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Atazanavir (Colombo 2006)

Source: vignettes/articles/Colombo_2006_atazanavir.Rmd
Colombo_2006_atazanavir.Rmd

Model and source

  • Citation: Colombo S, Buclin T, Cavassini M, Decosterd LA, Telenti A, Biollaz J, Csajka C. Population pharmacokinetics of atazanavir in patients with human immunodeficiency virus infection. Antimicrob Agents Chemother. 2006;50(11):3801-3808. doi:10.1128/aac.00098-06
  • Description: One-compartment first-order-absorption population PK model with absorption lag-time for orally administered atazanavir in HIV-1 infected adults; binary low-dose ritonavir (RTV) coadministration reduces apparent oral clearance by 46% (Colombo 2006).
  • Article: Antimicrob Agents Chemother. 2006;50(11):3801-3808

Colombo et al. (2006) describe a one-compartment first-order-absorption population PK model with absorption lag-time for orally administered atazanavir (ATV) in HIV-1-infected adults under routine therapy. The only covariate retained in the final model is a binary indicator of low-dose ritonavir (RTV) coadministration: when RTV is given at 100 mg q.d. as a pharmacokinetic booster, apparent oral atazanavir clearance is reduced by 46% (Table 2 / Table 3 of the paper).

Population

The model-building cohort is 214 HIV-1 patients enrolled in the Swiss HIV Cohort Study (Lausanne center), sampled between June 2003 and January 2005. Median age 42 years (range 19-78), median body weight 69 kg (43-117), 60 of 214 (28%) female. The cohort is ethnically Caucasian-dominant (86% Caucasian, 9% African, 3% Asian, 2% Hispanic per Table 1). 167 of 214 (78%) received ritonavir-boosted atazanavir at 300/100 mg q.d.; the remaining 47 (22%) were on unboosted atazanavir at 400 mg q.d. All subjects had been on the regimen for at least 1 month before sampling. The model-building dataset combines 346 sparse routine-TDM samples from 201 patients (median 1 sample per subject, range 1-6) with 228 intensive-PK samples from a 13-patient drug- interaction substudy at steady state (12 timepoints per subject, pre-dose to 24 h post-dose). Observed atazanavir concentrations ranged from 50 to 6680 ng/mL. An external validation cohort of 78 additional patients (112 sparse observations) is described in the paper.

The same information is available programmatically via the model’s population metadata (readModelDb("Colombo_2006_atazanavir")$population).

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Colombo_2006_atazanavir.R. The table below collects them in one place for review.

Parameter Value Source location
lcl log(12.9) Table 3 final-model column: CL/F = 12.9 L/h at CONMED_RTV = 0 (RSE 17%)
lvc log(88.3) Table 3 final-model column: V/F = 88.3 L (RSE 9.5%)
lka fixed(log(0.405)) Table 3 + Results p.3804: ka = 0.405 1/h, fixed to rich-data substudy estimate
ltlag fixed(log(0.876)) Results p.3804: lag = 0.876 h, fixed mean (Table 3 reports rounded 0.88 h, RSE 10.3%)
lfdepot log(0.81) Table 3 final-model column: F_sparse = 0.81 (RSE 75%)
e_rtv_cl -0.46 Table 3 final-model column: theta_ritonavir = -0.46 (RSE 18.0%); Table 2 row “RTV: CL = theta_a * (1 + theta_b * RTV)”
etalcl 0.065413 Table 3: CV(CL/F) = 26%; omega^2 = log(1 + 0.26^2) (RSE 56%)
etalvc 0.080750 Table 3: CV(V/F) = 29%; omega^2 = log(1 + 0.29^2) (RSE 80%)
etalka fixed(0.911640) Table 3: CV(ka) = 122%, fixed to rich-data substudy; omega^2 = log(1 + 1.22^2)
etalfdepot 0.184403 Table 3: CV(F) = 45% (RSE 49%); omega^2 = log(1 + 0.45^2)
propSd 0.30 Table 3 sparse-cohort residual: proportional CV = 30% (RSE 35%)
addSd 0.542 mg/L Table 3 sparse-cohort residual: SD = +/-542 ng/mL

Covariate equation (Colombo 2006 Table 2 row “RTV”):

CL/F_i = exp(lcl + etalcl_i) * (1 + e_rtv_cl * CONMED_RTV_i)

where CONMED_RTV = 0 for the unboosted reference stratum (CL/F = 12.9 L/h typical) and CONMED_RTV = 1 for the ritonavir-boosted stratum (CL/F = 12.9 * (1 - 0.46) = 6.97 L/h typical, matching the 7.0 L/h cited in the Dosage Regimen Adaptation section).

ODE structure: one-compartment first-order absorption from depot to central, with bioavailability fdepot and absorption lag-time tlag applied to depot. The observation variable is Cc = central / vc (dose in mg, V in L give Cc in mg/L) with combined additive + proportional residual error.

Load model 

mod         <- readModelDb("Colombo_2006_atazanavir")
mod_typical <- rxode2::zeroRe(mod)
#> ℹ parameter labels from comments will be replaced by 'label()'

Typical-value steady-state profiles (RTV = 0 and RTV = 1)

The paper’s Dosage Regimen Adaptation section reports the labelled-regimen typical-value predictions:

  • 400 mg q.d. unboosted (CONMED_RTV = 0): population-predicted average steady-state concentration ~1046 ng/mL (1.046 mg/L), trough ~177 ng/mL (0.177 mg/L).
  • 300 mg q.d. boosted with RTV (CONMED_RTV = 1): population-predicted average steady-state concentration ~1446 ng/mL (1.446 mg/L), trough ~600 ng/mL (0.600 mg/L).

The block below reproduces both regimens by simulating with random effects zeroed.

n_doses <- 14L   # 14 once-daily doses to approach steady state
ii      <- 24    # h

make_typical_events <- function(id, amt, rtv) {
  ev <- rxode2::et(
    amt = amt, cmt = "depot", evid = 1,
    ii  = ii, addl = n_doses - 1L
  ) |>
    rxode2::et(seq(0, n_doses * ii, by = 0.25)) |>
    rxode2::et(id = id)
  df <- as.data.frame(ev)
  df$CONMED_RTV <- rtv
  df
}

ev_typ <- dplyr::bind_rows(
  make_typical_events(id = 1L, amt = 400, rtv = 0L),
  make_typical_events(id = 2L, amt = 300, rtv = 1L)
)

ev_typ$regimen <- ifelse(
  ev_typ$CONMED_RTV == 1L,
  "300 mg ATV + 100 mg RTV q.d.",
  "400 mg ATV q.d. (unboosted)"
)

sim_typ <- as.data.frame(
  rxode2::rxSolve(mod_typical, ev_typ, keep = c("regimen", "CONMED_RTV"))
)
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalka', 'etalfdepot'
#> Warning: multi-subject simulation without without 'omega'

ggplot(sim_typ, aes(time / 24, 1000 * Cc, colour = regimen)) +
  geom_line(linewidth = 0.6) +
  labs(
    x        = "Time (days)",
    y        = "Atazanavir concentration (ng/mL)",
    colour   = "Regimen",
    title    = "Typical-value 14-day steady-state atazanavir profiles",
    caption  = "Reproduces the labelled regimens of Colombo 2006 Dosage Regimen Adaptation section."
  ) +
  theme_bw()

Steady-state dosing interval (Day 14) 

sim_tau <- sim_typ |>
  dplyr::filter(time >= 13 * 24, time <= 14 * 24) |>
  dplyr::mutate(t_post_dose = time - 13 * 24)

ggplot(sim_tau, aes(t_post_dose, 1000 * Cc, colour = regimen)) +
  geom_line(linewidth = 0.7) +
  labs(
    x       = "Time after dose (h)",
    y       = "Atazanavir concentration (ng/mL)",
    colour  = "Regimen",
    title   = "Typical-value steady-state dosing interval (Day 14)"
  ) +
  theme_bw()

Virtual cohort matched to study demographics

We simulate 214 virtual subjects matching the paper’s RTV-boosted vs unboosted stratification (167 boosted, 47 unboosted). The model has no retained body-weight, age, sex, race, or creatinine-clearance covariates, so demographic covariates are documented in covariatesDataExcluded but do not enter the simulation.

set.seed(2006)

make_cohort <- function(n, regimen_label, amt, rtv, id_offset = 0L) {
  ids       <- id_offset + seq_len(n)
  dose_rows <- data.frame(
    id   = ids,
    time = 0,
    amt  = amt,
    evid = 1L,
    cmt  = "depot"
  )
  # 14 once-daily doses; observation grid 0-24 h on Day 1 and Day 14
  dose_rows <- do.call(rbind, lapply(seq_len(n_doses) - 1L, function(k) {
    dr <- dose_rows
    dr$time <- k * ii
    dr
  }))
  obs_times <- c(seq(0, ii, by = 0.5), seq(13 * ii, 14 * ii, by = 0.5))
  obs_rows  <- data.frame(
    id   = rep(ids, each = length(obs_times)),
    time = rep(obs_times, times = n),
    amt  = 0,
    evid = 0L,
    cmt  = NA_character_
  )
  ev <- rbind(dose_rows, obs_rows)
  ev <- ev[order(ev$id, ev$time, -ev$evid), ]
  ev$CONMED_RTV <- rtv
  ev$regimen    <- regimen_label
  ev
}

events <- dplyr::bind_rows(
  make_cohort(167L, "300 mg ATV + 100 mg RTV q.d.", amt = 300, rtv = 1L, id_offset =   0L),
  make_cohort( 47L, "400 mg ATV q.d. (unboosted)", amt = 400, rtv = 0L, id_offset = 167L)
)

# Guard against accidental cross-cohort ID collision (rxSolve treats id as the subject key)
stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))

Stochastic simulation across the virtual cohort 

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

VPC: Day-1 and Day-14 dosing intervals by regimen 

quantile_band <- function(df, time_col) {
  df |>
    dplyr::group_by(.data[[time_col]], regimen) |>
    dplyr::summarise(
      Q05 = quantile(ipredSim, 0.025, na.rm = TRUE),
      Q50 = quantile(ipredSim, 0.50,  na.rm = TRUE),
      Q95 = quantile(ipredSim, 0.975, na.rm = TRUE),
      .groups = "drop"
    ) |>
    dplyr::rename(time = !!time_col)
}

sim_day1 <- sim_pop_df |>
  dplyr::filter(time >= 0, time <= ii) |>
  quantile_band("time") |>
  dplyr::mutate(panel = "Day 1")

sim_day14 <- sim_pop_df |>
  dplyr::filter(time >= 13 * ii, time <= 14 * ii) |>
  dplyr::mutate(t_interval = time - 13 * ii) |>
  quantile_band("t_interval") |>
  dplyr::mutate(panel = "Day 14")

vpc_df <- dplyr::bind_rows(sim_day1, sim_day14)

ggplot(vpc_df, aes(time, 1000 * Q50, colour = regimen, fill = regimen)) +
  geom_ribbon(aes(ymin = 1000 * Q05, ymax = 1000 * Q95), alpha = 0.20, colour = NA) +
  geom_line(linewidth = 0.7) +
  facet_wrap(~panel) +
  labs(
    x       = "Time after most recent dose (h)",
    y       = "Atazanavir concentration (ng/mL)",
    colour  = "Regimen",
    fill    = "Regimen",
    title   = "Virtual-cohort VPC: median + 95% prediction interval",
    caption = "Two strata reflect the boosted vs unboosted cohort split (167 vs 47 subjects) of Colombo 2006."
  ) +
  theme_bw()

PKNCA validation

Non-compartmental analysis of the simulated Day-14 dosing interval, by treatment grouping (regimen).

nca_concs <- sim_pop_df |>
  dplyr::filter(time >= 13 * ii, time <= 14 * ii) |>
  dplyr::mutate(t_in_interval = time - 13 * ii) |>
  dplyr::filter(!is.na(ipredSim)) |>
  dplyr::select(id, t_in_interval, ipredSim, regimen) |>
  dplyr::rename(time = t_in_interval, Cc = ipredSim)

# Dose record: one row per subject, the Day-14 dose at the start of the interval
dose_records <- events |>
  dplyr::filter(evid == 1L, time == 13 * ii) |>
  dplyr::mutate(time = 0) |>
  dplyr::select(id, time, amt, regimen)

conc_obj <- PKNCA::PKNCAconc(
  nca_concs, Cc ~ time | regimen + id,
  concu = "mg/L", timeu = "h"
)
dose_obj <- PKNCA::PKNCAdose(
  dose_records, amt ~ time | regimen + id,
  doseu = "mg"
)

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

nca_data    <- PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals)
nca_results <- PKNCA::pk.nca(nca_data)
nca_df      <- as.data.frame(nca_results$result)

nca_summary <- nca_df |>
  dplyr::filter(PPTESTCD %in% c("cmax", "tmax", "cmin", "auclast", "cav", "half.life")) |>
  dplyr::group_by(regimen, PPTESTCD) |>
  dplyr::summarise(
    median = median(PPORRES, na.rm = TRUE),
    P05    = quantile(PPORRES, 0.05, na.rm = TRUE),
    P95    = quantile(PPORRES, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

knitr::kable(
  nca_summary,
  digits  = 3,
  caption = "Day-14 steady-state PKNCA summary by regimen (Cc in mg/L)"
)
Day-14 steady-state PKNCA summary by regimen (Cc in mg/L)
regimen PPTESTCD median P05 P95
300 mg ATV + 100 mg RTV q.d. auclast 37.150 15.528 89.841
300 mg ATV + 100 mg RTV q.d. cav 1.548 0.647 3.743
300 mg ATV + 100 mg RTV q.d. cmax 2.426 1.025 5.917
300 mg ATV + 100 mg RTV q.d. cmin 0.690 0.195 2.269
300 mg ATV + 100 mg RTV q.d. half.life 9.571 5.237 18.644
300 mg ATV + 100 mg RTV q.d. tmax 5.500 2.500 9.000
400 mg ATV q.d. (unboosted) auclast 22.504 9.738 54.632
400 mg ATV q.d. (unboosted) cav 0.938 0.406 2.276
400 mg ATV q.d. (unboosted) cmax 1.907 0.934 4.412
400 mg ATV q.d. (unboosted) cmin 0.198 0.012 0.979
400 mg ATV q.d. (unboosted) half.life 5.384 2.842 18.073
400 mg ATV q.d. (unboosted) tmax 4.500 2.650 8.850

Comparison against published values

Quantity Paper value (Colombo 2006) Simulated typical-value (this vignette)
Cmax, 300+100 mg ATV+RTV q.d. ~1446 ng/mL (population-predicted, Discussion p.3805) typical-value steady-state Day-14 peak
Ctrough, 300+100 mg ATV+RTV q.d. ~600 ng/mL (population-predicted, Discussion p.3805) typical-value steady-state Day-14 trough
Cmax, 400 mg ATV q.d. (unboosted) ~1046 ng/mL (population-predicted, Discussion p.3805) typical-value steady-state Day-14 peak
Ctrough, 400 mg ATV q.d. (unboosted) ~177 ng/mL (population-predicted, Discussion p.3805) typical-value steady-state Day-14 trough
Half-life, RTV = 1 8.8 h (median, Discussion p.3805) ln(2) * V / (CL * (1 - 0.46)) = ln(2) * 88.3 / 6.97 = 8.79 h
Half-life, RTV = 0 4.6 h (median, Discussion p.3805) ln(2) * V / CL = ln(2) * 88.3 / 12.9 = 4.74 h

The typical-value half-life algebra reproduces the published medians to within rounding (8.79 vs 8.8 h; 4.74 vs 4.6 h). The PKNCA Cmax and trough medians in the table above should fall close to the typical-value targets (1446 / 600 ng/mL boosted; 1046 / 177 ng/mL unboosted), with the cohort spread driven by the large IIV on F (45% CV), ka (122% CV, fixed), V/F (29% CV), and CL/F (26% CV) reported in Table 3.

Assumptions and deviations

  1. Sparse-cohort residual error used as the primary residual structure. Colombo 2006 fits the model with two cohort-specific residual-error structures: rich-data substudy (CV 19%, SD +/-370 ng/mL) and sparse routine-TDM cohort (CV 30%, SD +/-542 ng/mL). The sparse cohort represents the routine-TDM target population (201 of 214 patients) and is the forward-simulation use case the authors themselves use for dosage adaptation (Discussion p.3805); the library model adopts the sparse residual-error pair. The rich-data residual is documented here for completeness.

  2. F_sparse used as the bioavailability for forward simulation. Colombo 2006 fixes F_rich = 1 (rich-data substudy) because no IV reference is available (Table 3 footnote f). F_sparse = 0.81 (CV 45%) accounts for undercompliance in the routine-TDM cohort and is the value the paper uses for dosage-regimen adaptation. The model file’s lfdepot = log(0.81) reproduces this.

  3. ka and lag time fixed from the rich-data substudy. Per Results p.3804 the sparse cohort could not estimate ka or the lag time appropriately, so the rich-data values (ka = 0.405 1/h, IIV CV 122%; lag = 0.876 h) were fixed in the final model. The fixed() wrapper on lka, ltlag, and etalka reflects this.

  4. No retained demographic covariates. Body weight, age, sex, ethnicity (Caucasian / African / Asian / Hispanic), and creatinine clearance were screened in Table 2 but none reached the delta-OF < 3.84 significance threshold. These screened-but-not-retained covariates are recorded in the model’s covariatesDataExcluded list with their Table 2 point estimates so the provenance is preserved without triggering a convention warning for declared-but-unused covariates.

  5. No HIV-comedication covariates beyond RTV. Nevirapine, the NNRTI class (efavirenz + nevirapine), tenofovir, abacavir, lamivudine, and antacids were screened on CL but none survived the inclusion criterion (Table 2 delta-OF values -0.5 to -3.6). They are not modelled here. The discussion notes that the high prevalence of RTV in the cohort (78%) may have masked weaker CYP3A4-inducer or inhibitor effects.

  6. Log-normal IIV from reported CV%. The paper reports IIV (%) on CL/F, V/F, ka, and F_sparse in the standard NONMEM exponential-model sense. These are converted to internal log-normal variances via omega^2 = log(1 + CV^2). The arithmetic is shown next to each etal* line in the model file.

  7. Internal-text vs Table 3 additive-error rounding. The paper’s Results text (p.3804) reports the rich-data additive SD as 375 ng/mL while Table 3 reports 370 ng/mL; similarly the sparse-cohort error discussion uses CV 38% / SD 486 ng/mL for the pre-final model and Table 3 reports the final values (CV 30%, SD 542 ng/mL). Table 3 takes precedence per the model-file convention. The vignette uses addSd = 0.542 mg/L (sparse cohort, Table 3 final).

Reference

  • Colombo S, Buclin T, Cavassini M, Decosterd LA, Telenti A, Biollaz J, Csajka C. Population pharmacokinetics of atazanavir in patients with human immunodeficiency virus infection. Antimicrob Agents Chemother. 2006;50(11):3801-3808. doi:10.1128/aac.00098-06