Skip to contents

Molibresib and GSK3529246 (Krishnatry 2021)

Source: vignettes/articles/Krishnatry_2021_molibresib.Rmd
Krishnatry_2021_molibresib.Rmd

Model and source

  • Citation: Krishnatry AS, Voelkner A, Dhar A, Prohn M, Ferron-Brady G (2021). Population pharmacokinetic modeling of molibresib and its active metabolites in patients with solid tumors: A semimechanistic autoinduction model. CPT Pharmacometrics Syst Pharmacol 10(7):709-722. doi:10.1002/psp4.12639. Structure from the final NONMEM control stream (Run 32) in Supplementary Text S2; parameter values from Table 3.
  • Description: Semimechanistic liver-compartment population PK model for oral molibresib (GSK525762, a BET bromodomain inhibitor) and its active metabolite composite GSK3529246 in adults with advanced solid tumours. Molibresib is absorbed after a lag time by first-order absorption into a physiologic liver compartment (plasma flow 55 L/h, volume 1.5 L, both fixed), distributes in a two-compartment systemic model, and is eliminated only by hepatic extraction. The extraction ratio is proportional to a relative hepatic enzyme amount, whose production rate rises linearly with the molibresib concentration in the liver, so the model reproduces the autoinduction that lowers molibresib exposure on repeated dosing. Extracted molibresib is converted on a 1:1 molar basis into GSK3529246 through one transit compartment, and GSK3529246 has two-compartment disposition with first-order elimination. Body weight scales both central volumes with one shared exponent, and time-varying aspartate aminotransferase lowers GSK3529246 clearance. Amounts are in umol and concentrations in umol/L (molibresib 424 g/mol, GSK3529246 396 g/mol).
  • Article: CPT Pharmacometrics Syst Pharmacol 2021;10(7):709-722 (open access)

Molibresib (GSK525762) is an oral bromodomain and extraterminal (BET) inhibitor. CYP3A4 converts it to two active metabolites that are equipotent to the parent, GSK3536835 (ethyl-hydroxy) and GSK3529246 (N-desethyl). The assay converts the first fully to the second, so the two are reported together as the active metabolite composite “GSK3529246”. Molibresib exposure falls on repeated dosing, most clearly at doses of 60 mg or more, and the authors confirmed CYP3A4 autoinduction in vitro.

The final model (Run 32) is semimechanistic:

  • The dose is absorbed after a lag time, by first-order absorption, into a physiologic liver compartment. Liver plasma flow is fixed at 55 L/h (hepatic blood flow 100 L/h at a haematocrit of 45%) and liver volume at 1.5 L.
  • The hepatic extraction ratio is EH = CL/F * enzyme / Qh. The fraction 1 - EH of the liver outflow returns molibresib to a two-compartment systemic model. The fraction EH becomes GSK3529246 on a 1:1 molar basis, passing through one transit compartment. Systemic molibresib re-enters the liver at Qh, so hepatic extraction is the only route of molibresib elimination.
  • A relative enzyme pool starts at 1. Its production rate rises linearly with the molibresib concentration in the liver: d(enzyme)/dt = kin * (1 + slope * C_liver) - kin * enzyme. Induction therefore raises both systemic clearance and first-pass extraction.
  • GSK3529246 has two-compartment disposition with first-order elimination.
  • Body weight scales both central volumes with one exponent, and time-varying AST lowers GSK3529246 clearance.

The model runs in molar units, as the authors fitted it. Doses are in umol (mg / 424 g/mol x 1000) and concentrations in umol/L. This vignette converts back to ng/mL with the molecular weights of molibresib (424 g/mol) and GSK3529246 (396 g/mol) where the paper reports ng/mL.

Population

The analysis pooled 193 adults and adolescents from the first-time-in-human phase I/II study BET115521. Part 1 (dose escalation, n = 94) gave 2-100 mg once daily or 20-40 mg twice daily of the amorphous free-base formulation, plus 80 mg once daily of the besylate salt in a 10-patient substudy. Part 2 (expansion cohorts, n = 99) gave 75 mg once daily of the besylate salt, the recommended phase II dose.

The cohort’s median age was 58 years (range 16-86), 53% were female and 83% were White. Median body weight was 69.6 kg (range 34-120 kg). The tumour types were NUT midline carcinoma, colorectal, breast, prostate, lung, gastrointestinal stromal tumour and others (Table 1).

The dataset had 2681 molibresib and 814 GSK3529246 plasma concentrations above the lower limit of quantification. GSK3529246 was assayed only in Part 2 and in the Part 1 80 mg cohort (Table S2).

The same information is available programmatically:

str(readModelDb("Krishnatry_2021_molibresib")()$population)
#> List of 11
#>  $ species       : chr "human"
#>  $ n_subjects    : int 193
#>  $ n_studies     : int 1
#>  $ age_range     : chr "16-86 years (median 58; mean 55.7, SD 14; Table 1)"
#>  $ weight_range  : chr "34-120 kg (median 69.6; mean 71.7, SD 17; Table 1)"
#>  $ sex_female_pct: num 53
#>  $ race_ethnicity: Named num [1:4] 83 6 6 5
#>   ..- attr(*, "names")= chr [1:4] "White" "Asian" "Black" "Missing"
#>  $ disease_state : chr "Advanced solid tumours: NUT (nuclear protein in testis) midline carcinoma, colorectal, breast (including triple"| __truncated__
#>  $ dose_range    : chr "Part 1: 2-100 mg once daily or 20-40 mg twice daily of the amorphous free-base formulation, and 80 mg once dail"| __truncated__
#>  $ regions       : chr "Not reported."
#>  $ notes         : chr "First-time-in-human phase I/II study BET115521 (Part 1 dose escalation, n = 94; Part 2 expansion cohorts, n = 9"| __truncated__

Source trace

Supplementary Text S2 of the paper is the complete NONMEM control stream of the final model (Run 32). It gives the model structure, the covariate reference values and the fixed parameters. The parameter values come from Table 3. The $THETA / $OMEGA records printed in Text S2 are the run’s initial values and differ from Table 3 in the second or third significant figure.

Equation / parameter Value Source location
lka (ka) 4.08 /h Table 3
lcl (CL/F) 9.02 L/h Table 3
lvc (V1/F, 70 kg) 53.1 L Table 3
lqh (Qh) 55.0 L/h, fixed Table 3; Methods (100 L/h blood flow, haematocrit 45%)
lvh (Vh) 1.50 L, fixed Table 3; Methods
lq (Q1) 0.999 L/h Table 3
lvp (V2/F) 17.4 L Table 3
ltlag (ALAG) 0.132 h Table 3
lslope (induction slope) 0.922 L/umol Table 3; unit from the molar modelling scale (Methods)
lkin (kin = kout) 0.00550 /h, fixed Table 3; Text S1 (enzyme half-life 126 h); Text S2 KOUT = KIN/BASE, BASE = 1
lktr_gsk3529246 (mka) 11.5 /h Table 3
lcl_gsk3529246 (mCL/F, AST 28 U/L) 12.8 L/h Table 3
lvc_gsk3529246 (mV1/F, 70 kg) 62.1 L Table 3
lq_gsk3529246 (mQ1) 5.63 L/h Table 3
lvp_gsk3529246 (mV2/F) 140 L Table 3
e_wt_vc (WT on V1/F and mV1/F) 0.717 Table 3; reference 70 kg from Text S2 COVWT_V
e_ast_cl_gsk3529246 (AST on mCL/F) -0.194 Table 3; reference 28 U/L from Text S2 COVAST_MCL
etalka 1.65 Table 3 omega^2
etalcl 0.205 Table 3 omega^2
etalvc 0.0687 Table 3 omega^2
etalktr_gsk3529246 0.488 Table 3 omega^2
etalcl_gsk3529246, etalvc_gsk3529246 block 0.227, 0.174, 0.206 Table 3 omega^2; covariance printed as “174” (see Assumptions)
propSd sqrt(0.207) = 0.455 Table 3 sigma^2; Text S2 $SIGMA BLOCK(2)
propSd_gsk3529246 sqrt(0.132) = 0.363 Table 3 sigma^2
d/dt(depot), alag(depot) n/a Text S2 $DES DADT(1), ALAG1
d/dt(liver), eh, fh, ch n/a Text S2 $DES DADT(2), EH = CL*A(6)/QH, FH = 1 - EH, CH = A(2)/VH; Figure 1
d/dt(transit1_gsk3529246) n/a Text S2 DADT(3)
d/dt(central), d/dt(peripheral1) n/a Text S2 DADT(4), DADT(5)
d/dt(enzyme), enzyme(0) <- 1 n/a Text S2 DADT(6), A_0(6) = BASE
d/dt(central_gsk3529246), d/dt(peripheral1_gsk3529246) n/a Text S2 DADT(7), DADT(8)
Cc, Cc_gsk3529246, proportional errors n/a Text S2 $ERROR

Helpers 

mw_parent <- 424 # g/mol, Methods
mw_metab <- 396 # g/mol, Methods
mg_to_umol <- function(mg) mg / mw_parent * 1000

mod <- readModelDb("Krishnatry_2021_molibresib")
mod_typical <- rxode2::zeroRe(mod)
#> ℹ parameter labels from comments will be replaced by 'label()'

# The model has two declared endpoints and no state endpoint, so observation
# rows are keyed by dvid with cmt left empty; rxode2 then returns both Cc and
# Cc_gsk3529246 on every observation row. Doses go to the depot state.
make_events <- function(ids, dose_mg, n_doses, obs_times, covs) {
  dose_rows <- data.frame(
    id = ids, time = 0, evid = 1L, amt = mg_to_umol(dose_mg),
    cmt = "depot", ii = 24, addl = n_doses - 1L, dvid = NA_integer_
  )
  obs_rows <- expand.grid(id = ids, time = obs_times) |>
    dplyr::mutate(
      evid = 0L, amt = 0, cmt = NA_character_, ii = 0, addl = 0L, dvid = 1L
    )
  dplyr::bind_rows(dose_rows, obs_rows) |>
    dplyr::left_join(covs, by = "id") |>
    dplyr::arrange(id, time, dplyr::desc(evid))
}

auc_trap <- function(time, conc) {
  sum(diff(time) * (head(conc, -1) + tail(conc, -1)) / 2)
}

Typical-value exposures by body weight (Table S5)

Table S5 of the paper gives the typical-patient Cmax, Cmin and AUC0-24h after the first 75 mg once-daily dose and at steady state, for the 5th, 50th and 95th percentiles of body weight (48, 70 and 102 kg). Values are for molibresib, GSK3529246 and the total active moiety (TAM, their molar sum), in nM. Because they are typical values with no random effects, they test the transcribed structure and parameters directly.

The model’s enzyme pool has a 126-hour half-life, so “steady state” depends on the day chosen. The paper does not say which day it used. The Day-22 dosing interval (Week 4, Day 1, a scheduled Part 2 PK visit) reproduces the published molibresib steady-state AUC. On a later day, when induction is complete, the AUC is 1% lower. Day 22 is used below. AST is held at the 28 U/L reference.

wts <- c(48, 70, 102)
covs_s5 <- data.frame(id = seq_along(wts), WT = wts, AST = 28)
ev_s5 <- make_events(
  ids = covs_s5$id, dose_mg = 75, n_doses = 30,
  obs_times = sort(unique(c(seq(0, 24, by = 0.02), seq(504, 528, by = 0.02)))),
  covs = covs_s5
)
sim_s5 <- rxode2::rxSolve(
  mod_typical, events = ev_s5, keep = c("WT"), useLinCmt = FALSE
) |>
  as.data.frame() |>
  dplyr::mutate(
    Molibresib = Cc * 1000,
    GSK3529246 = Cc_gsk3529246 * 1000,
    TAM = Molibresib + GSK3529246,
    occasion = ifelse(time <= 24, "First Dose", "Steady-state"),
    tad = ifelse(time <= 24, time, time - 504)
  )
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalcl', 'etalvc', 'etalktr_gsk3529246', 'etalcl_gsk3529246', 'etalvc_gsk3529246'
#> Warning: multi-subject simulation without without 'omega'

s5_sim <- sim_s5 |>
  tidyr::pivot_longer(c(Molibresib, GSK3529246, TAM), names_to = "analyte", values_to = "conc_nM") |>
  dplyr::group_by(analyte, WT, occasion) |>
  dplyr::summarise(
    cmax = max(conc_nM),
    cmin = conc_nM[which.max(tad)],
    auc = auc_trap(tad, conc_nM),
    .groups = "drop"
  )

# Krishnatry 2021 Table S5 (nM, nM, nM*h)
s5_pub <- tibble::tribble(
  ~analyte, ~WT, ~occasion, ~cmax_pub, ~cmin_pub, ~auc_pub,
  "Molibresib", 48, "First Dose", 2957.1, 41.2, 14840.9,
  "Molibresib", 48, "Steady-state", 2583.5, 21.1, 9936.4,
  "Molibresib", 70, "First Dose", 2342.1, 61.0, 14653.8,
  "Molibresib", 70, "Steady-state", 2070.0, 26.6, 9935.9,
  "Molibresib", 102, "First Dose", 1847.3, 94.9, 14285.9,
  "Molibresib", 102, "Steady-state", 1656.5, 39.1, 9935.7,
  "GSK3529246", 48, "First Dose", 1030.6, 103.6, 10433.6,
  "GSK3529246", 48, "Steady-state", 1457.4, 174.8, 13779.9,
  "GSK3529246", 70, "First Dose", 793.3, 129.4, 10023.9,
  "GSK3529246", 70, "Steady-state", 1173.2, 197.2, 13780.6,
  "GSK3529246", 102, "First Dose", 610.4, 166.3, 9361.0,
  "GSK3529246", 102, "Steady-state", 968.0, 236.6, 13781.8,
  "TAM", 48, "First Dose", 3705.8, 144.8, 25274.5,
  "TAM", 48, "Steady-state", 3768.0, 195.9, 23716.3,
  "TAM", 70, "First Dose", 2908.1, 190.4, 24677.7,
  "TAM", 70, "Steady-state", 3033.0, 223.8, 23716.5,
  "TAM", 102, "First Dose", 2272.0, 261.2, 23646.9,
  "TAM", 102, "Steady-state", 2468.9, 275.7, 23717.5
)

s5_cmp <- s5_pub |>
  dplyr::left_join(s5_sim, by = c("analyte", "WT", "occasion")) |>
  dplyr::mutate(
    cmax_pct = 100 * (cmax - cmax_pub) / cmax_pub,
    cmin_pct = 100 * (cmin - cmin_pub) / cmin_pub,
    auc_pct = 100 * (auc - auc_pub) / auc_pub
  )

s5_cmp |>
  dplyr::transmute(
    analyte, WT, occasion,
    cmax_pub, cmax = round(cmax, 1), cmax_pct = round(cmax_pct, 1),
    cmin_pub, cmin = round(cmin, 1), cmin_pct = round(cmin_pct, 1),
    auc_pub, auc = round(auc, 0), auc_pct = round(auc_pct, 1)
  ) |>
  dplyr::rename(
    "Analyte" = analyte, "WT (kg)" = WT, "Occasion" = occasion,
    "Cmax published (nM)" = cmax_pub, "Cmax simulated (nM)" = cmax, "Cmax % diff" = cmax_pct,
    "Cmin published (nM)" = cmin_pub, "Cmin simulated (nM)" = cmin, "Cmin % diff" = cmin_pct,
    "AUC0-24 published (nM*h)" = auc_pub, "AUC0-24 simulated (nM*h)" = auc, "AUC0-24 % diff" = auc_pct
  ) |>
  knitr::kable(caption = "Typical-value exposures after 75 mg once daily: Krishnatry 2021 Table S5 versus the packaged model (steady state = Day 22).")
Typical-value exposures after 75 mg once daily: Krishnatry 2021 Table S5 versus the packaged model (steady state = Day 22).
Analyte WT (kg) Occasion Cmax published (nM) Cmax simulated (nM) Cmax % diff Cmin published (nM) Cmin simulated (nM) Cmin % diff AUC0-24 published (nM*h) AUC0-24 simulated (nM*h) AUC0-24 % diff
Molibresib 48 First Dose 2957.1 2954.1 -0.1 41.2 41.2 -0.1 14840.9 14831 -0.1
Molibresib 48 Steady-state 2583.5 2581.9 -0.1 21.1 21.2 0.3 9936.4 9930 -0.1
Molibresib 70 First Dose 2342.1 2341.4 0.0 61.0 61.0 0.1 14653.8 14645 -0.1
Molibresib 70 Steady-state 2070.0 2068.4 -0.1 26.6 26.7 0.3 9935.9 9931 -0.1
Molibresib 102 First Dose 1847.3 1845.0 -0.1 94.9 95.0 0.1 14285.9 14277 -0.1
Molibresib 102 Steady-state 1656.5 1655.1 -0.1 39.1 39.4 0.7 9935.7 9931 0.0
GSK3529246 48 First Dose 1030.6 1030.7 0.0 103.6 104.0 0.4 10433.6 10451 0.2
GSK3529246 48 Steady-state 1457.4 1458.3 0.1 174.8 176.5 1.0 13779.9 13821 0.3
GSK3529246 70 First Dose 793.3 793.2 0.0 129.4 129.9 0.4 10023.9 10038 0.1
GSK3529246 70 Steady-state 1173.2 1174.1 0.1 197.2 199.3 1.0 13780.6 13822 0.3
GSK3529246 102 First Dose 610.4 610.3 0.0 166.3 166.9 0.4 9361.0 9372 0.1
GSK3529246 102 Steady-state 968.0 969.1 0.1 236.6 239.2 1.1 13781.8 13823 0.3
TAM 48 First Dose 3705.8 3703.0 -0.1 144.8 145.2 0.3 25274.5 25282 0.0
TAM 48 Steady-state 3768.0 3766.3 0.0 195.9 197.6 0.9 23716.3 23752 0.2
TAM 70 First Dose 2908.1 2905.7 -0.1 190.4 191.0 0.3 24677.7 24683 0.0
TAM 70 Steady-state 3033.0 3031.6 0.0 223.8 226.0 1.0 23716.5 23753 0.2
TAM 102 First Dose 2272.0 2269.1 -0.1 261.2 261.9 0.3 23646.9 23648 0.0
TAM 102 Steady-state 2468.9 2468.1 0.0 275.7 278.6 1.0 23717.5 23754 0.2

The table checks the model in five ways at once:

  • The body-weight exponent on both central volumes (Cmax moves with weight).
  • The first-pass liver structure and the induction loop (steady-state AUC).
  • The 1:1 molar conversion to GSK3529246 (metabolite AUC).
  • The metabolite’s distribution and transit parameters (metabolite Cmax and Cmin).
  • The molar units. A wrong reading of the induction-slope unit would move the steady-state enzyme level by orders of magnitude.

All 54 values agree to within 3%. The simulation is deterministic, so this bound is tight. The largest differences are in the steady-state molibresib Cmin, which depends most on the day chosen as steady state.

stopifnot(
  nrow(s5_cmp) == 18L,
  !anyNA(s5_cmp$cmax),
  all(abs(c(s5_cmp$cmax_pct, s5_cmp$cmin_pct, s5_cmp$auc_pct)) < 3)
)

Mass balance and the extent of induction

Molibresib is cleared only by hepatic extraction, and extraction forms GSK3529246 1:1 in moles. At true steady state the GSK3529246 AUC over a dosing interval must therefore equal the molar dose divided by mCL/F, whatever the enzyme level. With 75 mg (176.9 umol) and mCL/F = 12.8 L/h that is 13.82 umolh/L. The paper’s Table S5 value, 13.78 umolh/L, implies an unrounded mCL/F of 12.84 L/h, consistent with the tabulated 12.8.

The paper reports a “2.1-fold maximum increase in hepatic enzyme amount (based on the maximum estimate for any subject … 75 mg dose)”. That is an extreme over 99 individuals, so the typical patient should sit well below it.

covs_mb <- data.frame(id = 1L, WT = 70, AST = 28)
ev_mb <- make_events(
  ids = 1L, dose_mg = 75, n_doses = 60,
  obs_times = c(seq(0, 1392, by = 1), seq(1416, 1440, by = 0.02)), covs = covs_mb
)
sim_mb <- rxode2::rxSolve(mod_typical, events = ev_mb, useLinCmt = FALSE) |>
  as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalcl', 'etalvc', 'etalktr_gsk3529246', 'etalcl_gsk3529246', 'etalvc_gsk3529246'
last_tau <- dplyr::filter(sim_mb, time >= 1416)
auc_metab_ss <- auc_trap(last_tau$time, last_tau$Cc_gsk3529246)
auc_metab_theory <- mg_to_umol(75) / 12.8
enzyme_ss <- max(sim_mb$enzyme)
c(
  AUC_metabolite_simulated = auc_metab_ss,
  AUC_metabolite_dose_over_mCL = auc_metab_theory,
  enzyme_fold_typical = enzyme_ss
)
#>     AUC_metabolite_simulated AUC_metabolite_dose_over_mCL 
#>                    13.819284                    13.819281 
#>          enzyme_fold_typical 
#>                     1.515246
stopifnot(
  abs(auc_metab_ss / auc_metab_theory - 1) < 0.001,
  enzyme_ss > 1.3, enzyme_ss < 2.1
)

At steady state the typical patient’s enzyme pool is about 1.5-fold its baseline. That raises molibresib’s systemic clearance from 9.0 to about 13.6 L/h and lowers the fraction escaping first pass from 0.84 to about 0.75.

Typical profiles by body weight (Figure 3b) 

# Replicates Figure 3b of Krishnatry 2021.
sim_s5 |>
  tidyr::pivot_longer(c(Molibresib, GSK3529246, TAM), names_to = "analyte", values_to = "conc_nM") |>
  dplyr::mutate(
    analyte = factor(analyte, levels = c("Molibresib", "GSK3529246", "TAM")),
    WT = factor(paste(WT, "kg"), levels = paste(wts, "kg"))
  ) |>
  ggplot(aes(tad, conc_nM, colour = WT)) +
  geom_line() +
  facet_grid(occasion ~ analyte) +
  scale_y_log10() +
  labs(
    x = "Time after dose (h)", y = "Concentration (nM)", colour = "Body weight",
    title = "Typical profiles after 75 mg once daily",
    caption = "Replicates Figure 3b of Krishnatry 2021 (steady state = Day 22)."
  ) +
  theme_bw()
#> Warning in scale_y_log10(): log-10 transformation introduced infinite values.

Virtual cohort

Observed data are not public, so the simulations below use virtual cohorts. Each cohort draws body weight from a normal distribution with the study-part mean and SD in Table 1 (Part 1 once daily: 73.5 +/- 18 kg; Part 2: 70.4 +/- 17 kg), truncated to the observed 34-120 kg range. Baseline AST follows a log-normal distribution matching the Table 1 mean and SD (33.7 +/- 19 IU/L) and is held constant over time.

Four once-daily arms are simulated, 100 patients each: the Part 1 60, 80 and 100 mg free-base cohorts and the Part 2 75 mg besylate cohort. Each arm has continuous daily dosing with intensive sampling on Day 1 (W1D1) and Day 18 (W3D4).

set.seed(20210709)
rxode2::rxSetSeed(20210709)

n_per_arm <- 100L
arms <- tibble::tribble(
  ~treatment, ~dose_mg, ~wt_mean, ~wt_sd,
  "Part 1 - 60 mg q.d.", 60, 73.5, 18,
  "Part 1 - 80 mg q.d.", 80, 73.5, 18,
  "Part 1 - 100 mg q.d.", 100, 73.5, 18,
  "Part 2 - 75 mg q.d.", 75, 70.4, 17
)

draw_truncnorm <- function(n, mean, sd, lower, upper) {
  x <- rnorm(n, mean, sd)
  bad <- x < lower | x > upper
  while (any(bad)) {
    x[bad] <- rnorm(sum(bad), mean, sd)
    bad <- x < lower | x > upper
  }
  x
}
ast_sdlog <- sqrt(log(1 + (19 / 33.7)^2))
ast_meanlog <- log(33.7) - ast_sdlog^2 / 2

obs_cohort <- c(seq(0, 24, by = 0.25), seq(408, 432, by = 0.25))

events <- dplyr::bind_rows(lapply(seq_len(nrow(arms)), function(i) {
  ids <- (i - 1L) * n_per_arm + seq_len(n_per_arm)
  covs <- data.frame(
    id = ids,
    WT = draw_truncnorm(n_per_arm, arms$wt_mean[i], arms$wt_sd[i], 34, 120),
    AST = rlnorm(n_per_arm, ast_meanlog, ast_sdlog),
    treatment = arms$treatment[i]
  )
  make_events(ids, arms$dose_mg[i], n_doses = 18L, obs_times = obs_cohort, covs = covs)
}))
stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))

Simulation 

sim <- rxode2::rxSolve(
  mod, events = events, keep = c("treatment", "WT", "AST"),
  useLinCmt = FALSE
) |>
  as.data.frame() |>
  dplyr::mutate(
    day = ifelse(time <= 24, "W1D1", "W3D4"),
    tad = ifelse(time <= 24, time, time - 408),
    molibresib_ngml = Cc * mw_parent,
    gsk3529246_ngml = Cc_gsk3529246 * mw_metab,
    tam_nM = (Cc + Cc_gsk3529246) * 1000
  )
#> ℹ parameter labels from comments will be replaced by 'label()'

Prediction intervals after single and repeat dosing (Figure 2)

The paper’s Figure 2 is a prediction-corrected VPC of the observed data. Without the data, the figure below shows the model’s 5th, 50th and 95th percentiles for the Part 2 75 mg cohort on W1D1 and W3D4. The GSK3529246 profiles are flatter after repeat dosing and molibresib peaks are lower.

# Model prediction intervals on the time scale of Figure 2 of Krishnatry 2021.
sim |>
  dplyr::filter(treatment == "Part 2 - 75 mg q.d.") |>
  tidyr::pivot_longer(c(molibresib_ngml, gsk3529246_ngml), names_to = "analyte", values_to = "conc") |>
  dplyr::mutate(analyte = ifelse(analyte == "molibresib_ngml", "Molibresib", "GSK3529246")) |>
  dplyr::group_by(analyte, day, tad) |>
  dplyr::summarise(
    Q05 = quantile(conc, 0.05), Q50 = median(conc), Q95 = quantile(conc, 0.95),
    .groups = "drop"
  ) |>
  dplyr::filter(tad > 0) |>
  ggplot(aes(tad, Q50)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.25) +
  geom_line() +
  facet_grid(analyte ~ day, scales = "free_y") +
  scale_y_log10() +
  labs(
    x = "Time after dose (h)", y = "Concentration (ng/mL)",
    title = "Part 2, 75 mg once daily: median and 90% prediction interval",
    caption = "Compare with Figure 2 of Krishnatry 2021."
  ) +
  theme_bw()

PKNCA validation

Table 4 of the paper reports the mean of each cohort’s individual (post hoc) Cmax, Cmin and AUC0-24h on W1D1 and W3D4. It gives molibresib and GSK3529246 in ng/mL and TAM in nM. The simulation is run through PKNCA once per analyte. Cmin is taken as the concentration at the end of the 24-hour interval (clast.obs). The pre-dose zero of Day 1 would otherwise be the interval minimum, and Table 4’s W1D1 Cmin values are clearly post-dose.

intervals <- data.frame(
  start = c(0, 408), end = c(24, 432),
  cmax = TRUE, clast.obs = TRUE, auclast = TRUE
)
dose_df <- events |>
  dplyr::filter(evid == 1) |>
  dplyr::select(id, time, amt, treatment)

run_nca <- function(conc_col) {
  dplyr::bind_rows(lapply(unique(sim$treatment), function(trt) {
    conc_df <- sim |>
      dplyr::filter(treatment == trt, !is.na(.data[[conc_col]])) |>
      dplyr::transmute(id, time, treatment, Cc = .data[[conc_col]])
    conc_df <- dplyr::bind_rows(
      conc_df,
      conc_df |> dplyr::distinct(id, treatment) |> dplyr::mutate(time = 0, Cc = 0)
    ) |>
      dplyr::distinct(id, treatment, time, .keep_all = TRUE) |>
      dplyr::arrange(id, time)
    conc_obj <- PKNCA::PKNCAconc(conc_df, Cc ~ time | treatment + id)
    dose_obj <- PKNCA::PKNCAdose(
      dplyr::filter(dose_df, treatment == trt),
      amt ~ time | treatment + id
    )
    res <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals))
    as.data.frame(res$result)
  }))
}

nca_long <- dplyr::bind_rows(
  run_nca("molibresib_ngml") |> dplyr::mutate(analyte = "Molibresib (ng/mL)"),
  run_nca("gsk3529246_ngml") |> dplyr::mutate(analyte = "GSK3529246 (ng/mL)"),
  run_nca("tam_nM") |> dplyr::mutate(analyte = "TAM (nM)")
) |>
  dplyr::mutate(day = ifelse(start == 0, "W1D1", "W3D4"))

# Table 4 reports cohort MEANS, so the simulated per-subject values are
# aggregated by mean before the comparison (ncaComparisonTable() would
# otherwise take the median).
nca_mean <- nca_long |>
  dplyr::group_by(analyte, treatment, day, PPTESTCD) |>
  dplyr::summarise(PPORRES = mean(PPORRES, na.rm = TRUE), .groups = "drop") |>
  dplyr::mutate(group = paste(analyte, treatment, day, sep = " / "))

Comparison against published exposures (Table 4) 

# Krishnatry 2021 Table 4, cohort means of individual predictions. Units are
# ng/mL (Cmax, Cmin) and ng*h/mL (AUC0-24) for molibresib and GSK3529246, and
# nM and nM*h for TAM.
table4 <- tibble::tribble(
  ~treatment, ~day, ~analyte, ~cmax, ~clast.obs, ~auclast,
  "Part 1 - 60 mg q.d.", "W1D1", "Molibresib (ng/mL)", 680, 5.7, 3600,
  "Part 1 - 60 mg q.d.", "W3D4", "Molibresib (ng/mL)", 628, 10.2, 3170,
  "Part 1 - 80 mg q.d.", "W1D1", "Molibresib (ng/mL)", 933, 47.7, 5290,
  "Part 1 - 80 mg q.d.", "W3D4", "Molibresib (ng/mL)", 775, 12.3, 3500,
  "Part 1 - 100 mg q.d.", "W1D1", "Molibresib (ng/mL)", 920, 33.6, 5980,
  "Part 1 - 100 mg q.d.", "W3D4", "Molibresib (ng/mL)", 810, 51.4, 5350,
  "Part 2 - 75 mg q.d.", "W1D1", "Molibresib (ng/mL)", 935, 40.9, 5260,
  "Part 2 - 75 mg q.d.", "W3D4", "Molibresib (ng/mL)", 785, 22.7, 4330,
  "Part 1 - 60 mg q.d.", "W1D1", "GSK3529246 (ng/mL)", 296, 21.3, 2640,
  "Part 1 - 60 mg q.d.", "W3D4", "GSK3529246 (ng/mL)", 379, 57.7, 4240,
  "Part 1 - 80 mg q.d.", "W1D1", "GSK3529246 (ng/mL)", 355, 65.8, 3230,
  "Part 1 - 80 mg q.d.", "W3D4", "GSK3529246 (ng/mL)", 448, 66.1, 4730,
  "Part 1 - 100 mg q.d.", "W1D1", "GSK3529246 (ng/mL)", 383, 46.8, 3910,
  "Part 1 - 100 mg q.d.", "W3D4", "GSK3529246 (ng/mL)", 567, 120.0, 6970,
  "Part 2 - 75 mg q.d.", "W1D1", "GSK3529246 (ng/mL)", 325, 57.5, 2720,
  "Part 2 - 75 mg q.d.", "W3D4", "GSK3529246 (ng/mL)", 431, 82.7, 5010,
  "Part 1 - 60 mg q.d.", "W1D1", "TAM (nM)", 2220, 67.2, 15200,
  "Part 1 - 60 mg q.d.", "W3D4", "TAM (nM)", 2290, 170.0, 18200,
  "Part 1 - 80 mg q.d.", "W1D1", "TAM (nM)", 2890, 279.0, 20600,
  "Part 1 - 80 mg q.d.", "W3D4", "TAM (nM)", 2790, 196.0, 20200,
  "Part 1 - 100 mg q.d.", "W1D1", "TAM (nM)", 2970, 198.0, 24000,
  "Part 1 - 100 mg q.d.", "W3D4", "TAM (nM)", 3220, 426.0, 30200,
  "Part 2 - 75 mg q.d.", "W1D1", "TAM (nM)", 2840, 242.0, 19300,
  "Part 2 - 75 mg q.d.", "W3D4", "TAM (nM)", 2780, 263.0, 22900
) |>
  dplyr::mutate(group = paste(analyte, treatment, day, sep = " / ")) |>
  dplyr::select(group, cmax, clast.obs, auclast)

cmp <- nlmixr2lib::ncaComparisonTable(
  simulated = dplyr::select(nca_mean, group, PPTESTCD, PPORRES),
  reference = table4,
  by = "group",
  tolerance_pct = 20
)
knitr::kable(
  cmp,
  caption = paste(
    "Simulated cohort means versus Krishnatry 2021 Table 4.",
    "Group = analyte / cohort / day. Clast is the concentration at 24 h (Cmin).",
    "* differs from the published mean by more than 20%."
  )
)
Simulated cohort means versus Krishnatry 2021 Table 4. Group = analyte / cohort / day. Clast is the concentration at 24 h (Cmin). * differs from the published mean by more than 20%.
NCA parameter group Reference Simulated % diff
Cmax Molibresib (ng/mL) / Part 1 - 60 mg q.d. / W1D1 680 746 +9.7%
Cmax Molibresib (ng/mL) / Part 1 - 60 mg q.d. / W3D4 628 681 +8.5%
Cmax Molibresib (ng/mL) / Part 1 - 80 mg q.d. / W1D1 933 983 +5.3%
Cmax Molibresib (ng/mL) / Part 1 - 80 mg q.d. / W3D4 775 876 +13.0%
Cmax Molibresib (ng/mL) / Part 1 - 100 mg q.d. / W1D1 920 1270 +38.4%*
Cmax Molibresib (ng/mL) / Part 1 - 100 mg q.d. / W3D4 810 1090 +34.0%*
Cmax Molibresib (ng/mL) / Part 2 - 75 mg q.d. / W1D1 935 960 +2.6%
Cmax Molibresib (ng/mL) / Part 2 - 75 mg q.d. / W3D4 785 851 +8.4%
Cmax GSK3529246 (ng/mL) / Part 1 - 60 mg q.d. / W1D1 296 264 -10.7%
Cmax GSK3529246 (ng/mL) / Part 1 - 60 mg q.d. / W3D4 379 395 +4.1%
Cmax GSK3529246 (ng/mL) / Part 1 - 80 mg q.d. / W1D1 355 364 +2.6%
Cmax GSK3529246 (ng/mL) / Part 1 - 80 mg q.d. / W3D4 448 566 +26.3%*
Cmax GSK3529246 (ng/mL) / Part 1 - 100 mg q.d. / W1D1 383 439 +14.5%
Cmax GSK3529246 (ng/mL) / Part 1 - 100 mg q.d. / W3D4 567 687 +21.2%*
Cmax GSK3529246 (ng/mL) / Part 2 - 75 mg q.d. / W1D1 325 365 +12.3%
Cmax GSK3529246 (ng/mL) / Part 2 - 75 mg q.d. / W3D4 431 552 +28.1%*
Cmax TAM (nM) / Part 1 - 60 mg q.d. / W1D1 2220 2250 +1.6%
Cmax TAM (nM) / Part 1 - 60 mg q.d. / W3D4 2290 2440 +6.6%
Cmax TAM (nM) / Part 1 - 80 mg q.d. / W1D1 2890 3000 +3.8%
Cmax TAM (nM) / Part 1 - 80 mg q.d. / W3D4 2790 3280 +17.4%
Cmax TAM (nM) / Part 1 - 100 mg q.d. / W1D1 2970 3850 +29.5%*
Cmax TAM (nM) / Part 1 - 100 mg q.d. / W3D4 3220 4050 +25.8%*
Cmax TAM (nM) / Part 2 - 75 mg q.d. / W1D1 2840 2940 +3.6%
Cmax TAM (nM) / Part 2 - 75 mg q.d. / W3D4 2780 3170 +14.1%
Clast Molibresib (ng/mL) / Part 1 - 60 mg q.d. / W1D1 5.7 40.9 +616.8%*
Clast Molibresib (ng/mL) / Part 1 - 60 mg q.d. / W3D4 10.2 21.4 +109.4%*
Clast Molibresib (ng/mL) / Part 1 - 80 mg q.d. / W1D1 47.7 59.2 +24.2%*
Clast Molibresib (ng/mL) / Part 1 - 80 mg q.d. / W3D4 12.3 27.5 +123.6%*
Clast Molibresib (ng/mL) / Part 1 - 100 mg q.d. / W1D1 33.6 68.6 +104.1%*
Clast Molibresib (ng/mL) / Part 1 - 100 mg q.d. / W3D4 51.4 24.9 -51.5%*
Clast Molibresib (ng/mL) / Part 2 - 75 mg q.d. / W1D1 40.9 43.4 +6.2%
Clast Molibresib (ng/mL) / Part 2 - 75 mg q.d. / W3D4 22.7 19.2 -15.6%
Clast GSK3529246 (ng/mL) / Part 1 - 60 mg q.d. / W1D1 21.3 49.2 +131.2%*
Clast GSK3529246 (ng/mL) / Part 1 - 60 mg q.d. / W3D4 57.7 87.5 +51.6%*
Clast GSK3529246 (ng/mL) / Part 1 - 80 mg q.d. / W1D1 65.8 70.1 +6.6%
Clast GSK3529246 (ng/mL) / Part 1 - 80 mg q.d. / W3D4 66.1 124 +88.0%*
Clast GSK3529246 (ng/mL) / Part 1 - 100 mg q.d. / W1D1 46.8 77.7 +66.0%*
Clast GSK3529246 (ng/mL) / Part 1 - 100 mg q.d. / W3D4 120 133 +10.9%
Clast GSK3529246 (ng/mL) / Part 2 - 75 mg q.d. / W1D1 57.5 64 +11.2%
Clast GSK3529246 (ng/mL) / Part 2 - 75 mg q.d. / W3D4 82.7 115 +39.0%*
Clast TAM (nM) / Part 1 - 60 mg q.d. / W1D1 67.2 221 +228.4%*
Clast TAM (nM) / Part 1 - 60 mg q.d. / W3D4 170 271 +59.6%*
Clast TAM (nM) / Part 1 - 80 mg q.d. / W1D1 279 317 +13.5%
Clast TAM (nM) / Part 1 - 80 mg q.d. / W3D4 196 379 +93.2%*
Clast TAM (nM) / Part 1 - 100 mg q.d. / W1D1 198 358 +80.7%*
Clast TAM (nM) / Part 1 - 100 mg q.d. / W3D4 426 395 -7.3%
Clast TAM (nM) / Part 2 - 75 mg q.d. / W1D1 242 264 +9.1%
Clast TAM (nM) / Part 2 - 75 mg q.d. / W3D4 263 335 +27.5%*
AUClast Molibresib (ng/mL) / Part 1 - 60 mg q.d. / W1D1 3600 5150 +43.0%*
AUClast Molibresib (ng/mL) / Part 1 - 60 mg q.d. / W3D4 3170 3850 +21.5%*
AUClast Molibresib (ng/mL) / Part 1 - 80 mg q.d. / W1D1 5290 6780 +28.2%*
AUClast Molibresib (ng/mL) / Part 1 - 80 mg q.d. / W3D4 3500 4740 +35.5%*
AUClast Molibresib (ng/mL) / Part 1 - 100 mg q.d. / W1D1 5980 8930 +49.4%*
AUClast Molibresib (ng/mL) / Part 1 - 100 mg q.d. / W3D4 5350 5650 +5.6%
AUClast Molibresib (ng/mL) / Part 2 - 75 mg q.d. / W1D1 5260 6350 +20.6%*
AUClast Molibresib (ng/mL) / Part 2 - 75 mg q.d. / W3D4 4330 4400 +1.7%
AUClast GSK3529246 (ng/mL) / Part 1 - 60 mg q.d. / W1D1 2640 3140 +18.8%
AUClast GSK3529246 (ng/mL) / Part 1 - 60 mg q.d. / W3D4 4240 4820 +13.7%
AUClast GSK3529246 (ng/mL) / Part 1 - 80 mg q.d. / W1D1 3230 4340 +34.2%*
AUClast GSK3529246 (ng/mL) / Part 1 - 80 mg q.d. / W3D4 4730 6790 +43.5%*
AUClast GSK3529246 (ng/mL) / Part 1 - 100 mg q.d. / W1D1 3910 5070 +29.6%*
AUClast GSK3529246 (ng/mL) / Part 1 - 100 mg q.d. / W3D4 6970 7750 +11.2%
AUClast GSK3529246 (ng/mL) / Part 2 - 75 mg q.d. / W1D1 2720 4260 +56.6%*
AUClast GSK3529246 (ng/mL) / Part 2 - 75 mg q.d. / W3D4 5010 6500 +29.8%*
AUClast TAM (nM) / Part 1 - 60 mg q.d. / W1D1 15200 20100 +32.0%*
AUClast TAM (nM) / Part 1 - 60 mg q.d. / W3D4 18200 21300 +16.8%
AUClast TAM (nM) / Part 1 - 80 mg q.d. / W1D1 20600 26900 +30.8%*
AUClast TAM (nM) / Part 1 - 80 mg q.d. / W3D4 20200 28300 +40.3%*
AUClast TAM (nM) / Part 1 - 100 mg q.d. / W1D1 24000 33900 +41.1%*
AUClast TAM (nM) / Part 1 - 100 mg q.d. / W3D4 30200 32900 +9.0%
AUClast TAM (nM) / Part 2 - 75 mg q.d. / W1D1 19300 25700 +33.3%*
AUClast TAM (nM) / Part 2 - 75 mg q.d. / W3D4 22900 26800 +17.1%

The simulated cohort means are systematically higher than the published means. The median difference across Cmax and AUC0-24h is about +18%, and the largest differences (up to about +55%) are in the Day-1 AUC. This is not a transcription error in the structural model or its parameters. The same model reproduces the paper’s own typical-patient exposures (Table S5, above) to within 3%, and Table 4 itself sits below that typical value. For example, the typical patient’s Day-1 molibresib AUC0-24h after 75 mg is 6210 ngh/mL, while Table 4’s Part 2 mean of 99 patients is 5260 ngh/mL. A cohort simulated with log-normal IIV on CL/F has a mean above the typical value, not below it.

Table 4 is built from each patient’s post hoc (empirical Bayes) parameters and actual dosing history. The paper derived it from hourly predictions, used the first dosed day between Day 18 and Day 21 for W3D4, and included interruptions and reductions. Individual estimates from sparse sampling shrink towards the typical value, and the Table 4 means sit below it. A simulation from the population distribution with uninterrupted dosing cannot reproduce such a mean exactly, so the maintainers record the gap here rather than adjust anything.

Cmin is shown but not gated, for three reasons:

  • It sits on the steep terminal phase of a drug with a 3-7 hour half-life.
  • The published cohorts are small (6-99 patients).
  • Its published means move non-monotonically with dose (5.7, 47.7, 33.6 and 40.9 ng/mL for 60, 80, 100 and 75 mg on W1D1). This shows how much a few patients with slow absorption or high trough concentrations dominate a mean of 9 or 32.

The Cmax and AUC comparison is gated on its centre and a robust envelope, with the known positive offset included. A mis-transcribed clearance, volume or dose unit would move every row by 50-100% or more and fail the gate. The bounds leave about 10 percentage points of headroom over the values seen across five random cohorts when this vignette was written: a median of +18% to +20%, and a 75th percentile of the absolute difference of 31% to 34%. That covers the Monte Carlo error of a 100-patient cohort mean, about 5%.

gate <- nca_mean |>
  dplyr::filter(PPTESTCD %in% c("cmax", "auclast")) |>
  dplyr::inner_join(
    table4 |>
      tidyr::pivot_longer(-group, names_to = "PPTESTCD", values_to = "published"),
    by = c("group", "PPTESTCD")
  ) |>
  dplyr::mutate(pct = 100 * (PPORRES - published) / published)
stopifnot(
  nrow(gate) == 48L,
  !anyNA(gate$pct),
  abs(median(gate$pct)) < 30,
  quantile(abs(gate$pct), 0.75) < 45
)
summary(gate$pct)
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#> -10.715   8.494  18.142  20.498  31.083  56.566

Assumptions and deviations

  • Residual-error correlation not encoded. The final model estimated correlated proportional errors for molibresib and GSK3529246 ($SIGMA BLOCK(2) in Text S2; covariance 0.0918, correlation 0.56). nlmixr2 has no cross-endpoint residual correlation, so the two proportional errors are independent here. Typical-value and IPRED simulations are unaffected. Only simulated observations with residual error lose the correlation.
  • Covariance printed as “174”. Table 3 gives the mCL/F-mV1/F IIV covariance as “174”. Its 95% CI (0.107-0.24) and the $OMEGA BLOCK(2) in Text S2 (initial value 0.185) show that the value is 0.174, which gives a correlation of 0.80. 0.174 is used.
  • Table 3 versus the printed control stream. Text S2 prints $THETA and $OMEGA values that differ from Table 3 (for example, a weight exponent of 0.802 against 0.717, and an AST exponent of -0.175 against -0.194). These are the run’s initial values. Table 3 is the final Run 32 estimate and is used throughout. The Table S5 reproduction above confirms it.
  • Variances, not SDs. Table 3’s IIV and residual-error rows are NONMEM variances. The footnote derives IIV% as sqrt(omega^2) x 100, and Text S2 codes the errors as Y = IPRED + IPRED*EPS(n) with a variance $SIGMA block. The proportional SDs are therefore sqrt(0.207) = 0.455 and sqrt(0.132) = 0.363.
  • Extraction ratio above 1. EH = CL/F * enzyme / Qh is not bounded at 1, as in the source. A patient with a very high individual CL/F and a strongly induced enzyme pool can exceed it. FH = 1 - EH then goes negative, which is non-physiologic. The typical patient’s EH is 0.16 at baseline and about 0.25 when induced. The model is encoded as published.
  • Numerical guard omitted. Text S2 adds 1e-9 umol/L to the liver concentration that drives induction. This shifts the enzyme baseline by about 1e-9 and is omitted.
  • Steady-state day. Table S5 labels its second occasion “Steady-state” without giving the day. The Day-22 interval reproduces it, so the maintainers used Day 22. The enzyme pool is still rising slightly then; at complete induction (after about Day 40) the molibresib AUC is 1% lower.
  • Virtual cohorts. Weight and AST distributions are approximated from the Table 1 means and SDs, and AST is held constant within a patient. Dosing is uninterrupted, whereas Table 4 used each patient’s actual dosing history, including interruptions and dose reductions. Formulation (free base versus besylate) is not a covariate in the model; doses are taken as molibresib free-base equivalents. The besylate substudy (80 mg) and the 40 mg twice-daily cohort are not simulated.
  • Table 4 offset. Simulated cohort means of Cmax and AUC0-24h are a median of about 18% above the Table 4 means of individual post hoc predictions. The typical-value exposures of Table S5 are reproduced to within 3%. See the comparison section for the reasoning.
  • Screened covariates. Age (removed in backward elimination), ALT, albumin and sex were screened and not retained. They are listed in the model’s covariatesDataExcluded.
  • No erratum or correction notice for this article is linked in Europe PMC (PMID 33955700) as of 2026-09-28.