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Raltegravir (Lee 2016)

Source: vignettes/articles/Lee_2016_raltegravir.Rmd
Lee_2016_raltegravir.Rmd

Model and source

  • Citation: Lee LS, Seng KY, Wang LZ, Yong WP, Hee KH, Soh TI, Wong A, Cheong PF, Soong R, Sapari NS, Soo R, Fan L, Lee SC, Goh BC. Phenotyping of UGT1A1 Activity Using Raltegravir Predicts Pharmacokinetics and Toxicity of Irinotecan in FOLFIRI. PLoS One. 2016 Jan 25;11(1):e0147681. doi:10.1371/journal.pone.0147681.
  • Description: Population PK model for oral raltegravir (a UGT1A1 phenotyping probe) and its glucuronide metabolite in 24 East Asian patients with advanced solid tumours receiving FOLFIRI chemotherapy (Lee 2016). Raltegravir absorption is described with a depot, a single transit compartment (the paper estimates a non-integer NN = 1.07 in the Savic 2007 transit-chain framework; the packaged model approximates this with one explicit transit compartment), and a one-compartment central compartment with first-order elimination (CL/F, V/F). Raltegravir glucuronide is described by a one-compartment metabolite compartment (central_gluc) with V_GLU fixed at 1 L (a structural identifiability anchor) and a first-order metabolite clearance CL_GLU. The formation rate constant kmet maps to the source paper’s FMET, which the authors define as the formation rate of glucuronide divided by V_GLU; with V_GLU fixed at 1 L, kmet has units 1/h and drives dA_gluc / dt = kmet * V_GLU * C_RAL_central - CL_GLU * C_gluc. Bioavailability F is fixed at 1 (single oral dose; absolute F not identifiable). IIV is reported on CL/F, MTT, F, V/F, kmet (FMET), and CL_GLU with a single off-diagonal covariance between CL/F and V/F (correlation 0.567). The residual error was reported as additive on log-transformed observations for both raltegravir and glucuronide, which maps to a proportional residual on the linear-concentration scale. No baseline covariates (age, sex, weight, body surface area, serum albumin / creatinine / bilirubin / liver enzymes, ethnicity, or UGT1A1 * 6 / * 28 / * 60 and CYP3A5 * 3 genotypes) were retained in the final model.
  • Article: https://doi.org/10.1371/journal.pone.0147681

Lee 2016 used raltegravir as an in vivo phenotyping probe for UGT1A1 activity in 24 East Asian patients receiving FOLFIRI chemotherapy for advanced gastrointestinal cancer. A single 400 mg oral raltegravir dose was given the day before FOLFIRI cycle 1, and the formation rate constant of raltegravir glucuronide derived from the population PK fit was used as an individual-level phenotyping metric correlated with subsequent neutropenia.

Population

Twenty-four Asian cancer patients (Singapore, single centre) were enrolled. The cohort was 79% male, age range 39 to 79 years (median 59), body weight 42.4 to 81.1 kg (median 55), all of East Asian or South Asian background (75% Chinese, 21% Malay, 4% Indian; Table 1 of the source). All patients had advanced-stage gastrointestinal malignancies (7 first-line, 13 second-line, 3 third-line, 1 fourth-line chemotherapy). UGT1A1 6, 28, and 60 and CYP3A5 3 genotypes were determined; no UGT1A1 28 homozygotes or 28 / 6 compound heterozygotes were observed in the cohort (consistent with the lower UGT1A1 28 prevalence in East Asians).

The same metadata is available programmatically via the model’s population list:

rxode2::rxode(readModelDb("Lee_2016_raltegravir"))$population[c(
  "species", "n_subjects", "age_range", "weight_range",
  "sex_female_pct", "race_ethnicity", "disease_state", "regions"
)]
#> ℹ parameter labels from comments will be replaced by 'label()'
#> $species
#> [1] "human"
#> 
#> $n_subjects
#> [1] 24
#> 
#> $age_range
#> [1] "39-79 years"
#> 
#> $weight_range
#> [1] "42.4-81.1 kg"
#> 
#> $sex_female_pct
#> [1] 21
#> 
#> $race_ethnicity
#> [1] "Asian: 75% Chinese, 21% Malay, 4% Indian (Singapore-recruited cohort; Table 1)"
#> 
#> $disease_state
#> [1] "Asian patients with advanced-stage gastro-intestinal cancers requiring FOLFIRI chemotherapy (folinic acid, 5-fluorouracil, irinotecan). Inclusion required Karnofsky performance status > 70% and adequate haematologic / renal / hepatic function. Recruited in Singapore between 2009 and 2011."
#> 
#> $regions
#> [1] "Singapore (single centre, National University Health System)"

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Lee_2016_raltegravir.R. The table below collects them in one place for review.

Equation / parameter Value Source location
lka (ka) log(4.23) Table 2, CL_RAL/F block: ka = 4.23 1/h (RSE 19.3%)
lmtt (MTT) log(1.04) Table 2: MTT = 1.04 h (RSE 25.8%)
lfdepot (F) fixed(log(1)) Table 2: F = 1 FIXED
lcl (CL_RAL/F) log(41.7) Table 2: CL_RAL/F = 41.7 L/h (RSE 24.9%)
lvc (V_RAL/F) log(157) Table 2: V_RAL/F = 157 L (RSE 32.4%)
lkmet_gluc (FMET) log(0.0324) Table 2: FMET = 0.0324 (RSE 10.4%)
lcl_gluc (CL_GLU) log(0.715) Table 2: CL_GLU = 0.715 L/h (RSE 10.2%)
lvc_gluc (V_GLU) fixed(log(1)) Table 2: V_GLU = 1 L FIXED
etalcl + etalvc block c(0.0890, 0.1206, 0.5085) Table 2: CV(CL_RAL/F) = 30.5%, CV(V_RAL/F) = 81.4%, correlation = 0.567
etalmtt 0.7651 Table 2: CV(MTT) = 107.2%
etalfdepot 0.9283 Table 2: CV(F) = 123.7%
etalkmet_gluc 0.1329 Table 2: CV(FMET) = 37.7%
etalcl_gluc 0.0183 Table 2: CV(CL_GLU) = 13.6%
propSd (sigma_RAL) 0.15 Table 2: sigma_RAL = 0.15 (RSE 3.2%)
propSd_gluc (sigma_GLU) 0.18 Table 2: sigma_GLU = 0.18 (RSE 2.6%)
Transit chain (ka, ktr, NN approx 1) – Fig 2; Methods page 5; Savic 2007 (reference [19] of source)
d/dt(central_gluc) = kmet * V_GLU * C_RAL - CL_GLU/V_GLU * central_gluc – Fig 2 caption; Methods page 5
Residual model: additive on log-transformed observations – Results “Population pharmacokinetic analyses” paragraph 1

The original publication does not tabulate per-patient observed Cmax / Tmax / AUC for raltegravir, only the population-typical parameters in Table 2 and the individual-level K23 values used in the downstream toxicity-correlation analyses.

Virtual cohort

Original observed plasma concentrations are not publicly available. The figures below use a 24-subject virtual cohort matching the published demographics in broad strokes (single 400 mg oral dose, sampling at 0, 0.5, 1, 2, 4, 6, 8, and 24 h post-dose as in the source). No covariates were retained in the final Lee 2016 model, so a single dosing scheme suffices.

set.seed(20160125)  # PLoS ONE publication date 2016-01-25

n_sub <- 24L
sample_times <- c(0, 0.5, 1, 2, 4, 6, 8, 24)

make_cohort <- function(n, id_offset = 0L) {
  ids <- id_offset + seq_len(n)

  dose_rows <- data.frame(
    id   = ids,
    time = 0,
    amt  = 400,
    evid = 1L,
    cmt  = "depot"
  )

  obs_rows <- expand.grid(id = ids, time = sample_times) |>
    dplyr::mutate(amt = 0, evid = 0L, cmt = "Cc")

  dplyr::bind_rows(dose_rows, obs_rows) |>
    dplyr::arrange(id, time, evid)
}

events <- make_cohort(n = n_sub)
head(events, 4)
#>   id time amt evid   cmt
#> 1  1  0.0   0    0    Cc
#> 2  1  0.0 400    1 depot
#> 3  1  0.5   0    0    Cc
#> 4  1  1.0   0    0    Cc

Simulation 

mod <- rxode2::rxode(readModelDb("Lee_2016_raltegravir"))
#> ℹ parameter labels from comments will be replaced by 'label()'

# Stochastic simulation including IIV. nlmixr2lib models declare the
# residual via `~ prop(...)`; rxode2 returns `Cc` / `Cc_gluc` as the
# model predictions and `sim` / `ipredSim` as the residual-augmented
# samples (only `sim` corresponds to the first declared endpoint, so
# `Cc` and `Cc_gluc` are used directly below).
sim <- rxode2::rxSolve(mod, events = events, returnType = "data.frame")

The deterministic (typical-value) prediction zeroes out the random effects using rxode2::zeroRe() so the curve traces the population-typical PK profile implied by Table 2 of the source.

mod_typical <- mod |> rxode2::zeroRe()

# A denser time grid for plotting the typical-value curve.
ev_typical <- data.frame(
  id   = 1L,
  time = c(0, seq(0.05, 24, by = 0.1)),
  amt  = c(400, rep(0, length(seq(0.05, 24, by = 0.1)))),
  evid = c(1L, rep(0L, length(seq(0.05, 24, by = 0.1)))),
  cmt  = c("depot", rep("Cc", length(seq(0.05, 24, by = 0.1))))
)

sim_typical <- rxode2::rxSolve(mod_typical, events = ev_typical,
                               returnType = "data.frame")
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalmtt', 'etalfdepot', 'etalkmet_gluc', 'etalcl_gluc'

Typical-value concentration-time profile

The source paper (Lee 2016) does not include a concentration-time figure for raltegravir; the published deliverable is Table 2 of population parameters and the downstream K23-vs-ANC correlation figures (Figures 3 and 4). The plot below traces the typical-value prediction of raltegravir parent and glucuronide plasma concentrations after a single 400 mg oral dose at the Table 2 fixed effects.

sim_typical |>
  tidyr::pivot_longer(c(Cc, Cc_gluc), names_to = "analyte", values_to = "C") |>
  dplyr::mutate(analyte = dplyr::recode(analyte,
    Cc       = "Raltegravir (mg/L)",
    Cc_gluc  = "Raltegravir glucuronide (mg, in V_GLU = 1 L frame)"
  )) |>
  ggplot(aes(time, C)) +
  geom_line(linewidth = 0.7) +
  facet_wrap(~ analyte, scales = "free_y", ncol = 1) +
  labs(x = "Time after 400 mg oral dose (h)", y = "Concentration",
       title = "Typical-value PK profile (Lee 2016 Table 2 fixed effects)",
       caption = paste("Glucuronide concentrations live in the V_GLU = 1 L",
                       "scaled frame and are not directly comparable to",
                       "physical plasma glucuronide.", sep = " "))

Visual predictive check

A 5th / 50th / 95th percentile envelope from the 24-subject simulation with full IIV applied:

quantile_envelope <- sim |>
  dplyr::group_by(time) |>
  dplyr::summarise(
    Q05 = quantile(Cc, 0.05, na.rm = TRUE),
    Q50 = quantile(Cc, 0.50, na.rm = TRUE),
    Q95 = quantile(Cc, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(quantile_envelope, aes(time, Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.25) +
  geom_line(linewidth = 0.7) +
  scale_y_log10() +
  labs(x = "Time after 400 mg oral dose (h)",
       y = "Raltegravir parent Cc (mg/L, log scale)",
       title = "Simulated 5 / 50 / 95 percentile envelope (n = 24)",
       caption = "Solid: median; band: 5 to 95th percentile from IIV.")
#> Warning in scale_y_log10(): log-10 transformation introduced infinite values.
#> log-10 transformation introduced infinite values.
#> log-10 transformation introduced infinite values.
#> log-10 transformation introduced infinite values.

PKNCA validation

PKNCA is run on the raltegravir parent only. The glucuronide compartment is in the V_GLU = 1 L scaled frame (see Assumptions and deviations) and is not suitable for absolute-NCA computation.

sim_nca <- sim |>
  dplyr::filter(!is.na(Cc)) |>
  dplyr::mutate(treatment = "raltegravir_400mg_po") |>
  dplyr::select(id, time, Cc, treatment)

conc_obj <- PKNCA::PKNCAconc(sim_nca, Cc ~ time | treatment + id)

dose_df <- events |>
  dplyr::filter(evid == 1L, cmt == "depot") |>
  dplyr::mutate(treatment = "raltegravir_400mg_po") |>
  dplyr::select(id, time, amt, treatment)

dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | treatment + id)

intervals <- data.frame(
  start = 0,
  end   = 24,
  cmax  = TRUE,
  tmax  = TRUE,
  auclast = TRUE,
  aucinf.obs = TRUE,
  half.life  = TRUE,
  cl.obs     = TRUE
)

nca_data <- PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals)
nca_res  <- PKNCA::pk.nca(nca_data)
nca_summary <- summary(nca_res)
knitr::kable(nca_summary,
             caption = "Simulated NCA parameters for raltegravir parent after a single 400 mg oral dose.")
Simulated NCA parameters for raltegravir parent after a single 400 mg oral dose.
start end treatment N auclast cmax tmax half.life aucinf.obs cl.obs
0 24 raltegravir_400mg_po 24 10.8 [113] 2.23 [89.4] 1.50 [0.500, 4.00] 2.69 [2.00] 10.9 [117] 36.5 [117]

Comparison against published NCA

Lee 2016 does not tabulate per-patient NCA parameters (Cmax / Tmax / AUC) for raltegravir; the published deliverable is Table 2 with the population PK estimates. The most direct cross-check is that the simulated apparent oral clearance (Dose / AUC_inf) should reproduce the published CL_RAL/F = 41.7 L/h and the simulated terminal half-life should reproduce the log(2) / (CL_RAL/F / V_RAL/F) = 2.61 h implied by Table 2.

cl_pub <- 41.7
v_pub  <- 157
t_half_implied <- log(2) * v_pub / cl_pub

# Median NCA-derived CL and half-life across simulated subjects.
nca_subj <- as.data.frame(nca_res) |>
  dplyr::filter(PPTESTCD %in% c("cl.obs", "half.life"))

if (nrow(nca_subj) > 0) {
  med_cl     <- median(nca_subj$PPORRES[nca_subj$PPTESTCD == "cl.obs"], na.rm = TRUE)
  med_thalf  <- median(nca_subj$PPORRES[nca_subj$PPTESTCD == "half.life"], na.rm = TRUE)
} else {
  med_cl <- NA
  med_thalf <- NA
}

knitr::kable(
  data.frame(
    metric = c("CL/F (L/h)", "Terminal half-life (h)"),
    published   = c(cl_pub, round(t_half_implied, 2)),
    simulated_median = c(round(med_cl, 2), round(med_thalf, 2))
  ),
  caption = "Published vs simulated derived parameters."
)
Published vs simulated derived parameters.
metric published simulated_median
CL/F (L/h) 41.70 36.79
Terminal half-life (h) 2.61 2.16

The simulated CL/F is computed from the AUC over a 24 h window and so depends on the extrapolation of the terminal phase; small deviations from the published CL_RAL/F are expected because of the AUC extrapolation tail. Because the model parameters were extracted directly from Table 2, any large deviation (more than 20%) would point to an encoding error in the model file rather than a biological signal.

Assumptions and deviations

  • Transit-chain discretisation. The source uses the Savic 2007 transit compartment formulation with the number of transit compartments estimated as a non-integer NN = 1.07. nlmixr2lib does not implement the Savic 2007 continuous transit chain with non-integer NN, so the packaged model approximates the chain with one explicit transit compartment between depot and central. The transit rate constant is computed as ktr = (NN + 1) / MTT = 2 / MTT with NN = 1 (rather than 1.07). Because NN = 1.07 is within 7% of the integer 1, the absorption-profile distortion is small; users needing the exact Savic 2007 input shape can rewrite the model to use the analytic gamma-distributed input function.

  • Separate ka and ktr. The source paper reports both a first-order absorption rate constant ka = 4.23 1/h and a transit-chain MTT = 1.04 h (with NN = 1.07). Figure 2 of Lee 2016 labels ka as “the absorption rate constant from the hypothetical drug depot compartment to plasma” and ktr as the inter-transit rate. The exact mapping of ka onto the depot-to-first- transit vs last-transit-to-central transition is not given in the paper text; the packaged model applies ka to depot to transit1 and ktr to transit1 to central. With NN approximated as 1 this distinction has only a minor effect on the resulting input shape.

  • Glucuronide compartment lives in V_GLU = 1 L scaled frame. The metabolite distribution volume V_GLU was fixed to 1 L in the source NONMEM fit (Fig 2 caption: “V_M, the distribution volume of the metabolite, was fixed to 1”). With this anchor, the simulated Cc_gluc represents the glucuronide amount in a 1 L “scaled” compartment rather than the physical plasma glucuronide concentration. The simulated Cc_gluc values from this model are intended for relative kinetics (e.g. peak time, half-life of formation decay, ratio across simulated subjects) and should not be compared to measured plasma glucuronide concentrations on an absolute scale.

  • FMET as a 1/h rate constant. The source paper describes FMET in two ways: (a) “the fraction of raltegravir clearance for the formation of glucuronide” and (b) “the ratio of the formation rate of glucuronide to V_GLU”. Interpretation (a) (a unitless fraction) is biologically implausible given FMET = 0.0324 – raltegravir is primarily glucuronidated in vivo, so a 3% formation fraction is inconsistent with the known biotransformation. Interpretation (b) gives FMET units of 1/h and drives the formation flux via kmet_gluc * V_GLU * C_RAL_central. The packaged model uses interpretation (b) and maps the source parameter to the canonical paper-named parameter kmet (formation rate constant from parent central to metabolite; see R/conventions.R::paperNamedParams).

  • No covariates in the final model. The source paper tested age, sex, body weight, body surface area, serum albumin / creatinine / total bilirubin / ALP / ALT / AST, ethnicity, and the UGT1A1 6 / 28 / 60 and CYP3A5 3 genotypes as candidate covariates. None was retained in the final model (Table 2). The packaged model therefore declares covariateData = list() – the model is covariate-free.

  • Reported NCA is not tabulated in the source. Lee 2016 performed non-compartmental analysis using Phoenix WinNonlin for AUC and CL but does not report per-patient or summary Cmax / Tmax / AUC values in the publication text or Tables 1 to 2. The “Comparison against published NCA” section above therefore uses model-implied derived parameters (CL/F = 41.7 L/h and t1/2 = 2.61 h from Table 2 of the source) rather than independently published NCA values.

  • Single dose only. The source paper administers a single 400 mg oral dose of raltegravir as a UGT1A1 phenotyping probe. Steady-state predictions via multiple dosing are outside the validation envelope of the published model; users simulating clinical raltegravir regimens (typically 400 mg twice daily for HIV indication) should validate against a steady-state- specific raltegravir model.