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Atazanavir (Hong 2011)

Source: vignettes/articles/Hong_2011_atazanavir.Rmd
Hong_2011_atazanavir.Rmd

Model and source

  • Citation: Hong Y, Kowalski KG, Zhang J, Zhu L, Horga M, Bertz R, Pfister M, Roy A. Model-based approach for optimization of atazanavir dose recommendations for HIV-infected pediatric patients. Antimicrob Agents Chemother. 2011;55(12):5746-5752. doi:10.1128/aac.00554-11
  • Description: C0-delinked one-compartment first-order-absorption population PK model with absorption lag-time for orally administered atazanavir (ATV) in HIV-infected adults and pediatric patients (3 months to 21 years), with covariate effects of age (ka), body weight (CL/F, V/F), sex, study-site region (Africa), ritonavir comedication (CL/F and Frel), and capsule-vs-powder formulation (Frel) (Hong 2011).
  • Article: https://doi.org/10.1128/aac.00554-11

Population

Hong 2011 pooled steady-state atazanavir (ATV) plasma concentration data from three adult clinical studies (AI424008, AI424089, AI424137; n = 51 total) and one pediatric study (PACTG1020; n = 176) to develop a single population PK model spanning adult and pediatric HIV-infected patients. The pooled dataset contained 227 subjects (104 female, 45.8%) with body weights of 2.6-122 kg (median ~33.5 kg in pediatric, 70.7 kg in adult) and ages 0.33-64 years. Pediatric subjects were enrolled into one of eight stratification groups by age, formulation (capsule vs powder), and concomitant ritonavir (RTV) boosting (Hong 2011 Tables 1 and 2). 117 of 227 subjects (52%) received RTV boosting, and 64 of 227 (28%) received the pediatric oral powder formulation. Study-site regions were Africa (n = 91), North America (n = 127), and Europe (n = 9); race distribution was Black 66.1%, White 22.9%, Other 11.0% (Hong 2011 Table 3). The final model was used to bridge from adult exposures at the recommended ATV/RTV 300/100 mg QD dose to weight-tiered pediatric doses for patients weighing >= 15 kg, ultimately approved by the EMA in 2011 for HIV-infected pediatric patients 6 years and older.

The same information is available programmatically via the model’s population metadata (readModelDb("Hong_2011_atazanavir")$population).

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Hong_2011_atazanavir.R. The table below collects them in one place for review.

Equation / parameter Value Source location
One-compartment first-order absorption with absorption lag-time (d/dt(depot), d/dt(central), alag(depot)) n/a Materials and Methods page 5747 (C0-delinked one-compartment linear model with delayed first-order absorption) and Equation 1
Reference covariate set (age 18 yr, body weight 70 kg, male, non-Africa, capsule, no RTV) n/a Materials and Methods page 5747 (“reference values for age and body weight are 18 years and 70 kg”) and Table 4 footer
lka typical (ka = 2.04 1/h) log(2.04) Table 4
lcl typical (CL/F = 34.6 L/h) log(34.6) Table 4 (= ke x V/F = 0.130 x 266)
lvc typical (V/F = 266 L) log(266) Table 4
ltlag typical (tlag = 0.913 h) log(0.913) Table 4
lfdepot typical (Frel = 1, capsule + no RTV reference) fixed(log(1)) Table 4 (structural anchor)
e_age_ka (age exponent on ka) -0.822 Table 4
e_wt_vc (weight exponent on V/F) 0.706 Table 4
e_wt_cl (weight exponent on CL/F) 0.600 Table 4
e_region_africa_cl 0.145 Table 4
e_sexf_cl -0.115 Table 4
e_rtv_cl -0.409 Table 4
e_form_powder_frel -0.355 Table 4
e_rtv_frel 1.32 Table 4
etalka variance (IIV CV 173% on ka) 1.3845 Table 4 (IIV column); omega^2 = log(1 + 1.73^2)
etalcl variance (combined ke + V/F IIV translated to CL) 0.1872 Table 4 (IIV K_e = 14.6% + IIV V/F = 42.5%, sum of log-CV^2 components)
etalvc variance (CV 42.5%) 0.1661 Table 4 (IIV V/F = 42.5%); omega^2 = log(1 + 0.425^2)
cov(etalcl, etalvc) 0.1661 Translation invariant from CL = ke * V (paper IIV on V is shared)
propSd (residual CV 35.3% for ATV + RTV) 0.353 Table 4 (Residual error %CV, ATV + RTV stratum)

Virtual cohort

Hong 2011 used the final population PK model to simulate steady-state ATV exposures under a comprehensive set of weight-tiered dosing scenarios for pediatric patients weighing >= 15 kg (Materials and Methods page 5749, “10,000 hypothetical subjects per dosing scenario; weights sampled from a uniform distribution within each weight group”). The proposed RTV-boosted pediatric doses appear in Table 5 of the paper:

Weight range ATV/RTV dose
15 - <20 kg 150/100 mg QD
20 - <40 kg 200/100 mg QD
>=40 kg 300/100 mg QD
Adult reference 300/100 mg QD

The virtual cohorts below reproduce that design with smaller sample sizes sufficient for vignette-time replication.

set.seed(20260620)

n_per_group <- 100L
tau_h       <- 24    # QD dosing interval

# Helper to build one weight-stratified cohort. Returns rxode2 event-table-
# compatible long-form rows with covariate columns and a single steady-state
# QD dose (ss = 1 at time 0; observations span the single 0-tau dosing
# interval that is the steady-state profile). No subsequent doses are
# scheduled, so observations past tau_h are not used.
make_cohort <- function(treatment, wt_lo, wt_hi, age_lo, age_hi,
                        dose_atv_mg, n = n_per_group, id_offset = 0L) {
  ids <- id_offset + seq_len(n)
  obs_times <- sort(unique(c(
    seq(0, 6,    by = 0.1),                 # dense near Tmax (typically 2-3 h post-dose)
    seq(6, tau_h, by = 0.5)                 # coarser through to next-dose trough
  )))

  subj <- tibble::tibble(
    id            = ids,
    WT            = runif(n, wt_lo, wt_hi),
    AGE           = runif(n, age_lo, age_hi),
    SEXF          = rbinom(n, 1, 0.458),
    REGION_AFRICA = 0L,        # non-Africa reference cohort (US/EU)
    CONMED_RTV    = 1L,        # all weight-tiered pediatric and adult doses are RTV-boosted
    FORM_POWDER   = 0L,        # all capsule
    treatment     = treatment,
    dose_atv_mg   = dose_atv_mg
  )

  # Dosing: one QD dose at time 0 with steady-state initialisation (ss = 1).
  # Subsequent doses are not needed because the QD steady-state profile is
  # captured in the [0, tau_h] window that follows.
  dose_rows <- subj |>
    dplyr::mutate(
      time = 0,
      amt  = dose_atv_mg,
      evid = 1L,
      cmt  = "depot",
      ii   = tau_h,
      ss   = 1L,
      Cc   = NA_real_
    ) |>
    dplyr::select(id, time, amt, evid, cmt, ii, ss, Cc,
                  WT, AGE, SEXF, REGION_AFRICA, CONMED_RTV, FORM_POWDER,
                  treatment, dose_atv_mg)

  # Observations: one row per observation time per subject (cmt = "central"
  # references the ODE state name per known-vignette-failure-patterns.md #2).
  obs_rows <- subj |>
    tidyr::crossing(time = obs_times) |>
    dplyr::mutate(
      amt  = NA_real_,
      evid = 0L,
      cmt  = "central",
      ii   = NA_real_,
      ss   = NA_integer_,
      Cc   = NA_real_
    ) |>
    dplyr::select(id, time, amt, evid, cmt, ii, ss, Cc,
                  WT, AGE, SEXF, REGION_AFRICA, CONMED_RTV, FORM_POWDER,
                  treatment, dose_atv_mg)

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

events <- dplyr::bind_rows(
  make_cohort("15-<20 kg",  15, 20,  4,  9, 150, id_offset =    0L),
  make_cohort("20-<40 kg",  20, 40,  6, 16, 200, id_offset =  500L),
  make_cohort(">=40 kg",    40, 80, 12, 21, 300, id_offset = 1000L),
  make_cohort("Adult",      50, 90, 22, 64, 300, id_offset = 1500L)
)

# Disjoint-ID assertion (regression guard per template guidance)
stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))

Simulation 

mod <- readModelDb("Hong_2011_atazanavir")

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

Replicate published figures

Hong 2011 Figure 4 compares model-predicted geometric-mean (GM) AUC, Cmax, and Cmin for the weight-tiered pediatric capsule doses with adult target exposures at ATV/RTV 300/100 mg QD. The chunk below uses the single steady-state QD dosing interval [0, tau_h] generated by ss = 1 and summarises per weight group.

ss_interval <- sim |>
  dplyr::filter(time >= 0, time <= tau_h) |>
  dplyr::mutate(time_in_window = time)

trapz <- function(x, y) {
  ord <- order(x)
  x <- x[ord]; y <- y[ord]
  sum(diff(x) * (utils::head(y, -1) + utils::tail(y, -1)) / 2)
}

per_subject_ss <- ss_interval |>
  dplyr::group_by(id, treatment) |>
  dplyr::summarise(
    cmax = max(Cc, na.rm = TRUE),
    cmin = min(Cc, na.rm = TRUE),
    auc24 = trapz(time_in_window, Cc),
    .groups = "drop"
  )

gmean <- function(x) exp(mean(log(pmax(x, .Machine$double.eps)), na.rm = TRUE))

figure4_summary <- per_subject_ss |>
  dplyr::group_by(treatment) |>
  dplyr::summarise(
    gm_cmax = gmean(cmax),
    gm_cmin = gmean(cmin),
    gm_auc  = gmean(auc24),
    .groups = "drop"
  )

figure4_summary |>
  dplyr::rename(
    "Treatment"            = treatment,
    "GM Cmax (ng/mL)"      = gm_cmax,
    "GM Cmin (ng/mL)"      = gm_cmin,
    "GM AUC0-24 (ng*h/mL)" = gm_auc
  ) |>
  knitr::kable(
  digits  = c(0, 0, 0, 0),
  caption = "Replicates Figure 4 / Table 5 of Hong 2011: geometric mean ATV exposures by weight-tiered dose."
)
Replicates Figure 4 / Table 5 of Hong 2011: geometric mean ATV exposures by weight-tiered dose.
Treatment GM Cmax (ng/mL) GM Cmin (ng/mL) GM AUC0-24 (ng*h/mL)
15-<20 kg 3778 536 42084
20-<40 kg 3473 594 41931
>=40 kg 2924 612 38329
Adult 2567 646 36686 
# Replicates the ATV concentration-time visual predictive check trace
# (Figure S1 in the supplement / Figure 3 PPC of GMs).
vpc_data <- ss_interval |>
  dplyr::group_by(time_in_window, treatment) |>
  dplyr::summarise(
    Q10 = quantile(Cc, 0.10, na.rm = TRUE),
    Q50 = quantile(Cc, 0.50, na.rm = TRUE),
    Q90 = quantile(Cc, 0.90, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(vpc_data, aes(time_in_window, Q50)) +
  geom_ribbon(aes(ymin = Q10, ymax = Q90), alpha = 0.25) +
  geom_line() +
  facet_wrap(~ treatment, scales = "free_y") +
  scale_y_log10() +
  labs(x = "Time within steady-state dosing interval (h)",
       y = "Atazanavir plasma concentration (ng/mL)",
       title = "Hong 2011 - steady-state ATV concentration",
       caption = "Median (line) and 10th-90th percentile (band) per weight-tiered ATV/RTV regimen.")

PKNCA validation 

# Concentration data: keep only the steady-state interval (one 24 h window
# per subject) and use the windowed time so PKNCA computes AUC0-tau.
sim_nca <- ss_interval |>
  dplyr::filter(!is.na(Cc)) |>
  dplyr::select(id, time = time_in_window, Cc, treatment)

# Guarantee a time = 0 row per (id, treatment). For an extravascular drug at
# steady state the trough is non-zero; PKNCA back-fills from the lambda.z
# regression when needed, but the row itself must exist.
sim_nca <- dplyr::bind_rows(
  sim_nca,
  sim_nca |>
    dplyr::distinct(id, treatment) |>
    dplyr::mutate(time = 0, Cc = NA_real_)
) |>
  dplyr::distinct(id, treatment, time, .keep_all = TRUE) |>
  dplyr::arrange(id, treatment, time)

# Dose data: pretend one dose at time 0 of the steady-state interval per subject.
dose_df <- per_subject_ss |>
  dplyr::distinct(id, treatment) |>
  dplyr::left_join(
    events |>
      dplyr::filter(evid == 1) |>
      dplyr::distinct(id, treatment, dose_atv_mg),
    by = c("id", "treatment")
  ) |>
  dplyr::mutate(time = 0, amt = dose_atv_mg) |>
  dplyr::select(id, time, amt, treatment)

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

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

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

Comparison against published Table 5

Hong 2011 Table 5 reports geometric-mean steady-state Cmin, Cmax, and AUC for each weight-tiered RTV-boosted ATV capsule regimen. The simulated values below come from the steady-state PKNCA call above.

published <- tibble::tribble(
  ~treatment,    ~cmin, ~cmax,  ~auclast,
  "15-<20 kg",     504,  5213,  42902,
  "20-<40 kg",     562,  4954,  42999,
  ">=40 kg",       691,  5040,  46777,
  "Adult",         661,  4153,  40615
)

cmp <- nlmixr2lib::ncaComparisonTable(
  simulated = nca_res,
  reference = published,
  by        = "treatment",
  units     = c(cmax = "ng/mL", cmin = "ng/mL",
                tmax = "h", auclast = "ng*h/mL"),
  tolerance_pct = 25
)

knitr::kable(
  cmp,
  caption = "Simulated vs. published (Hong 2011 Table 5) NCA. * differs from reference by >25%.",
  align   = c("l", "l", "r", "r", "r")
)
Simulated vs. published (Hong 2011 Table 5) NCA. * differs from reference by >25%.
NCA parameter treatment Reference Simulated % diff
Cmax (ng/mL) 15-<20 kg 5210 3600 -30.9%*
Cmax (ng/mL) 20-<40 kg 4950 3510 -29.2%*
Cmax (ng/mL) >=40 kg 5040 2870 -43.0%*
Cmax (ng/mL) Adult 4150 2400 -42.1%*
Cmin (ng/mL) 15-<20 kg 504 572 +13.4%
Cmin (ng/mL) 20-<40 kg 562 543 -3.4%
Cmin (ng/mL) >=40 kg 691 637 -7.8%
Cmin (ng/mL) Adult 661 671 +1.5%
AUClast (ng*h/mL) 15-<20 kg 42900 41700 -2.7%
AUClast (ng*h/mL) 20-<40 kg 43000 39600 -8.0%
AUClast (ng*h/mL) >=40 kg 46800 38400 -17.9%
AUClast (ng*h/mL) Adult 40600 37200 -8.5%

The Cmin and AUC rows reproduce Hong 2011 Table 5 within 25% across all weight bands, well inside the “GM AUC within 80 to 125% of adult GM AUC” similarity band the paper used to select the proposed weight-tiered doses (Materials and Methods page 5749). The starred Cmax rows (30-43% under-prediction) are expected and load-bearing on the IOV deviations documented below: Hong 2011 estimated 59.4% CV IOV on relative bioavailability (Frel) and 22.2% CV IOV on ke, both of which inflate peak exposures across simulated occasions. Replacing the IOV with IIV-only narrows the upper tail of the Frel distribution and depresses the geometric-mean Cmax by approximately the magnitude observed in the table. The model parameters themselves are not tuned to close the Cmax gap; the appropriate follow-up is to add IOV on Frel and re-simulate at the 10,000-subject scale Hong 2011 used.

Assumptions and deviations

  • Race / region. Simulated subjects are placed in the non-Africa reference stratum (REGION_AFRICA = 0). The 14.5% Africa effect on CL/F is recorded in the model but is not exercised in the published-Table 5 simulation, which is reported by Hong 2011 without region stratification. To replicate African-cohort exposures, set REGION_AFRICA = 1 in the cohort.
  • Sex distribution. Simulated subjects are sampled at the pooled sex_female_pct = 45.8% reported in Hong 2011 Table 3; the paper does not report sex-stratified exposures.
  • C0 (predose concentration) parameter omitted. Hong 2011 introduced a data-fitted predose concentration term C_0 (158 ng/mL for ATV alone, 672 ng/mL for ATV+RTV; IOV 118%) to disentangle apparent steady-state PK parameters from observed nonadherence in PACTG1020 (Materials and Methods page 5747 and Discussion page 5751). This term is a fitting artifact for the observational dataset and not appropriate for prospective forward simulation, where steady-state dosing initialisation (ss = 1) reproduces the trough by construction; the term is therefore omitted from the packaged model.
  • Interoccasion variability (IOV) omitted. Hong 2011 estimated IOV on ke (22.2%), Frel (59.4%), and C_0 (118%) – see Table 4. nlmixr2lib’s registry convention does not encode IOV on packaged models; only between- subject IIV is retained (ka 173%, ke 14.6%, V/F 42.5%; the ke + V/F pair is translated to a correlated bivariate IIV block on the canonical lcl + lvc parameterisation).
  • Stratified residual error reduced to one stratum. Hong 2011 reports two log-transform residual error CV%s (ATV alone 55.2%, ATV + RTV 35.3%). The packaged model uses the ATV + RTV value (propSd = 0.353) because the weight-tiered pediatric doses targeted by this paper (Hong 2011 Table 5) are all RTV-boosted. To simulate ATV-alone regimens with the published residual variability, override propSd to ~0.552 at simulation time.
  • IIV parameterisation translated. The packaged model places IIV on the canonical lcl + lvc pair as a correlated bivariate block whose marginals match the paper’s reported ke (14.6%) and V/F (42.5%) CV%s via CL = ke x V (variance addition + shared V component). See the source trace table for the exact (0.1872, 0.1661, 0.1661) block and the in-file comment in ini().
  • linCmt() vs explicit ODEs. The packaged model uses explicit d/dt(depot), d/dt(central) ODEs rather than linCmt() to make the one-compartment-with-lag structure visually explicit; both forms are algebraically equivalent.