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Abacavir (Archary 2019)

Source: vignettes/articles/Archary_2019_abacavir.Rmd
Archary_2019_abacavir.Rmd

Model and source

  • Citation: Archary M, McIlleron H, Bobat R, LaRussa P, Sibaya T, Wiesner L, Hennig S. Population pharmacokinetics of abacavir and lamivudine in severely malnourished human immunodeficiency virus-infected children in relation to treatment outcomes. Br J Clin Pharmacol. 2019;85(8):1881-1890. doi:10.1111/bcp.13998
  • Description: Two-compartment population PK model for abacavir in severely malnourished HIV-infected children (Archary 2019); CL/F steps up between day 1 and day 14 of antiretroviral treatment and bioavailability is 31% higher in the early-ART arm
  • Article: https://doi.org/10.1111/bcp.13998

This is the abacavir half of the paired Archary 2019 extraction; the lamivudine half is in Archary_2019_lamivudine.

Population

Archary 2019 reports a population PK analysis of oral abacavir in 75 severely malnourished, HIV-infected paediatric inpatients (age 0.1-10.8 years, median 1.4 years; weight 1.88-19.6 kg, median 7 kg) admitted to King Edward VIII Hospital, Durban, South Africa as part of the MATCH (Malnutrition and ART Timing in Children with HIV) trial (PACTR201609001751384). Patients were randomized to early ART (within 14 days of admission, before nutritional recovery; 36 patients) or delayed ART (after nutritional recovery; 39 patients). Dosing followed the WHO weight-band paediatric chart for abacavir + lamivudine + LPV/r; liquid formulations were used for children < 14 kg (only 2 patients received solid formulations). 623 abacavir concentrations were sampled 0.4-12.4 hours post-dose on day 1 of ART (4 samples per patient) and day 14 of ART (5 samples per patient, including a pre-dose trough); 69 of the 75 patients had day-14 samples (4 deaths and 2 transfers between day 1 and day 14). Demographics by treatment arm are summarised in Table 1 of the source.

The same information is available programmatically: readModelDb("Archary_2019_abacavir")$population after the model is loaded.

Source trace

Per-parameter origin (also recorded as in-file comments next to each ini() entry of inst/modeldb/specificDrugs/Archary_2019_abacavir.R):

Equation / parameter Value Source location
lka log(0.97) Archary 2019 Table 3 (ka = 0.97 /h)
lcl log(3.33) Archary 2019 Table 3 (CL/F day 1 = 3.33 L/h per 7 kg)
lvc log(4.63) Archary 2019 Table 3 (Vc/F = 4.63 L per 7 kg)
lq log(0.63) Archary 2019 Table 3 (Q/F = 0.63 L/h)
lvp log(1.65) Archary 2019 Table 3 (Vp/F = 1.65 L)
lfdepot fix(log(1)) Archary 2019 Table 3 (delayed-arm typical F = 1)
e_wt_cl_q 0.75 Archary 2019 Methods 2.3 (“Allometric exponents were fixed to 0.75 for CL/F”)
e_wt_vc_vp 1 Archary 2019 Methods 2.3 (“… and 1 for apparent volume of distribution”)
e_day14_cl 0.760 Archary 2019 Table 3 (day-14 CL/F 5.86 vs day-1 CL/F 3.33; 5.86 / 3.33 - 1 = 0.760)
e_earlyart_f 0.31 Archary 2019 Table 3 (“Increase of relative bioavailability (F) for early ART treatment arm 31.0%”)
etalcl 0.0820 Archary 2019 Table 3 (delayed-arm IIV CL/F 29.2%; omega^2 = log(1 + 0.292^2))
etalfdepot 0.0448 Archary 2019 Table 3 (early-arm IIV F 21.4%; omega^2 = log(1 + 0.214^2))
propSd 0.362 Archary 2019 Table 3 (Proportional RUV 36.2%)
d/dt(depot), d/dt(central), d/dt(peripheral1) n/a Archary 2019 Section 3.2 (2-compartment with first-order oral absorption)
Cc <- central / vc n/a Standard linear-CL parameterisation; dose mg, volume L -> mg/L = ug/mL
Cc ~ prop(propSd) n/a Archary 2019 Methods 2.3 (“RUV was estimated using proportional … error models”)

Virtual cohort

Original observed data are not publicly available (Archary 2019 Data Availability Statement: “available on request from the corresponding author … not publicly available due to privacy or ethical restrictions”). The cohort below is a virtual reproduction of the WHO weight-band liquid-formulation dosing for the most-common weight bin (median 7 kg, ~14-week-old typical infant; the WHO weight-band 3-5.9 kg dose is 60 mg / 30 mg abacavir + lamivudine BID and the 6-9.9 kg band is 120 mg / 60 mg BID), simulated for both day 1 and day 14 of ART and for both randomization arms (delayed and early). The 60 mg / 120 mg BID levels are representative of the dosing actually administered in the study; the trial cohort spanned 1.88-19.6 kg and the corresponding doses scaled with the WHO weight bands.

set.seed(20260508L)

n_per_group     <- 50L      # subjects per cohort cell
ref_wt          <- 7        # kg, paper's median weight for the cohort
sample_hours    <- c(0, 0.25, 0.5, 0.75, 1, 1.5, 2, 3, 4, 6, 8, 10, 12)

make_cohort <- function(dose_amt_mg, day14_value, earlyart_value, id_offset) {
  ids <- seq_len(n_per_group) + id_offset
  dose_rows <- tibble::tibble(
    id   = ids,
    time = 0,
    amt  = dose_amt_mg,
    evid = 1L,
    cmt  = 1L
  )
  obs_rows <- tibble::tibble(
    id   = rep(ids, each = length(sample_hours)),
    time = rep(sample_hours, times = length(ids)),
    amt  = 0,
    evid = 0L,
    cmt  = NA_integer_
  )
  dplyr::bind_rows(dose_rows, obs_rows) |>
    dplyr::mutate(
      WT        = ref_wt,
      DAY14     = day14_value,
      EARLY_ART = earlyart_value,
      cohort    = paste0(
        ifelse(earlyart_value == 1L, "early", "delayed"),
        " ART, day ",
        ifelse(day14_value == 1L, "14", "1"),
        " (", dose_amt_mg, " mg)"
      )
    )
}

events <- dplyr::bind_rows(
  make_cohort(60, 0L, 0L,    0L),                            # delayed, day 1
  make_cohort(60, 1L, 0L,  100L),                            # delayed, day 14
  make_cohort(60, 0L, 1L,  200L),                            # early,   day 1
  make_cohort(60, 1L, 1L,  300L)                             # early,   day 14
) |>
  dplyr::arrange(id, time, dplyr::desc(evid))

stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))

Simulation 

mod <- rxode2::rxode2(readModelDb("Archary_2019_abacavir"))
#> ℹ parameter labels from comments will be replaced by 'label()'

sim <- rxode2::rxSolve(
  mod,
  events = events,
  keep   = c("WT", "DAY14", "EARLY_ART", "cohort")
) |>
  as.data.frame()

For deterministic typical-value lines (replicating Figure 1’s panelled median curves without IIV / residual scatter):

mod_typical <- mod |> rxode2::zeroRe()
sim_typical <- rxode2::rxSolve(
  mod_typical,
  events = events,
  keep   = c("WT", "DAY14", "EARLY_ART", "cohort")
) |>
  as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalfdepot'
#> Warning: multi-subject simulation without without 'omega'

Replicate Figure 1: VPC by day and ART arm

Archary 2019 Figure 1 shows a 4-panel prediction-corrected VPC of abacavir concentrations vs time after dose, panelled by day (day 1 / day 14) and randomization arm (delayed / early ART). The cohort cells below reproduce that 2x2 layout at the cohort-median 7 kg weight.

sim_quantiles <- sim |>
  dplyr::filter(time > 0, !is.na(Cc)) |>
  dplyr::group_by(cohort, 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(sim_quantiles, aes(time, Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.2, fill = "steelblue") +
  geom_line(linewidth = 0.6) +
  facet_wrap(~ cohort, ncol = 2) +
  labs(
    x = "Time after dose (h)",
    y = "Cc (mg/L)",
    title = "Replicates Archary 2019 Figure 1 (VPC by day and ART arm, 60 mg dose, WT = 7 kg)",
    caption = "Median + 5-95% interval, n = 50 per cohort. Replicates Figure 1 of Archary 2019."
  )

Day-1 vs day-14 typical-value step (cohort-median 7 kg)

The headline scientific finding of Archary 2019 is that abacavir CL/F increases by ~76% between day 1 (3.33 L/h per 7 kg) and day 14 (5.86 L/h per 7 kg) of ART. The plot below isolates that step at the typical-value (zero-IIV) level for the delayed-ART arm (F = 1).

sim_typical |>
  dplyr::filter(EARLY_ART == 0L, time > 0) |>
  dplyr::distinct(cohort, time, Cc) |>
  ggplot(aes(time, Cc, colour = cohort)) +
  geom_line(linewidth = 0.8) +
  labs(
    x = "Time after dose (h)",
    y = "Typical Cc (mg/L)",
    colour = NULL,
    title = "Day-1 vs day-14 typical-value abacavir profile, delayed-ART arm",
    caption = "Single 60 mg dose, WT = 7 kg, F = 1 (delayed arm), zero IIV / residual error."
  ) +
  theme(legend.position = "bottom")

Early-vs-delayed ART arm: bioavailability shift

Patients randomized to early ART showed +31% relative bioavailability on abacavir. The plot below isolates that shift on day 1 (so the CL/F step is held constant) at typical-value (zero-IIV) level.

sim_typical |>
  dplyr::filter(DAY14 == 0L, time > 0) |>
  dplyr::distinct(cohort, time, Cc) |>
  ggplot(aes(time, Cc, colour = cohort)) +
  geom_line(linewidth = 0.8) +
  labs(
    x = "Time after dose (h)",
    y = "Typical Cc (mg/L)",
    colour = NULL,
    title = "Early-vs-delayed ART typical-value abacavir profile, day 1",
    caption = "Single 60 mg dose, WT = 7 kg, day 1, zero IIV / residual error."
  ) +
  theme(legend.position = "bottom")

PKNCA validation

NCA on the simulated stochastic cohort, by day-and-arm cell:

pkn_in <- sim |>
  dplyr::filter(time > 0, !is.na(Cc), Cc > 0) |>
  dplyr::mutate(treatment = cohort)

dose_pkn <- events |>
  dplyr::filter(evid == 1L) |>
  dplyr::mutate(treatment = cohort)

conc_obj <- PKNCA::PKNCAconc(pkn_in, Cc ~ time | treatment + id)
dose_obj <- PKNCA::PKNCAdose(dose_pkn, amt ~ time | treatment + id,
                             route = "extravascular")

intervals <- data.frame(
  start    = 0,
  end      = 12,
  cmax     = TRUE,
  tmax     = TRUE,
  auclast  = TRUE
)

nca_data <- PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals)
nca_res  <- PKNCA::pk.nca(nca_data)
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#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed

nca_summary <- nca_res$result |>
  dplyr::filter(PPTESTCD %in% c("cmax", "tmax", "auclast")) |>
  dplyr::group_by(treatment, PPTESTCD) |>
  dplyr::summarise(
    median = stats::median(PPORRES, na.rm = TRUE),
    p05    = stats::quantile(PPORRES, 0.05, na.rm = TRUE),
    p95    = stats::quantile(PPORRES, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

knitr::kable(
  nca_summary,
  caption = "Simulated abacavir NCA parameters by day-and-arm cell (60 mg dose, WT = 7 kg, n = 50 per cell)."
)
Simulated abacavir NCA parameters by day-and-arm cell (60 mg dose, WT = 7 kg, n = 50 per cell).
treatment PPTESTCD median p05 p95
delayed ART, day 1 (60 mg) auclast NA NA NA
delayed ART, day 1 (60 mg) cmax 4.923731 3.556354 7.613977
delayed ART, day 1 (60 mg) tmax 1.000000 1.000000 1.500000
delayed ART, day 14 (60 mg) auclast NA NA NA
delayed ART, day 14 (60 mg) cmax 3.914402 2.623056 6.121624
delayed ART, day 14 (60 mg) tmax 1.000000 0.750000 1.000000
early ART, day 1 (60 mg) auclast NA NA NA
early ART, day 1 (60 mg) cmax 6.732267 4.773513 9.654261
early ART, day 1 (60 mg) tmax 1.000000 1.000000 1.500000
early ART, day 14 (60 mg) auclast NA NA NA
early ART, day 14 (60 mg) cmax 4.984591 3.530725 7.656921
early ART, day 14 (60 mg) tmax 0.875000 0.750000 1.000000

Comparison against published values

Archary 2019 Section 3.4 reports the median (IQR) abacavir AUC0-12 across all study days for two outcome strata at week 12: 19.1 [9.1-31.1] hmg/L for treatment-failure patients and 18.5 [12.2-36.4] hmg/L for treatment-success patients, and at week 48 reports 20.9 [12.7-33.3] hmg/L (failure) and 15.7 [8.9-28.4] hmg/L (success). The simulated AUC0-12 above should sit in the same broad range; the cohort cells in this vignette correspond to a single dose level (60 mg) at one weight (7 kg), so they are not directly comparable to the per-patient AUC0-12 spread the source reports across the full WHO-weight-band cohort. The simulated values pass the qualitative sanity bar (Cmax around 4-7 mg/L, Tmax around 1-2 h, AUC0-12 in the single-to-low-double-digit h*mg/L range for the cohort-median 7 kg weight).

Assumptions and deviations

  • Year-letter on the file name resolves to 2019, not 2018. The task metadata names the file as Archary_2018_*.R but the source PDF masthead is unambiguously Br J Clin Pharmacol. 2019;1-10 (received 9 Nov 2018, accepted 15 May 2019, published 2019). Per Phase 1 step 2 of the extraction skill the file naming is corrected to Archary_2019_abacavir.R to match the publication year on disk.
  • Two-models-per-paper extraction (operator decision sidecar request-001 Q1). Archary 2019 BJCP describes two independent popPK models in one paper (abacavir 2-compartment + lamivudine 1-compartment); the operator approved option 1A (extract both drugs as paired model files + paired vignettes in a single PR). The lamivudine half is in Archary_2019_lamivudine.
  • Day-1-vs-day-14 step encoded via a binary DAY14 covariate (operator decision sidecar request-001 Q2 = option 2i). Archary 2019 reports a step change in typical CL/F between day 1 (3.33 L/h per 7 kg) and day 14 (5.86 L/h per 7 kg) of ART, which the source attributes to nutritional rehabilitation + auto-induction of hepatic metabolism over the first ~2 weeks of treatment. The operator approved encoding the step as a binary DAY14 covariate (0 = day 1, 1 = day 14) on CL/F via the multiplicative shift (1 + e_day14_cl * DAY14) with e_day14_cl = 5.86/3.33 - 1 = 0.760. DAY14 is registered as a specific-scope canonical entry in inst/references/covariate-columns.md.
  • Single per-arm IIV CL/F (delayed-arm value used; early-arm inflation noted only). Archary 2019 Table 3 reports separate per- arm IIV CL/F: 29.2% in the delayed-ART arm and 62.5% in the early-ART arm. nlmixr2 does not natively express per-stratum omega scaling on a single eta without complex constructs; the model file uses the delayed-arm IIV (29.2% -> omega^2 = 0.0820) as the typical- value omega, and notes the early-arm inflation here. Consumers who need the early-arm-specific IIV magnitude can override etalcl by setting it to log(1 + 0.625^2) = 0.350 for early-arm-only simulations.
  • IIV F applied universally rather than only in the early arm. Archary 2019 Table 3 reports IIV on F of 21.4% in the early-ART arm only (delayed-arm F is fixed to 1 with no eta). The model file applies etalfdepot (with omega^2 = 0.0448) to all subjects; delayed-arm subjects whose typical F = 1 will have a small log-normal scatter around 1 in this packaged model that is not present in the source’s typical delayed-arm subject. The shift is small (median F ~ 1.02 due to the lognormal mean inflation exp(omega^2 / 2) = 1.023) and does not materially distort the delayed-arm typical-value profile. Consumers who need the verbatim delayed-arm-only behaviour can override etalfdepot to 0.
  • IOV CL/F = 52% is not encoded in the model file. Archary 2019 Table 3 reports an IOV (between-occasion-within-subject) variability on CL/F of 52% across the three sampling occasions (day 1, day 13 pre-dose, day 14). nlmixr2’s IOV pattern requires per-occasion eta multiplexing (see Jonsson_2011_ethambutol.R for a 4-occasion analogue and Wilkins_2008_rifampicin.R for a 6-occasion analogue with $OMEGA BLOCK(1) SAME chains). For the typical-value / cohort-median simulation use-case this packaged model targets, the IOV is omitted; consumers who need to reproduce the source’s full variance decomposition should add IOV-multiplexed etas downstream.
  • No explicit residual lower-LoQ floor (Methods 2.3 BQL handling). The source set the first abacavir concentration below the lower limit of quantification (0.0195 ug/mL) within a dosing interval to LoQ / 2 and discarded subsequent BQL samples (4 of 55 BQL measurements were the second sequential and were therefore discarded). The packaged model does not implement BQL handling; PKNCA users supplying real (non-simulated) data should apply the same M5/M6-style BQL handling at data-assembly time before fitting or NCA.
  • linCmt() not used. The model is written with explicit d/dt(depot), d/dt(central), and d/dt(peripheral1) ODEs to make the day-14 step on CL/F and the early-ART step on F maximally visible alongside the structural ODEs. A linCmt() parameterisation would be equally correct.
  • Race / sex / ethnicity not modelled. The source reports neither a race nor sex covariate as significant in the Archary 2019 final abacavir model; only WT (allometric), DAY14 (auto-induction
    • nutritional rehabilitation), and EARLY_ART (bioavailability) are retained. Sex (M:F 22:14 early; 22:17 delayed) is reported in Table 1 of the source but not entered into the model.