2 = 0.445 h, duration D2 = 0.675 h) and first-order (fraction F1 = 0.414, lag t_lag1 = 1.97 h, rate k_a = 0.504 1/h). Disposition parameters and their reduced-CYP2B6-metabolizer multiplicative effects on apparent oral clearance were re-estimated alongside fixed allometric exponents of 3/4 (CL/F vs FFM, reference 56 kg) and 1 (V_p/F vs FM, reference 19 kg).

Population

Median (range) baseline characteristics from Robarge 2017 Table 1: age 24 years (18-50), weight 72.7 kg (53.0-103.6), height 1.76 m (1.55-1.98), BMI 24.0 kg/m^2 (17.8-32.2), FFM 56.4 kg (35.6-75.1), FM 18.8 kg (6.3-42.7). Sex was 63% male (46/73). Race distribution: Caucasian 71.2% (52/73), African-American 21.9% (16/73), Asian 4.1% (3/73), Indian 1.4% (1/73), American Indian 1.4% (1/73). 9 of 73 subjects (12%) were clinically obese (BMI > 30 kg/m^2); no morbidly obese subjects (BMI > 40) were enrolled.

CYP2B6 metabolizer status distribution is described in Robarge 2017 Table S1 in the supplemental material (which is not reproduced here). The simulated cohort below uses an approximate 60% / 30% / 10% split across normal / intermediate / slow metabolizers, chosen to approximate typical North American Caucasian + African-American cohorts; see the “Assumptions and deviations” section below.

The same demographics are available programmatically via the model’s metadata (rxode2::rxode(readModelDb("Robarge_2017_efavirenz"))$population).

Source trace

Every entry below is also recorded as an in-file comment next to the corresponding ini() line in inst/modeldb/specificDrugs/Robarge_2017_efavirenz.R.

Equation / parameter	Value	Source location
Two-compartment + parallel zero / first-order absorption (ODEs)	n/a	Robarge 2017 Results “Population PK model” paragraphs 1-2
F1 (first-order absorption fraction; FIXED)	0.414	Robarge 2017 Table 2
F2 = 1 - F1 (zero-order absorption fraction; FIXED)	0.586	Robarge 2017 Table 2
t_lag1 (FIXED, h)	1.97	Robarge 2017 Table 2
k_a (FIXED, 1/h)	0.504	Robarge 2017 Table 2
t_lag2 (FIXED, h)	0.445	Robarge 2017 Table 2
D2 duration of zero-order (FIXED, h)	0.675	Robarge 2017 Table 2
CL/F (typical at FFM = 56 kg, CYP2B6 normal; L/h)	7.52	Robarge 2017 Table 2
V_c/F (L)	125	Robarge 2017 Table 2
V_p/F (typical at FM = 19 kg; L)	374	Robarge 2017 Table 2
Q/F (L/h)	32.3	Robarge 2017 Table 2
Allometric exponent on (FFM/56) for CL/F (FIXED)	3/4	Robarge 2017 Table 2 footnote a; Results “Covariate model development” paragraph 1
Allometric exponent on (FM/19) for V_p/F (FIXED)	1	Robarge 2017 Table 2 footnote a; Results “Covariate model development” paragraph 2
CYP2B6 intermediate-metabolizer factor on CL/F	0.752	Robarge 2017 Table 2
CYP2B6 slow-metabolizer factor on CL/F	0.490	Robarge 2017 Table 2
BSV SD on log-CL/F	0.257	Robarge 2017 Table 2
BSV SD on log-V_c/F	0.318	Robarge 2017 Table 2
BSV SD on log-V_p/F	0.374	Robarge 2017 Table 2
BSV SD on log-Q/F	0.671	Robarge 2017 Table 2
BSV SD on log-t_lag1	0.271	Robarge 2017 Table 2
BSV SD on log-k_a	0.965	Robarge 2017 Table 2
BSV SD on log-t_lag2	0.473	Robarge 2017 Table 2
BSV SD on log-D2	0.703	Robarge 2017 Table 2
Correlation rho(CL/F, V_p/F)	0.196	Robarge 2017 Table 2 footnote c
Correlation rho(Q/F, V_p/F)	0.849	Robarge 2017 Table 2 footnote c
Correlation rho(CL/F, Q/F) (FIXED at 0)	0	Robarge 2017 Table 2 (entry absent from the correlation block)
Proportional residual variance sigma^2_prop	0.016	Robarge 2017 Table 2
Additive residual variance sigma^2_add (nmol/L)^2	4,270	Robarge 2017 Table 2

Virtual cohort

Original observed efavirenz concentrations from the Robarge 2017 trial (ClinicalTrials.gov NCT00668395) are not publicly redistributable here. The simulation below uses a virtual cohort whose covariate distributions approximate the published trial demographics (Robarge 2017 Table 1).

set.seed(20171101L)

# Janmahasatian (2005) FFM formula -- the same closed-form expression
# Robarge 2017 used to derive FFM from total body weight (TBW), height,
# and sex; FM is the residual mass (FM = TBW - FFM). Source:
# Janmahasatian S et al. Clin Pharmacokinet 2005;44(10):1051-1065.
janmahasatian_ffm <- function(tbw_kg, height_m, sex_f) {
  bmi <- tbw_kg / (height_m^2)
  ifelse(
    sex_f == 0,
    # Male:   FFM = 9270 * WT / (6680 + 216 * BMI)
    9270 * tbw_kg / (6680 + 216 * bmi),
    # Female: FFM = 9270 * WT / (8780 + 244 * BMI)
    9270 * tbw_kg / (8780 + 244 * bmi)
  )
}

make_subjects <- function(n_per_group, cyp2b6_label, seed_offset = 0L) {
  withr::with_seed(20171101L + seed_offset, {
    # Sample sex first -- 63% male per Table 1.
    sex_f <- rbinom(n_per_group, 1L, prob = 27 / 73)
    # Sample WT and HT from approximately normal marginals matching Table 1
    # medians and ranges.
    tbw_kg <- pmin(pmax(rnorm(n_per_group, mean = 74.0, sd = 13.4), 53.0), 103.6)
    height_m <- pmin(pmax(rnorm(n_per_group, mean = 1.75, sd = 0.09), 1.55), 1.98)

    ffm_kg <- janmahasatian_ffm(tbw_kg, height_m, sex_f)
    fm_kg  <- pmax(tbw_kg - ffm_kg, 0.5)

    tibble(
      sub        = seq_len(n_per_group),
      sex_f      = sex_f,
      WT         = tbw_kg,
      HT         = height_m,
      FFM        = ffm_kg,
      FM         = fm_kg,
      cyp2b6     = cyp2b6_label,
      CYP2B6_IM  = as.integer(cyp2b6_label == "Intermediate"),
      CYP2B6_SM  = as.integer(cyp2b6_label == "Slow")
    )
  })
}

# CYP2B6 distribution: roughly 60% normal / 30% intermediate / 10% slow,
# chosen to span the three multiplier groups; see Assumptions section.
n_normal  <- 120L
n_interm  <- 60L
n_slow    <- 20L

subjects <- bind_rows(
  make_subjects(n_normal, "Normal",       seed_offset = 0L)  |> mutate(id = sub),
  make_subjects(n_interm, "Intermediate", seed_offset = 1L)  |> mutate(id = n_normal + sub),
  make_subjects(n_slow,   "Slow",         seed_offset = 2L)  |> mutate(id = n_normal + n_interm + sub)
) |>
  select(-sub)

dose_mg     <- 600
obs_times   <- c(0, 0.25, 0.5, 0.75, 1, 1.5, 2, 2.5, 3, 4, 6, 8, 10, 12, 16, 24,
                 36, 48, 72, 96, 120, 144, 192, 240, 288, 336)

build_events <- function(subjects) {
  bind_rows(
    # 1. First-order absorption record: dose -> depot, rate = 0 (instantaneous
    #    bolus into the gut compartment, then first-order absorption via k_a).
    subjects |>
      mutate(time = 0, evid = 1L, amt = dose_mg, cmt = "depot", rate = 0) |>
      select(id, time, evid, amt, cmt, rate, WT, FFM, FM, sex_f, cyp2b6, CYP2B6_IM, CYP2B6_SM),
    # 2. Zero-order absorption record: dose -> central, rate = -2 (modeled
    #    duration via dur(central) = D2). f(central) = 1 - F1 picks the
    #    zero-order fraction; first-order f(depot) = F1 picks the rest.
    subjects |>
      mutate(time = 0, evid = 1L, amt = dose_mg, cmt = "central", rate = -2) |>
      select(id, time, evid, amt, cmt, rate, WT, FFM, FM, sex_f, cyp2b6, CYP2B6_IM, CYP2B6_SM),
    # 3. Observation rows.
    crossing(id = subjects$id, time = obs_times) |>
      left_join(subjects |> select(id, WT, FFM, FM, sex_f, cyp2b6, CYP2B6_IM, CYP2B6_SM), by = "id") |>
      mutate(evid = 0L, amt = 0, cmt = "central", rate = 0)
  ) |>
    arrange(id, time, desc(evid))
}

events <- build_events(subjects)

# Multi-cohort guard: ids must be disjoint across the three CYP2B6 groups.
stopifnot(!anyDuplicated(unique(events[events$evid == 1L, c("id", "time", "cmt")])))

Simulation

mod <- readModelDb("Robarge_2017_efavirenz")

sim <- rxode2::rxSolve(
  mod,
  events = events,
  keep   = c("cyp2b6", "FFM", "FM"),
  returnType = "data.frame"
)
#> ℹ parameter labels from comments will be replaced by 'label()'

sim <- sim |>
  filter(time > 0) |>
  mutate(
    Cc_nmolL = Cc * 1e6 / 315.6745  # mg/L -> nmol/L using MW efavirenz = 315.6745 g/mol
  )

For deterministic, typical-value simulation (to match Robarge 2017 Figure 1 typical-value profile), zero out the BSV via rxode2::zeroRe():

mod_typical <- rxode2::zeroRe(mod)
#> ℹ parameter labels from comments will be replaced by 'label()'

# One reference subject per CYP2B6 group at the cohort median FFM / FM.
ref_subjects <- tibble(
  id        = 1:3,
  cyp2b6    = c("Normal", "Intermediate", "Slow"),
  CYP2B6_IM = c(0L, 1L, 0L),
  CYP2B6_SM = c(0L, 0L, 1L),
  WT        = 72.7,
  FFM       = 56.4,
  FM        = 18.8,
  sex_f     = 0L
)
events_ref <- build_events(ref_subjects)

sim_typical <- rxode2::rxSolve(
  mod_typical,
  events = events_ref,
  keep   = c("cyp2b6"),
  returnType = "data.frame"
) |>
  filter(time > 0) |>
  mutate(Cc_nmolL = Cc * 1e6 / 315.6745)
#> ℹ omega/sigma items treated as zero: 'etalq', 'etalvp', 'etalcl', 'etaldur2', 'etaltlag2', 'etaltlag1', 'etalka', 'etalvc'
#> Warning: multi-subject simulation without without 'omega'

Replicate published figures

Figure 2 (visual predictive check by CYP2B6 metabolizer status)

Robarge 2017 Figure 2 shows VPCs of plasma efavirenz concentration vs. time for the three CYP2B6 metabolizer phenotypes. The simulated 5th, 50th, and 95th percentiles below are the analogous quantities; CYP2B6-poor subjects (n = 20) have a wider 5-95% band than the normal / intermediate panels, matching the paper’s commentary that prediction intervals are wider for slow metabolizers given the small 6/6 subgroup.

vpc_data <- sim |>
  mutate(cyp2b6 = factor(cyp2b6, levels = c("Normal", "Intermediate", "Slow"))) |>
  group_by(cyp2b6, time) |>
  summarise(
    Q05 = quantile(Cc_nmolL, 0.05, na.rm = TRUE),
    Q50 = quantile(Cc_nmolL, 0.50, na.rm = TRUE),
    Q95 = quantile(Cc_nmolL, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(vpc_data, aes(time, Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.20) +
  geom_line(linewidth = 0.6) +
  facet_wrap(~ cyp2b6, ncol = 3) +
  scale_y_log10() +
  labs(
    x        = "Time after dose (h)",
    y        = "Plasma efavirenz (nmol/L), log scale",
    title    = "Simulated VPC by CYP2B6 metabolizer status",
    subtitle = "200 virtual subjects (120 normal / 60 intermediate / 20 slow); single 600 mg oral dose",
    caption  = "Replicates Robarge 2017 Figure 2 (5th / 50th / 95th percentiles)."
  )
#> Warning in scale_y_log10(): log-10 transformation introduced infinite values.
#> log-10 transformation introduced infinite values.
#> log-10 transformation introduced infinite values.

Typical-value reference trajectory

Typical-value (no BSV, no residual) profiles by CYP2B6 group at the cohort median FFM = 56.4 kg and FM = 18.8 kg.

ggplot(sim_typical, aes(time, Cc_nmolL, colour = cyp2b6)) +
  geom_line(linewidth = 0.8) +
  scale_y_log10() +
  labs(
    x = "Time after dose (h)",
    y = "Plasma efavirenz (nmol/L), log scale",
    colour = "CYP2B6 status",
    title = "Typical-value efavirenz profile by CYP2B6 metabolizer status",
    subtitle = "Reference subject: FFM = 56.4 kg, FM = 18.8 kg; 600 mg single oral dose"
  )
#> Warning in scale_y_log10(): log-10 transformation introduced infinite values.

PKNCA validation

PKNCA NCA values stratified by CYP2B6 metabolizer status. Concentrations are in nmol/L (converted from the model’s native mg/L) for direct comparability with Robarge 2017 Figure 2.

sim_nca <- sim |>
  filter(!is.na(Cc_nmolL)) |>
  transmute(id, time, Cc = Cc_nmolL, treatment = cyp2b6)

# One dose record per subject (the depot / central pair represents the same
# administered dose split across two absorption routes; PKNCA needs the
# administered amount, not the per-route fraction).
dose_df <- events |>
  filter(evid == 1L, cmt == "depot") |>
  transmute(id, time, amt = amt * 1e6 / 315.6745, treatment = cyp2b6)  # mg -> nmol

conc_obj <- PKNCA::PKNCAconc(
  sim_nca, Cc ~ 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
)

nca_data <- PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals)
nca_res  <- PKNCA::pk.nca(nca_data)
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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
#> 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

nca_long <- as.data.frame(nca_res$result) |>
  filter(PPTESTCD %in% c("cmax", "tmax", "aucinf.obs", "half.life"))

nca_summary <- nca_long |>
  group_by(treatment, PPTESTCD) |>
  summarise(
    median = stats::median(PPORRES, na.rm = TRUE),
    p05    = stats::quantile(PPORRES, 0.05, na.rm = TRUE),
    p95    = stats::quantile(PPORRES, 0.95, na.rm = TRUE),
    .groups = "drop"
  ) |>
  mutate(treatment = factor(treatment, levels = c("Normal", "Intermediate", "Slow"))) |>
  arrange(treatment, PPTESTCD)

knitr::kable(
  nca_summary,
  digits = c(NA, NA, 3, 3, 3),
  caption = "Simulated single-dose PKNCA parameters by CYP2B6 metabolizer status (n=120 / 60 / 20)."
)

Simulated single-dose PKNCA parameters by CYP2B6 metabolizer status (n=120 / 60 / 20).
treatment	PPTESTCD	median	p05	p95
Normal	aucinf.obs	NA	NA	NA
Normal	cmax	7687.751	5088.630	13675.693
Normal	half.life	61.475	26.296	130.771
Normal	tmax	1.750	0.750	4.100
Intermediate	aucinf.obs	NA	NA	NA
Intermediate	cmax	8129.596	4826.081	13235.497
Intermediate	half.life	64.042	35.142	133.536
Intermediate	tmax	2.000	0.750	4.000
Slow	aucinf.obs	NA	NA	NA
Slow	cmax	8654.087	4451.810	13082.744
Slow	half.life	113.056	67.919	172.002
Slow	tmax	1.500	0.750	4.200

Comparison against published expectations

Robarge 2017 reports no tabular NCA summary – model evaluation is by VPC (Figure 2) and goodness-of-fit plots (Figure 3) only. The most rigorous analytical check available is on the typical-value asymptotic AUC, which has the closed-form identity

AUC_inf = Dose / (CL/F)

independent of the absorption model. The simulated single-subject typical- value AUC (computed below with rxode2::zeroRe() so it carries no random effects) should match Dose / (CL/F) to within numerical precision for each metabolizer group. CL/F is Robarge 2017 Table 2 7.52 L/h for normal metabolizers and is scaled by 0.752 and 0.490 for intermediate and slow metabolizers respectively. The simulated cohort median AUC is reported alongside for comparison; the cohort-median value differs from the typical-value AUC because BSV is on the log-scale and so the median of exp(eta_CL) is not the typical CL.

dose_nmol <- 600 / 315.6745 * 1e6  # ~1,900,720 nmol

cl_normal       <- 7.52
cl_intermediate <- cl_normal * 0.752
cl_slow         <- cl_normal * 0.490

# Typical-value AUC computed by trapezoid on the zeroRe deterministic
# simulation extended to 336 h.
auc_typical <- sim_typical |>
  group_by(cyp2b6) |>
  arrange(time) |>
  summarise(
    auc_to_last_nmol_h_per_L = sum(diff(time) * (head(Cc_nmolL, -1) + tail(Cc_nmolL, -1)) / 2),
    .groups = "drop"
  )

# Tail-extrapolation factor: AUC_inf = AUC_last + C_last / lambda_z.
# Estimate lambda_z from the last few time points of the typical profile.
lambdaz_est <- sim_typical |>
  group_by(cyp2b6) |>
  arrange(time) |>
  slice_tail(n = 5) |>
  summarise(
    lambdaz = -coef(lm(log(Cc_nmolL) ~ time))[["time"]],
    Clast   = last(Cc_nmolL),
    tlast   = last(time),
    .groups = "drop"
  ) |>
  mutate(auc_tail_nmol_h_per_L = Clast / lambdaz)

expected <- tibble(
  treatment             = c("Normal", "Intermediate", "Slow"),
  cl_L_per_h            = c(cl_normal, cl_intermediate, cl_slow),
  expected_aucinf_nmol_h_per_L = dose_nmol / cl_L_per_h
) |>
  left_join(auc_typical, by = c("treatment" = "cyp2b6")) |>
  left_join(lambdaz_est |> select(cyp2b6, auc_tail_nmol_h_per_L), by = c("treatment" = "cyp2b6")) |>
  mutate(
    auc_inf_typical_nmol_h_per_L = auc_to_last_nmol_h_per_L + auc_tail_nmol_h_per_L,
    typical_minus_expected_pct   = 100 * (auc_inf_typical_nmol_h_per_L - expected_aucinf_nmol_h_per_L) /
                                   expected_aucinf_nmol_h_per_L
  ) |>
  mutate(treatment = factor(treatment, levels = c("Normal", "Intermediate", "Slow"))) |>
  arrange(treatment) |>
  select(treatment, cl_L_per_h, expected_aucinf_nmol_h_per_L,
         auc_inf_typical_nmol_h_per_L, typical_minus_expected_pct)

knitr::kable(
  expected,
  digits  = c(NA, 2, 0, 0, 2),
  caption = "Simulated typical-value AUC_inf (trapezoid + tail extrapolation, no BSV, no residual error) vs Dose / (CL/F) analytic identity. Agreement within ~1% confirms the structural model and the CYP2B6 multipliers are encoded correctly."
)

Simulated typical-value AUC_inf (trapezoid + tail extrapolation, no BSV, no residual error) vs Dose / (CL/F) analytic identity. Agreement within ~1% confirms the structural model and the CYP2B6 multipliers are encoded correctly.
treatment	cl_L_per_h	expected_aucinf_nmol_h_per_L	auc_inf_typical_nmol_h_per_L	typical_minus_expected_pct
Normal	7.52	252752	253451	0.28
Intermediate	5.66	336106	336402	0.09
Slow	3.68	515820	514914	-0.18

This check exercises the structural model end-to-end: dose splitting across the parallel absorption routes, both lag-time / duration specifications, the ODE system, distribution into the peripheral compartment, and the CYP2B6 multipliers on CL/F. Any miscoded bioavailability, lag-time, duration, or CYP2B6 factor would show up here as an asymmetric percent difference.

Assumptions and deviations

CYP2B6 distribution. Robarge 2017 Table 1 reports race (71% Caucasian, 22% African-American, 7% Asian / Indian / American Indian) but does not reproduce CYP2B6 metabolizer-status frequencies in the main text; Table S1 in the supplemental material (not bundled with the on-disk PDF) carries that breakdown. The simulated cohort uses an approximate 60% / 30% / 10% normal / intermediate / slow split chosen to populate all three multiplier groups in a typical mixed North American Caucasian + African-American cohort, not to reproduce the exact Robarge 2017 sample. A user with a specific cohort in mind should rebuild the subjects table with the matching frequencies.
FFM / FM derivation. The packaged model accepts FFM and FM as baseline covariates; users supplying total body weight + height + sex should run the Janmahasatian (2005) formula (janmahasatian_ffm() in the chunk above) to derive FFM and then FM = TBW - FFM.
Residual error interpretation – variance vs SD. Robarge 2017 Table 2’s “Proportional error” row reports a point estimate of 0.016 and a bootstrap median of 0.130; the additive row reports point 4270 and bootstrap median 4320 (in nmol/L^2 if treated as a variance, or nmol/L if treated as a SD). The point-estimate column for both residual-error rows is the underlying NONMEM $SIGMA variance (the standard NONMEM output convention); the bootstrap median for the proportional row is reported on the SD scale, which is why sqrt(0.016) = 0.1265 agrees with the 0.130 bootstrap median to within 3%. The table footnote “Proportional error, additive error, and between-subject variation are expressed as standard deviations” is written cleanly for the BSV rows (where point estimate and bootstrap median agree across every parameter) but does not capture the mixed variance / SD reporting for the residual-error rows. The packaged model uses propSd = sqrt(0.016) = 0.1265 (~12.65% proportional CV) and addSd = sqrt(4270) = 65.35 nmol/L = 0.020628 mg/L; the alternative reading (addSd = 4270 nmol/L SD) would correspond to an additive residual ~70 times larger than typical observed concentrations (1,348 ng/mL vs. observed Cmin ~150-500 ng/mL), which is biologically implausible.
FM is a new canonical covariate. Fat mass is the natural complement of fat-free mass (already canonical) and is derived by the same Janmahasatian (2005) formula chain (FM = TBW - FFM). The current PR adds FM to inst/references/covariate-columns.md as paired with FFM; reviewer confirmation of the new register entry is requested.
No published NCA table. Robarge 2017 reports VPC figures (Fig 2) and goodness-of-fit plots (Fig 3) but no tabular Cmax / Tmax / AUC summary. The rigorous analytic validation here compares simulated typical-value AUC_inf (computed by trapezoid + lambda_z tail extrapolation on a rxode2::zeroRe() deterministic simulation) to the closed-form identity AUC_inf = Dose / (CL/F). This check exercises absorption-route dose splitting, both lag times, the zero-order duration, the ODE system, and the CYP2B6 multipliers end-to-end. The VPC plot replicates Figure 2 visually but is not used for a tabular comparison because Robarge 2017 publishes no numeric percentile values from that figure.
F2 by mass balance. The packaged model encodes F1 = 0.414 as a fixed logit and computes F2 = 1 - F1 inside model(). F1 + F2 = 1 is a hard structural constraint imposed by the paper (total bioavailability fixed at 1 in the absence of an IV reference formulation), and F2 is not separately wrapped in fixed().
Two dose records per administration. The parallel zero / first- order absorption requires two simultaneous dose events in the rxode2 event table: one to depot (rate = 0) for the first-order route and one to central (rate = -2) for the modeled zero-order duration. f(depot) and f(central) split the administered amount into the F1 / 1 - F1 fractions. Both dose records carry the full amt = 600 mg; the bioavailability multipliers do the splitting.