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Dapsone (Hall 2017)

Source: vignettes/articles/Hall_2017_dapsone.Rmd
Hall_2017_dapsone.Rmd

Model and source

  • Citation: Hall RG II, Pasipanodya JG, Swancutt MA, Meek C, Leff R, Gumbo T. Supervised machine-learning reveals that old and obese people achieve low dapsone concentrations. CPT Pharmacometrics Syst Pharmacol. 2017;6(8):552-559. doi:10.1002/psp4.12208
  • Description: One-compartment population PK model with first-order oral absorption for dapsone in healthy US adults across a wide weight range; covariate effects on Ka, CL, and Vc are encoded via the published MARS piecewise-linear basis functions of weight, age, and blood urea nitrogen (Hall 2017).
  • Article: https://doi.org/10.1002/psp4.12208

The structural model is a one-compartment disposition with first-order oral absorption. Hall 2017 fits the per-subject pharmacokinetic parameters with ADAPT 5 / MLEM and then applies Multivariate Adaptive Regression Splines (MARS) to the individual posthoc PK estimates to express each parameter as a piecewise-linear combination of hinge basis functions of body weight, age, and blood urea nitrogen (Table 2 of the paper). The packaged model encodes the MARS equations verbatim; the IIV and residual error magnitudes are documented under Assumptions and deviations below.

Population

35 healthy adult volunteers (NCT01165840) recruited at the University of Texas Southwestern Clinical Trials and Research Center between July 2010 and May 2012 received a single 100 mg oral dose of dapsone under directly observed therapy. Recruitment was stratified by BMI to enrol equal numbers of normal-weight (BMI < 25), overweight / class I-II obese (BMI 25-40), and class III obese (BMI > 40) participants, with equal numbers of men and women within each stratum (Hall 2017 Methods, “Recruitment”). Plasma dapsone concentrations were measured at eight timepoints over 72 h, with sampling times chosen by D-optimal design in ADAPT 5. Baseline demographics are in Hall 2017 Table 1; the same fields are available programmatically via readModelDb("Hall_2017_dapsone")$population.

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Hall_2017_dapsone.R. The table below collects them for reviewer audit.

Equation / parameter Value Source location
lka (Ka MARS intercept, 1/h) log(3.967) Table 2, Eq. (2) intercept
lcl (CL MARS intercept, L/h) log(2.048) Table 2, Eq. (3) intercept
lvc (Vc MARS intercept, L) log(36.648) Table 2, Eq. (4) intercept
e_bf3ka_ka (coef on BF3_Ka) -0.062 Table 2, Eq. (2) BF3 term
e_bf5ka_ka (coef on BF5_Ka) +0.162 Table 2, Eq. (2) BF5 term
e_bf3cl_cl (coef on BF3_CL) -0.002 Table 2, Eq. (3) BF3 term
e_bf4cl_cl (coef on BF4_CL) -0.005 Table 2, Eq. (3) BF4 term
e_bf8v_vc (coef on BF8_V) +8.894 Table 2, Eq. (4) BF8 term
e_bf10v_vc (coef on BF10_V) -8.818 Table 2, Eq. (4) BF10 term
Hinge BF1_Ka = max(0, BUN - 7) structural Table 2, BF1 definition
Hinge BF3_Ka = max(0, 63.7 - WT) * BF1_Ka structural Table 2, BF3 definition (Ka row)
Hinge BF5_Ka = max(0, 74.8 - WT) structural Table 2, BF5 definition (Ka row)
Hinge BF2_CL = max(0, 77.2 - WT) structural Table 2, BF2 definition (CL row)
Hinge BF3_CL = max(0, AGE - 27) * BF2_CL structural Table 2, BF3 definition (CL row)
Hinge BF4_CL = max(0, 27 - AGE) * BF2_CL structural Table 2, BF4 definition (CL row)
Hinge BF8_V = max(0, WT - 69.8) structural Table 2, BF8 definition (V row)
Hinge BF10_V = max(0, WT - 74.8) structural Table 2, BF10 definition (V row)
IIV omega^2 on Ka (CV 94.7%) 0.6402 Results, p. 553-554 (base model)
IIV omega^2 on CL (CV 37.6%) 0.1322 Results, p. 553-554 (base model)
IIV omega^2 on Vc (CV 50.5%) 0.2271 Results, p. 553-554 (base model)
propSd (proportional residual SD) 0.20 Figure 2b derivation (see Deviations)
1-compartment ODE with first-order absorption structural Methods, “Pharmacokinetic modeling”; Figure 2b model selection

Virtual cohort

Original observed concentrations are not publicly distributed. The cohort below approximates the published baseline demographics (Table 1) within the in-cohort covariate ranges, sized to give stable MARS-typical-value behavior without straying into the extrapolation regions where the linear-scale typical value would otherwise be clamped at the model’s safety floor.

set.seed(20260518)
n_sim <- 200

cohort <- tibble(
  id  = seq_len(n_sim),
  WT  = pmin(pmax(rnorm(n_sim, mean = 85.1, sd = 18.0), 58), 138),
  AGE = pmin(pmax(rgamma(n_sim, shape = 2.5, rate = 2.5 / 38), 21), 77),
  BUN = pmin(pmax(rnorm(n_sim, mean = 13.0, sd = 4.5), 7), 28),
  treatment = "100 mg PO"
)

obs_times <- c(0, 1, 2, 4, 8, 16, 24, 48, 72)

dose_rows <- cohort |>
  transmute(id, time = 0, amt = 100, evid = 1, cmt = "depot",
            WT, AGE, BUN, treatment)
obs_rows <- cohort |>
  tidyr::crossing(time = obs_times) |>
  mutate(amt = 0, evid = 0, cmt = "central") |>
  select(id, time, amt, evid, cmt, WT, AGE, BUN, treatment)
events <- bind_rows(dose_rows, obs_rows) |>
  arrange(id, time, desc(evid))

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

Simulation 

sim <- rxode2::rxSolve(mod, events = events, keep = c("treatment", "WT", "AGE", "BUN"))
#> ℹ parameter labels from comments will be replaced by 'label()'

For the typical-value replication used in the figures below, also simulate without between-subject variability:

mod_typical <- rxode2::zeroRe(mod)
#> ℹ parameter labels from comments will be replaced by 'label()'
sim_typical <- rxode2::rxSolve(mod_typical, events = events, keep = c("treatment", "WT", "AGE", "BUN"))
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalcl', 'etalvc'
#> Warning: multi-subject simulation without without 'omega'

Replicate published figures

Figure 2a – concentration-time envelope across subjects

Hall 2017 Figure 2a shows the dapsone concentration-time profiles in all 35 subjects after a single 100 mg oral dose, illustrating the order-of- magnitude variability in peak concentration that motivates the covariate analysis. The simulated 5th-50th-95th percentile envelope below reproduces that order-of-magnitude spread.

sim_summary <- sim |>
  filter(time > 0) |>
  group_by(time) |>
  summarise(
    Q05 = quantile(Cc, 0.05, na.rm = TRUE),
    Q50 = quantile(Cc, 0.50, na.rm = TRUE),
    Q95 = quantile(Cc, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(sim_summary, aes(time, Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.25) +
  geom_line(linewidth = 0.7) +
  scale_y_log10() +
  labs(x = "Time (h)", y = "Dapsone Cc (mg/L)",
       title = "Figure 2a - simulated concentration envelope",
       caption = "Replicates Figure 2a of Hall 2017 (5th-50th-95th percentile across 200 virtual subjects).")

Figure 3 – relationship between weight and volume of distribution

Hall 2017 Figure 3 depicts the MARS BF8 and BF10 hinges for weight versus volume of distribution. The figure below shows the simulated typical-value Vc versus weight at the median BUN and AGE, reproducing the two hinge break points at 69.8 kg and 74.8 kg.

wt_grid <- tibble(WT = seq(50, 150, length.out = 201), AGE = 36, BUN = 13)
vc_grid <- wt_grid |>
  mutate(
    BF8_V  = pmax(0, WT - 69.8),
    BF10_V = pmax(0, WT - 74.8),
    Vc     = pmax(0.1, 36.648 + 8.894 * BF8_V - 8.818 * BF10_V)
  )

ggplot(vc_grid, aes(WT, Vc)) +
  geom_vline(xintercept = c(69.8, 74.8), linetype = "dashed", colour = "grey50") +
  geom_line(linewidth = 0.7) +
  labs(x = "Weight (kg)", y = "Typical Vc (L)",
       title = "Figure 3 - typical-value Vc vs weight (hinges at 69.8 and 74.8 kg)",
       caption = "Replicates Figure 3 of Hall 2017 with BF8 and BF10 of Table 2.")

PKNCA validation 

sim_nca <- sim |>
  filter(!is.na(Cc), time > 0) |>
  select(id, time, Cc, treatment)

conc_obj <- PKNCA::PKNCAconc(
  sim_nca, Cc ~ time | treatment + id,
  concu = "mg/L", timeu = "hr"
)

dose_df <- events |>
  filter(evid == 1) |>
  select(id, time, amt, treatment)
dose_obj <- PKNCA::PKNCAdose(
  dose_df, amt ~ time | treatment + 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))
#> Warning: Requesting an AUC range starting (0) before the first measurement (1) is not allowed
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nca_summary <- summary(nca_res)
knitr::kable(nca_summary, caption = "Simulated NCA parameters (single 100 mg oral dose).")
Simulated NCA parameters (single 100 mg oral dose).
Interval Start Interval End treatment N Cmax (mg/L) Tmax (hr) Clast (mg/L) Half-life (hr) λz\lambda_z (1/hr) AUCinf,obs (hr*mg/L)
0 Inf 100 mg PO 200 1.36 [60.5] 1.00 [1.00, 8.00] 0.113 [337] 30.3 [20.8] 0.0282 [74.9] NC

Comparison against published NCA

Hall 2017 does not tabulate per-subject NCA parameters; only the base-model PK parameter point estimates and population half-life (25.2 +/- 7.7 h) are reported. The simulated half-life summary from the PKNCA block above should fall within roughly +/- 30% of 25.2 h. The simulated AUCinf median maps to 100 mg / typical CL (L/h) and should track the MARS-typical-value CL at the median weight / age (CL = 2.048 L/h, giving AUCinf ~= 49 mg.h/L).

Assumptions and deviations

  • Drug-name correction: the source task block reported drug: "CPT: Pharmacometrics & Sys", which is the journal name. The paper’s title and Abstract identify dapsone as the modeled drug; the file is named Hall_2017_dapsone.R accordingly.
  • MARS-style covariate model: Hall 2017 fit individual posthoc PK estimates with MLEM in ADAPT 5 and then applied a MARS regression to express Ka, CL, and Vc as additive linear combinations of hinge basis functions of WT, AGE, and BUN. This is unusual for nlmixr2 (the standard form is a multiplicative power-law on log-transformed parameters). The packaged model encodes the MARS equations verbatim in linear-parameter space, with the population intercept stored on the log scale (lka, lcl, lvc) so log-normal IIV can be applied multiplicatively around the MARS typical value.
  • In-cohort covariate range: the MARS hinges have no physical constraint outside the cohort’s covariate range (WT 58-138 kg, AGE 21-77 yr, BUN 7-28 mg/dL). The linear-scale typical value can go non-positive under extrapolation; the model() block clamps Ka, CL, and Vc at a small positive floor (0.01, 0.01, and 0.1 respectively) to keep the ODE well-posed. Stay inside the in-cohort range for virtual cohorts; outside that range the clamped values are not a meaningful PK prediction.
  • IIV from base model, not covariate-adjusted: Hall 2017 reports the base 1-compartment %CVs (94.7% Ka, 37.6% CL, 50.5% Vc) but does not report IIV after the MARS hinges are applied. The packaged model uses the base %CVs verbatim, which overstates the residual IIV the MARS covariates would leave unexplained (Table 3 reports MARS cross-validated r^2 = 0.36 / 0.48 / 0.64 for Ka / CL / Vc; the covariate-adjusted IIV would be smaller by roughly sqrt(1 - r^2)).
  • Residual error model: Hall 2017 does not report a residual-error specification. The packaged propSd <- fixed(0.20) is approximated from Figure 2b: observed vs predicted r^2 = 0.91, slope 0.90 +/- 0.02, observed mean 1.63 mg/L and SD 1.03 mg/L give a residual SD of approximately sqrt(1 - r^2) * SD(obs) / mean(obs) ~= 19%. This is a paper-derived approximation, not a directly reported value; documented here per the extract-literature-model skill’s non-paper-provenance rule.
  • Bioavailability: F is held at the structural anchor of 1 (not encoded explicitly as lfdepot). Hall 2017 does not estimate or constrain F, and the published parameter values are apparent (CL/F, V/F, ka/F).
  • Race / SEX / metabolic-syndrome covariates: Hall 2017 evaluated race (White vs non-White) and gender in bivariate analyses; gender showed a univariate effect on volume that did not survive multivariate MARS. The packaged model carries only the three covariates retained in the final MARS model (WT, AGE, BUN); race and gender are not used.
  • Supplement S1: Supplementary Table S1 (model selection AIC / BIC comparison across 1-, 2-, and 3-compartment structures) was referenced in the paper but is not on disk. The 1-compartment selection is reported in the Results text and is encoded as such; the supplement would only inform the model-comparison narrative, not the parameter values.