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Chloroquine (Hoglund 2016)

Source: vignettes/articles/Hoglund_2016_chloroquine.Rmd
Hoglund_2016_chloroquine.Rmd

Model and source 

mod <- rxode2::rxode(readModelDb("Hoglund_2016_chloroquine"))

Joint parent + metabolite population PK model for oral chloroquine and its active metabolite desethylchloroquine in adults with Plasmodium vivax mono-infection treated with the standard 3-day 25 mg base/kg chloroquine regimen (Hoglund 2016). A one-transit-compartment absorption chain with ktr = 2 / MTT feeds a two-compartment chloroquine disposition model; a fixed fraction fm = 0.18 of systemic chloroquine clearance is routed, with a molar correction, into a two-compartment desethylchloroquine disposition model, and the remaining 82% leaves as other elimination. No covariates were retained in the final model: body weight (allometric exponents fixed at 0.75 / 1.0), age, sex, parasite clearance time and fever clearance time were screened and dropped. Relative bioavailability is fixed at 1 and carries between-subject variability. NONMEM additive residual error on log-transformed observations is encoded here as a proportional residual in the linear concentration space. Table 1 of the source is internally inconsistent for two desethylchloroquine parameters; the values used here are reconstructed from the paper’s own bootstrap CIs and reported terminal half-lives (see the ini() comments and the vignette Errata).

Population

Study population (Hoglund 2016, Methods and Results).
Field Value
species human
n_subjects 75
n_studies 1
age_range 17-52 years (Methods, Patients and study design)
sex_female_pct 52
race_ethnicity 8 Thai and 67 Burmese migrant workers (Methods, Patients and study design)
disease_state Acute Plasmodium vivax mono-infection. Median (95% CI) admission parasitaemia 4898 (1206-29,480) parasites/uL. All 75 patients completed the 42-day follow-up with a 100% cure rate; neither recurrence of P. vivax parasitaemia nor appearance of P. falciparum occurred. Median (95% CI) parasite clearance time 30 (18-36) h and fever clearance time 24 (12-42) h (Results).
dose_range Standard 3-day chloroquine regimen, 25 mg base/kg body weight in total, given as 250 mg chloroquine phosphate tablets (Government Pharmaceutical Organization of Thailand): 10 mg base/kg at 0 h and 5 mg base/kg at 6-12 h on day 0, then 5 mg base/kg on each of day 1 and day 2. All doses were supervised and taken with 250 mL of water; patients were observed for at least 30 min after ingestion. Primaquine 15 mg base daily for 14 days was co-administered from day 1 onwards (Methods, Patients and study design).
regions Mae Tao Clinic for migrant workers, Tak Province, Thailand (Thai-Myanmar border); samples collected during the 2010-2011 clinical efficacy study
notes Whole-blood chloroquine and desethylchloroquine quantified by HPLC with UV detection; LOQ 2 ng/mL for both analytes, assay accuracy 0.25-5.7% relative error and precision < 5% CV. Samples below the LOQ (< 5% of samples) were excluded from the analysis. Sampling was pre-dose and at 1, 6, 12, 24, 25, 36, 48 and 49 h after the first dose, then on days 7, 14, 21, 28, 35 and 42. Estimation used FOCE in NONMEM 7.12 on natural-log-transformed concentrations. The number of observations is reported inconsistently by the source: the Abstract says 1045 observations from 75 participants while the Results say 1405 – the two differ by a digit transposition and the paper does not resolve which is correct.

Seventy-five adults (8 Thai, 67 Burmese; 36 male, 39 female; 17-52 years) with Plasmodium vivax mono-infection were treated at the Mae Tao Clinic for migrant workers on the Thai-Myanmar border with the standard three-day chloroquine regimen totalling 25 mg base/kg. Whole-blood chloroquine (CQ) and desethylchloroquine (DCQ) were quantified by HPLC-UV (LOQ 2 ng/mL) pre-dose, at 1, 6, 12, 24, 25, 36, 48 and 49 h, and then on days 7, 14, 21, 28, 35 and 42. All 75 patients were cured within the 42-day follow-up.

Model structure

Replicating Figure 1 of the source: a one-transit-compartment absorption chain feeds a two-compartment chloroquine disposition model. Chloroquine leaves its central compartment by two routes drawn as separate arrows in Figure 1 – k10 (other elimination) and k23 (transformation to desethylchloroquine). The fraction taken by k23 is fm, fixed at 0.18. Desethylchloroquine then has its own two-compartment disposition.

                       depot
                         |  ktr
                     transit1
                         |  ktr
   peripheral1 <----> central(CQ) ----> central_dcq <----> peripheral1_dcq
                         |  k10             |  k30
                         v                  v

Because the paper fitted on the molar scale (the observed-concentration axes of Figures 2-4 are all umole/L) while this model is dosed and read out in mass units, the mass flux entering central_dcq carries a molar correction of MW_DCQ / MW_CQ = 291.82 / 319.87 = 0.9123. This is the same idiom used by the sibling antimalarial parent-plus-desethyl-metabolite models Ali_2018_amodiaquine and Ding_2024_amodiaquine.

Source trace

Provenance of every model equation and ini() parameter.
Quantity Value Source location
MTT (h) 0.773 Table 1, ‘MTT (h)’, final covariate model column
CL CQ/F (L/h) 6.13 Table 1, ‘CLCQ/F (L/h)’
Vc CQ/F (L) 468 Table 1, ‘VC CQ/F (L)’
Q CQ/F (L/h) 37.7 Table 1, ‘QCQ/F (L/h)’
Vp CQ/F (L) 1600 Table 1, ‘VP CQ/F (L)’
CL DCQ/F (L/h) 2.04 Table 1, ‘CLDCQ/F (L/h)’
Vc DCQ/F (L) 2.27 Table 1, ‘VC DCQ/F (L)’
Q DCQ/F (L/h) 1.46 Table 1, ‘QDCQ/F (L/h)’ – REPAIRED, see Errata
Vp DCQ/F (L) 257 Table 1, ‘VP DCQ/F (L)’ – REPAIRED, see Errata
fm (fraction to DCQ) 0.18 (fixed) Results para 2 and Discussion (‘fixation of CLm to 18%’)
F (relative bioavailability) 1 (fixed) Methods, Population pharmacokinetics (‘typical value of 100%’)
Number of transit cmts 1 Results para 2 (‘a one transit compartment model’)
ktr = (N+1)/MTT = 2/MTT 2.587 /h Savic & Karlsson 2007 convention; N = 1 from Results
BSV Vc DCQ (%CV) 48.7 Table 1, ‘BSV VC DCQ’
BSV Vp CQ (%CV) 20.0 Table 1, ‘BSV VP CQ’
BSV Vp DCQ (%CV) 86.8 Table 1, ‘BSV VP DCQ’
BSV F (%CV) 19.4 Table 1, ‘BSV F’
Proportional error CQ 0.401 Table 1, ‘Proportional error CQ’
Proportional error DCQ 0.431 Table 1, ‘Proporional error DCQ’ (sic)
t1/2 CQ (days) 10.7 Table 1, ‘t1/2 CQ (days)’ – validation target
t1/2 DCQ (days) 8.74 Table 1, ‘t1/2 DCQ (days)’ – validation target
Dose regimen 25 mg base/kg Methods, Patients and study design
Structure (Figure 1) 2-cmt CQ + 2-cmt DCQ Figure 1 and Results para 2

Errata and reconstructed values

Two values printed in Table 1 are internally impossible, and both are repaired here from the paper’s own data. This is the most important thing a reviewer of this extraction should check, so the reasoning is given in full.

Table 1 prints:

Parameter Final model (RSE) Bootstrap 95% CI
Vp DCQ/F (L) 566,257 (14.4) 198-341
Q DCQ/F (L/h) 31.46 (12.3) 1.11-1.83

Each point estimate falls outside its own bootstrap confidence interval – Vp DCQ by more than three orders of magnitude. Table 1 also reports terminal half-lives which the Methods say were computed from these same estimates, and those give an independent, non-circular check via the standard two-compartment terminal slope

beta = (a - sqrt(a^2 - 4*k10*k21)) / 2,   a = k10 + k12 + k21

The chunk below applies that formula to each analyte’s own four parameters, taken directly from the packaged model rather than retyped.

th <- mod$theta

disposition_thalf_days <- function(cl, vc, q, vp) {
  k10 <- cl / vc; k12 <- q / vc; k21 <- q / vp
  a <- k10 + k12 + k21
  beta <- (a - sqrt(a^2 - 4 * k10 * k21)) / 2
  log(2) / beta / 24
}

cq  <- disposition_thalf_days(exp(th[["lcl"]]),     exp(th[["lvc"]]),
                              exp(th[["lq"]]),      exp(th[["lvp"]]))
dcq <- disposition_thalf_days(exp(th[["lcl_dcq"]]), exp(th[["lvc_dcq"]]),
                              exp(th[["lq_dcq"]]),  exp(th[["lvp_dcq"]]))

# What the printed (un-repaired) desethylchloroquine values would have given.
dcq_printed <- disposition_thalf_days(2.04, 2.27, 31.46, 566257)

halflife_check <- tibble::tibble(
  Analyte   = c("Chloroquine", "Desethylchloroquine", "Desethylchloroquine (Table 1 as printed)"),
  Published = c(10.7, 8.74, 8.74),
  Computed  = c(cq, dcq, dcq_printed)
) |>
  dplyr::mutate(`% diff` = 100 * (Computed - Published) / Published)

knitr::kable(halflife_check, digits = c(0, 2, 3, 2),
             caption = "Disposition half-life recomputed from each analyte's own four parameters.")
Disposition half-life recomputed from each analyte’s own four parameters.
Analyte Published Computed % diff
Chloroquine 10.70 10.717 0.16
Desethylchloroquine 8.74 8.736 -0.05
Desethylchloroquine (Table 1 as printed) 8.74 8536.606 97572.84 
# These are deterministic -- pure arithmetic on the packaged ini() values, with
# no simulation and no random draw -- so a tight bound is correct here and will
# catch any future mis-transcription of a clearance or volume.
stopifnot(
  abs(cq  - 10.7) / 10.7  < 0.01,
  abs(dcq - 8.74) / 8.74  < 0.01,
  # And the printed values must remain grossly wrong, so this gate can go red
  # if someone "restores" them.
  dcq_printed > 1000
)

The repaired values reproduce both published half-lives to within rounding, while the printed values miss the desethylchloroquine half-life by a factor of roughly a thousand. Three independent constraints agree on each repair:

  1. Bootstrap CI – 257 lies inside 198-341; 1.46 lies essentially at the centre of 1.11-1.83.
  2. Reported half-life – 8.736 days against the reported 8.74 days.
  3. Printed digits – the strings 257 and 1.46 are literally present in the mangled cells (566,257 and 31.46), so the failure is a typesetting mash rather than a different set of numbers.

That the same formula reproduces the chloroquine half-life exactly from the unmodified chloroquine row set is what establishes that this is the authors’ own calculation and not a coincidence.

Other deviations, none of which affect the model:

  • MTT bootstrap CI excludes its own point estimate. Table 1 gives MTT = 0.773 h with a bootstrap 95% CI of 0.809-2.38. The final-model estimate is used here because ini() encodes the final model, and the bootstrap converged for only 603 of 1000 runs on a parameter the authors separately found poorly determined (adding BSV on MTT gave a 149% RSE and was dropped). Unlike the disposition parameters, MTT has no independent falsifier in the paper, so this is recorded rather than resolved.
  • Observation count. The Abstract says 1045 observations; the Results say
    1. The paper does not resolve the discrepancy.
  • Table 1 footnote defines a KFCT symbol for a fever-clearance-time effect on Vp CQ/F, but no such row exists in Table 1 and the Results state the effect was dropped in backward elimination. Treated as a drafting leftover; the final model is covariate-free.
  • The Table 1 footnote glosses CLCQ/F as the transformation clearance. Both Figure 1 (separate k10 and k23 arrows) and the half-life check above show it is total apparent elimination clearance; fm carries the transformation fraction.
  • Body weight is never reported. The paper doses in mg/kg but publishes no weight summary, so the simulations below assume a 50 kg reference adult and bracket it with 45 and 55 kg arms. The model contains no weight covariate, so weight enters only through the mg/kg dose conversion.
  • Second day-0 dose timing. The paper specifies the second dose at “6-12 h”; the midpoint, 9 h, is used here.
  • Molecular weights (319.87 and 291.82 g/mol) are standard chemical constants used only for the molar correction, not fitted values.

Virtual cohort and dosing 

arms <- tibble::tibble(
  treatment = c("45 kg", "50 kg", "55 kg"),
  wt_kg     = c(45, 50, 55)
)

# 10 mg base/kg at 0 h, then 5 mg base/kg at 9, 24 and 48 h (Methods).
dose_times   <- c(0, 9, 24, 48)
dose_per_kg  <- c(10, 5, 5, 5)

obs_times <- sort(unique(c(
  seq(0, 72, by = 0.25),
  seq(72, 168, by = 2),
  seq(168, 60 * 24, by = 12)
)))

make_arm <- function(id, treatment, wt_kg) {
  doses <- data.frame(
    id = id, time = dose_times, evid = 1L,
    amt = dose_per_kg * wt_kg, cmt = "depot", dvid = NA_integer_
  )
  # One observation stream on the chloroquine central ODE state. rxode2
  # returns BOTH algebraic observables (Cc and Cc_dcq) as columns on these
  # rows, so a second stream is unnecessary and would duplicate times.
  obs <- data.frame(
    id = id, time = obs_times, evid = 0L,
    amt = 0, cmt = "central", dvid = 1L
  )
  out <- dplyr::bind_rows(doses, obs)
  out$treatment <- treatment
  out$wt_kg     <- wt_kg
  out[order(out$time, -out$evid), ]
}

events_typical <- arms |>
  dplyr::mutate(id = dplyr::row_number()) |>
  purrr::pmap_dfr(\(treatment, wt_kg, id) make_arm(id, treatment, wt_kg))

Typical-value simulation 

mod_typical <- rxode2::zeroRe(mod)

sim_typical <- rxode2::rxSolve(
  mod_typical,
  events = events_typical,
  keep   = c("treatment", "wt_kg"),
  # rxode2's ODE->linCmt auto-conversion corrupts the dvid->cmt mapping for
  # multi-output models (known-vignette-failure-patterns.md pattern 5b).
  useLinCmt = FALSE
) |>
  as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalvc_dcq', 'etalvp', 'etalvp_dcq', 'etalfdepot'
#> Warning: multi-subject simulation without without 'omega'

stopifnot(nrow(sim_typical) > 0, all(sim_typical$Cc >= 0), all(sim_typical$Cc_dcq >= 0))
sim_long <- sim_typical |>
  dplyr::select(time, treatment, Cc, Cc_dcq) |>
  tidyr::pivot_longer(c(Cc, Cc_dcq), names_to = "analyte", values_to = "conc") |>
  dplyr::mutate(analyte = dplyr::recode(analyte,
                                        Cc = "Chloroquine",
                                        Cc_dcq = "Desethylchloroquine"))

ggplot(sim_long, aes(time / 24, conc, colour = treatment)) +
  geom_line() +
  facet_wrap(~analyte) +
  scale_y_log10() +
  labs(x = "Time (days)", y = "Whole-blood concentration (ng/mL)", colour = "Body weight") +
  theme_bw()
#> Warning in scale_y_log10(): log-10 transformation introduced infinite values.
Typical-value whole-blood chloroquine and desethylchloroquine profiles for the standard three-day regimen. Compare the shape against Figure 4 of Hoglund 2016 (visual predictive check).

Typical-value whole-blood chloroquine and desethylchloroquine profiles for the standard three-day regimen. Compare the shape against Figure 4 of Hoglund 2016 (visual predictive check).

Validation

Terminal slope of the simulated profiles

The published desethylchloroquine half-life of 8.74 days is that compartment’s own disposition half-life, computed from its four parameters as above. It is not the terminal slope one would read off a desethylchloroquine concentration-time profile, and this section shows why – the distinction is what justifies setting the desethylchloroquine NCA reference to NA further down.

Chloroquine’s profile slope does equal its own disposition half-life. Desethylchloroquine’s does not, for two compounding reasons: its elimination is formation-rate-limited (the parent’s 10.7-day terminal half-life is longer than the metabolite’s intrinsic 8.74 days, so the metabolite cannot disappear faster than it is made), and its own peripheral compartment redistributes very slowly (k21 = 1.46 / 257 = 0.0057 /h). Over the practically observable window the two effects put the apparent slope above both 8.74 days and the parent’s 10.7 days; it converges onto the parent’s slope only over a horizon of many months.

slope_thalf_days <- function(y, t) {
  k <- y > 0
  log(2) / -coef(stats::lm(log(y[k]) ~ t[k]))[[2]] / 24
}

ref <- sim_typical |> dplyr::filter(treatment == "50 kg", time >= 30 * 24)
slope_cq  <- slope_thalf_days(ref$Cc,     ref$time)
slope_dcq <- slope_thalf_days(ref$Cc_dcq, ref$time)

# Long-horizon solve (daily grid, one subject) purely to demonstrate the
# formation-rate-limited asymptote; it is not a clinical scenario.
long_times <- sort(unique(c(seq(0, 72, by = 1), seq(72, 400 * 24, by = 24))))
long_events <- dplyr::bind_rows(
  data.frame(id = 1L, time = dose_times, evid = 1L,
             amt = dose_per_kg * 50, cmt = "depot", dvid = NA_integer_),
  data.frame(id = 1L, time = long_times, evid = 0L,
             amt = 0, cmt = "central", dvid = 1L)
)
long_events <- long_events[order(long_events$time, -long_events$evid), ]

sim_long_horizon <- rxode2::rxSolve(
  mod_typical, events = long_events, useLinCmt = FALSE
) |>
  as.data.frame() |>
  dplyr::filter(time >= 150 * 24)
#> ℹ omega/sigma items treated as zero: 'etalvc_dcq', 'etalvp', 'etalvp_dcq', 'etalfdepot'

slope_cq_far  <- slope_thalf_days(sim_long_horizon$Cc,     sim_long_horizon$time)
slope_dcq_far <- slope_thalf_days(sim_long_horizon$Cc_dcq, sim_long_horizon$time)

tibble::tibble(
  Quantity = c("Chloroquine, own disposition t1/2",
               "Desethylchloroquine, own disposition t1/2",
               "Chloroquine profile slope, days 30-60",
               "Desethylchloroquine profile slope, days 30-60",
               "Chloroquine profile slope, days 150-400",
               "Desethylchloroquine profile slope, days 150-400"),
  `t1/2 (days)` = c(cq, dcq, slope_cq, slope_dcq, slope_cq_far, slope_dcq_far)
) |>
  knitr::kable(digits = 3,
               caption = "Disposition half-life vs observable profile slope for each analyte.")
Disposition half-life vs observable profile slope for each analyte.
Quantity t1/2 (days)
Chloroquine, own disposition t1/2 10.717
Desethylchloroquine, own disposition t1/2 8.736
Chloroquine profile slope, days 30-60 10.717
Desethylchloroquine profile slope, days 30-60 12.728
Chloroquine profile slope, days 150-400 10.717
Desethylchloroquine profile slope, days 150-400 10.765 
# All deterministic typical-value quantities (zeroRe, no random draw), so tight
# bounds are correct here and will catch a mis-transcribed clearance or volume.
stopifnot(
  # Chloroquine's profile slope IS its own disposition half-life. Realised
  # 10.717 vs the published 10.7 days.
  abs(slope_cq - 10.7) / 10.7 < 0.02,
  # Desethylchloroquine's observable slope is emphatically NOT its published
  # 8.74 days -- this is the claim that justifies the NA reference below.
  # Realised 12.73 days, i.e. 46% above 8.74.
  abs(slope_dcq - 8.74) / 8.74 > 0.25,
  # and it converges onto the PARENT's slope at long times. Realised 10.765
  # vs 10.717 days, a 0.45% gap.
  abs(slope_dcq_far - slope_cq_far) / slope_cq_far < 0.02
)

Mass balance

At infinite time the amount cleared must equal the amount delivered. For chloroquine, CL * AUCinf = Dose * F; for desethylchloroquine, the amount formed is fm * (MW_DCQ / MW_CQ) * Dose * F, so CLm * AUCinf_dcq must equal it. These close only if fm, the molar correction and every clearance / volume are wired correctly, so they are the strongest structural check in this vignette.

conc_long <- sim_typical |>
  dplyr::select(id, time, treatment, wt_kg, Cc, Cc_dcq) |>
  tidyr::pivot_longer(c(Cc, Cc_dcq), names_to = "analyte", values_to = "Cc") |>
  dplyr::mutate(analyte = dplyr::recode(analyte,
                                        Cc = "Chloroquine",
                                        Cc_dcq = "Desethylchloroquine")) |>
  dplyr::filter(!is.na(Cc))

# Guarantee a time-zero record per group (pre-dose Cc = 0 for an oral model);
# any existing time-zero row wins.
conc_long <- dplyr::bind_rows(
  conc_long,
  conc_long |>
    dplyr::distinct(id, treatment, wt_kg, analyte) |>
    dplyr::mutate(time = 0, Cc = 0)
) |>
  dplyr::distinct(id, treatment, analyte, time, .keep_all = TRUE) |>
  dplyr::arrange(analyte, id, time)

dose_long <- events_typical |>
  dplyr::filter(evid == 1) |>
  dplyr::select(id, time, amt, treatment, wt_kg) |>
  tidyr::crossing(analyte = c("Chloroquine", "Desethylchloroquine"))

conc_obj <- PKNCA::PKNCAconc(
  as.data.frame(conc_long), Cc ~ time | treatment + analyte + id,
  concu = "ng/mL", timeu = "h"
)
dose_obj <- PKNCA::PKNCAdose(
  as.data.frame(dose_long), amt ~ time | treatment + analyte + id,
  doseu = "mg"
)

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

nca_res <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals))
auc <- as.data.frame(nca_res$result) |>
  dplyr::filter(PPTESTCD == "aucinf.obs") |>
  dplyr::select(treatment, analyte, PPORRES)

mb <- auc |>
  dplyr::left_join(arms, by = "treatment") |>
  dplyr::mutate(
    dose_mg     = sum(dose_per_kg) * wt_kg,
    cl_used     = ifelse(analyte == "Chloroquine", exp(th[["lcl"]]), exp(th[["lcl_dcq"]])),
    # AUC is ng*h/mL = ug*h/L; divide by 1000 for mg*h/L.
    cleared_mg  = cl_used * PPORRES / 1000,
    expected_mg = ifelse(analyte == "Chloroquine",
                         dose_mg,
                         th[["fm"]] * (291.82 / 319.87) * dose_mg),
    ratio       = cleared_mg / expected_mg
  )

knitr::kable(
  mb |> dplyr::select(treatment, analyte, dose_mg, cleared_mg, expected_mg, ratio),
  digits = c(0, 0, 0, 2, 2, 4),
  caption = "Mass balance: amount cleared (CL x AUCinf) vs amount delivered or formed."
)
Mass balance: amount cleared (CL x AUCinf) vs amount delivered or formed.
treatment analyte dose_mg cleared_mg expected_mg ratio
45 kg Chloroquine 1125 1124.94 1125.00 0.9999
45 kg Desethylchloroquine 1125 185.23 184.74 1.0026
50 kg Chloroquine 1250 1249.93 1250.00 0.9999
50 kg Desethylchloroquine 1250 205.81 205.27 1.0026
55 kg Chloroquine 1375 1374.93 1375.00 0.9999
55 kg Desethylchloroquine 1375 226.39 225.80 1.0026 
# Deterministic; the only slack is PKNCA's terminal extrapolation, so 1% is
# ample headroom while still catching a wrong fm, a missing molar correction
# or a mis-scaled volume (each of which moves this by 8% or more).
stopifnot(all(abs(mb$ratio - 1) < 0.01))

Dose proportionality

The model is linear and carries no weight covariate, so exposure must scale exactly with the mg/kg dose.

dp <- mb |>
  dplyr::group_by(analyte) |>
  dplyr::mutate(auc_norm = PPORRES / dose_mg) |>
  dplyr::summarise(cv_pct = 100 * sd(auc_norm) / mean(auc_norm), .groups = "drop")

knitr::kable(dp, digits = 6,
             caption = "Coefficient of variation of dose-normalised AUCinf across the three weight arms (must be ~0).")
Coefficient of variation of dose-normalised AUCinf across the three weight arms (must be ~0).
analyte cv_pct
Chloroquine 3e-06
Desethylchloroquine 1e-06 
stopifnot(all(dp$cv_pct < 0.1))

Comparison against the published NCA values

Hoglund 2016 reports no Cmax, Tmax or AUC, so the only published NCA-comparable quantity is the chloroquine terminal half-life. The desethylchloroquine reference is deliberately set to NA: as shown above, the published 8.74 days is a disposition half-life, not an observable terminal slope, so comparing it against an NCA slope would manufacture a spurious ~23% discrepancy. It is validated instead by the parameter-level check in the Errata section.

published <- tibble::tribble(
  ~treatment, ~analyte,               ~half.life,
  "45 kg",    "Chloroquine",          10.7 * 24,
  "50 kg",    "Chloroquine",          10.7 * 24,
  "55 kg",    "Chloroquine",          10.7 * 24,
  "45 kg",    "Desethylchloroquine",  NA_real_,
  "50 kg",    "Desethylchloroquine",  NA_real_,
  "55 kg",    "Desethylchloroquine",  NA_real_
)

cmp <- nlmixr2lib::ncaComparisonTable(
  simulated     = nca_res,
  reference     = published,
  by            = c("treatment", "analyte"),
  units         = c(half.life = "h"),
  tolerance_pct = 20
)

knitr::kable(
  cmp,
  caption = "Simulated vs published NCA. * marks rows differing by more than 20%."
)
Simulated vs published NCA. * marks rows differing by more than 20%.
NCA parameter treatment analyte Reference Simulated % diff
t½ (h) 45 kg Chloroquine 257 256 -0.1%
t½ (h) 45 kg Desethylchloroquine — 298 —
t½ (h) 50 kg Chloroquine 257 256 -0.1%
t½ (h) 50 kg Desethylchloroquine — 298 —
t½ (h) 55 kg Chloroquine 257 256 -0.1%
t½ (h) 55 kg Desethylchloroquine — 298 —

Simulated exposures against concentrations quoted in the Discussion

The Discussion cites a Bolivian cohort in which day-7 whole-blood chloroquine and desethylchloroquine were 197-535 and 75-223 ng/mL, and notes a suggested minimum effective chloroquine concentration of 90 ng/mL in whole blood. These come from other studies, so they are a magnitude sanity check rather than a gate on this model.

day7 <- sim_typical |>
  dplyr::filter(treatment == "50 kg", time == 168) |>
  dplyr::select(Cc, Cc_dcq) |>
  dplyr::mutate(ratio = Cc_dcq / Cc)

knitr::kable(day7, digits = 2,
             caption = "Day-7 whole-blood concentrations (ng/mL), 50 kg reference adult.")
Day-7 whole-blood concentrations (ng/mL), 50 kg reference adult.
Cc Cc_dcq ratio
332.17 136.07 0.41

Both fall inside the quoted ranges, the day-7 chloroquine concentration sits well above the 90 ng/mL minimum effective concentration (consistent with the 100% cure rate observed), and the metabolite-to-parent ratio matches the ratio implied by those two ranges.

Visual predictive check 

n_vpc <- 100L   # cap is 200 per arm

vpc_events <- purrr::map_dfr(seq_len(n_vpc), \(i) make_arm(i, "50 kg", 50))

sim_vpc <- rxode2::rxSolve(
  mod, events = vpc_events, keep = c("treatment", "wt_kg"), useLinCmt = FALSE
) |>
  as.data.frame()
vpc_long <- sim_vpc |>
  dplyr::select(id, time, Cc, Cc_dcq) |>
  tidyr::pivot_longer(c(Cc, Cc_dcq), names_to = "analyte", values_to = "conc") |>
  dplyr::mutate(analyte = dplyr::recode(analyte,
                                        Cc = "Chloroquine",
                                        Cc_dcq = "Desethylchloroquine")) |>
  dplyr::group_by(analyte, time) |>
  dplyr::summarise(
    median = median(conc),
    lo     = quantile(conc, 0.05),
    hi     = quantile(conc, 0.95),
    .groups = "drop"
  )

ggplot(vpc_long, aes(time / 24, median)) +
  geom_ribbon(aes(ymin = lo, ymax = hi), alpha = 0.25, fill = "steelblue") +
  geom_line(colour = "steelblue4") +
  facet_wrap(~analyte) +
  scale_y_log10() +
  labs(x = "Time (days)", y = "Whole-blood concentration (ng/mL)") +
  theme_bw()
#> Warning in scale_y_log10(): log-10 transformation introduced infinite values.
#> log-10 transformation introduced infinite values.
#> log-10 transformation introduced infinite values.
#> log-10 transformation introduced infinite values.
Simulated between-subject variability for the 50 kg reference arm (median and 5th-95th percentiles), replicating the layout of Figure 4 of Hoglund 2016.

Simulated between-subject variability for the 50 kg reference arm (median and 5th-95th percentiles), replicating the layout of Figure 4 of Hoglund 2016. 

# Cohort-derived, so assert on the CENTRE and on robust quantiles rather than
# on extremes, which are not reproducible across rxode2 builds or thread counts.
vpc_day7 <- sim_vpc |>
  dplyr::filter(time == 168) |>
  dplyr::summarise(
    med_cq  = median(Cc),
    med_dcq = median(Cc_dcq),
    q90_cq  = quantile(Cc, 0.9)
  )

stopifnot(
  # The cohort median must sit near the typical-value prediction; BSV in this
  # model is on volumes and F only, so the median moves little.
  abs(vpc_day7$med_cq - day7$Cc) / day7$Cc < 0.25,
  # Structural: a mis-transcribed clearance or dose moves the whole
  # distribution by tens of percent.
  vpc_day7$med_cq > 150, vpc_day7$med_cq < 700,
  vpc_day7$med_dcq > 50,  vpc_day7$med_dcq < 350
)

Assumptions and deviations

  • Two Table 1 values are reconstructed (Vp DCQ/F = 257 L, Q DCQ/F = 1.46 L/h). See the Errata section for the full three-way justification.
  • Body weight is assumed (50 kg reference, bracketed 45-55 kg) because the paper reports none. The model has no weight covariate, so this affects only the mg/kg-to-mg dose conversion and scales exposure linearly.
  • The second day-0 dose is placed at 9 h, the midpoint of the paper’s “6-12 h” window.
  • fm = 0.18 is treated as a molar fraction, consistent with the authors fitting in umole/L and with the fraction being derived from urinary recovery. The molecular weights used for the correction are standard chemical constants.
  • The residual error is encoded as proportional in linear concentration space, which is the equivalent of the paper’s additive-on-log-transformed-data model; the paper states this equivalence explicitly.
  • The final model is covariate-free. Body weight (allometric, exponents fixed at 0.75 and 1.0), age, sex, parasite clearance time and fever clearance time were screened and dropped; they are recorded in the model file’s covariatesDataExcluded for provenance.
  • No correlation between the etas is modelled, as none is reported.
  • The VPC uses 100 subjects, below the 200-per-arm cap; it illustrates the model’s between-subject variability and is not a reproduction of the paper’s 1000-replicate VPC. ```