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Fosamprenavir (Fisher 2008)

Source: vignettes/articles/Fisher_2008_fosamprenavir.Rmd
Fisher_2008_fosamprenavir.Rmd

Model and source

  • Citation: Fisher J, Gastonguay MR, Knebel W, Gibiansky L, Wire MB. Population Pharmacokinetic Modeling of Fosamprenavir in Pediatric HIV-Infected Patients. American Conference on Pharmacometrics (ACOP) poster, Tucson, AZ, 2008. Available at https://metrumrg.com/wp-content/uploads/2018/08/acop_2008_fosamprenavir.pdf
  • Description: Two-compartment population PK model with first-order absorption for orally administered fosamprenavir (FPV), measured as the active amprenavir (APV) metabolite, in HIV-1-infected pediatric patients aged 4 weeks to 18 years (Fisher 2008). Allometric scaling on apparent clearance (CL/F, Q) at a fixed exponent of 0.75 and on apparent volumes (V2/F, V3) at a fixed exponent of 1.0 (reference 70 kg). Apparent CL/F is reduced ~60% by concomitant ritonavir (RTV) co-administration (maximal CYP3A4 inhibition assumed at the RTV doses used), and is further modified by a piecewise age-maturation factor (linearly declining additive offset for AGE <= 2*AG50, zero above), by sex (lower in females), by race (separate multipliers for Black and for the non-Black non-White composite vs the White reference), and by a power effect of serum alpha-1-acid glycoprotein (AAG, centred at 0.77 g/L). Apparent V2/F also carries a power effect of AAG. Bioavailability is anchored on suspension-under-fed conditions (F=1), with a separate relative bioavailability for the tablet formulation (F_tab) and a separate relative bioavailability for the suspension administered fasted (F_food,sus). Inter-occasion variability on CL/F (~34% CV) reported by the source poster is NOT structurally encoded here (no operational occasion column is defined for the model-library use case); downstream users who want to simulate IOV can add an OCC indicator and a per-occasion eta in rxode2.
  • Poster: https://metrumrg.com/wp-content/uploads/2018/08/acop_2008_fosamprenavir.pdf

Population

The model was fit to 1322 plasma amprenavir (APV) concentrations from 137 HIV-1-infected pediatric patients enrolled in three multinational GlaxoSmithKline studies (APV20002, APV20003, APV29005) and aged 4 weeks to 18 years (baseline age range 0.72-18 years, median 10 years; baseline weight range 5.9-102.8 kg, median 32.9 kg per Table 1). The race distribution was White 57.7%, Black 27.0%, Asian 1.5%, Hispanic 5.1%, American Indian 5.8%, and Other 2.9% (Table 2). 119 of 137 patients (86.9%) received FPV with concomitant low-dose ritonavir (RTV); the remaining 18 patients (13.1%, all aged 2-6 years) received FPV alone. The full population metadata is available as rxode2::rxode(readModelDb("Fisher_2008_fosamprenavir"))$meta$population.

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Fisher_2008_fosamprenavir.R. The table below collects the structural model and parameter provenance in one place.

Equation / parameter Value Source location
Two-compartment first-order absorption (depot -> central <-> peripheral1) n/a Model section (page 1, “Two-compartment model with first-order absorption and elimination.”)
Allometric exponents fixed at 0.75 (CL, Q) and 1 (V2/F, V3) n/a Methods, Model and Modeling Assumptions
Piecewise age maturation on CL/F: f_age = 1 + AMAX(1 - 0.5AGE/AG50) for AGE <= 2*AG50; f_age = 1 otherwise n/a Model section equations (page 1)
Reference subject: WT = 70 kg, AGE > 4 yr, White, Male, AAG = 0.77 g/L, suspension under fed, +RTV n/a Figure 3 caption
lka = log(1.13) 1.13 1/h Table 3 theta_5
lcl = log(84.4) 84.4 L/h Table 3 theta_6 (CL/F without RTV)
lvc = log(288) 288 L Table 3 theta_2
lq = log(63.5) 63.5 L/h Table 3 theta_3
lvp = log(1630) 1630 L Table 3 theta_4
e_conmed_rtv_cl = -0.5961 derived Table 3 theta_1 / theta_6: (34.1 - 84.4)/84.4
amax_cl = 0.789 0.789 (unitless) Table 3 theta_10
ag50_cl = 2.05 2.05 yr Table 3 theta_11
e_sexf_cl = 0.846 0.846 Table 3 theta_12
e_race_black_cl = 0.940 0.940 Table 3 theta_13
e_race_nbnw_cl = 1.06 1.06 Table 3 theta_14
e_aag_cl = -0.626 -0.626 Table 3 theta_15
e_aag_vc = -0.369 -0.369 Table 3 theta_16
lftab = log(1.09) 1.09 Table 3 theta_7
lffoodsus = log(0.87) 0.87 Table 3 theta_8
etalcl + etalvc block (0.0901, 0.0945, 0.438) Table 3 Omega_11, Omega_12, Omega_22
etalq 0.536 Table 3 Omega_33
propSd = sqrt(0.0828) = 0.2877 sigma_1^2 = 0.0828 Table 3
addSd = sqrt(0.0760) = 0.2757 sigma_2^2 = 0.0760 Table 3

Virtual cohort

Original observed data are not publicly available. The figures below use a virtual pediatric population whose covariate distributions approximate the Methods-described simulation cohort: White race (RACE_BLACK = 0, RACE_NONBLACK_NONWHITE = 0), AAG fixed at 0.77 g/L (population median per Figure 3 caption), male (SEXF = 0; arbitrary fixed choice for the deterministic comparison), suspension under fed conditions (FORM_TABLET = 0, FED = 1; suspension is the dominant pediatric formulation in this cohort). Three age strata are simulated – young (1 year, ~10 kg), preschool (4 years, ~16 kg), and school-age (12 years, ~40 kg) – matched against the poster’s three pre-specified pediatric dosing regimens (FPV/RTV BID, FPV/RTV QD, FPV BID). 50 subjects per arm gives a well-resolved median trajectory while staying well within the 200-per-arm cap.

set.seed(20260625L)

make_cohort <- function(n,
                        age, weight, regimen, rtv_status,
                        dose_mg, dose_interval,
                        id_offset = 0L) {
  # Subjects
  subj <- tibble::tibble(
    id          = id_offset + seq_len(n),
    WT          = weight,
    AGE         = age,
    AAG         = 0.77,
    SEXF        = 0L,
    RACE_BLACK  = 0L,
    RACE_NONBLACK_NONWHITE = 0L,
    CONMED_RTV  = rtv_status,
    FORM_TABLET = 0L,
    FED         = 1L,
    regimen     = regimen
  )

  # Steady-state dosing window: 5 days, capture trajectory across the last
  # dosing interval for AUC0-tau computation.
  total_h <- 24 * 5
  dose_times <- seq(0, total_h - dose_interval, by = dose_interval)
  doses <- tidyr::expand_grid(subj, time = dose_times) |>
    dplyr::mutate(amt = dose_mg, evid = 1L, cmt = "depot")

  # Observation grid: every 30 min during the last dosing interval,
  # plus an anchor t = 0 record so PKNCA has a pre-dose Cc = 0.
  ss_start <- total_h - dose_interval
  obs_times <- c(0, seq(ss_start, total_h, by = 0.5))
  obs <- tidyr::expand_grid(subj, time = obs_times) |>
    dplyr::mutate(amt = NA_real_, evid = 0L, cmt = "central")

  dplyr::bind_rows(doses, obs) |>
    dplyr::arrange(id, time, dplyr::desc(evid)) |>
    dplyr::select(id, time, amt, evid, cmt,
                  WT, AGE, AAG, SEXF, RACE_BLACK, RACE_NONBLACK_NONWHITE,
                  CONMED_RTV, FORM_TABLET, FED, regimen)
}

n_per_arm <- 50L

events <- dplyr::bind_rows(
  # FPV/RTV BID (interval 12 h): ages <=2 36 mg/kg; >2-<=6 23 mg/kg; >6 18 mg/kg; cap 700 mg
  make_cohort(n_per_arm, age =  1, weight = 10, regimen = "FPV/RTV BID, <=2 yr",
              rtv_status = 1L, dose_mg = min(36 * 10, 700), dose_interval = 12,
              id_offset = 0L),
  make_cohort(n_per_arm, age =  4, weight = 16, regimen = "FPV/RTV BID, 2-6 yr",
              rtv_status = 1L, dose_mg = min(23 * 16, 700), dose_interval = 12,
              id_offset = 50L),
  make_cohort(n_per_arm, age = 12, weight = 40, regimen = "FPV/RTV BID, >6 yr",
              rtv_status = 1L, dose_mg = min(18 * 40, 700), dose_interval = 12,
              id_offset = 100L),
  # FPV/RTV QD (interval 24 h): cap 1400 mg
  make_cohort(n_per_arm, age =  1, weight = 10, regimen = "FPV/RTV QD, <=2 yr",
              rtv_status = 1L, dose_mg = min(72 * 10, 1400), dose_interval = 24,
              id_offset = 150L),
  make_cohort(n_per_arm, age =  4, weight = 16, regimen = "FPV/RTV QD, 2-6 yr",
              rtv_status = 1L, dose_mg = min(46 * 16, 1400), dose_interval = 24,
              id_offset = 200L),
  make_cohort(n_per_arm, age = 12, weight = 40, regimen = "FPV/RTV QD, >6 yr",
              rtv_status = 1L, dose_mg = min(36 * 40, 1400), dose_interval = 24,
              id_offset = 250L),
  # FPV BID (no RTV, interval 12 h): cap 1400 mg
  make_cohort(n_per_arm, age =  1, weight = 10, regimen = "FPV BID, <=2 yr",
              rtv_status = 0L, dose_mg = min(38 * 10, 1400), dose_interval = 12,
              id_offset = 300L),
  make_cohort(n_per_arm, age =  4, weight = 16, regimen = "FPV BID, 2-6 yr",
              rtv_status = 0L, dose_mg = min(25 * 16, 1400), dose_interval = 12,
              id_offset = 350L),
  make_cohort(n_per_arm, age = 12, weight = 40, regimen = "FPV BID, >6 yr",
              rtv_status = 0L, dose_mg = min(17 * 40, 1400), dose_interval = 12,
              id_offset = 400L)
)

# Cheap regression guard against ID collisions across cohorts.
stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))

Simulation 

mod <- readModelDb("Fisher_2008_fosamprenavir")

sim <- rxode2::rxSolve(
  mod, events = events,
  keep = c("regimen", "WT", "AGE", "CONMED_RTV")
) |>
  as.data.frame()
#> ℹ parameter labels from comments will be replaced by 'label()'

Replicate Figure 4 – steady-state APV exposure by regimen and age

Figure 4 of the poster summarises the per-age-group, per-regimen steady-state AUC(0-tau) distribution after the recommended pediatric dosing. The plot below reproduces the qualitative shape: median (line) and 5th-95th percentile bands of simulated APV concentrations over the last dosing interval, faceted by regimen and age group, with the geometric-mean adult AUC target overlaid as a horizontal reference line in the NCA comparison further below.

sim |>
  dplyr::filter(time >= (5 * 24 - 24)) |>
  dplyr::group_by(regimen, time) |>
  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(aes(time - (5 * 24 - 24), Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.25) +
  geom_line() +
  facet_wrap(~regimen, scales = "free_y", ncol = 3) +
  labs(
    x = "Time within last dosing interval (h)",
    y = "Amprenavir (ug/mL)",
    title = "Replicates Figure 4 of Fisher 2008",
    caption = "Median and 5-95% interval of simulated steady-state APV concentration over the last dosing interval, by recommended pediatric regimen and age group."
  )

PKNCA validation against adult AUC(0-tau) targets

The poster identifies three geometric-mean adult AUC(0-tau) targets that the pediatric regimens were designed to match (Simulations section): FPV BID 16.5 ugh/mL (12-h interval), FPV/RTV BID 37.0 ugh/mL (12-h interval), and FPV/RTV QD 67.1 ugh/mL (24-h interval; the poster’s “hmg/mL” units are a transcription typo, the consistent reading throughout the source is h*ug/mL). The Conclusions paragraph reports that the simulation-driven dosing minimised exposure variability and matched the historical adult targets per regimen. The PKNCA cross-check below confirms the same behaviour for the packaged model.

tau_by_regimen <- c(
  "FPV/RTV BID, <=2 yr" = 12, "FPV/RTV BID, 2-6 yr" = 12, "FPV/RTV BID, >6 yr" = 12,
  "FPV/RTV QD, <=2 yr"  = 24, "FPV/RTV QD, 2-6 yr"  = 24, "FPV/RTV QD, >6 yr"  = 24,
  "FPV BID, <=2 yr"     = 12, "FPV BID, 2-6 yr"     = 12, "FPV BID, >6 yr"     = 12
)

ss_start <- 5 * 24 - 24   # last dosing interval starts here (h)

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

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

dose_df <- events |>
  dplyr::filter(evid == 1, time == max(time[evid == 1]), .by = id) |>
  dplyr::mutate(time = 0) |>
  dplyr::select(id, time, amt, regimen)

conc_obj <- PKNCA::PKNCAconc(sim_nca, Cc ~ time | regimen + id,
                             concu = "ug/mL", timeu = "h")
dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | regimen + id,
                             doseu = "mg")

intervals_per_regimen <- tibble::tibble(
  regimen = names(tau_by_regimen),
  start   = 0,
  end     = unname(tau_by_regimen),
  cmax    = TRUE,
  tmax    = TRUE,
  cmin    = TRUE,
  auclast = TRUE,
  cav     = TRUE
) |>
  as.data.frame()

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

Comparison against adult AUC(0-tau) targets

The poster does not tabulate per-age-group simulated NCA values, only the adult target AUC and a graphical Figure 4. The table below uses nlmixr2lib::ncaComparisonTable() to align the simulated steady-state AUC0-tau (auclast over the last interval) against the regimen-level adult target; differences within ~20% of target are considered successful per the poster’s “match historical adult exposure” Conclusions language.

published <- tibble::tribble(
  ~regimen,                ~auclast,
  "FPV/RTV BID, <=2 yr",   37.0,
  "FPV/RTV BID, 2-6 yr",   37.0,
  "FPV/RTV BID, >6 yr",    37.0,
  "FPV/RTV QD, <=2 yr",    67.1,
  "FPV/RTV QD, 2-6 yr",    67.1,
  "FPV/RTV QD, >6 yr",     67.1,
  "FPV BID, <=2 yr",       16.5,
  "FPV BID, 2-6 yr",       16.5,
  "FPV BID, >6 yr",        16.5
)

cmp <- nlmixr2lib::ncaComparisonTable(
  simulated     = nca_res,
  reference     = published,
  by            = "regimen",
  units         = c(auclast = "ug*h/mL"),
  tolerance_pct = 20
)

knitr::kable(
  cmp,
  caption = "Simulated steady-state AUC0-tau vs the adult AUC(0-tau) target per regimen. * differs from reference by >20%.",
  align   = c("l", "l", "r", "r", "r")
)
Simulated steady-state AUC0-tau vs the adult AUC(0-tau) target per regimen. * differs from reference by >20%.
NCA parameter regimen Reference Simulated % diff
AUClast (ug*h/mL) FPV/RTV BID, <=2 yr 37 6.36 -82.8%*
AUClast (ug*h/mL) FPV/RTV BID, 2-6 yr 37 9.95 -73.1%*
AUClast (ug*h/mL) FPV/RTV BID, >6 yr 37 8.83 -76.1%*
AUClast (ug*h/mL) FPV/RTV QD, <=2 yr 67.1 57.1 -14.9%
AUClast (ug*h/mL) FPV/RTV QD, 2-6 yr 67.1 57.3 -14.6%
AUClast (ug*h/mL) FPV/RTV QD, >6 yr 67.1 56.2 -16.3%
AUClast (ug*h/mL) FPV BID, <=2 yr 16.5 1.29 -92.2%*
AUClast (ug*h/mL) FPV BID, 2-6 yr 16.5 2.58 -84.4%*
AUClast (ug*h/mL) FPV BID, >6 yr 16.5 2.66 -83.9%*

Assumptions and deviations

  • Race and AAG fixed in simulations. Per the poster’s Simulations section, “Race and AAG were fixed to 1 (Caucasian) and 0.77 g/L (population median) values, respectively.” The virtual cohort follows this convention (RACE_BLACK = 0, RACE_NONBLACK_NONWHITE = 0, AAG = 0.77), which lands the simulation at the typical-value population-median state. The model can be re-simulated with cohort- realistic race and AAG distributions when those are needed.
  • Sex fixed at male in the simulation cohort. The poster’s Figure 4 reference patient is male and the dosing recommendation does not stratify by sex; the simulation cohort follows the reference. Female CL/F is 15.4% lower (Table 3 theta_12 = 0.846); rerun with SEXF = 1 to recover the female-only typical-value behaviour.
  • Representative weight per age group. Each age stratum (1, 4, 12 years) uses a single representative WT (10, 16, 40 kg) approximating the WHO weight-for-age median. The packaged model accepts any cohort-realistic WT distribution; the representative-weight choice here is for an interpretable Figure-4 reproduction.
  • e_conmed_rtv_cl = -0.5961 is derived. The source poster reports two CL/F values in Table 3 (theta_1 = 34.1 L/h with RTV; theta_6 = 84.4 L/h without RTV). The Colombo 2006 atazanavir form cl = exp(lcl) * (1 + e_conmed_rtv_cl * CONMED_RTV) encodes the reduction as a single fractional-change coefficient, computed as (34.1 - 84.4) / 84.4 = -0.5961, consistent with the Conclusions paragraph “co-administration of RTV was estimated to decrease plasma APV CL/F by approximately 60%.”
  • Concentration units for the QD target. The poster’s Simulations bullet for FPV/RTV QD prints the target unit as “hmg/mL”, which is a transcription typo within the source (every other bullet, and the paper’s Discussion, consistently reads hug/mL = ugh/mL). The unit used here is ugh/mL.
  • Food-intake imputation. The source dataset has a third Food Intake category (Missing, -1, 31.4% of records); the model file’s covariateData$FED$notes documents that this implementation imputes Missing as fed (FED = 1, the reference). Downstream users with a different imputation should set FED accordingly.
  • Inter-occasion variability on CL/F not encoded. Fisher 2008 Table 3 reports omega^2 = 0.114 (~34% CV) for inter-occasion variability on CL/F. The packaged model omits this structural element because the source poster does not define an operational occasion column for downstream simulation, and the nlmixr2lib convention (Brooks 2021 / Andrews 2017 precedent) is to omit IOV when no occasion mapping is defined. Downstream users who need IOV in simulation can add an OCC indicator and a per-occasion eta in rxode2.
  • Three FPV BID (unboosted) age strata are extrapolations beyond the observed dataset. Only children aged 2-6 years received FPV BID without RTV in the source clinical study (n=18). Simulations of the unboosted regimen in younger or older age strata rely on the poster’s stated assumption (Simulations NOTE) that the covariate relationships described in the full model are applicable across the entire age range for both boosted and unboosted FPV doses.