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Lumefantrine (Francis 2020)

Source: vignettes/articles/Francis_2020_lumefantrine.Rmd
Francis_2020_lumefantrine.Rmd

Model and source 

mod <- rxode2::rxode2(readModelDb("Francis_2020_lumefantrine"))
#> ℹ parameter labels from comments will be replaced by 'label()'
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_fdepot_4, etaiov_fdepot_5, etaiov_fdepot_6, etaiov_fdepot_7, etaiov_fdepot_8, etaiov_fdepot_9, etaiov_fdepot_10, etaiov_fdepot_11, etaiov_fdepot_12, etaiov_mtt_1, etaiov_mtt_2, etaiov_mtt_3, etaiov_mtt_4, etaiov_mtt_5, etaiov_mtt_6, etaiov_mtt_7, etaiov_mtt_8, etaiov_mtt_9, etaiov_mtt_10, etaiov_mtt_11, etaiov_mtt_12, etaiov_ka_1, etaiov_ka_2, etaiov_ka_3, etaiov_ka_4, etaiov_ka_5, etaiov_ka_6, etaiov_ka_7, etaiov_ka_8, etaiov_ka_9, etaiov_ka_10, etaiov_ka_11, etaiov_ka_12
#> as a work-around try putting the mu-referenced expression on a simple line
  • Citation: Francis J, Barnes KI, Workman L, Kredo T, Vestergaard LS, Hoglund RM, Byakika-Kibwika P, Lamorde M, Walimbwa SI, Chijioke-Nwauche I, Sutherland CJ, Merry C, Scarsi KK, Nyagonde N, Lemnge MM, Khoo SH, Bygbjerg IC, Parikh S, Aweeka FT, Tarning J, Denti P (2020). An individual participant data population pharmacokinetic meta-analysis of drug-drug interactions between lumefantrine and commonly used antiretroviral treatment. Antimicrobial Agents and Chemotherapy 64(5):e02394-19. doi:10.1128/AAC.02394-19.
  • Description: Population PK model for oral lumefantrine from an individual participant data meta-analysis of 10 studies (793 non-pregnant adults, 6,100 concentrations; HIV-malaria coinfected, malaria-infected, HIV-infected and healthy volunteers from sub-Saharan Africa and the USA) treated with artemether-lumefantrine (Francis 2020 Antimicrob Agents Chemother). Savic transit-compartment absorption (MTT 2.86 h, 7.58 transit compartments, separate first-order ka) into three-compartment disposition with first-order elimination; allometric body-weight scaling (exponent 0.75 on clearances, 1 on volumes) centred at 57 kg. Drug-drug interactions: lopinavir-ritonavir-based ART (-50.1% CL/F, +67.2% F, -47.6% ka), efavirenz-based ART (+89.9% CL/F) and rifampicin-based antituberculosis treatment (+142% CL/F). Study- and dose-occasion-specific relative bioavailability (evening doses of InterACT/SEACAT = reference), a 2.28-fold dried-blood-spot matrix factor and an estimated 4.3 h delay of the unobserved 5th dose in two studies. BSV on CL/F, F and Q1/F, between-visit variability on CL/F and between-occasion (per-dose) variability on F, MTT and ka; combined additive and proportional residual error.
  • Article: doi:10.1128/AAC.02394-19

Artemether-lumefantrine is the most widely used treatment for uncomplicated falciparum malaria, and lumefantrine is cleared mainly by CYP3A4, which many antiretrovirals induce or inhibit. Francis 2020 pooled the individual participant data of 10 studies collected by the WorldWide Antimalarial Resistance Network (WWARN) to quantify these drug-drug interactions in one population pharmacokinetic model, and used it to predict the probability of a day-7 lumefantrine concentration below the 200 ng/mL efficacy threshold.

Population

The pooled data set contains 6,100 lumefantrine concentrations from 793 non-pregnant adults: 41% HIV-malaria coinfected, 36% malaria-infected, 20% HIV-infected and 3% healthy volunteers (Abstract; Table 1). 341 samples (5.59%) were below the LLOQ and were handled with the M6 method. The studies were SEACAT 2.4.1 and 2.4.2 (South Africa), InterACT (Tanzania), four Ugandan studies, two Nigerian studies and a U.S. healthy-volunteer study (Table 2). Concomitant treatments were no ART, nevirapine-, efavirenz-, dolutegravir- or lopinavir-ritonavir-based ART, and rifampicin-based antituberculosis treatment (13 participants). All participants received Coartem, 4 tablets (480 mg lumefantrine) per dose, twice daily for 3 days, except for two single-dose study phases. The median body weight was 57 kg, which is the allometric reference.

Source trace

Model element Value Source
Three-compartment disposition, first-order elimination – Results ‘(i) Structural model’
Savic transit absorption plus first-order ka – Results ‘(i)’; Methods
CL/F 3.28 L/h Table 3
Vc/F 60 L Table 3
Q1/F, Vp1/F 0.63 L/h, 182 L Table 3
Q2/F, Vp2/F 1.55 L/h, 39.1 L Table 3
MTT, NN, ka 2.86 h, 7.58, 0.727 1/h Table 3
F 1 (fixed) Table 3
Allometry on WT/57, exponents 0.75 / 1 (fixed) – Methods; Table 3 footnote c
LPV/r on CL/F, F, ka -50.1%, +67.2%, -47.6% Table 3
Efavirenz on CL/F +89.9% Table 3
Rifampicin on CL/F +142% Table 3
SEACAT first (morning) dose on F -48.6% Table 3
SEACAT consecutive morning doses on F -77.2% Table 3
Uganda studies on F -26.9% Table 3
Nigeria study 1, 6th dose, on F -60.8% Table 3 (Results text: 60.1%)
Delay of the unobserved 5th dose 4.30 h Table 3, footnote d; Results ‘(c)’
DBS scaling factor 2.28 Table 3, footnote e; Results ‘(b)’
BSV CL, F, Q1 20.8%, 30.2%, 29.1% Table 3
BVV CL 15.4% Table 3
BOV F, MTT, ka 56.5%, 31.9%, 73.8% Table 3
Additive, proportional error 32.9 ng/mL, 14.2% Table 3

Model structure checks

The transit input is the Savic gamma density with ktr = (NN + 1) / MTT, written out explicitly. A single dose in a typical subject must deliver exactly the administered amount, so AUC(0-inf) * CL / Dose must equal 1.

cov_zero <- c(
  CONMED_LPV = 0, CONMED_EFV = 0, CONMED_RIF = 0, STUDY_SEACAT = 0,
  STUDY_UGANDA = 0, STUDY_NIGERIA1 = 0, STUDY_USHV = 0, SAMPLE_DBS = 0
)

# Event table for n subjects on an AL regimen of `days` days (doses at 0 and
# 8 h, then every 12 h), observations at `tobs`. OCC is the dose number and is
# carried forward onto the observations that follow each dose.
make_events <- function(n, wt, tobs, days = 3, id0 = 0, covs = list()) {
  dose_t <- c(0, 8, if (days > 1) seq(24, 24 * days - 12, by = 12))
  ev <- expand.grid(id = id0 + seq_len(n), k = seq_along(dose_t))
  ev <- data.frame(
    id = ev$id, time = dose_t[ev$k], evid = 1, amt = 480, cmt = "depot",
    OCC = ev$k
  )
  ob <- expand.grid(id = id0 + seq_len(n), time = tobs)
  ob <- data.frame(id = ob$id, time = ob$time, evid = 0, amt = 0, cmt = "central")
  ob$OCC <- pmax(findInterval(ob$time, dose_t), 1)
  d <- rbind(ev, ob)
  d$WT <- wt
  for (nm in names(cov_zero)) d[[nm]] <- cov_zero[[nm]]
  for (nm in names(covs)) d[[nm]] <- covs[[nm]]
  d[order(d$id, d$time, -d$evid), ]
}

mod_typ <- rxode2::zeroRe(mod)
#> Warning: some etas defaulted to non-mu referenced, possible parsing error: etaiov_fdepot_1, etaiov_fdepot_2, etaiov_fdepot_3, etaiov_fdepot_4, etaiov_fdepot_5, etaiov_fdepot_6, etaiov_fdepot_7, etaiov_fdepot_8, etaiov_fdepot_9, etaiov_fdepot_10, etaiov_fdepot_11, etaiov_fdepot_12, etaiov_mtt_1, etaiov_mtt_2, etaiov_mtt_3, etaiov_mtt_4, etaiov_mtt_5, etaiov_mtt_6, etaiov_mtt_7, etaiov_mtt_8, etaiov_mtt_9, etaiov_mtt_10, etaiov_mtt_11, etaiov_mtt_12, etaiov_ka_1, etaiov_ka_2, etaiov_ka_3, etaiov_ka_4, etaiov_ka_5, etaiov_ka_6, etaiov_ka_7, etaiov_ka_8, etaiov_ka_9, etaiov_ka_10, etaiov_ka_11, etaiov_ka_12
#> as a work-around try putting the mu-referenced expression on a simple line
tgrid <- c(seq(0, 48, by = 0.1), seq(48.5, 400, by = 0.5), seq(410, 30000, by = 10))
d_sd <- make_events(1, 57, tgrid, days = 1)
d_sd <- d_sd[!(d_sd$evid == 1 & d_sd$time > 0), ]
sim_sd <- rxode2::rxSolve(mod_typ, d_sd, returnType = "data.frame")
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etabvv_cl', 'etalfdepot', 'etalq', 'etaiov_fdepot_1', 'etaiov_fdepot_2', 'etaiov_fdepot_3', 'etaiov_fdepot_4', 'etaiov_fdepot_5', 'etaiov_fdepot_6', 'etaiov_fdepot_7', 'etaiov_fdepot_8', 'etaiov_fdepot_9', 'etaiov_fdepot_10', 'etaiov_fdepot_11', 'etaiov_fdepot_12', 'etaiov_mtt_1', 'etaiov_mtt_2', 'etaiov_mtt_3', 'etaiov_mtt_4', 'etaiov_mtt_5', 'etaiov_mtt_6', 'etaiov_mtt_7', 'etaiov_mtt_8', 'etaiov_mtt_9', 'etaiov_mtt_10', 'etaiov_mtt_11', 'etaiov_mtt_12', 'etaiov_ka_1', 'etaiov_ka_2', 'etaiov_ka_3', 'etaiov_ka_4', 'etaiov_ka_5', 'etaiov_ka_6', 'etaiov_ka_7', 'etaiov_ka_8', 'etaiov_ka_9', 'etaiov_ka_10', 'etaiov_ka_11', 'etaiov_ka_12'
auc_sd <- sum(diff(sim_sd$time) * (head(sim_sd$Cc, -1) + tail(sim_sd$Cc, -1)) / 2)
mb <- auc_sd / 1000 * 3.28 / 480
mb
#> [1] 1.000007
stopifnot(max(sim_sd$Cc) > 1, abs(mb - 1) < 0.005)

The most-recent-dose semantics of tad() / podo() restart the transit input at every new dose. With MTT = 2.86 h against an 8-12 h dosing interval nothing is lost; the multiple-dose AUC matches the total dose over CL.

tgrid_md <- sort(unique(c(seq(0, 72, by = 0.1), seq(72.5, 400, by = 0.5), seq(410, 30000, by = 10))))
sim_md <- rxode2::rxSolve(mod_typ, make_events(1, 57, tgrid_md), returnType = "data.frame")
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etabvv_cl', 'etalfdepot', 'etalq', 'etaiov_fdepot_1', 'etaiov_fdepot_2', 'etaiov_fdepot_3', 'etaiov_fdepot_4', 'etaiov_fdepot_5', 'etaiov_fdepot_6', 'etaiov_fdepot_7', 'etaiov_fdepot_8', 'etaiov_fdepot_9', 'etaiov_fdepot_10', 'etaiov_fdepot_11', 'etaiov_fdepot_12', 'etaiov_mtt_1', 'etaiov_mtt_2', 'etaiov_mtt_3', 'etaiov_mtt_4', 'etaiov_mtt_5', 'etaiov_mtt_6', 'etaiov_mtt_7', 'etaiov_mtt_8', 'etaiov_mtt_9', 'etaiov_mtt_10', 'etaiov_mtt_11', 'etaiov_mtt_12', 'etaiov_ka_1', 'etaiov_ka_2', 'etaiov_ka_3', 'etaiov_ka_4', 'etaiov_ka_5', 'etaiov_ka_6', 'etaiov_ka_7', 'etaiov_ka_8', 'etaiov_ka_9', 'etaiov_ka_10', 'etaiov_ka_11', 'etaiov_ka_12'
auc_md <- sum(diff(sim_md$time) * (head(sim_md$Cc, -1) + tail(sim_md$Cc, -1)) / 2)
mb_md <- auc_md / 1000 * 3.28 / (6 * 480)
mb_md
#> [1] 1.000001
stopifnot(abs(mb_md - 1) < 0.005)

Typical concentration-time profiles

The typical 57-kg patient on the standard 3-day regimen at the reference bioavailability (InterACT, and SEACAT evening doses), by concomitant treatment.

scen <- list(
  "AL alone" = list(),
  "Lopinavir-ritonavir" = list(CONMED_LPV = 1),
  "Efavirenz" = list(CONMED_EFV = 1),
  "Rifampicin" = list(CONMED_RIF = 1)
)
tprof <- sort(unique(c(seq(0, 72, by = 0.25), seq(73, 336, by = 1))))
typ <- bind_rows(lapply(seq_along(scen), function(i) {
  s <- rxode2::rxSolve(mod_typ, make_events(1, 57, tprof, covs = scen[[i]]),
    returnType = "data.frame"
  )
  data.frame(time = s$time, Cc = s$Cc, treatment = names(scen)[i])
}))
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etabvv_cl', 'etalfdepot', 'etalq', 'etaiov_fdepot_1', 'etaiov_fdepot_2', 'etaiov_fdepot_3', 'etaiov_fdepot_4', 'etaiov_fdepot_5', 'etaiov_fdepot_6', 'etaiov_fdepot_7', 'etaiov_fdepot_8', 'etaiov_fdepot_9', 'etaiov_fdepot_10', 'etaiov_fdepot_11', 'etaiov_fdepot_12', 'etaiov_mtt_1', 'etaiov_mtt_2', 'etaiov_mtt_3', 'etaiov_mtt_4', 'etaiov_mtt_5', 'etaiov_mtt_6', 'etaiov_mtt_7', 'etaiov_mtt_8', 'etaiov_mtt_9', 'etaiov_mtt_10', 'etaiov_mtt_11', 'etaiov_mtt_12', 'etaiov_ka_1', 'etaiov_ka_2', 'etaiov_ka_3', 'etaiov_ka_4', 'etaiov_ka_5', 'etaiov_ka_6', 'etaiov_ka_7', 'etaiov_ka_8', 'etaiov_ka_9', 'etaiov_ka_10', 'etaiov_ka_11', 'etaiov_ka_12'
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etabvv_cl', 'etalfdepot', 'etalq', 'etaiov_fdepot_1', 'etaiov_fdepot_2', 'etaiov_fdepot_3', 'etaiov_fdepot_4', 'etaiov_fdepot_5', 'etaiov_fdepot_6', 'etaiov_fdepot_7', 'etaiov_fdepot_8', 'etaiov_fdepot_9', 'etaiov_fdepot_10', 'etaiov_fdepot_11', 'etaiov_fdepot_12', 'etaiov_mtt_1', 'etaiov_mtt_2', 'etaiov_mtt_3', 'etaiov_mtt_4', 'etaiov_mtt_5', 'etaiov_mtt_6', 'etaiov_mtt_7', 'etaiov_mtt_8', 'etaiov_mtt_9', 'etaiov_mtt_10', 'etaiov_mtt_11', 'etaiov_mtt_12', 'etaiov_ka_1', 'etaiov_ka_2', 'etaiov_ka_3', 'etaiov_ka_4', 'etaiov_ka_5', 'etaiov_ka_6', 'etaiov_ka_7', 'etaiov_ka_8', 'etaiov_ka_9', 'etaiov_ka_10', 'etaiov_ka_11', 'etaiov_ka_12'
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etabvv_cl', 'etalfdepot', 'etalq', 'etaiov_fdepot_1', 'etaiov_fdepot_2', 'etaiov_fdepot_3', 'etaiov_fdepot_4', 'etaiov_fdepot_5', 'etaiov_fdepot_6', 'etaiov_fdepot_7', 'etaiov_fdepot_8', 'etaiov_fdepot_9', 'etaiov_fdepot_10', 'etaiov_fdepot_11', 'etaiov_fdepot_12', 'etaiov_mtt_1', 'etaiov_mtt_2', 'etaiov_mtt_3', 'etaiov_mtt_4', 'etaiov_mtt_5', 'etaiov_mtt_6', 'etaiov_mtt_7', 'etaiov_mtt_8', 'etaiov_mtt_9', 'etaiov_mtt_10', 'etaiov_mtt_11', 'etaiov_mtt_12', 'etaiov_ka_1', 'etaiov_ka_2', 'etaiov_ka_3', 'etaiov_ka_4', 'etaiov_ka_5', 'etaiov_ka_6', 'etaiov_ka_7', 'etaiov_ka_8', 'etaiov_ka_9', 'etaiov_ka_10', 'etaiov_ka_11', 'etaiov_ka_12'
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etabvv_cl', 'etalfdepot', 'etalq', 'etaiov_fdepot_1', 'etaiov_fdepot_2', 'etaiov_fdepot_3', 'etaiov_fdepot_4', 'etaiov_fdepot_5', 'etaiov_fdepot_6', 'etaiov_fdepot_7', 'etaiov_fdepot_8', 'etaiov_fdepot_9', 'etaiov_fdepot_10', 'etaiov_fdepot_11', 'etaiov_fdepot_12', 'etaiov_mtt_1', 'etaiov_mtt_2', 'etaiov_mtt_3', 'etaiov_mtt_4', 'etaiov_mtt_5', 'etaiov_mtt_6', 'etaiov_mtt_7', 'etaiov_mtt_8', 'etaiov_mtt_9', 'etaiov_mtt_10', 'etaiov_mtt_11', 'etaiov_mtt_12', 'etaiov_ka_1', 'etaiov_ka_2', 'etaiov_ka_3', 'etaiov_ka_4', 'etaiov_ka_5', 'etaiov_ka_6', 'etaiov_ka_7', 'etaiov_ka_8', 'etaiov_ka_9', 'etaiov_ka_10', 'etaiov_ka_11', 'etaiov_ka_12'
stopifnot(all(tapply(typ$Cc, typ$treatment, max) > 1))

ggplot(typ, aes(time, Cc, colour = treatment)) +
  geom_line() +
  geom_hline(yintercept = 200, linetype = "dashed") +
  scale_y_log10(limits = c(10, NA)) +
  labs(
    x = "Time after first dose (h)", y = "Lumefantrine (ng/mL)", colour = NULL,
    caption = "Typical 57-kg adult, 480 mg twice daily for 3 days; dashed line 200 ng/mL."
  ) +
  theme_bw()
#> Warning in scale_y_log10(limits = c(10, NA)): log-10 transformation introduced
#> infinite values.

Exposure ratios of the drug-drug interactions

The Results report AUC changes of about 3.4-fold with lopinavir-ritonavir, -47% with efavirenz and -59% with rifampicin. For the typical patient these follow from F / CL alone, so they are exact checks of the encoding.

auc_typ <- function(covs) {
  s <- rxode2::rxSolve(mod_typ, make_events(1, 57, tgrid_md, covs = covs), returnType = "data.frame")
  sum(diff(s$time) * (head(s$Cc, -1) + tail(s$Cc, -1)) / 2)
}
auc_ref <- auc_typ(list())
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etabvv_cl', 'etalfdepot', 'etalq', 'etaiov_fdepot_1', 'etaiov_fdepot_2', 'etaiov_fdepot_3', 'etaiov_fdepot_4', 'etaiov_fdepot_5', 'etaiov_fdepot_6', 'etaiov_fdepot_7', 'etaiov_fdepot_8', 'etaiov_fdepot_9', 'etaiov_fdepot_10', 'etaiov_fdepot_11', 'etaiov_fdepot_12', 'etaiov_mtt_1', 'etaiov_mtt_2', 'etaiov_mtt_3', 'etaiov_mtt_4', 'etaiov_mtt_5', 'etaiov_mtt_6', 'etaiov_mtt_7', 'etaiov_mtt_8', 'etaiov_mtt_9', 'etaiov_mtt_10', 'etaiov_mtt_11', 'etaiov_mtt_12', 'etaiov_ka_1', 'etaiov_ka_2', 'etaiov_ka_3', 'etaiov_ka_4', 'etaiov_ka_5', 'etaiov_ka_6', 'etaiov_ka_7', 'etaiov_ka_8', 'etaiov_ka_9', 'etaiov_ka_10', 'etaiov_ka_11', 'etaiov_ka_12'
ratios <- data.frame(
  treatment = c("Lopinavir-ritonavir", "Efavirenz", "Rifampicin"),
  simulated = c(auc_typ(scen[[2]]), auc_typ(scen[[3]]), auc_typ(scen[[4]])) / auc_ref,
  published = c(3.4, 1 - 0.47, 1 - 0.59)
)
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etabvv_cl', 'etalfdepot', 'etalq', 'etaiov_fdepot_1', 'etaiov_fdepot_2', 'etaiov_fdepot_3', 'etaiov_fdepot_4', 'etaiov_fdepot_5', 'etaiov_fdepot_6', 'etaiov_fdepot_7', 'etaiov_fdepot_8', 'etaiov_fdepot_9', 'etaiov_fdepot_10', 'etaiov_fdepot_11', 'etaiov_fdepot_12', 'etaiov_mtt_1', 'etaiov_mtt_2', 'etaiov_mtt_3', 'etaiov_mtt_4', 'etaiov_mtt_5', 'etaiov_mtt_6', 'etaiov_mtt_7', 'etaiov_mtt_8', 'etaiov_mtt_9', 'etaiov_mtt_10', 'etaiov_mtt_11', 'etaiov_mtt_12', 'etaiov_ka_1', 'etaiov_ka_2', 'etaiov_ka_3', 'etaiov_ka_4', 'etaiov_ka_5', 'etaiov_ka_6', 'etaiov_ka_7', 'etaiov_ka_8', 'etaiov_ka_9', 'etaiov_ka_10', 'etaiov_ka_11', 'etaiov_ka_12'
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etabvv_cl', 'etalfdepot', 'etalq', 'etaiov_fdepot_1', 'etaiov_fdepot_2', 'etaiov_fdepot_3', 'etaiov_fdepot_4', 'etaiov_fdepot_5', 'etaiov_fdepot_6', 'etaiov_fdepot_7', 'etaiov_fdepot_8', 'etaiov_fdepot_9', 'etaiov_fdepot_10', 'etaiov_fdepot_11', 'etaiov_fdepot_12', 'etaiov_mtt_1', 'etaiov_mtt_2', 'etaiov_mtt_3', 'etaiov_mtt_4', 'etaiov_mtt_5', 'etaiov_mtt_6', 'etaiov_mtt_7', 'etaiov_mtt_8', 'etaiov_mtt_9', 'etaiov_mtt_10', 'etaiov_mtt_11', 'etaiov_mtt_12', 'etaiov_ka_1', 'etaiov_ka_2', 'etaiov_ka_3', 'etaiov_ka_4', 'etaiov_ka_5', 'etaiov_ka_6', 'etaiov_ka_7', 'etaiov_ka_8', 'etaiov_ka_9', 'etaiov_ka_10', 'etaiov_ka_11', 'etaiov_ka_12'
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etabvv_cl', 'etalfdepot', 'etalq', 'etaiov_fdepot_1', 'etaiov_fdepot_2', 'etaiov_fdepot_3', 'etaiov_fdepot_4', 'etaiov_fdepot_5', 'etaiov_fdepot_6', 'etaiov_fdepot_7', 'etaiov_fdepot_8', 'etaiov_fdepot_9', 'etaiov_fdepot_10', 'etaiov_fdepot_11', 'etaiov_fdepot_12', 'etaiov_mtt_1', 'etaiov_mtt_2', 'etaiov_mtt_3', 'etaiov_mtt_4', 'etaiov_mtt_5', 'etaiov_mtt_6', 'etaiov_mtt_7', 'etaiov_mtt_8', 'etaiov_mtt_9', 'etaiov_mtt_10', 'etaiov_mtt_11', 'etaiov_mtt_12', 'etaiov_ka_1', 'etaiov_ka_2', 'etaiov_ka_3', 'etaiov_ka_4', 'etaiov_ka_5', 'etaiov_ka_6', 'etaiov_ka_7', 'etaiov_ka_8', 'etaiov_ka_9', 'etaiov_ka_10', 'etaiov_ka_11', 'etaiov_ka_12'
ratios |>
  mutate(simulated = signif(simulated, 3)) |>
  dplyr::rename("Treatment" = treatment, "Simulated AUC ratio" = simulated, "Published AUC ratio" = published) |>
  knitr::kable()
Treatment Simulated AUC ratio Published AUC ratio
Lopinavir-ritonavir 3.350 3.40
Efavirenz 0.527 0.53
Rifampicin 0.413 0.41 
stopifnot(
  abs(ratios$simulated[1] - 1.672 / 0.499) < 0.01,
  abs(ratios$simulated[2] - 1 / 1.899) < 0.005,
  abs(ratios$simulated[3] - 1 / 2.42) < 0.005,
  abs(ratios$simulated / ratios$published - 1) < 0.03
)

Study and dose-occasion effects

The bioavailability reference is the evening dose of InterACT and SEACAT. SEACAT morning doses (the first, and the consecutive ones) have much lower bioavailability; all Ugandan doses are 26.9% lower; in Nigeria study 1 the observed 6th dose is 60.8% lower and the unobserved 5th dose is delayed by 4.3 h (as in the U.S. healthy-volunteer study). Nigeria study 2 measured dried blood spots, which read 2.28-fold higher than plasma.

st <- list(
  "Reference (InterACT)" = list(),
  "SEACAT" = list(STUDY_SEACAT = 1),
  "Uganda" = list(STUDY_UGANDA = 1),
  "Nigeria study 1" = list(STUDY_NIGERIA1 = 1),
  "Nigeria study 2 (DBS)" = list(SAMPLE_DBS = 1)
)
stp <- bind_rows(lapply(seq_along(st), function(i) {
  s <- rxode2::rxSolve(mod_typ, make_events(1, 57, tprof, covs = st[[i]]), returnType = "data.frame")
  data.frame(time = s$time, Cc = s$Cc, study = names(st)[i])
}))
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etabvv_cl', 'etalfdepot', 'etalq', 'etaiov_fdepot_1', 'etaiov_fdepot_2', 'etaiov_fdepot_3', 'etaiov_fdepot_4', 'etaiov_fdepot_5', 'etaiov_fdepot_6', 'etaiov_fdepot_7', 'etaiov_fdepot_8', 'etaiov_fdepot_9', 'etaiov_fdepot_10', 'etaiov_fdepot_11', 'etaiov_fdepot_12', 'etaiov_mtt_1', 'etaiov_mtt_2', 'etaiov_mtt_3', 'etaiov_mtt_4', 'etaiov_mtt_5', 'etaiov_mtt_6', 'etaiov_mtt_7', 'etaiov_mtt_8', 'etaiov_mtt_9', 'etaiov_mtt_10', 'etaiov_mtt_11', 'etaiov_mtt_12', 'etaiov_ka_1', 'etaiov_ka_2', 'etaiov_ka_3', 'etaiov_ka_4', 'etaiov_ka_5', 'etaiov_ka_6', 'etaiov_ka_7', 'etaiov_ka_8', 'etaiov_ka_9', 'etaiov_ka_10', 'etaiov_ka_11', 'etaiov_ka_12'
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etabvv_cl', 'etalfdepot', 'etalq', 'etaiov_fdepot_1', 'etaiov_fdepot_2', 'etaiov_fdepot_3', 'etaiov_fdepot_4', 'etaiov_fdepot_5', 'etaiov_fdepot_6', 'etaiov_fdepot_7', 'etaiov_fdepot_8', 'etaiov_fdepot_9', 'etaiov_fdepot_10', 'etaiov_fdepot_11', 'etaiov_fdepot_12', 'etaiov_mtt_1', 'etaiov_mtt_2', 'etaiov_mtt_3', 'etaiov_mtt_4', 'etaiov_mtt_5', 'etaiov_mtt_6', 'etaiov_mtt_7', 'etaiov_mtt_8', 'etaiov_mtt_9', 'etaiov_mtt_10', 'etaiov_mtt_11', 'etaiov_mtt_12', 'etaiov_ka_1', 'etaiov_ka_2', 'etaiov_ka_3', 'etaiov_ka_4', 'etaiov_ka_5', 'etaiov_ka_6', 'etaiov_ka_7', 'etaiov_ka_8', 'etaiov_ka_9', 'etaiov_ka_10', 'etaiov_ka_11', 'etaiov_ka_12'
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etabvv_cl', 'etalfdepot', 'etalq', 'etaiov_fdepot_1', 'etaiov_fdepot_2', 'etaiov_fdepot_3', 'etaiov_fdepot_4', 'etaiov_fdepot_5', 'etaiov_fdepot_6', 'etaiov_fdepot_7', 'etaiov_fdepot_8', 'etaiov_fdepot_9', 'etaiov_fdepot_10', 'etaiov_fdepot_11', 'etaiov_fdepot_12', 'etaiov_mtt_1', 'etaiov_mtt_2', 'etaiov_mtt_3', 'etaiov_mtt_4', 'etaiov_mtt_5', 'etaiov_mtt_6', 'etaiov_mtt_7', 'etaiov_mtt_8', 'etaiov_mtt_9', 'etaiov_mtt_10', 'etaiov_mtt_11', 'etaiov_mtt_12', 'etaiov_ka_1', 'etaiov_ka_2', 'etaiov_ka_3', 'etaiov_ka_4', 'etaiov_ka_5', 'etaiov_ka_6', 'etaiov_ka_7', 'etaiov_ka_8', 'etaiov_ka_9', 'etaiov_ka_10', 'etaiov_ka_11', 'etaiov_ka_12'
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etabvv_cl', 'etalfdepot', 'etalq', 'etaiov_fdepot_1', 'etaiov_fdepot_2', 'etaiov_fdepot_3', 'etaiov_fdepot_4', 'etaiov_fdepot_5', 'etaiov_fdepot_6', 'etaiov_fdepot_7', 'etaiov_fdepot_8', 'etaiov_fdepot_9', 'etaiov_fdepot_10', 'etaiov_fdepot_11', 'etaiov_fdepot_12', 'etaiov_mtt_1', 'etaiov_mtt_2', 'etaiov_mtt_3', 'etaiov_mtt_4', 'etaiov_mtt_5', 'etaiov_mtt_6', 'etaiov_mtt_7', 'etaiov_mtt_8', 'etaiov_mtt_9', 'etaiov_mtt_10', 'etaiov_mtt_11', 'etaiov_mtt_12', 'etaiov_ka_1', 'etaiov_ka_2', 'etaiov_ka_3', 'etaiov_ka_4', 'etaiov_ka_5', 'etaiov_ka_6', 'etaiov_ka_7', 'etaiov_ka_8', 'etaiov_ka_9', 'etaiov_ka_10', 'etaiov_ka_11', 'etaiov_ka_12'
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etabvv_cl', 'etalfdepot', 'etalq', 'etaiov_fdepot_1', 'etaiov_fdepot_2', 'etaiov_fdepot_3', 'etaiov_fdepot_4', 'etaiov_fdepot_5', 'etaiov_fdepot_6', 'etaiov_fdepot_7', 'etaiov_fdepot_8', 'etaiov_fdepot_9', 'etaiov_fdepot_10', 'etaiov_fdepot_11', 'etaiov_fdepot_12', 'etaiov_mtt_1', 'etaiov_mtt_2', 'etaiov_mtt_3', 'etaiov_mtt_4', 'etaiov_mtt_5', 'etaiov_mtt_6', 'etaiov_mtt_7', 'etaiov_mtt_8', 'etaiov_mtt_9', 'etaiov_mtt_10', 'etaiov_mtt_11', 'etaiov_mtt_12', 'etaiov_ka_1', 'etaiov_ka_2', 'etaiov_ka_3', 'etaiov_ka_4', 'etaiov_ka_5', 'etaiov_ka_6', 'etaiov_ka_7', 'etaiov_ka_8', 'etaiov_ka_9', 'etaiov_ka_10', 'etaiov_ka_11', 'etaiov_ka_12'
ggplot(stp, aes(time, Cc, colour = study)) +
  geom_line() +
  scale_y_log10(limits = c(10, NA)) +
  labs(x = "Time after first dose (h)", y = "Lumefantrine (ng/mL)", colour = NULL) +
  theme_bw()
#> Warning in scale_y_log10(limits = c(10, NA)): log-10 transformation introduced
#> infinite values.


c168 <- stp |>
  filter(time == 168) |>
  mutate(ratio = Cc / Cc[study == "Reference (InterACT)"]) |>
  select(study, Cc, ratio)
knitr::kable(c168 |> dplyr::rename("Study" = study, "Day-7 concentration (ng/mL)" = Cc, "Ratio to reference" = ratio), digits = 3)
Study Day-7 concentration (ng/mL) Ratio to reference
Reference (InterACT) 679.072 1.000
SEACAT 459.383 0.676
Uganda 496.402 0.731
Nigeria study 1 585.887 0.863
Nigeria study 2 (DBS) 1548.284 2.280 
stopifnot(
  abs(c168$ratio[c168$study == "Uganda"] - (1 - 0.269)) < 1e-3,
  abs(c168$ratio[c168$study == "Nigeria study 2 (DBS)"] - 2.28) < 1e-3,
  c168$ratio[c168$study == "SEACAT"] < 1
)

Replication of Table 4 and Figure 2

Francis 2020 simulated 10,000 patients per scenario (typical patient of 40, 57 and 80 kg) and reported the median (95% prediction interval) day-7 concentration with, in brackets, a range whose width (about 1.5-fold either side of the median) identifies it as the interquartile range, and the percentage below 200 ng/mL. Here 200 virtual patients per scenario are simulated with full between-subject, between-visit and between-occasion variability at the reference bioavailability. Day 7 is taken as 168 h after the first dose.

rxode2::rxSetSeed(20200421)
t4_scen <- bind_rows(
  expand.grid(treatment = names(scen), days = 3, wt = c(40, 57, 80), stringsAsFactors = FALSE),
  expand.grid(treatment = "Efavirenz", days = 4:5, wt = c(40, 57, 80), stringsAsFactors = FALSE),
  expand.grid(treatment = "Rifampicin", days = 4:6, wt = c(40, 57, 80), stringsAsFactors = FALSE)
)
n_arm <- 200
t4_scen$arm <- seq_len(nrow(t4_scen))
ev_t4 <- bind_rows(lapply(t4_scen$arm, function(a) {
  r <- t4_scen[a, ]
  d <- make_events(n_arm, r$wt, 168, days = r$days, id0 = (a - 1) * n_arm, covs = scen[[r$treatment]])
  d$arm <- a
  d
}))
sim_t4 <- rxode2::rxSolve(mod, ev_t4, keep = "arm", returnType = "data.frame")
stopifnot(all(is.finite(sim_t4$Cc)), median(sim_t4$Cc) > 1)

t4 <- sim_t4 |>
  group_by(arm) |>
  summarise(
    med = median(Cc), q25 = quantile(Cc, 0.25), q75 = quantile(Cc, 0.75),
    pct_below = 100 * mean(Cc < 200), .groups = "drop"
  ) |>
  left_join(t4_scen, by = "arm")

# Francis 2020 Table 4: median day-7 concentration (ng/mL), the bracketed
# range (read as IQR) and % below 200 ng/mL, by regimen and body weight.
# Only the 3-day rows' brackets are transcribed; they check the spread.
pub_t4 <- tibble::tribble(
  ~treatment, ~days, ~wt, ~pub_med, ~pub_pct,
  "AL alone", 3, 40, 999, 0, "AL alone", 3, 57, 811, 1, "AL alone", 3, 80, 671, 2,
  "Lopinavir-ritonavir", 3, 40, 5823, 0, "Lopinavir-ritonavir", 3, 57, 4626, 0, "Lopinavir-ritonavir", 3, 80, 3686, 0,
  "Efavirenz", 3, 40, 250, 37, "Efavirenz", 3, 57, 203, 49, "Efavirenz", 3, 80, 166, 62,
  "Efavirenz", 4, 40, 410, 11, "Efavirenz", 4, 57, 336, 18, "Efavirenz", 4, 80, 279, 28,
  "Efavirenz", 5, 40, 700, 1, "Efavirenz", 5, 57, 576, 3, "Efavirenz", 5, 80, 479, 5,
  "Rifampicin", 3, 40, 144, 69, "Rifampicin", 3, 57, 118, 80, "Rifampicin", 3, 80, 99, 87,
  "Rifampicin", 4, 40, 243, 38, "Rifampicin", 4, 57, 201, 50, "Rifampicin", 4, 80, 166, 62,
  "Rifampicin", 5, 40, 419, 10, "Rifampicin", 5, 57, 343, 16, "Rifampicin", 5, 80, 282, 26,
  "Rifampicin", 6, 40, 812, 0, "Rifampicin", 6, 57, 656, 2, "Rifampicin", 6, 80, 547, 3
)
cmp_t4 <- left_join(t4, pub_t4, by = c("treatment", "days", "wt")) |>
  mutate(pct_diff_med = 100 * (med / pub_med - 1))

cmp_t4 |>
  transmute(
    treatment, days, wt,
    sim = sprintf("%.0f (%.0f-%.0f) (%.0f%%)", med, q25, q75, pct_below),
    pub = sprintf("%.0f (%.0f%%)", pub_med, pub_pct),
    pct_diff_med = round(pct_diff_med, 1)
  ) |>
  dplyr::rename(
    "Treatment" = treatment, "AL regimen (days)" = days, "Weight (kg)" = wt,
    "Simulated median (IQR) (% < 200)" = sim, "Published median (% < 200)" = pub,
    "Median difference (%)" = pct_diff_med
  ) |>
  knitr::kable()
Treatment AL regimen (days) Weight (kg) Simulated median (IQR) (% < 200) Published median (% < 200) Median difference (%)
AL alone 3 40 1119 (683-1741) (4%) 999 (0%) 12.0
Lopinavir-ritonavir 3 40 5728 (3967-8477) (0%) 5823 (0%) -1.6
Efavirenz 3 40 236 (140-354) (43%) 250 (37%) -5.7
Rifampicin 3 40 141 (85-233) (68%) 144 (69%) -1.8
AL alone 3 57 815 (529-1333) (3%) 811 (1%) 0.5
Lopinavir-ritonavir 3 57 4457 (3086-6219) (0%) 4626 (0%) -3.6
Efavirenz 3 57 191 (134-335) (55%) 203 (49%) -6.1
Rifampicin 3 57 110 (67-187) (80%) 118 (80%) -6.8
AL alone 3 80 668 (450-969) (2%) 671 (2%) -0.4
Lopinavir-ritonavir 3 80 3642 (2351-5184) (0%) 3686 (0%) -1.2
Efavirenz 3 80 170 (118-260) (58%) 166 (62%) 2.6
Rifampicin 3 80 87 (49-147) (86%) 99 (87%) -12.3
Efavirenz 4 40 461 (246-780) (17%) 410 (11%) 12.4
Efavirenz 5 40 759 (471-1098) (3%) 700 (1%) 8.4
Efavirenz 4 57 389 (215-604) (20%) 336 (18%) 15.9
Efavirenz 5 57 577 (390-981) (6%) 576 (3%) 0.2
Efavirenz 4 80 297 (183-499) (30%) 279 (28%) 6.6
Efavirenz 5 80 495 (329-832) (12%) 479 (5%) 3.3
Rifampicin 4 40 258 (155-425) (34%) 243 (38%) 6.1
Rifampicin 5 40 463 (286-681) (11%) 419 (10%) 10.5
Rifampicin 6 40 859 (599-1532) (2%) 812 (0%) 5.7
Rifampicin 4 57 224 (132-358) (46%) 201 (50%) 11.6
Rifampicin 5 57 408 (255-627) (18%) 343 (16%) 19.1
Rifampicin 6 57 771 (529-1220) (3%) 656 (2%) 17.5
Rifampicin 4 80 175 (114-272) (55%) 166 (62%) 5.4
Rifampicin 5 80 306 (211-516) (22%) 282 (26%) 8.6
Rifampicin 6 80 591 (389-948) (5%) 547 (3%) 8.0 

stopifnot(
  # Structural: a mis-transcribed clearance, bioavailability or DDI effect
  # moves every median by tens of percent.
  abs(median(cmp_t4$pct_diff_med)) < 10,
  # Envelope, robust to which scenarios land in the tails of n = 200.
  quantile(abs(cmp_t4$pct_diff_med), 0.9) < 20,
  quantile(abs(cmp_t4$pct_below - cmp_t4$pub_pct), 0.9) < 12
)

# Spread: the published 3-day brackets for the 57-kg patient, read as the IQR.
pub_iqr <- tibble::tribble(
  ~treatment, ~pub_q25, ~pub_q75,
  "AL alone", 548, 1194, "Lopinavir-ritonavir", 3294, 6407,
  "Efavirenz", 132, 310, "Rifampicin", 77, 182
)
iqr_cmp <- cmp_t4 |>
  filter(days == 3, wt == 57) |>
  inner_join(pub_iqr, by = "treatment") |>
  mutate(sim_ratio = q75 / q25, pub_ratio = pub_q75 / pub_q25)
iqr_cmp |>
  select(treatment, q25, q75, pub_q25, pub_q75, sim_ratio, pub_ratio) |>
  dplyr::rename(
    "Treatment" = treatment, "Simulated Q25" = q25, "Simulated Q75" = q75,
    "Published Q25" = pub_q25, "Published Q75" = pub_q75,
    "Simulated Q75/Q25" = sim_ratio, "Published Q75/Q25" = pub_ratio
  ) |>
  knitr::kable(digits = 2)
Treatment Simulated Q25 Simulated Q75 Published Q25 Published Q75 Simulated Q75/Q25 Published Q75/Q25
AL alone 529.39 1332.90 548 1194 2.52 2.18
Lopinavir-ritonavir 3086.20 6218.54 3294 6407 2.01 1.95
Efavirenz 134.08 334.82 132 310 2.50 2.35
Rifampicin 66.94 186.67 77 182 2.79 2.36 
stopifnot(abs(median(iqr_cmp$sim_ratio / iqr_cmp$pub_ratio) - 1) < 0.35)

The extended 4- to 6-day regimens are simulated as a continuation of twice-daily dosing (every 12 h after the 8-h second dose) with day 7 at 168 h after the first dose. Their simulated medians run about 10% above the published values, more than the 3-day rows; the paper does not describe its extended-regimen dosing times, so a small difference in the assumed schedule is the likely reason.

sim_t4 |>
  left_join(t4_scen, by = "arm") |>
  mutate(scenario = paste0(treatment, ", ", days, "-day")) |>
  ggplot(aes(factor(wt), Cc)) +
  geom_boxplot(outlier.shape = NA, coef = 0) +
  stat_summary(fun.data = function(x) data.frame(ymin = quantile(x, 0.025), ymax = quantile(x, 0.975)), geom = "errorbar", width = 0.3) +
  geom_hline(yintercept = 200, linetype = "dashed") +
  scale_y_log10() +
  facet_wrap(~scenario, nrow = 2) +
  labs(
    x = "Body weight (kg)", y = "Day-7 lumefantrine (ng/mL)",
    caption = "Replicates Figure 2 of Francis 2020: box 25th-75th, whiskers 2.5th-97.5th percentiles; n = 200 per scenario."
  ) +
  theme_bw()

PKNCA validation

Non-compartmental analysis of the standard 3-day regimen in 200 virtual 57-kg patients per concomitant treatment, over 0-336 h after the first dose (a dense grid, without residual error). The paper reports no NCA table; the check is that the ratio of the NCA AUC to the AL-alone arm reproduces the published fold changes on the median.

rxode2::rxSetSeed(20200422)
tnca <- c(0, 0.5, 1, 2, 3, 4, 6, 8, 12, 24, 36, 48, 60, 61, 62, 63, 64, 66, 68, 72, 96, 120, 168, 216, 264, 336)
ev_nca <- bind_rows(lapply(seq_along(scen), function(i) {
  d <- make_events(n_arm, 57, tnca, id0 = (i - 1) * n_arm, covs = scen[[i]])
  d$treatment <- names(scen)[i]
  d
}))
sim_nca <- rxode2::rxSolve(mod, ev_nca, keep = "treatment", returnType = "data.frame")

conc <- sim_nca |>
  dplyr::filter(!is.na(Cc)) |>
  select(id, time, Cc, treatment) |>
  distinct(id, time, .keep_all = TRUE)
doses <- ev_nca |>
  dplyr::filter(evid == 1) |>
  select(id, time, amt, treatment)

o_conc <- PKNCA::PKNCAconc(conc, Cc ~ time | treatment + id)
o_dose <- PKNCA::PKNCAdose(doses, amt ~ time | treatment + id)
intervals <- data.frame(start = 0, end = 336, cmax = TRUE, tmax = TRUE, auclast = TRUE)
nca <- PKNCA::pk.nca(PKNCA::PKNCAdata(o_conc, o_dose, intervals = intervals))
nca_res <- as.data.frame(nca$result)

nca_sum <- nca_res |>
  dplyr::filter(PPTESTCD %in% c("cmax", "tmax", "auclast")) |>
  group_by(treatment, PPTESTCD) |>
  summarise(median = median(PPORRES), .groups = "drop") |>
  tidyr::pivot_wider(names_from = PPTESTCD, values_from = median)
nca_sum <- nca_sum |>
  mutate(auc_ratio = auclast / auclast[treatment == "AL alone"])
nca_sum |>
  dplyr::rename(
    "Treatment" = treatment, "Cmax (ng/mL)" = cmax, "Tmax (h)" = tmax,
    "AUC0-336 (h*ng/mL)" = auclast, "AUC ratio vs AL alone" = auc_ratio
  ) |>
  knitr::kable(digits = 2)
Treatment AUC0-336 (h*ng/mL) Cmax (ng/mL) Tmax (h) AUC ratio vs AL alone
AL alone 828593.2 13759.48 64 1.00
Efavirenz 470765.9 10013.92 48 0.57
Lopinavir-ritonavir 2684329.8 30283.53 64 3.24
Rifampicin 328378.9 9190.93 60 0.40 

r_nca <- setNames(nca_sum$auc_ratio, nca_sum$treatment)
stopifnot(
  abs(r_nca[["Lopinavir-ritonavir"]] / 3.4 - 1) < 0.2,
  abs(r_nca[["Efavirenz"]] / 0.53 - 1) < 0.2,
  abs(r_nca[["Rifampicin"]] / 0.41 - 1) < 0.2
)

Assumptions and deviations

  • Approximate CV. Table 3 reports variability as “approximate CV%” (footnote b). For log-normal random effects the approximate CV is sqrt(omega^2), so the variances are encoded as (CV/100)^2.
  • Occasion definition. The paper does not define the between-occasion level. One occasion per dose is assumed; this is the level at which the dose-specific bioavailability effects are also defined. OCC is the dose number (1-12 slots, covering the 4-, 5- and 6-day regimens of Table 4) and must be carried forward onto the observation records after each dose.
  • Between-visit variability. BVV on CL/F (between phase 1 and phase 2 of SEACAT 2.4.2, the Uganda studies and the U.S. study) is carried as one subject-level random effect, etabvv_cl, which is correct for a simulation of a single visit. Redraw it to simulate a second visit of the same subject.
  • Dose-occasion mapping. SEACAT doses at 0, 8 and 24 h and every 12 h thereafter starting in the morning, so odd dose numbers are morning doses: OCC = 1 receives the first-dose effect and OCC = 3, 5, ... the consecutive-morning effect. The Nigeria study 1 effect applies to the 6th dose only and the unobserved-dose delay to the 5th dose only (Table 3, footnote d; Results ‘(c) Dosing time’).
  • Delay implementation. The 4.3 h delay is applied to the start of the transit input of the 5th dose (a dosing-time shift), matching the Results description of “a delay in the absorption for this specific occasion”.
  • Nigeria study 1 value. Table 3 gives -60.8% while the Results text gives 60.1%; the table value is used.
  • Table 4 simulations are taken at the reference bioavailability (F = 1 for every dose); the paper does not state the dosing-condition assumptions of its simulations, and this reading reproduces the published medians.
  • Rifampicin plus efavirenz. The two clearance effects combine multiplicatively, as in the final model; the paper notes a non-significant trend toward an even stronger effect with the combination.
  • Covariates not retained (nevirapine- and dolutegravir-based ART, HIV and malaria infection, fat-free mass) are documented in covariatesDataExcluded and are not part of the model.
  • Residual error for DBS. The paper does not report a separate residual error for the dried-blood-spot samples; the DBS scaling factor multiplies the prediction and the same combined residual error applies.