Skip to contents

Lumefantrine (Kay 2020)

Source: vignettes/articles/Kay_2020_lumefantrine.Rmd
Kay_2020_lumefantrine.Rmd

Model and source

  • Citation: Kay K, Goodwin J, Mwebaza N, Ruiz A, Ehrlich H, Ou J, Freeman T, Wade M, Huang L, Wang K, Li F, Aweeka FT, Riggs M, Kajubi R, Parikh S (2020). Modeling and simulation of lumefantrine pharmacokinetics in HIV-infected and HIV-uninfected children with malaria and the role of lumefantrine exposure as a potential driver of drug resistance. American Society of Tropical Medicine and Hygiene (ASTMH) Annual Meeting, 16-18 November 2020, poster 2167.
  • Poster PDF: https://metrumrg.com/wp-content/uploads/2020/11/KAY_2167_ASTMH.pdf

Kay 2020 is an ASTMH 2020 conference poster (abstract 2167; Metrum Research Group, Yale School of Public Health, Infectious Diseases Research Collaboration, UCSF) presenting a population PK / PD analysis of lumefantrine in Ugandan children with uncomplicated malaria. The poster reports:

  • a 2-compartment lumefantrine popPK model with first-order absorption, body-weight allometric scaling on all CL and V terms, age-dependent CL allometric exponent, age effect on bioavailability F, and ART (efavirenz / lopinavir-ritonavir / nevirapine) drug-drug interactions on CL/F and the absorption rate constant KA (Table 1, the model packaged here); and
  • a separately developed repeated-time-to-event (RTTE) hazard model of malaria reinfection driven by HIV status and time-varying lumefantrine concentration (Preliminary Results; no parameter table reported on the poster – the present Kay_2020_lumefantrine model packages only the popPK layer).

The related companion model from the same Aweeka / Kampala lineage in HIV-infected Ugandan adults is modellib("Hoglund_2015_lumefantrine"); the present model extends Hoglund 2015 to a pediatric cohort with body-weight and age covariates and piecewise age-dependent allometric clearance scaling.

mod_fn <- readModelDb("Kay_2020_lumefantrine")
mod <- rxode2::rxode2(mod_fn())

Population

The poster’s Methods section describes a cohort of 277 children with 364 episodes of uncomplicated malaria recruited from a high-transmission area of eastern Uganda. The cohort comprises 161 HIV-uninfected children and 116 HIV-infected children. All children received standard-of-care artemether-lumefantrine (AL) for malaria treatment; HIV-infected children were additionally on daily ART (efavirenz EFV, lopinavir/ritonavir LPV/r, or nevirapine NVP) and on trimethoprim-sulfamethoxazole (TS) prophylaxis. The sub-population of 140 children with recurrent parasitemia during 42-day follow-up (176 episodes) was genotyped at pfcrt K76, pfmdr1 N86, and pfmdr1 Y184F via Luminex; the pfcrt K76 sub-population had 102 HIV-uninfected children (119 episodes) and 38 HIV-infected children (57 episodes: 13 EFV, 11 LPV/r, 14 NVP). The popPK model and the first hazard sub-model used the full dataset; the second (genotype-stratified) hazard sub-model used the pfcrt K76 sub-population.

The poster does not tabulate baseline demographics by age band, weight band, or sex; the cohort is characterised qualitatively as pediatric uncomplicated-malaria patients spanning the standard pediatric weight-band AL dosing range (approximately 3 months to ~10 years, body weight from ~5 kg infants to ~30 kg older children).

Programmatic access to the population metadata is available via readModelDb("Kay_2020_lumefantrine")()$population.

Source trace

Per-parameter source locations are recorded inline next to each ini() entry in inst/modeldb/specificDrugs/Kay_2020_lumefantrine.R. The table below collects them in one place for review. All parameter values come from Table 1 of the ASTMH 2020 poster (“Lumefantrine parameter summary”), “Estimate” column. The 95% confidence intervals (from the poster’s Table 1) are listed for cross-reference.

Parameter Value (95% CI) Source location
lcl <- log(1.20) (CL/F, L/h at WT_REF = 14 kg) 1.20 (0.952, 1.45) Table 1 theta_1
lvc <- log(24.1) (V2/F, L at WT_REF = 14 kg) 24.1 (19.0, 29.2) Table 1 theta_2
lq <- log(0.380) (Q/F, L/h at WT_REF = 14 kg) 0.380 (0.258, 0.501) Table 1 theta_3
lvp <- log(767) (V3/F, L at WT_REF = 14 kg) 767 (174, 1360) Table 1 theta_4
lka <- log(0.0215) (KA, 1/h) 0.0215 (0.0197, 0.0234) Table 1 theta_5
lfdepot <- fixed(log(1)) (F anchor at AGE_REF / no ART) 1 (fixed by convention) apparent-CL/F parameterisation
e_age_f <- 0.204 (AGE on F) 0.204 (-0.0586, 0.467) Table 1 theta_6 (CI spans zero)
e_efv_cl <- 0.982 (EFV on CL/F) 0.982 (0.163, 1.80) Table 1 theta_7
e_lpv_cl <- -0.514 (LPV/r on CL/F) -0.514 (-0.696, -0.332) Table 1 theta_8
e_nvp_cl <- 0.0191 (NVP on CL/F) 0.0191 (-0.324, 0.362) Table 1 theta_9 (CI spans zero)
e_efv_ka <- 0.484 (EFV on KA) 0.484 (0.282, 0.685) Table 1 theta_10
e_lpv_ka <- -0.212 (LPV/r on KA) -0.212 (-0.305, -0.120) Table 1 theta_11
e_nvp_ka <- -0.0589 (NVP on KA) -0.0589 (-0.207, 0.0891) Table 1 theta_12 (CI spans zero)
etalcl ~ 0.735 (IIV CL/F, log-scale variance) CV 104% Table 1 Omega_{1,1} (shrinkage 5.86%)
etalvc ~ 0.813 (IIV V2/F) CV 112% Table 1 Omega_{2,2} (shrinkage 32.6%)
etalq ~ 0.0250 (IIV Q/F) CV 15.9% Table 1 Omega_{3,3} (shrinkage 67.5%)
etalvp ~ 0.956 (IIV V3/F) CV 127% Table 1 Omega_{4,4} (shrinkage 36.4%)
etalka ~ 0.0280 (IIV KA) CV 16.9% Table 1 Omega_{5,5} (shrinkage 58.2%)
propSd <- sqrt(0.200) (proportional residual SD) CV 44.7% Table 1 Sigma_{1,1}
Piecewise CL allometric exponent (V exp = 1; CL exp 0.75 / 0.9 / 1.0 / 1.2 for >60 / >24-60 / >3-24 / <=3 months) – Final Results paragraph
2-cmt LF disposition with 1st-order absorption (depot -> central, central <-> peripheral1) – Final Results paragraph

Assumptions and deviations

The Kay 2020 poster reports Table 1 numerical values but does not print the explicit covariate equations or the reference centering values. Three assumptions are documented here and in the model file’s covariateData notes:

  • Reference body weight WT_REF = 14 kg. Not reported in the poster. Chosen as a plausible pediatric median for the 3 months to ~10 years cohort. Cross-check: back-extrapolation to a 70-kg adult with the >60-month allometric exponent of 0.75 yields CL = 1.20 * (70/14)^0.75 = 4.0 L/h, which matches the published adult lumefantrine CL/F of ~4-5 L/h (e.g., Hoglund 2015 adults CL/F = 4.77 L/h).
  • Reference age AGE_REF = 5 years. Not reported in the poster. Chosen as the upper boundary of one piecewise-allometric age bin (>24 to 60 months), also a plausible study-population median age.
  • Age effect on F encoded as a centered fractional-deviation form F = exp(lfdepot) * (1 + e_age_f * (AGE / AGE_REF - 1)). The exact functional form is not printed on the poster; Table 1 lists only the coefficient (AGE_F = 0.204). The centered fractional-deviation form is the natural continuous-covariate extension of the binary linear-deviation form (1 + e * IND) used by the related Hoglund 2015 Ugandan-adult lumefantrine model from the same Aweeka / Kampala lineage. It is dimensionless, anchored to F = 1 at the reference age, and produces sensible bounded behaviour across the observed age range (F = 0.81 at age 3 months; F = 1.20 at age 10 years).
  • ART covariate effects on CL/F and KA encoded as linear-deviation form 1 + e * IND. Same lineage rationale; the EFV-on-CL coefficient +0.982 corresponds to a 1.98-fold CL/F increase, consistent with the 2.1- to 3.4-fold EFV-driven LF-exposure reduction reported by Parikh 2016 (reference [1] of the poster), and the LPV/r-on-CL coefficient -0.514 corresponds to a 2.06-fold CL/F decrease, consistent with the 2.1-fold LPV/r-driven LF-exposure increase reported by Parikh 2016.
  • The RTTE (repeated time-to-event) hazard model is NOT packaged. The poster’s RTTE section is preliminary, gives only qualitative effect sizes (6.6% increase, 64% decrease, etc.), and does not tabulate baseline hazard parameters; the present Kay_2020_lumefantrine model packages only the popPK layer reported in Table 1. The PK model is sufficient on its own to drive downstream exposure-response analyses.

Virtual cohort

The cohort is built across four ART arms (no ART; EFV; LPV/r; NVP) with disjoint subject IDs across arms so the multi-cohort bind_rows() collapses cleanly into a single rxSolve input. Each arm has 50 subjects (200 total; below the 200-per-arm cohort cap). Age is drawn approximately uniformly across the four piecewise-allometric age bins so the model’s age-dependent allometric structure is exercised. Body weight is drawn from a WHO-style age-weight curve (see make_arm below).

set.seed(20260624L)
n_per_arm <- 50L

# Standard pediatric Coartem dosing weight bands (WHO 2015, Table 1):
#   5-<15 kg  -> 1 tablet (20 mg artemether / 120 mg lumefantrine) BID for 3 days
#   15-<25 kg -> 2 tablets BID
#   25-<35 kg -> 3 tablets BID
# Each tablet = 120 mg lumefantrine. The simulation uses a single lumefantrine
# dose value per subject derived from baseline body weight.
lf_per_tablet_mg <- 120

tablets_for_weight <- function(wt_kg) {
  dplyr::case_when(
    wt_kg <  15 ~ 1L,
    wt_kg <  25 ~ 2L,
    wt_kg <  35 ~ 3L,
    TRUE        ~ 4L
  )
}

# Simple age -> WHO-style typical weight (kg) for boys ~50th percentile;
# adequate for an illustrative virtual cohort.
typical_weight_for_age <- function(age_yr) {
  pmax(3.5, 3.5 + 1.5 * age_yr ^ 1.05)
}

make_arm <- function(arm_label, conmed_efv, conmed_lpv, conmed_nvp, id_offset) {
  # Distribute ages across the four piecewise-allometric bins so the
  # age-dependent CL exponent is exercised. Age in years.
  ages <- runif(n_per_arm, min = 0.25, max = 10)
  wts  <- pmin(pmax(rnorm(n_per_arm, mean = typical_weight_for_age(ages),
                          sd = 1.5), 3.5), 35)
  tibble::tibble(
    id         = id_offset + seq_len(n_per_arm),
    arm        = arm_label,
    AGE        = ages,
    WT         = round(wts, 2),
    CONMED_EFV = conmed_efv,
    CONMED_LPV = conmed_lpv,
    CONMED_NVP = conmed_nvp
  )
}

subjects <- dplyr::bind_rows(
  make_arm("No ART", 0L, 0L, 0L, id_offset =   0L),
  make_arm("EFV",    1L, 0L, 0L, id_offset =  50L),
  make_arm("LPV/r",  0L, 1L, 0L, id_offset = 100L),
  make_arm("NVP",    0L, 0L, 1L, id_offset = 150L)
)
stopifnot(!anyDuplicated(subjects$id))
subjects |>
  dplyr::group_by(arm) |>
  dplyr::summarise(
    n            = dplyr::n(),
    age_median   = median(AGE),
    age_range    = sprintf("%.2f - %.2f", min(AGE), max(AGE)),
    wt_median    = median(WT),
    wt_range     = sprintf("%.1f - %.1f", min(WT), max(WT)),
    .groups      = "drop"
  ) |>
  knitr::kable(caption = "Virtual cohort by ART arm (50 subjects per arm).")
Virtual cohort by ART arm (50 subjects per arm).
arm n age_median age_range wt_median wt_range
EFV 50 4.313758 0.29 - 9.70 10.915 3.5 - 20.4
LPV/r 50 5.798677 0.32 - 9.96 12.665 3.5 - 22.2
NVP 50 5.008919 0.87 - 9.92 11.825 3.5 - 21.4
No ART 50 6.162732 0.62 - 9.82 14.245 4.0 - 20.6

Event table and simulation

The standard 3-day pediatric Coartem regimen is 6 doses at 0, 8, 24, 36, 48, 60 hours. Lumefantrine has a long terminal half-life (the poster’s Figure 1 extends through ~40 days), so observations are kept dense early and progressively sparser through 42 days post first-dose so the long elimination tail is captured.

dose_times <- c(0, 8, 24, 36, 48, 60)
obs_times  <- sort(unique(c(
  seq(0,   72,   by = 1),       # absorption + early disposition
  seq(73,  168,  by = 3),       # day-7 endpoint window
  seq(171, 500,  by = 12),      # multi-day elimination
  seq(504, 1008, by = 24)       # tail through day 42
)))

build_events <- function(subjects, obs_times, dose_times) {
  out <- vector("list", nrow(subjects))
  for (i in seq_len(nrow(subjects))) {
    s <- subjects[i, ]
    dose_mg <- tablets_for_weight(s$WT) * lf_per_tablet_mg
    dose_rows <- data.frame(
      id         = s$id,
      time       = dose_times,
      evid       = 1L,
      amt        = dose_mg,
      cmt        = "depot",
      arm        = s$arm,
      AGE        = s$AGE,
      WT         = s$WT,
      CONMED_EFV = s$CONMED_EFV,
      CONMED_LPV = s$CONMED_LPV,
      CONMED_NVP = s$CONMED_NVP
    )
    obs_rows <- data.frame(
      id         = s$id,
      time       = obs_times,
      evid       = 0L,
      amt        = 0,
      cmt        = "central",
      arm        = s$arm,
      AGE        = s$AGE,
      WT         = s$WT,
      CONMED_EFV = s$CONMED_EFV,
      CONMED_LPV = s$CONMED_LPV,
      CONMED_NVP = s$CONMED_NVP
    )
    out[[i]] <- rbind(dose_rows, obs_rows)
  }
  ev <- dplyr::bind_rows(out)
  ev[order(ev$id, ev$time, -ev$evid), ]
}

events <- build_events(subjects, obs_times, dose_times)
stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))

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

Replicate Figure 1 – Lumefantrine exposure by treatment arm

Kay 2020 Figure 1 shows median lumefantrine concentration vs. time over ~40 days post-dose for each of the four arms. The visual predictive check below replicates the same structure: median + 5th-95th percentile envelope per arm.

sim |>
  dplyr::filter(!is.na(Cc), time > 0, Cc > 0) |>
  dplyr::group_by(arm, time) |>
  dplyr::summarise(
    p05 = quantile(Cc, 0.05, na.rm = TRUE),
    p50 = quantile(Cc, 0.50, na.rm = TRUE),
    p95 = quantile(Cc, 0.95, na.rm = TRUE),
    .groups = "drop"
  ) |>
  dplyr::filter(p50 > 0.1) |>
  ggplot(aes(time / 24, p50, colour = arm, fill = arm)) +
  geom_ribbon(aes(ymin = p05, ymax = p95), alpha = 0.20, colour = NA) +
  geom_line(linewidth = 0.6) +
  scale_y_log10() +
  labs(x = "Time after first dose (days)",
       y = "Lumefantrine plasma concentration (ng/mL)",
       title = "Lumefantrine VPC by HIV/ART arm",
       caption = "Replicates Kay 2020 Figure 1: LF exposure by treatment arm.") +
  theme_bw()

The qualitative ranking of arms by exposure agrees with the abstract narrative and with Parikh 2016 (poster reference [1]):

  • LPV/r markedly elevates lumefantrine exposure (CL/F reduced 51.4% by ritonavir-driven CYP3A4 inhibition; KA reduced 21.2%).
  • No-ART and NVP arms are similar (NVP coefficients are small and statistically non-significant).
  • EFV markedly lowers lumefantrine exposure (CL/F increased 98.2% by CYP3A4 induction; KA increased 48.4%).

PKNCA validation

PKNCA is used to compute Cmax, Tmax, AUC, and apparent terminal half-life from the simulated lumefantrine concentrations, with the four ART arms as the treatment grouping.

sim_nca <- sim |>
  dplyr::filter(!is.na(Cc)) |>
  dplyr::select(id, time, Cc, arm)

# Guarantee a time = 0 row per (id, arm); for extravascular pre-dose Cc = 0
# is the correct value.
sim_nca <- dplyr::bind_rows(
  sim_nca,
  sim_nca |> dplyr::distinct(id, arm) |>
    dplyr::mutate(time = 0, Cc = 0)
) |>
  dplyr::distinct(id, arm, time, .keep_all = TRUE) |>
  dplyr::arrange(id, arm, time)

conc_obj <- PKNCA::PKNCAconc(sim_nca, Cc ~ time | arm + id)

dose_df <- events |>
  dplyr::filter(evid == 1L) |>
  dplyr::select(id, time, amt, arm)

dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | arm + id)

intervals <- data.frame(
  start      = 0,
  end        = Inf,
  cmax       = TRUE,
  tmax       = TRUE,
  aucinf.obs = TRUE,
  half.life  = TRUE
)

nca_data <- PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals)
nca_res  <- PKNCA::pk.nca(nca_data)
nca_summary <- as.data.frame(nca_res) |>
  dplyr::filter(PPTESTCD %in% c("cmax", "tmax", "aucinf.obs", "half.life")) |>
  dplyr::group_by(arm, 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"
  )

nca_summary |>
  dplyr::mutate(
    parameter = dplyr::case_when(
      PPTESTCD == "cmax"       ~ "Cmax (ng/mL)",
      PPTESTCD == "tmax"       ~ "Tmax (h)",
      PPTESTCD == "aucinf.obs" ~ "AUCinf (ng*h/mL)",
      PPTESTCD == "half.life"  ~ "Half-life (h)"
    )
  ) |>
  dplyr::transmute(
    arm,
    `NCA parameter` = parameter,
    `Median (P05, P95)` = sprintf("%.1f (%.1f, %.1f)", median, p05, p95)
  ) |>
  tidyr::pivot_wider(names_from = arm, values_from = `Median (P05, P95)`) |>
  knitr::kable(caption = "Simulated lumefantrine NCA parameters by ART arm (median, P05, P95).")
Simulated lumefantrine NCA parameters by ART arm (median, P05, P95).
NCA parameter EFV LPV/r NVP No ART
AUCinf (ng*h/mL) 538928.7 (129437.0, 1585367.0) 1823589.0 (579566.6, 5936026.7) 1014967.0 (283494.1, 3465979.4) 965901.3 (233447.0, 3253967.3)
Cmax (ng/mL) 5161.3 (1535.6, 12565.8) 7851.7 (3618.5, 17918.4) 6517.8 (2635.2, 12371.4) 7265.2 (2069.6, 13664.7)
Half-life (h) 1650.5 (379.2, 10240.6) 1840.0 (298.5, 16088.9) 1890.1 (422.1, 9807.0) 1777.2 (362.3, 10456.4)
Tmax (h) 67.0 (63.5, 73.0) 76.0 (67.0, 115.3) 72.0 (65.0, 101.6) 72.0 (64.5, 98.9)

The relative ranking across arms (LPV/r exposure > no-ART ~ NVP exposure > EFV exposure) is consistent with Kay 2020 Figure 1, the abstract narrative, and Parikh 2016 (poster reference [1]).

The Kay 2020 poster does not tabulate NCA parameter values for direct numerical comparison, so a side-by-side ncaComparisonTable() against published values cannot be rendered here. The qualitative ranking and the magnitude of arm-to-arm exposure differences serve as the validation check.