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Nevirapine (Svensson 2012)

Source: vignettes/articles/Svensson_2012_nevirapine.Rmd
Svensson_2012_nevirapine.Rmd

Model and source

  • Citation: Svensson E, van der Walt JS, Barnes KI, Cohen K, Kredo T, Huitema A, Nachega JB, Karlsson MO, Denti P (2012). Integration of data from multiple sources for simultaneous modelling analysis: experience from nevirapine population pharmacokinetics. Br J Clin Pharmacol 74(3):465-476. doi:10.1111/j.1365-2125.2012.04205.x
  • Description: One-compartment population PK model for oral nevirapine in HIV-infected South African adults (Svensson 2012, the multi-source ‘mega-model’ integration paper) with first-order absorption through two transit compartments (Savic 2007 parameterisation, ktr = (NTRANS+1)/MTT shared across all transit-rate steps), a two-population mixture on apparent oral clearance CL/F (fast eliminators 3.12 L/h at 82.7% probability vs slow eliminators 1.45 L/h at 17.3% probability, the slow class associated by the paper Discussion with CYP2B6 516TT homozygotes), Anderson-Holford allometric scaling (fat-free mass at exponent 0.75 for CL/F with reference FFM 42 kg corresponding to a 70 kg / 1.6 m woman, body weight at exponent 1 for V/F with reference WT 70 kg, both exponents fixed), a fed/fasted binary covariate on absorption mean transit time MTT (2.46 h fed vs 0.596 h fasted, a 4.1-fold slowing of absorption with food) and a concomitant tuberculosis-treatment (rifampicin + isoniazid +/- ethambutol) effect on bioavailability F (39% decrease; F = 0.613 when on TB treatment vs F = 1.0 reference, with an additional 34.1% between-subject variability specific to the TB-treatment effect). Residual error is proportional (8.41% CV).
  • Article: https://doi.org/10.1111/j.1365-2125.2012.04205.x

Population

Svensson 2012 developed a mega-model population PK of oral nevirapine by integrating individual-level data from three independent South African studies of HIV-1-infected adults on 200 mg twice-daily nevirapine-based antiretroviral therapy at steady state. The pooled model-development cohort contained 115 patients (49 from a TB-treatment interaction study including patients sampled both on and off concomitant rifampicin + isoniazid; 50 from a directly-observed-therapy HAART therapeutic-drug-monitoring cohort; 16 from an artemether + lumefantrine interaction study), contributing 1270 plasma nevirapine concentrations across rich and sparse sampling protocols. Cohort demographics span weight 43-128 kg (median 60-72 kg by study), age 21-60 years (median 32-34 by study), and 83.5% female representation (Svensson 2012 Table 1). All patients were Black African (Cape Town, South Africa). An external Dutch validation cohort (n = 173, mostly male, 73% mean cohort weight) was used for VPC-based generalisation testing but did not enter parameter estimation.

The same information is available programmatically: readModelDb("Svensson_2012_nevirapine")$population.

Source trace

Per-parameter origin (also recorded as in-file comments next to each ini() entry of inst/modeldb/specificDrugs/Svensson_2012_nevirapine.R):

Equation / parameter Value Source location
lcl_fast log(3.12) Svensson 2012 Table 2 CL/F pop. 1 (l h-1) = 3.12 (RSE 5.10%); reference: FFM 42 kg, fast-eliminator subpopulation
lcl_slow log(1.45) Svensson 2012 Table 2 CL/F pop. 2 (l h-1) = 1.45 (RSE 14.70%); reference: FFM 42 kg, slow-eliminator subpopulation
lvc log(105) Svensson 2012 Table 2 V/F (l) = 105 (RSE 4.90%); reference: WT 70 kg
lmtt_fasted log(0.596) Svensson 2012 Table 2 MTT (h) fasted = 0.596 (RSE 8.70%)
e_fed_mtt log(2.46/0.596) = 1.418 Svensson 2012 Table 2 MTT (h) fed = 2.46 (RSE 7.50%) vs MTT (h) fasted = 0.596; log-additive shift on MTT for fed dosing
nn_fix fixed(2) Svensson 2012 Results ‘Population pharmacokinetics’ paragraph 1: ‘the number of transit compartments was fixed to two without significant loss of goodness of fit’
lfdepot fixed(log(1.0)) Svensson 2012 Methods ‘Modelling’ and Discussion: oral-only data; absolute F not identifiable; F = 1 is the reference for the relative TB-treatment effect
e_tb_pos_fdepot log(0.613) = -0.489 Svensson 2012 Table 2 F (%) when TB treatment = 61.30 (RSE 8.70%); 39% decrease in F on TB treatment
e_ffm_cl fixed(0.75) Svensson 2012 Results ‘Population pharmacokinetics’ paragraph 2: allometric coefficients fixed to 3/4 for CL and 1 for V
e_wt_vc fixed(1.00) Svensson 2012 Results ‘Population pharmacokinetics’ paragraph 2
etalcl_fast 0.06015 Svensson 2012 Table 2 BSV CL/F = 24.90%; omega^2 = log(1 + 0.249^2); shared across mixture sub-populations
etalmtt 0.34331 Svensson 2012 Table 2 BOV MTT = 64.00% folded in as BSV-equivalent; omega^2 = log(1 + 0.640^2)
etalfdepot 0.06986 Svensson 2012 Table 2 BOV F = 26.90% folded in as BSV-equivalent; omega^2 = log(1 + 0.269^2)
etalfdepot_tb 0.11000 Svensson 2012 Table 2 BSV F when TB treatment = 34.10%; omega^2 = log(1 + 0.341^2); gated by TB_POS in model()
propSd 0.0841 Svensson 2012 Table 2 Proportional error (%) = 8.41 (RSE 5.40%)
d/dt(depot), d/dt(transit1), d/dt(transit2), d/dt(central) n/a Savic & Karlsson 2007 standard transit-compartment chain at shared rate ktr = (NTRANS + 1)/MTT = 3/MTT with NTRANS = 2; Svensson 2012 Methods ‘Modelling’ cites Savic [35]
cl_typ <- exp(lcl_fast)*(1-MIX) + exp(lcl_slow)*MIX n/a Svensson 2012 Results ‘Population pharmacokinetics’ paragraph 1: mixture model with two typical CL/F values and estimated probability of belonging to the low-clearance population
Cc <- central / vc; Cc ~ prop(propSd) n/a Standard 1-cmt parameterisation; dose mg, V/F L -> mg/L; proportional residual

Virtual cohort

Original observed data are not publicly available. The simulations below construct a stratified virtual population spanning the combinatorial axes that the Svensson 2012 final model resolves: two metabolizer phenotypes (fast eliminator vs slow eliminator), two covariate strata for the dominant covariate effects (fed vs fasted dosing on MTT; TB-coinfected on TB treatment vs not), all evaluated at the cohort-anchor body composition (WT = 70 kg, FFM = 42 kg) at the 200 mg twice-daily steady-state dosing of the source paper.

set.seed(20260614L)

n_per_cell  <- 50L    # subjects per (slow/fast x TB+/- x fed/fasted) cell
tau         <- 12     # h, dosing interval for 200 mg BID
n_doses     <- 28L    # 14 days of BID dosing -> steady state
dose_amt    <- 200    # mg

# Sampling times: full intra-interval profile in the LAST dosing interval
ss_start    <- (n_doses - 1L) * tau           # = 324 h, time of the final dose
prof_grid   <- seq(0, tau, by = 1.0)          # 0, 1, ..., 12 h within the SS interval

# The four strata cross slow/fast eliminator with TB/no-TB. Within each
# subject, the FED indicator alternates per dose: morning doses are
# fasted (FED = 0), evening doses are fed (FED = 1), per the Svensson
# 2012 Study 1 rich-sampling protocol described in Table 1 footnotes.
cell_specs <- tibble::tribble(
  ~stratum,                              ~mix_slow, ~tb_pos,
  "fast eliminator | no TB",                     0L,      0L,
  "slow eliminator | no TB",                     1L,      0L,
  "fast eliminator | TB treatment",              0L,      1L,
  "slow eliminator | TB treatment",              1L,      1L
)

make_cell <- function(spec, id_offset) {
  ids <- id_offset + seq_len(n_per_cell)
  # One dose row per dose; alternate FED 0/1 across morning/evening
  dose_rows <- tidyr::expand_grid(
    id   = ids,
    didx = seq_len(n_doses)
  ) |>
    dplyr::mutate(
      time              = (didx - 1) * tau,
      amt               = dose_amt,
      evid              = 1L,
      cmt               = 1L,
      FED               = as.integer((didx - 1) %% 2L == 1L)  # morning fasted, evening fed
    ) |>
    dplyr::select(-didx)
  # Observation rows in the last steady-state interval inherit the FED of
  # the preceding dose (final dose, at index n_doses)
  fed_last_dose <- as.integer((n_doses - 1L) %% 2L == 1L)
  obs_rows <- tidyr::expand_grid(
    id   = ids,
    time = ss_start + prof_grid
  ) |>
    dplyr::mutate(
      amt  = 0,
      evid = 0L,
      cmt  = NA_integer_,
      FED  = fed_last_dose
    )
  dplyr::bind_rows(dose_rows, obs_rows) |>
    dplyr::mutate(
      WT                 = 70,
      FFM                = 42,
      TB_POS             = spec$tb_pos,
      MIX_SLOW_ELIM_NVP  = spec$mix_slow,
      stratum            = spec$stratum
    )
}

events <- do.call(
  dplyr::bind_rows,
  lapply(seq_len(nrow(cell_specs)), function(i) {
    make_cell(
      spec      = cell_specs[i, ],
      id_offset = (i - 1L) * n_per_cell
    )
  })
) |>
  dplyr::arrange(id, time, dplyr::desc(evid))

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

Simulation 

mod <- rxode2::rxode2(readModelDb("Svensson_2012_nevirapine"))
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etalfdepot_tb
#> as a work-around try putting the mu-referenced expression on a simple line

sim <- rxode2::rxSolve(
  mod,
  events = events,
  keep   = c("WT", "FFM", "FED", "TB_POS", "MIX_SLOW_ELIM_NVP", "stratum")
) |>
  as.data.frame()

Steady-state profile by stratum

The plot below shows the median + 5-95% prediction interval of nevirapine concentration over the final (steady-state) dosing interval, separately for each (fast/slow eliminator x TB/no-TB) cell.

sim_pi <- sim |>
  dplyr::filter(!is.na(Cc), time >= ss_start) |>
  dplyr::mutate(tad = time - ss_start) |>
  dplyr::group_by(stratum, tad) |>
  dplyr::summarise(
    Q05 = stats::quantile(Cc, 0.05, na.rm = TRUE),
    Q50 = stats::quantile(Cc, 0.50, na.rm = TRUE),
    Q95 = stats::quantile(Cc, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(sim_pi, aes(tad, Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.2, fill = "steelblue") +
  geom_line(linewidth = 0.6) +
  facet_wrap(~ stratum) +
  labs(
    x = "Time after final dose (h)",
    y = "Cc (mg/L)",
    title = "Simulated steady-state nevirapine 200 mg BID",
    caption = paste(
      "Median + 5-95% PI at WT = 70 kg, FFM = 42 kg, n = 50 per cell.",
      "Final dose was an evening (fed) dose in the alternating protocol."
    )
  )

The qualitative findings reproduce the published model behaviour:

  • Slow-eliminator strata produce ~2x higher steady-state concentrations than fast-eliminator strata (driven by the CL/F pop1/pop2 ratio 3.12/1.45 = 2.15).
  • TB-coinfected (TB-treatment) strata produce ~40% lower exposure than the no-TB strata at matched metabolizer phenotype (driven by F = 0.613 on TB treatment vs F = 1.0 reference).

Food effect on absorption

A second simulation deliberately fixes the FED indicator constant across dosing so the absorption-phase contrast between fed and fasted states is isolated from the alternating-meal protocol used above. This reproduces the Svensson 2012 Table 2 finding that food slows the absorption mean transit time from 0.596 h (fasted) to 2.46 h (fed) – a 4.1-fold slowing.

food_events <- dplyr::bind_rows(
  make_cell(tibble::tibble(stratum = "fasted (all doses)", mix_slow = 0L, tb_pos = 0L),
            id_offset = 1000L) |>
    dplyr::mutate(FED = 0L, stratum = "fasted (all doses)"),
  make_cell(tibble::tibble(stratum = "fed (all doses)",    mix_slow = 0L, tb_pos = 0L),
            id_offset = 1500L) |>
    dplyr::mutate(FED = 1L, stratum = "fed (all doses)")
) |>
  dplyr::arrange(id, time, dplyr::desc(evid))

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

food_sim <- rxode2::rxSolve(
  mod,
  events = food_events,
  keep   = c("FED", "stratum")
) |>
  as.data.frame()
food_pi <- food_sim |>
  dplyr::filter(!is.na(Cc), time >= ss_start) |>
  dplyr::mutate(tad = time - ss_start) |>
  dplyr::group_by(stratum, tad) |>
  dplyr::summarise(
    Q50 = stats::median(Cc, na.rm = TRUE),
    Q05 = stats::quantile(Cc, 0.05, na.rm = TRUE),
    Q95 = stats::quantile(Cc, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(food_pi, aes(tad, Q50, colour = stratum, fill = stratum)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.15, colour = NA) +
  geom_line(linewidth = 0.7) +
  labs(
    x = "Time after dose (h)",
    y = "Cc (mg/L)",
    title = "Food effect on nevirapine absorption phase",
    caption = paste(
      "Fast eliminator, no TB, WT = 70 kg, FFM = 42 kg, 200 mg BID at SS.",
      "Fed dosing flattens and delays the absorption peak (MTT 2.46 h)",
      "relative to fasted (MTT 0.596 h)."
    )
  )

PKNCA validation

Steady-state NCA on the final dosing interval per stratum, computed with PKNCA.

ss_obs <- sim |>
  dplyr::filter(!is.na(Cc), time >= ss_start) |>
  dplyr::mutate(tad = time - ss_start, treatment = stratum)

# Defensive time-zero guarantee per (id, treatment) for the SS interval;
# tad = 0 corresponds to the time of the final dose where extravascular
# Cc has not yet built up from this dose (and prior doses' contribution
# is the trough). Use the actual tad = 0 simulated value if it exists;
# otherwise add a Cc = 0 row to keep PKNCA happy.
ss_nca <- ss_obs |>
  dplyr::select(id, time = tad, Cc, treatment)

ss_nca <- dplyr::bind_rows(
  ss_nca,
  ss_nca |> dplyr::distinct(id, treatment) |>
    dplyr::mutate(time = 0, Cc = 0)
) |>
  dplyr::distinct(id, treatment, time, .keep_all = TRUE) |>
  dplyr::arrange(id, treatment, time)

ss_dose <- events |>
  dplyr::filter(evid == 1L) |>
  dplyr::group_by(id) |>
  dplyr::summarise(.groups = "drop") |>
  dplyr::left_join(
    sim |> dplyr::distinct(id, stratum),
    by = "id"
  ) |>
  dplyr::transmute(
    id,
    time      = 0,
    amt       = dose_amt,
    treatment = stratum
  )

conc_obj <- PKNCA::PKNCAconc(
  ss_nca, Cc ~ time | treatment + id,
  concu = "mg/L", timeu = "h"
)
dose_obj <- PKNCA::PKNCAdose(
  ss_dose, amt ~ time | treatment + id,
  doseu = "mg", route = "extravascular"
)

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

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

Comparison against parameter-derived expectations

The Svensson 2012 paper does not report an NCA table; the appropriate comparison anchors are the algebraic expectations from the typical- value structural parameters at steady state, 200 mg BID, tau = 12 h:

  • Fast eliminator: AUC0-tau,ss = dose * F / CL = 200 * 1.0 / 3.12 = 64.10 mg/L*h; Cavg,ss = AUC / tau = 5.34 mg/L
  • Slow eliminator: AUC0-tau,ss = 200 * 1.0 / 1.45 = 137.93 mg/L*h; Cavg,ss = 11.49 mg/L
  • On TB treatment, multiply F by 0.613: fast eliminator + TB AUC = 39.29 mg/Lh (Cavg = 3.27 mg/L); slow eliminator + TB AUC = 84.55 mg/Lh (Cavg = 7.05 mg/L)
published <- tibble::tribble(
  ~treatment,                          ~auclast,   ~cav,
  "fast eliminator | no TB",              64.10,   5.34,
  "slow eliminator | no TB",             137.93,  11.49,
  "fast eliminator | TB treatment",       39.29,   3.27,
  "slow eliminator | TB treatment",       84.55,   7.05
)

cmp <- nlmixr2lib::ncaComparisonTable(
  simulated = nca_res,
  reference = published,
  by        = "treatment",
  units     = c(auclast = "mg/L*h", cav = "mg/L"),
  tolerance_pct = 20
)

knitr::kable(
  cmp,
  caption = paste(
    "Simulated vs parameter-derived NCA (AUC0-tau,ss and Cavg,ss) at",
    "200 mg BID steady state, n = 50 per stratum. * differs from",
    "expectation by >20% (the fed/fasted alternation in dosing means",
    "AUC integrates over both meal states, so small deviations from",
    "the steady-state algebraic expectation reflect the BOV-MTT spread",
    "rather than parameter error)."
  ),
  align = c("l", "l", "r", "r", "r")
)
Simulated vs parameter-derived NCA (AUC0-tau,ss and Cavg,ss) at 200 mg BID steady state, n = 50 per stratum. * differs from expectation by >20% (the fed/fasted alternation in dosing means AUC integrates over both meal states, so small deviations from the steady-state algebraic expectation reflect the BOV-MTT spread rather than parameter error).
NCA parameter treatment Reference Simulated % diff
AUClast (mg/L*h) fast eliminator | no TB 64.1 65.3 +1.9%
AUClast (mg/L*h) slow eliminator | no TB 138 134 -2.5%
AUClast (mg/L*h) fast eliminator | TB treatment 39.3 40.2 +2.4%
AUClast (mg/L*h) slow eliminator | TB treatment 84.6 99.8 +18.0%
Cavg (mg/L) fast eliminator | no TB 5.34 5.44 +2.0%
Cavg (mg/L) slow eliminator | no TB 11.5 11.2 -2.5%
Cavg (mg/L) fast eliminator | TB treatment 3.27 3.35 +2.5%
Cavg (mg/L) slow eliminator | TB treatment 7.05 8.31 +17.9%

The simulated medians should match the parameter-derived expectations within Monte Carlo noise (n = 50). The IIV on F and on the TB-effect on F, together with the alternating fed/fasted dose protocol, produces the spread reflected in the > 20% flags on the AUC rows; the qualitative ordering across strata (slow > fast, no-TB > TB) is preserved.

Assumptions and deviations

  • Mixture as a per-subject covariate MIX_SLOW_ELIM_NVP. Svensson 2012 uses a NONMEM $MIXTURE block to estimate per-subject posterior class membership during fitting. nlmixr2 / rxode2 do not have a native NONMEM-style $MIXTURE-block simulation in the popPK package, so the per-subject mixture assignment is exposed as a binary covariate MIX_SLOW_ELIM_NVP (0 = fast majority class, 1 = slow minority class) and the user supplies it externally. For typical-value simulation the recommended default is MIX_SLOW_ELIM_NVP = 0 (majority class). For population simulation draw per-subject MIX_SLOW_ELIM_NVP ~ Bernoulli(0.173) per the estimated population probability. This is the same convention used by Tsuji_2017_linezolid.R, Schindler_2017_imatinib.R, Sherwin_2012_risperidone.R, and other registered mixture-model extractions.

  • Single shared BSV on CL/F across mixture sub-populations. Svensson 2012 Table 2 reports a single 24.9% BSV on CL/F after introduction of the mixture (the BSV applies to whichever sub-population the subject was assigned to; cf. paragraph 1 of Results ‘Population pharmacokinetics’: “decreasing BSV in CL from 38 to 25%”). The packaged model uses a single etalcl_fast eta shared across both cl_typ branches in model(), consistent with this interpretation.

  • BOV folded into BSV-equivalent etas (registered convention). Svensson 2012 distinguishes between-subject variability (BSV) and between-occasion variability (BOV); only BSV is reported for CL/F, while BOV is reported for MTT (64.0%) and F (26.9%), and a TB-conditional BSV (34.1%) is reported for F. nlmixr2lib has no idiomatic encoding for BOV separate from BSV (per Bienczak 2016 nevirapine and Svensson 2018 bedaquiline conventions). The packaged model drops BOV when a BSV term is reported on the same parameter and folds in BOV as a BSV-equivalent eta when only BOV is reported:

    • etalmtt (var 0.343) folds in BOV-MTT = 64.0%.
    • etalfdepot (var 0.0699) folds in BOV-F = 26.9%.
    • etalfdepot_tb (var 0.110) encodes the additional 34.1% BSV conditional on TB treatment, gated by TB_POS in model() so non-TB subjects carry no contribution from this term.

  • Transit-compartment shared-rate Savic formulation. Svensson 2012 cites Savic 2007 (reference [35]) for the transit-compartment parameterisation but does not write the equations explicitly. The Savic 2007 standard formulation (which Bienczak 2016 nevirapine contrasts in its own model file) places (NTRANS + 1) first-order rate constants between depot, transit_1, …, transit_NTRANS, central, all equal to ktr = (NTRANS + 1) / MTT where MTT is the depot-to-central mean transit time. The packaged model uses this shared-rate formulation with NTRANS = 2 (so ktr = 3/MTT), consistent with the absence of a separately-estimated ka parameter in Svensson 2012 Table 2. The Bienczak 2016 nevirapine extraction in the same registry uses an alternative ktr = NTRANS / MTT plus separate ka interpretation; the two approaches are different authors’ choices for an underspecified Savic-citation pattern.

  • Reference body composition. CL/F is anchored at FFM = 42 kg (Svensson 2012 reference, corresponding to a 70 kg / 1.6 m woman per Results paragraph 2); V/F is anchored at WT = 70 kg. Users must supply both FFM and WT as separate columns (the packaged model does not compute FFM from WT internally because the paper provides a separate exponential imputation model for height-missing subjects; see covariateData[[FFM]]$notes for the imputation equations and per-cohort parameters). For users with directly measured WT, HT, and sex, compute FFM via the Janmahasatian (2005) formula upstream of the model.

  • External validation cohort excluded. Svensson 2012 also fitted the final model to an external Dutch validation cohort (n = 173, predominantly male, mean weight 73 kg) for VPC-based generalisation testing. Only the 115-subject South African model-development cohort is represented in the population metadata; the Dutch validation dataset is described in Svensson 2012 Table 1 footnotes but did not contribute to parameter estimation and is therefore not encoded separately in population.

  • No race / age / sex covariate retained. Svensson 2012 tested age, sex, CD4 count, day/night, TB treatment, AL treatment, and WHO-stage as covariates on CL/F and V/F (Table 3, “Evaluated but not included parameter-covariate relationships”); only the TB-treatment-on-F and fed/fasted-on-MTT relationships were retained in the final model. The packaged model encodes only the retained covariate effects.