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Atazanavir (Dickinson 2009)

Source: vignettes/articles/Dickinson_2009_atazanavir.Rmd
Dickinson_2009_atazanavir.Rmd

Model and source

  • Citation: Dickinson L, Boffito M, Back D, Waters L, Else L, Davies G, Khoo S, Pozniak A, Aarons L. Population pharmacokinetics of ritonavir-boosted atazanavir in HIV-infected patients and healthy volunteers. J Antimicrob Chemother. 2009;63(6):1233-1243. doi:10.1093/jac/dkp102
  • Description: One-compartment first-order-absorption population PK model with absorption lag-time for oral ritonavir-boosted atazanavir in HIV-infected adults and healthy volunteers; ritonavir AUC0-24 (median 7.52 mg*h/L) enters CL/F via a power function (Dickinson 2009).
  • Article: J Antimicrob Chemother. 2009;63(6):1233-1243

Dickinson et al. (2009) describe a one-compartment first-order-absorption population PK model with absorption lag-time for orally administered ritonavir-boosted atazanavir in HIV-infected adults and healthy volunteers. The only covariate retained in the final model is ritonavir AUC over the 0-24 h dosing interval (RTVAUC0-24), which enters atazanavir CL/F via a power function centred at the cohort median of 7.52 mg*h/L (Table 2 / Table 3 of the paper).

Population

The analysis dataset pools three single-centre UK studies in adults (St Stephen’s Centre, Chelsea and Westminster Foundation Trust, London): 16 healthy volunteers (10 male / 6 female) and 30 HIV-infected patients (27 male / 3 female), all >=18 years old and stable on atazanavir/ritonavir for at least two weeks prior to PK sampling (Dickinson 2009 Table 1).

Baseline demographics from Table 1 (median and range pooled across cohorts):

Variable All (n = 46)
Sex (M:F) 37:9 (19.6% female)
Age (years) 43 (22-62)
Weight (kg) 76 (46-115)
BMI (kg/m^2) 24 (15-38)
Ritonavir AUC0-24 (mg*h/L) 7.52 (2.41-22.05)
Ethnicity Caucasian 33 (72%), Black-African 7 (15%), Hispanic 6 (13%)

Atazanavir/ritonavir was dosed 300/100 mg once daily under fed conditions (16-20 g fat). 18 of 46 patients also received saquinavir 1600 mg once daily; 6 of 46 received tenofovir 300 mg once daily. Sampling at pre-dose and 0.5, 1, 2, 3, 4, 6, 8, 10, 12, 24 h post-dose; healthy volunteers had additional samples at 16 and 20 h. A total of 538 atazanavir concentrations (range 0.077-8.763 mg/L) were used in model building. Lower-dose regimens (200/100 and 150/100 mg once daily) were used only in external validation (Figure 2 of the paper) and are not part of the model-building dataset; they can be simulated by changing the dose amount in the event table below.

The same information is available programmatically via the model’s population metadata (readModelDb("Dickinson_2009_atazanavir")$population).

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Dickinson_2009_atazanavir.R. The table below collects them in one place for review.

Parameter Value Source location
lcl log(7.7) Table 2 final-model column: CL/F = 7.7 L/h (RSE 5%)
lvc log(103) Table 2 final-model column: V/F = 103 L (RSE 13%)
lka log(3.4) Table 2 final-model column: ka = 3.4 1/h (RSE 34%)
ltlag log(0.96) Table 2 final-model column: Lag-time = 0.96 h (RSE 1%)
e_aucrtv_cl -0.8 Table 2 final-model column / Table 3 row 1: factor on RTVAUC0-24 power form (RSE 13%)
etalcl 0.0807 Table 2 IIV CL/F = 29% (RSE 59%); omega^2 = log(1 + 0.29^2)
etalvc 0.2074 Table 2 IIV V/F = 48% (RSE 37%); omega^2 = log(1 + 0.48^2)
etalka 1.2155 Table 2 IIV ka = 154% (RSE 51%); omega^2 = log(1 + 1.54^2)
propSd 0.23 Table 2 final-model column: proportional residual error 23% (RSE 27%)
addSd 0.08 Table 2 final-model column: additive residual error 0.08 mg/L (RSE 38%)

Covariate equation (paper Results page 1236, with Table 3 row 1 reporting the estimate):

CL/F_i = exp(lcl + etalcl_i) * (AUC_RTV_i / 7.52)^(-0.8)

ODE structure: one-compartment first-order absorption from depot to central, with an absorption lag-time tlag applied to depot. The observation variable is Cc = central / vc with combined additive + proportional residual error.

Load model 

mod <- readModelDb("Dickinson_2009_atazanavir")
mod_typical <- rxode2::zeroRe(mod)
#> ℹ parameter labels from comments will be replaced by 'label()'

Typical-value steady-state profile (300/100 mg once daily)

Replicates the labelled adult regimen with the cohort-median ritonavir AUC0-24 (7.52 mgh/L). The typical steady-state AUC0-24 should be approximately dose / CL/F = 300 / 7.7 = 38.96 mgh/L.

n_doses <- 14L     # 14 once-daily doses to reach steady state
ii      <- 24      # h
ev_ss <- rxode2::et(
  amt = 300, cmt = "depot", evid = 1,
  ii = ii, addl = n_doses - 1L
) |>
  rxode2::et(seq(0, n_doses * ii, by = 0.25)) |>
  rxode2::et(id = 1)
ev_ss$AUC_RTV <- 7.52

sim_ss <- rxode2::rxSolve(mod_typical, ev_ss)
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc', 'etalka'

ggplot(as.data.frame(sim_ss), aes(time / 24, Cc)) +
  geom_line(linewidth = 0.6) +
  labs(
    x = "Time (days)",
    y = "Atazanavir concentration (mg/L)",
    title = "Typical-value 14-day once-daily 300/100 mg ATV/RTV profile (AUC_RTV = 7.52 mg*h/L)"
  ) +
  theme_bw()

Typical-value steady-state dosing interval (Day 14, 24 h) 

sim_tau <- as.data.frame(sim_ss) |>
  dplyr::filter(time >= 13 * 24, time <= 14 * 24) |>
  dplyr::mutate(t_post_dose = time - 13 * 24)

ggplot(sim_tau, aes(t_post_dose, Cc)) +
  geom_line(linewidth = 0.7) +
  labs(
    x = "Time after dose (h)",
    y = "Atazanavir concentration (mg/L)",
    title = "Typical-value steady-state dosing interval (Day 14)"
  ) +
  theme_bw()

Virtual cohort matched to study demographics

We sample 80 virtual subjects whose covariate distributions reproduce the published baseline demographics. RTVAUC0-24 is sampled from approximately log-normal centred on 7.52 mg*h/L spanning the Table 1 range (2.41-22.05).

set.seed(2009)
n_subj <- 80L

# Ritonavir AUC0-24 ~ log-normal centred at the cohort median 7.52 mg*h/L,
# spanning the Table 1 range (2.41-22.05).
log_med   <- log(7.52)
log_sd    <- 0.45
AUC_RTV   <- pmin(22.05, pmax(2.41, exp(rnorm(n_subj, log_med, log_sd))))

cohort <- data.frame(
  ID      = seq_len(n_subj),
  AUC_RTV = AUC_RTV
)
summary(cohort$AUC_RTV)
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>   2.509   5.613   7.148   8.112   9.861  22.050

Stochastic simulation across the virtual cohort

Each subject receives 14 once-daily doses; observations are at 30-min resolution during the first dosing interval and once per dose interval through Day 14.

build_subject_events <- function(id, auc_rtv) {
  ev <- rxode2::et(
    amt = 300, cmt = "depot", evid = 1,
    ii = 24, addl = 13
  ) |>
    rxode2::et(c(seq(0, 24, by = 0.5), seq(13 * 24, 14 * 24, by = 0.5))) |>
    rxode2::et(id = id)
  df <- as.data.frame(ev)
  df$AUC_RTV <- auc_rtv
  df
}

ev_all <- do.call(
  rbind,
  Map(build_subject_events, cohort$ID, cohort$AUC_RTV)
)

set.seed(2009)
sim_pop <- rxode2::rxSolve(mod, ev_all)
#> ℹ parameter labels from comments will be replaced by 'label()'
sim_pop_df <- as.data.frame(sim_pop)

VPC: Day-1 vs Day-14 dosing intervals 

sim_day1 <- sim_pop_df |>
  filter(time >= 0, time <= 24) |>
  group_by(time) |>
  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"
  ) |>
  mutate(panel = "Day 1")

sim_day14 <- sim_pop_df |>
  filter(time >= 13 * 24, time <= 14 * 24) |>
  mutate(time_in_panel = time - 13 * 24) |>
  group_by(time_in_panel) |>
  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"
  ) |>
  rename(time = time_in_panel) |>
  mutate(panel = "Day 14")

vpc_df <- bind_rows(sim_day1, sim_day14)

ggplot(vpc_df, aes(time, Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), fill = "steelblue", alpha = 0.25) +
  geom_line(linewidth = 0.7) +
  facet_wrap(~panel) +
  labs(
    x = "Time after most recent dose (h)",
    y = "Atazanavir concentration (mg/L)",
    title = "Virtual-cohort VPC: median + 95% prediction interval",
    caption = "Replicates Figure 2(a) of Dickinson 2009 (300/100 mg ATV/RTV) qualitatively; the published figure is the 95% PI over 1000 simulated 24-h intervals."
  ) +
  theme_bw()

PKNCA validation

Non-compartmental analysis of the simulated steady-state (Day-14) dosing interval. The paper does not tabulate observed Cmax / Tmax / AUC0-24 from the NCA, but the typical-value AUC0-24 expected from dose / CL/F = 300 / 7.7 is 38.96 mg*h/L; the Day-14 simulated cohort median should fall close to that value.

nca_concs <- sim_pop_df |>
  filter(time >= 13 * 24, time <= 14 * 24) |>
  mutate(t_in_interval = time - 13 * 24) |>
  filter(!is.na(ipredSim))

dose_records <- cohort |>
  mutate(time = 0, amt = 300) |>
  select(id = ID, time, amt)

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

intervals <- data.frame(
  start    = 0,
  end      = 24,
  cmax     = TRUE,
  tmax     = TRUE,
  cmin     = TRUE,
  auclast  = TRUE,
  cav      = 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 |>
  filter(PPTESTCD %in% c("cmax", "tmax", "cmin", "auclast", "cav")) |>
  group_by(PPTESTCD) |>
  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 across the virtual cohort"
)
Day-14 steady-state PKNCA summary across the virtual cohort
PPTESTCD median P05 P95
auclast 38.883 19.354 70.085
cav 1.620 0.806 2.920
cmax 3.152 1.760 5.708
cmin 0.565 0.065 1.716
tmax 2.000 1.500 5.525

Comparison against published values

Quantity Paper value Simulated (median, 5th-95th)
Typical AUC0-24 (mg*h/L) dose / CL/F = 300 / 7.7 = 38.96 mg*h/L nca_summary auclast median (should fall within approximately 30-50 mg*h/L)
Atazanavir Cmax range (mg/L) observed range 0.077-8.763 mg/L (538 samples) virtual-cohort cmax 5th-95th should overlap this range
Typical half-life (h) 8.9 h (median individual estimate, Discussion) t1/2 = ln(2) * V/F / CL/F = 0.693 * 103 / 7.7 = 9.3 h (typical-value algebraic)

Dickinson 2009 does not report observed Cmax / Tmax / AUC0-24 NCA tables in the main paper. Where the paper does report a quantitative simulation summary (Discussion, page 1239), the model predicts 14% of trough concentrations at 300/100 mg once daily would fall below the 0.15 mg/L viral-suppression threshold. The simulated cohort cmin distribution above should reproduce that order of magnitude.

Assumptions and deviations

  1. Lag-time IIV omitted. The paper retains a typical lag-time of 0.96 h in the final model but reports that adding IIV on lag-time did not improve fit (delta-OFV = -0.8; Results page 1235). The library model follows the published final model and omits IIV on ltlag.
  2. Inter-laboratory error split omitted. The paper considered separate residual-error models for the two analytical laboratories and found no improvement (delta-OFV = -1.2; Results page 1235). A single combined proportional + additive residual-error model is used here.
  3. Ritonavir AUC0-24 supplied as a per-subject data column. The paper derives RTVAUC0-24 from observed ritonavir concentration-time data via non-compartmental analysis (WinNonlin 5.2). For simulation users without observed ritonavir concentrations, supplying the cohort median 7.52 mg*h/L reproduces typical-value behaviour. A future model could integrate the Dickinson 2008 (J Antimicrob Chemother) ritonavir PK model to compute RTVAUC0-24 endogenously.
  4. Concomitant medications (saquinavir, tenofovir) not modelled. Univariate tests of saquinavir and tenofovir status did not survive multivariate backwards elimination (Table 3; saquinavir significant on V/F and CL/F at p < 0.01 alone, but dropped during stepwise elimination because the model already accounted for ritonavir AUC). Body weight, sex, HIV status, and ethnicity (Black-African, Hispanic) were similarly excluded from the final model. None of these are included in the library model.
  5. Log-normal IIV from reported CV%. The paper reports IIV (%) on CL/F, V/F, and ka in the standard NONMEM exponential-model sense. These are converted to internal log-normal variances via omega^2 = log(1 + CV^2).
  6. Single-laboratory assumption. The paper uses two HPLC-MS/MS laboratories that participate in the same external QA programme and shows that inter-laboratory error stratification does not improve fit (Results page 1235). The library model uses a single residual-error block.

Reference

  • Dickinson L, Boffito M, Back D, Waters L, Else L, Davies G, Khoo S, Pozniak A, Aarons L. Population pharmacokinetics of ritonavir-boosted atazanavir in HIV-infected patients and healthy volunteers. J Antimicrob Chemother. 2009;63(6):1233-1243. doi:10.1093/jac/dkp102