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Exemestane (Valle 2005)

Source: vignettes/articles/Valle_2005_exemestane.Rmd
Valle_2005_exemestane.Rmd

Model and source

  • Citation: Valle M, Di Salle E, Jannuzzo MG, Poggesi I, Rocchetti M, Spinelli R, Verotta D. A predictive model for exemestane pharmacokinetics/pharmacodynamics incorporating the effect of food and formulation. Br J Clin Pharmacol. 2005;59(3):355-364. doi:10.1111/j.1365-2125.2005.02335.x
  • Description: Three-compartment population PK with first-order absorption + lag time, coupled to an indirect-response PD model on plasma estrone sulphate (E1S), for oral exemestane (25 mg single dose) in healthy postmenopausal women. Crossover study comparing a sugar-coated tablet (SCT) under fasting versus an extemporaneous tablet-suspended-in-water suspension under fasting versus a SCT taken after a standard high-fat breakfast. Disposition is independent of formulation and food; absorption rate ka and apparent bioavailability F depend on formulation (suspension: ka 7.6 vs SCT 2.35 1/h, F 1.2x) and on the high-fat meal (ka 1.13 1/h, F 1.6x). Exemestane inhibits E1S synthesis via a sigmoid Imax function with IC50 22.1 pg/mL and Hill coefficient 1.73.
  • Article: Br J Clin Pharmacol 2005;59(3):355-364 (open access via PMC1884790)

Valle 2005 is a 3-period randomized crossover bioequivalence study comparing a sugar-coated tablet (SCT, swallowed whole) of exemestane under fasting conditions, an extemporaneously-prepared suspension of the same 25 mg dose under fasting, and a SCT taken 15 min after a standard high-fat breakfast. The published PK model is a 3-compartment mammillary system with first-order absorption + lag time, with formulation- and food-dependent ka and apparent bioavailability F. Disposition (kel, k12, k21, k13, k31) is the same across all three treatments. The PD model is an indirect-response model: plasma estrone sulphate (E1S) is produced at a zero-order rate ks (= rbase * kout) and eliminated first-order at rate kout; exemestane inhibits E1S synthesis via a sigmoid Imax function with IC50 22.1 pg/mL and Hill exponent g = 1.73.

Population

Twelve healthy postmenopausal women, age 45-68 years (mean 55 years), weight 46-66 kg (mean 54.9 kg), enrolled at Pontchaillou Hospital (Rennes, France). Each woman received three treatments according to a repeated 3x3 Latin-square design separated by a 4-5 week washout (Valle 2005 Methods, Subjects and Study design). Subjects were healthy by physical examination, electrocardiography, and routine laboratory tests, and avoided concomitant medication beyond occasional paracetamol. Race / ethnicity composition is not reported.

Exemestane plasma sampling: 15 timepoints over 0.25-168 h post-dose. Plasma E1S sampling: 7 timepoints over 0-336 h post-dose (14-day follow-up window). Estimation by NONMEM V FOCE INTERACTION; the population PK fit was performed first, with individual empirical-Bayes parameter estimates serving as input to the subsequent population PD fit.

The same information is available programmatically via readModelDb("Valle_2005_exemestane")$population.

Source trace

Every parameter, covariate effect, IIV element, and residual-error term below is taken from Valle 2005 Tables 2-4 and the accompanying Results narrative. The per-parameter origin is also recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Valle_2005_exemestane.R.

Equation / parameter Value Source location
lka (SCT/fasting ka1) log(2.35) 1/h Table 2, ka1 SCT/fasting row, RSE 25%
lvc (V intrinsic; V/F at SCT/fasting) log(1360) L Table 2, V/F SCT/fasting row, RSE 10%
ltlag (absorption lag) log(0.21) h Table 2, Lag row (common to all treatments), RSE 10%
lkel (k, elimination from central) log(0.738) 1/h Table 3, k row, RSE 7%
lk12 log(0.454) 1/h Table 3, k12 row, RSE 19%
lk21 log(0.158) 1/h Table 3, k21 row, RSE 6%
lk13 log(0.174) 1/h Table 3, k13 row, RSE 9%
lk31 log(0.016) 1/h Table 3, k31 row, RSE 10%
e_form_suspension_ka log(7.6 / 2.35) Table 2, suspension/fasting ka1 = 7.6 vs SCT/fasting reference 2.35
e_fed_highfat_ka log(1.13 / 2.35) Table 2, SCT/food ka1 = 1.13 vs SCT/fasting reference 2.35
e_form_suspension_fdepot log(1.2) Results: “suspension formulation showed a 1.2 times higher F than the SCT after fasting”
e_fed_highfat_fdepot log(1.6) Results: “food effect translated into an increase of the F of 1.6 times”
lrbase (Baseline E1S) log(203) pg/mL Table 4, Baseline row, RSE 8%
lkout (E1S elimination ko) log(0.032) 1/h Table 4, ko row, RSE 9%
lic50 (C50 of exemestane on E1S) log(22.1) pg/mL Table 4, C50 row, RSE 10%
lhill (Hill exponent g) log(1.73) Table 4, g row, RSE 12% (IIV not estimated, N.E.)
var(etalka) log(1 + 0.92^2) Results: “rate of absorption (ka1) had a higher coefficient of variation (92%)”
var(etalvc) log(1 + 0.22^2) Results: “significant interindividual variability in the V/F (coefficient of variation = 22%)”
var(etalkel) log(1 + 0.11^2) Results: “the elimination rate constant (k) from the central compartment (11%)”
var(etalrbase) log(1 + 0.56^2) Table 4: Baseline CV 56% (RSE 19%)
var(etalkout) log(1 + 0.41^2) Table 4: ko CV 41% (RSE 47%)
var(etalic50) log(1 + 0.47^2) Table 4: C50 CV 47% (RSE 32%)
propSd (exemestane proportional RE) 0.04 Results: “proportional part was estimated to be 4%”
addSd (exemestane additive RE, FIXED) fixed(0.0024) ng/mL Results: “additive part was fixed to the SD of the analytical technique” – paper does not report the SD value; approximated as LLOQ (13.5 pg/mL) x inter-assay CV (17.7%) ~= 2.4 pg/mL = 0.0024 ng/mL (see Assumptions and deviations)
propSd_e1s (E1S proportional RE) 0.35 Results: PD residual variability 35%
Structure – PK (3-cmt mammillary + first-order absorption + lag) n/a Methods, Pharmacokinetic model section and Eq. 1
Structure – PD (indirect response with sigmoid Imax on synthesis) n/a Methods, Pharmacodynamic model section, Eq. 3-4
Choice of indirect response over irreversible inactivation (Eq. 5-7) n/a Results: OFV decrease for Eq. 5-7 was less than 3.9 points – not statistically better

Parameterization notes

  • Rate-constant (vs CL/V) parameterization. Valle 2005 reports micro-constants k, k12, k21, k13, k31 together with the apparent central volume V/F, and reports IIV separately on k, V/F, and ka (with no IIV on inter-compartmental constants or on the absorption lag). To preserve that IIV structure faithfully, the model is parameterised on lkel, lk12, lk21, lk13, lk31, and lvc as primary ini() parameters rather than on lcl + lvc + lq + lvp + lq2 + lvp2 (the standard CL/V form), since the rate-constant IIV structure does not factorise cleanly through cl = kel * vc. Precedent: the same parameterisation is used by Reijers_2016_trastuzumab.R and Krause_2017_selexipag.R.
  • Intrinsic V vs treatment-specific V/F. Valle 2005 Table 2 reports three V/F values (1360, 1120, 844 L for SCT/fasting, suspension/fasting, and SCT/food respectively) but explicitly interprets the differences as F differences with V intrinsic (“The differences observed in the ratio of volume of distribution to bioavailability (V/F), indicate that the latter for the three treatments is different”). The model is built with vc = exp(lvc) constant across treatments and the F multipliers (1.0 / 1.2 / 1.6) applied via f(depot) <- fdepot. The implied V/F values are 1360 / 1 = 1360, 1360 / 1.2 = 1133 (paper 1120, +1% difference), and 1360 / 1.6 = 850 (paper 844, +1% difference) – within the published rounding precision.
  • Hill-coefficient name. Valle 2005 calls the Hill exponent g in Eq. 4 and Table 4. The canonical nlmixr2lib name is lhill; the value and role are unchanged.
  • PD synthesis rate as a derived quantity. Valle 2005 abstract gives ks = 6.5 pg/mL/h; Table 4 reports Baseline = 203 pg/mL and ko = 0.032 1/h. The relation ks = Baseline * ko = 6.496 ~= 6.5 identifies Baseline as the estimated parameter and ks as derived in model(). The compartment e1s is initialised at its steady-state baseline (e1s(0) <- rbase).
  • CV% to log-normal variance. IIV is reported in Valle 2005 as CV% on the linear parameter scale. nlmixr2’s convention is log-normal IIV on the log-transformed parameter; the conversion omega^2 = log(CV^2 + 1) is applied in ini().

Virtual cohort

The crossover design is reproduced by simulating each treatment arm independently with the typical-value parameters; the published trial has N = 12 subjects with limited demographic spread (postmenopausal women, weight 46-66 kg) so the stochastic VPC adds N = 30 virtual subjects per arm to approximate the observed scatter.

set.seed(20260604)
n_subj_arm <- 30L

build_events <- function(n, treatment, suspension, food, id_offset = 0L,
                         pk_obs_times = NULL, pd_obs_times = NULL,
                         dose_mg = 25, dose_times = 0) {
  if (is.null(pk_obs_times)) pk_obs_times <- sort(unique(c(
    0, 0.25, 0.5, 1, 1.5, 2, 4, 6, 8, 12, 16, 24, 48, 72, 120, 168
  )))
  if (is.null(pd_obs_times)) pd_obs_times <- sort(unique(c(
    0, 24, 48, 72, 96, 120, 168, 240, 336
  )))
  ids <- id_offset + seq_len(n)
  cov <- tibble::tibble(
    id              = ids,
    FORM_SUSPENSION = as.integer(suspension),
    FED_HIGHFAT     = as.integer(food),
    treatment       = treatment
  )
  ev_dose <- cov |>
    tidyr::crossing(time = dose_times) |>
    dplyr::mutate(amt = dose_mg, cmt = "depot", evid = 1L)
  ev_cc <- cov |>
    tidyr::crossing(time = pk_obs_times) |>
    dplyr::mutate(amt = 0, cmt = "Cc", evid = 0L)
  ev_e1s <- cov |>
    tidyr::crossing(time = pd_obs_times) |>
    dplyr::mutate(amt = 0, cmt = "e1s", evid = 0L)
  dplyr::bind_rows(ev_dose, ev_cc, ev_e1s) |>
    dplyr::arrange(id, time, dplyr::desc(evid)) |>
    dplyr::select(id, time, amt, cmt, evid, FORM_SUSPENSION, FED_HIGHFAT,
                  treatment)
}

Simulation

The simulation block builds two event tables per treatment: a fine time-grid for typical-value (IIV-zeroed) trajectories used to replicate the figures, and a sparse time-grid (matching the published sampling schedule) for the stochastic VPC and NCA.

mod <- rxode2::rxode2(readModelDb("Valle_2005_exemestane"))
#> ℹ parameter labels from comments will be replaced by 'label()'
mod_typ <- mod |> rxode2::zeroRe()

fine_pk <- seq(0, 168, by = 0.1)
fine_pd <- seq(0, 336, by = 1)

typ_args <- list(
  SCT_fasting     = list(s = 0, f = 0),
  Suspension_fast = list(s = 1, f = 0),
  SCT_food        = list(s = 0, f = 1)
)

sim_typ <- lapply(names(typ_args), function(name) {
  a <- typ_args[[name]]
  ev <- build_events(1, name, a$s, a$f, id_offset = 0L,
                     pk_obs_times = fine_pk, pd_obs_times = fine_pd)
  as.data.frame(rxode2::rxSolve(mod_typ, events = ev,
                                keep = c("treatment")))
}) |> dplyr::bind_rows()
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalvc', 'etalkel', 'etalrbase', 'etalkout', 'etalic50'
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalvc', 'etalkel', 'etalrbase', 'etalkout', 'etalic50'
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalvc', 'etalkel', 'etalrbase', 'etalkout', 'etalic50'

# Stochastic cohort: N = 30 per arm, sparse sampling at the published times.
sim_cohort <- dplyr::bind_rows(
  as.data.frame(rxode2::rxSolve(mod,
    events = build_events(n_subj_arm, "SCT_fasting",     0, 0,
                          id_offset = 0L * n_subj_arm),
    keep = c("treatment"))),
  as.data.frame(rxode2::rxSolve(mod,
    events = build_events(n_subj_arm, "Suspension_fast", 1, 0,
                          id_offset = 1L * n_subj_arm),
    keep = c("treatment"))),
  as.data.frame(rxode2::rxSolve(mod,
    events = build_events(n_subj_arm, "SCT_food",        0, 1,
                          id_offset = 2L * n_subj_arm),
    keep = c("treatment")))
)

Replicate published figures

Figure 1 – typical-value exemestane plasma concentration

Valle 2005 Figure 1 plots the observed exemestane concentration profiles (0-168 h) for each of the three treatments alongside the typical population model prediction (solid line). The block below shows the typical-value (IIV-zeroed) PK simulation for the same three treatments on a log y-axis.

sim_typ |>
  dplyr::filter(!is.na(Cc), time <= 168, time > 0) |>
  ggplot(aes(time, Cc, colour = treatment)) +
  geom_line(linewidth = 0.9) +
  scale_y_log10() +
  scale_x_continuous(breaks = c(0, 4, 12, 24, 48, 72, 120, 168)) +
  labs(
    x = "Time post dose (h)",
    y = "Exemestane Cc (ng/mL, log10 scale)",
    title = "Valle 2005 Figure 1 -- typical-value exemestane Cc by treatment",
    caption = paste(
      "Single 25 mg oral dose under three formulation/meal conditions.",
      "Typical-value (IIV zeroed); replicates Figure 1 of Valle 2005."
    )
  ) +
  theme_minimal()
#> Warning in scale_y_log10(): log-10 transformation introduced infinite values.

Figure 2 – typical-value E1S concentration

Valle 2005 Figure 2 plots E1S plasma concentrations over the 0-336 h follow-up period for the three treatments alongside the typical population PD model prediction. The block below reproduces the typical-value (IIV-zeroed) E1S trajectories on a linear y-axis.

sim_typ |>
  dplyr::filter(!is.na(e1s)) |>
  ggplot(aes(time, e1s, colour = treatment)) +
  geom_line(linewidth = 0.9) +
  geom_hline(yintercept = 203, linetype = "dotted") +
  scale_x_continuous(breaks = c(0, 24, 48, 72, 120, 168, 240, 336)) +
  labs(
    x = "Time post dose (h)",
    y = "E1S (pg/mL)",
    title = "Valle 2005 Figure 2 -- typical-value E1S by treatment",
    caption = paste(
      "Dotted horizontal line marks the typical baseline (203 pg/mL).",
      "Typical-value (IIV zeroed); replicates Figure 2 of Valle 2005."
    )
  ) +
  theme_minimal()

Figure 4 – steady-state daily-dosing E1S response

Valle 2005 Figure 4 simulates E1S concentrations as a percentage of baseline after 15 days of once-daily oral exemestane at 0.5, 1, 2.5, 5, and 25 mg under non-fasting conditions. The paper reports the model’s predicted week-2 (steady-state) E1S nadir as:

Dose (mg/day) Model prediction (% baseline) Comparison (% baseline) Source
0.5 ~70% 56% (Bajetta et al.) Discussion
1.0 ~45% 34% (Bajetta et al.) Discussion
2.5 ~14% 16% (Bajetta et al.) Discussion
5.0 ~10% 18% (Bajetta et al.) Discussion
25.0 <10% 8.1-9.2% (Kaufmann et al.) Discussion

The block below replicates Figure 4 by simulating typical-value once-daily dosing under SCT/food conditions (since the source figure used non-fasting administration). E1S is expressed as a percentage of the typical baseline (203 pg/mL).

ss_doses <- c(0.5, 1, 2.5, 5, 25)
ss_horizon <- 15 * 24  # 15 days in hours
dose_times_ss <- seq(0, by = 24, length.out = 15)

sim_ss <- lapply(ss_doses, function(d) {
  ev <- build_events(
    1, sprintf("%g mg/day", d), suspension = 0, food = 1,
    id_offset = 0L,
    pk_obs_times = seq(0, ss_horizon, by = 1),
    pd_obs_times = seq(0, ss_horizon, by = 1),
    dose_mg = d, dose_times = dose_times_ss
  )
  out <- as.data.frame(rxode2::rxSolve(mod_typ, events = ev,
                                       keep = c("treatment")))
  out$dose_mg <- d
  out
}) |> dplyr::bind_rows()
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalvc', 'etalkel', 'etalrbase', 'etalkout', 'etalic50'
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalvc', 'etalkel', 'etalrbase', 'etalkout', 'etalic50'
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalvc', 'etalkel', 'etalrbase', 'etalkout', 'etalic50'
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalvc', 'etalkel', 'etalrbase', 'etalkout', 'etalic50'
#> ℹ omega/sigma items treated as zero: 'etalka', 'etalvc', 'etalkel', 'etalrbase', 'etalkout', 'etalic50'

sim_ss |>
  dplyr::filter(!is.na(e1s)) |>
  dplyr::mutate(pct_baseline = 100 * e1s / 203,
                dose_label = factor(sprintf("%g mg/day", dose_mg),
                                    levels = sprintf("%g mg/day", ss_doses))) |>
  ggplot(aes(time / 24, pct_baseline, colour = dose_label)) +
  geom_line(linewidth = 0.9) +
  scale_x_continuous(breaks = seq(0, 15, by = 3)) +
  scale_y_continuous(limits = c(0, 110), breaks = seq(0, 100, by = 20)) +
  labs(
    x = "Time (days)",
    y = "E1S (% of baseline)",
    colour = "Dose",
    title = "Valle 2005 Figure 4 -- steady-state E1S after 15 days of daily dosing",
    caption = paste(
      "SCT under fed conditions (FED_HIGHFAT = 1); typical-value, IIV zeroed.",
      "Replicates Figure 4 of Valle 2005."
    )
  ) +
  theme_minimal()

PKNCA validation

Valle 2005 Table 1 reports non-compartmental PK parameters by treatment arm. The block below runs PKNCA on the stochastic-cohort simulated exemestane profiles and compares the per-arm means against the published NCA values.

# The stochastic-cohort simulation emits one output row per observation
# event (Cc rows + e1s rows). For NCA, deduplicate by (treatment, id,
# time) so PKNCA receives one Cc reading per timepoint.
sim_nca <- sim_cohort |>
  dplyr::filter(!is.na(Cc), time > 0) |>
  dplyr::distinct(treatment, id, time, .keep_all = TRUE) |>
  dplyr::select(id, time, Cc, treatment)

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

dose_df <- sim_cohort |>
  dplyr::distinct(id, treatment) |>
  dplyr::mutate(time = 0, amt = 25)
dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | treatment + 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)
#> Warning: Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
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#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
#> Requesting an AUC range starting (0) before the first measurement (0.25) is not allowed
nca_tab  <- as.data.frame(nca_res$result)

nca_summary <- nca_tab |>
  dplyr::group_by(treatment, PPTESTCD) |>
  dplyr::summarise(mean = mean(PPORRES, na.rm = TRUE),
                   sd   = stats::sd(PPORRES, na.rm = TRUE),
                   .groups = "drop") |>
  dplyr::filter(PPTESTCD %in% c("cmax", "tmax", "aucinf.obs", "half.life"))

knitr::kable(nca_summary, digits = 2,
  caption = paste("Simulated NCA parameters by treatment arm",
                  "(N =", n_subj_arm, "virtual subjects per arm,",
                  "stochastic VPC)."))
Simulated NCA parameters by treatment arm (N = 30 virtual subjects per arm, stochastic VPC).
treatment PPTESTCD mean sd
SCT_fasting aucinf.obs NaN NA
SCT_fasting cmax 8.86 2.93
SCT_fasting half.life 54.20 1.31
SCT_fasting tmax 0.85 0.27
SCT_food aucinf.obs NaN NA
SCT_food cmax 10.80 4.18
SCT_food half.life 54.40 1.22
SCT_food tmax 1.03 0.32
Suspension_fast aucinf.obs NaN NA
Suspension_fast cmax 15.73 4.36
Suspension_fast half.life 54.51 1.36
Suspension_fast tmax 0.52 0.15

Comparison against Valle 2005 Table 1

The table below pairs the simulated NCA means with the corresponding published values from Valle 2005 Table 1 (means with SEM in parenthesis; SEM converted to SD via SD = SEM * sqrt(12) for the n = 12 cohort).

published_nca <- tibble::tribble(
  ~treatment,        ~param,        ~published_mean, ~published_sem,
  "SCT_fasting",     "tmax",            0.97,             0.28,
  "SCT_fasting",     "cmax",           11.1,              1.3,
  "SCT_fasting",     "aucinf.obs",     29.7,              2.2,
  "SCT_fasting",     "half.life",      24.0,              2.8,
  "Suspension_fast", "tmax",            0.71,             0.07,
  "Suspension_fast", "cmax",           15.4,              2.3,
  "Suspension_fast", "aucinf.obs",     34.5,              3.3,
  "Suspension_fast", "half.life",      21.9,              3.7,
  "SCT_food",        "tmax",            1.88,             0.5,
  "SCT_food",        "cmax",           17.7,              4.5,
  "SCT_food",        "aucinf.obs",     41.3,              3.4,
  "SCT_food",        "half.life",      21.4,              3.1
)

sim_means <- nca_summary |>
  dplyr::transmute(treatment, param = PPTESTCD, simulated_mean = mean)

comparison <- published_nca |>
  dplyr::left_join(sim_means, by = c("treatment", "param")) |>
  dplyr::mutate(pct_diff = 100 * (simulated_mean - published_mean) /
                          published_mean)

knitr::kable(comparison, digits = 2,
  caption = paste("Simulated vs published NCA values per treatment arm",
                  "(Valle 2005 Table 1)."))
Simulated vs published NCA values per treatment arm (Valle 2005 Table 1).
treatment param published_mean published_sem simulated_mean pct_diff
SCT_fasting tmax 0.97 0.28 0.85 -12.37
SCT_fasting cmax 11.10 1.30 8.86 -20.15
SCT_fasting aucinf.obs 29.70 2.20 NaN NaN
SCT_fasting half.life 24.00 2.80 54.20 125.84
Suspension_fast tmax 0.71 0.07 0.52 -27.23
Suspension_fast cmax 15.40 2.30 15.73 2.13
Suspension_fast aucinf.obs 34.50 3.30 NaN NaN
Suspension_fast half.life 21.90 3.70 54.51 148.90
SCT_food tmax 1.88 0.50 1.03 -45.04
SCT_food cmax 17.70 4.50 10.80 -38.99
SCT_food aucinf.obs 41.30 3.40 NaN NaN
SCT_food half.life 21.40 3.10 54.40 154.19

Differences > 20 %% between simulated and published NCA parameters are discussed in the Assumptions and deviations section below.

Comparison against published PD nadir

Valle 2005 Results reports the maximum observed E1S decrease (expressed as percentage of the baseline concentrations) per arm. The block below extracts the typical-value E1S nadir per arm from the typical-value simulation and compares it against the published values.

pd_compare <- sim_typ |>
  dplyr::filter(!is.na(e1s)) |>
  dplyr::group_by(treatment) |>
  dplyr::summarise(
    nadir_pgml      = min(e1s),
    nadir_pct_base  = 100 * min(e1s) / 203,
    .groups = "drop"
  ) |>
  dplyr::mutate(
    published_pct_base = dplyr::case_when(
      treatment == "SCT_fasting"     ~ 27.0,
      treatment == "Suspension_fast" ~ 28.5,
      treatment == "SCT_food"        ~ 24.6
    )
  )

knitr::kable(pd_compare, digits = 2,
  caption = paste("Typical-value E1S nadir (% of baseline) vs Valle 2005",
                  "Results (mean across n = 12 observed subjects)."))
Typical-value E1S nadir (% of baseline) vs Valle 2005 Results (mean across n = 12 observed subjects).
treatment nadir_pgml nadir_pct_base published_pct_base
SCT_fasting 60.25 29.68 27.0
SCT_food 43.93 21.64 24.6
Suspension_fast 54.18 26.69 28.5

Assumptions and deviations

  • Additive residual SD approximated from the assay’s LLOQ and inter-assay CV. Valle 2005 Results states that the additive component of the exemestane residual error was fixed to “the SD of the analytical technique” but does not report the numeric SD value. The assay’s LLOQ is 13.5 pg/mL and the inter-assay CV is 17.7 %% (Methods). The model fixes addSd = 0.0024 ng/mL (= 13.5 pg/mL x 0.177 ~= 2.4 pg/mL), representing the typical assay SD at the LLOQ end of the calibration range. Because the proportional component is 4 %% of Cc and exemestane Cmax is in the 8-15 ng/mL range, the proportional component dominates the residual SD above ~60 pg/mL (~0.06 ng/mL) and the precise additive value affects only near-LLOQ residuals.
  • Intrinsic V (not V/F) is held constant across treatments. Valle 2005 Table 2 reports three separate V/F values (1360 / 1120 / 844 L) but interprets the differences as F differences with V intrinsic. The model encodes V = 1360 L (the V/F reference for SCT/fasting with F = 1) and applies F = 1.0 / 1.2 / 1.6 multiplicatively on the depot dose for SCT/fasting / suspension/fasting / SCT/food respectively. The implied per-treatment V/F values (1360 / 1133 / 850) are within 1 %% of the published values (1360 / 1120 / 844).
  • Food effect encoded generically per dose record. The crossover protocol did not test a suspension-after-food condition, so the food effect on ka and F was estimated only on the SCT arm. The model applies the FED_HIGHFAT indicator generically per dose record so any combination of FORM_SUSPENSION and FED_HIGHFAT produces a prediction; downstream users should restrict to combinations the protocol covers (SCT/fasting, suspension/fasting, SCT/food) unless they have an external justification for extrapolating outside the protocol.
  • Cmax for SCT/food is under-predicted vs the published NCA. The typical-value (IIV-zeroed) simulation under-predicts Valle 2005 Table 1 Cmax for SCT/food by ~40 %% (~10 vs 18 ng/mL). The cause is the 3-compartment disposition’s rapid early-distribution phase (k12 + k13 = 0.628 1/h, comparable to ka - kel = 1.612 1/h at SCT/fasting and larger than ka - kel = 0.392 1/h at SCT/food), which removes exemestane from the central compartment during absorption and damps Cmax. The Cmax in the stochastic cohort simulation (with IIV) is higher than the typical-value Cmax because the log-normal IIV on lka (CV 92 %%) inflates individual peaks. The published Table 1 Cmax means reflect observed individual Cmax values, which are inflated by the same IIV. The popPK fit chose to match the longitudinal profile rather than the mean observed Cmax – this is a documented characteristic of the published model, not a transcription error in this implementation.
  • AUC for SCT/fasting and suspension/fasting is under-predicted vs the published NCA by ~15-17 %%. The popPK CL/F at the SCT/fasting reference is kel * V/F = 0.738 * 1360 = 1004 L/h, larger than the Table 1 NCA CL/F of 902 L/h. This is the standard popPK-vs-NCA difference; the popPK fit minimises a likelihood that weights all observations whereas NCA derives CL/F from observed AUC alone. No parameter tuning is performed.
  • Hill exponent has no IIV per the source. Valle 2005 Table 4 marks the IIV on g as N.E. (not estimated) because the data did not support its estimation. The model uses a single typical-value Hill exponent (hill = exp(lhill) = 1.73) with no etalhill.
  • No data on race / ethnicity. Valle 2005 Methods does not report race or ethnicity for the 12 subjects. The model does not carry a race covariate.
  • Steady-state Figure 4 simulation uses FED_HIGHFAT = 1. Valle 2005 Discussion describes the Figure 4 simulation as “0.5, 1, 2.5, 5, and 25 mg day^-1 of exemestane for a period of 15 days… under non-fasting conditions”, so the typical-value simulation in the Figure 4 block uses FED_HIGHFAT = 1 (with FORM_SUSPENSION = 0 since the figure refers to the sugar-coated tablet).
  • E1S nadir interpretation. Valle 2005 Results reports “the maximum observed decrease in E1S plasma concentrations (expressed as percentage of the baseline concentrations: 27 (12.6 SD), 28.5 (8.7) and 24.6 (6.8)…” which is interpreted here as the residual E1S expressed as a percent of baseline (i.e., E1S nadir at 27 %% of baseline = 73 %% suppression for SCT/fasting), based on consistency with the paper’s steady-state observation “lower than 10 %% for the 25 mg day^-1 dose” and the Kaufmann reference “8.1-9.2 %% reported by Kaufmann et al.”, which both refer to the residual fraction.