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Rosuvastatin + ezetimibe with enterohepatic recirculation (An 2025)

Source: vignettes/articles/An_2025_rosuvastatin_ezetimibe.Rmd
An_2025_rosuvastatin_ezetimibe.Rmd

Model and source 

ui <- rxode2::rxode(readModelDb("An_2025_rosuvastatin_ezetimibe"))
  • Citation: An H, Shin D. Population pharmacokinetics and pharmacodynamics with enterohepatic recirculation of co-medication of rosuvastatin and ezetimibe. Drug Des Devel Ther. 2025;19:4775-4787. doi:10.2147/DDDT.S522863.
  • Article: https://doi.org/10.2147/DDDT.S522863
  • Description: Joint population PK/PD model of co-administered rosuvastatin and ezetimibe with enterohepatic recirculation, fitted to a two-part open-label multiple-dose crossover drug-interaction study in 50 healthy Korean male volunteers (An 2025 Table 2). Rosuvastatin has first-order absorption and two-compartment disposition. Total ezetimibe (unchanged ezetimibe plus its phenolic glucuronide, which together are the measured analyte) has a four-compartment structure: a gastrointestinal / absorption compartment, central and peripheral compartments, and a gallbladder reservoir. Drug moves from the ezetimibe central compartment into the gallbladder continuously at kbm, and is released back into the GASTROINTESTINAL compartment (not the central compartment) during three 0.75 h post-prandial windows, from which it is re-absorbed at ka - this GI-linked return is the structure the authors found superior on goodness-of-fit. The two PK models drive one shared LDL-cholesterol indirect-response compartment through independent, multiplicative (Bliss-independent) inhibition of LDL-C production, with Imax fixed at 1 and the Hill coefficient fixed at 1; there is no PK or PD interaction term. The meal gate is anchored to TIME AFTER DOSE, matching the protocol’s standard meals 4, 10 and 24 h after an administration, so a single-dose event table reproduces the paper’s Equations 3-6 indicator exactly. No covariate was significant on any PK or PD parameter; the screened covariates are recorded in covariatesDataExcluded. Concentrations are in ng/mL and LDL-C in mg/dL, so model() scales amount/volume by 1000 to convert mg/L to ng/mL.

An 2025 fits one joint system to three endpoints measured in the same subjects: rosuvastatin plasma concentration, total ezetimibe plasma concentration, and serum LDL-cholesterol. Because the LDL-C compartment is driven by both drugs at once, the paper’s structure is a single model, and it is packaged as a single .R file rather than split per drug.

Population

The analysis dataset comes from a two-part, open-label, multiple-dose, two-treatment, two-period, two-sequence crossover drug-interaction study (ClinicalTrials.gov NCT02289430) in healthy Korean male volunteers. Fifty-six subjects were enrolled, 28 in each part, and 50 (25 per part) contributed to the population analysis, giving 25 rosuvastatin-monotherapy, 25 ezetimibe-monotherapy and 50 co-therapy concentration-time profiles. Part A compared rosuvastatin 20 mg once daily with rosuvastatin 20 mg + ezetimibe 10 mg once daily; Part B compared ezetimibe 10 mg once daily with the same combination. Each treatment ran for 7 days, separated by a 14-day washout.

Subjects were 19-45 years old and within 20% of ideal body weight, with creatinine clearance at or above 80 mL/min. An 2025 Table 1 reports medians (ranges) of 24 years (19-33 / 19-37), 69.1 and 68.8 kg, 173 and 174 cm, serum creatinine 0.7 and 0.8 mg/dL, albumin 4.5 g/dL, and baseline LDL-C 91 (43-137) and 99 (53-175) mg/dL across Parts A and B. The cohort’s homogeneity is the paper’s own explanation for finding no significant covariate on any PK or PD parameter, so the packaged model has an empty covariateData and records the eight screened covariates under covariatesDataExcluded.

Steady-state PK sampling ran on day 7 at 0, 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 5, 6, 8, 12, 24, 48 and 72 h post-dose. Standard meals were given 4, 10 and 24 h after the final dose; these define the gallbladder-emptying windows in the model. LDL-C was measured pre-dose on day 1 and 24 h after the final dose.

The same information is available programmatically via ui$population.

Source trace

Every ini() entry in inst/modeldb/specificDrugs/An_2025_rosuvastatin_ezetimibe.R carries an in-file comment naming its source location. They are collected here for review. All display equations were read from the typeset PDF: the publisher renders them as vector artwork, so both pdftotext and the preprocessed markdown drop them.

Equation / parameter Value Source location
d/dt(depot_rosuvastatin), d/dt(central_rosuvastatin), d/dt(peripheral1_rosuvastatin) n/a Figure 2 (left half), p. 4781 – first-order absorption into two-compartment disposition
d/dt(depot_ezetimibe) n/a Equation 3, p. 4782
d/dt(central_ezetimibe) n/a Equation 4, p. 4782
d/dt(peripheral1_ezetimibe) n/a Equation 5, p. 4782
d/dt(gallbladder_ezetimibe) n/a Equation 6, p. 4782
d/dt(ldl) n/a Equation 1, p. 4779 (repeated in Figure 2)
residual-error form n/a Equation 2, p. 4781: C = f + (a + b * f) * e
lka_rosuvastatin 0.21 1/h Table 2, ka,R (RSE 9.3%)
lcl_rosuvastatin 92.27 L/h Table 2, Cl,R (RSE 8.5%)
lvc_rosuvastatin 222.23 L Table 2, Vc,R (RSE 13.0%)
lq_rosuvastatin 24.16 L/h Table 2, Q,R (RSE 12.9%)
lvp_rosuvastatin 650.71 L Table 2, Vp,R (RSE 24.1%)
lka_ezetimibe 0.64 1/h Table 2, ka,E (RSE 6.5%)
lcl_ezetimibe 20.04 L/h Table 2, Cl,E (RSE 6.7%)
lvc_ezetimibe 31.98 L Table 2, Vc,E (RSE 9.8%)
lq_ezetimibe 44.53 L/h Table 2, Q,E (RSE 8.9%)
lvp_ezetimibe 363.06 L Table 2, Vp,E (RSE 9.5%)
lkbm_ezetimibe 0.013 1/h Table 2, kb,E (RSE 5.3%)
lkehc_ezetimibe 1.33 1/h, fixed Table 2, ke,E (“Fix”); Results p. 4782, “fixed as the inverse of duration”
tmeal1, tmeal2, tmeal3 4, 10, 24 h, fixed Methods p. 4778, “A standard meal was provided at 4, 10, and 24 h after the final dose”; Results p. 4783, “Three intermittent bile release periods (at 4, 10, and 24 h post-dose)”
dge 0.75 h, fixed Results p. 4782, “the duration of bile release in each EHC cycle was set to 0.75 h”
lbase 92.2 mg/dL Table 2, Baseline LDL (RSE 3.9%)
lkin 1.9 mg/dL/h Table 2, kin (RSE 22.2%)
kout derived Not tabulated; recovered as kin / base from the drug-free steady state of Equation 1
lic50_rosuvastatin 4.6 ng/mL Table 2, IC50,R (RSE 7.8%)
lic50_ezetimibe 36.9 ng/mL Table 2, IC50,E (RSE 11.8%)
Imax, Hill coefficient 1, fixed Methods p. 4779 (“The model assumes Imax = 1 … fixed rather than estimated”); Discussion p. 4784 (“Hill coefficient … is simply fixed at 1”)
all eta variances see model file Table 2 IIV block, read as CV% and converted by omega^2 = log(1 + CV^2)
eta correlations -0.87; 0.74 / 0.58 / 0.74 Table 2 Correlation block
addSd_rosuvastatin, propSd_rosuvastatin 0.17 ng/mL, 0.20 Table 2, a,R and b,R
addSd_ezetimibe 0.33 ng/mL Table 2, a,E; b,E is zero per Results p. 4783
addSd_ldl, propSd_ldl 0.73 mg/dL, 0.12 Table 2, a,LDL and b,LDL

Virtual cohort

Original observed data are not publicly available. The cohort below reproduces the trial’s three treatment arms at the published doses and schedule: 7 once-daily doses, with the day-7 dose at 144 h. PK is read over the 72 h following that dose, matching the paper’s day-7 sampling window; LDL-C is read pre-dose (0 h, the day-1 baseline) and 24 h after the final dose (168 h), matching the paper’s PD sampling.

The model has no covariates, so the arms differ only in which drugs are dosed.

# `set.seed()` seeds R's RNG, not rxode2's. rxode2 partitions its streams per
# solver thread, so this cohort is reproducible on this machine and different on
# a machine with a different thread count. Every assertion below is written to
# hold for ANY cohort the model can produce.
set.seed(20250908)

n_arm      <- 200L                          # per-arm cap; 200 is the skill's maximum
dose_times <- seq(0, 144, by = 24)          # 7 once-daily doses; day-7 dose at 144 h
pk_times   <- 144 + c(seq(0, 8, by = 0.25), seq(8.5, 12, by = 0.5),
                      seq(13, 24, by = 1), 30, 36, 48, 60, 72)
ldl_times  <- c(0, 168)                     # day-1 pre-dose baseline, and 24 h after the last dose

make_arm <- function(arm, rosuvastatin, ezetimibe, id_offset) {
  ids <- id_offset + seq_len(n_arm)
  doses <- dplyr::bind_rows(
    if (rosuvastatin) {
      tidyr::expand_grid(id = ids, time = dose_times) |>
        dplyr::mutate(amt = 20, evid = 1L, cmt = "depot_rosuvastatin")
    },
    if (ezetimibe) {
      tidyr::expand_grid(id = ids, time = dose_times) |>
        dplyr::mutate(amt = 10, evid = 1L, cmt = "depot_ezetimibe")
    }
  )
  obs <- dplyr::bind_rows(
    tidyr::expand_grid(id = ids, time = pk_times)  |> dplyr::mutate(cmt = "Cc_rosuvastatin"),
    tidyr::expand_grid(id = ids, time = pk_times)  |> dplyr::mutate(cmt = "Cc_ezetimibe"),
    tidyr::expand_grid(id = ids, time = ldl_times) |> dplyr::mutate(cmt = "ldl")
  ) |>
    dplyr::mutate(amt = NA_real_, evid = 0L)
  dplyr::bind_rows(doses, obs) |>
    dplyr::mutate(arm = arm) |>
    dplyr::arrange(id, time, dplyr::desc(evid))
}

events <- dplyr::bind_rows(
  make_arm("Rosuvastatin 20 mg", TRUE,  FALSE, id_offset =   0L),
  make_arm("Ezetimibe 10 mg",    FALSE, TRUE,  id_offset = 200L),
  make_arm("Co-therapy",         TRUE,  TRUE,  id_offset = 400L)
)

# Disjoint IDs across arms: duplicate ids would silently merge into one subject
# receiving the summed dose.
stopifnot(
  length(unique(events$id)) == 3L * n_arm,
  !anyDuplicated(unique(events[, c("id", "time", "evid", "cmt")]))
)

The observation rows above set cmt to an endpoint name (Cc_rosuvastatin, Cc_ezetimibe, ldl) rather than to an ODE state. That is required here: with three declared endpoints rxode2 rejects cmt = "<ODE state>" and rejects dvid-only rows, and asks the observation to name which endpoint it belongs to. Because each of these names is a declared endpoint (it appears on the left of a ~ residual line), rxode2 already owns a compartment slot for it and nothing is injected or renumbered. The guard chunk after the simulation proves that.

Simulation 

mod <- readModelDb("An_2025_rosuvastatin_ezetimibe")

sim <- rxode2::rxSolve(
  mod,
  events      = events,
  keep        = "arm",
  useLinCmt   = FALSE,   # ODE->linCmt auto-conversion corrupts multi-endpoint dvid mapping
  addDosing   = FALSE,
  returnType  = "data.frame"
)

# rxode2 returns `CMT` as the NUMERIC compartment slot, not the endpoint name it
# was given in the event table. Derive the mapping from the model rather than
# hardcoding it, so this cannot silently go stale (and so a mismatch fails here
# instead of producing a zero-row filter downstream).
endpoint_map  <- setNames(ui$predDf$var, as.character(ui$predDf$cmt))
sim$endpoint  <- unname(endpoint_map[as.character(sim$CMT)])
stopifnot(!anyNA(sim$endpoint), setequal(unique(sim$endpoint), ui$predDf$var))
# Proof that naming endpoints on the observation rows did NOT renumber the ODE
# compartment slots. `ui$predDf` shows the two purely-algebraic observables
# taking slots 9 and 10 -- ABOVE all 8 declared states -- while `ldl`, which is
# itself an ODE state, keeps its own slot 8. Nothing was inserted among the
# states, so no state reference shifted.
knitr::kable(ui$predDf[, c("var", "dvid", "cmt")],
             caption = "Endpoint-to-compartment-slot mapping; 8 ODE states occupy slots 1-8.")
Endpoint-to-compartment-slot mapping; 8 ODE states occupy slots 1-8.
var dvid cmt
Cc_rosuvastatin 1 9
Cc_ezetimibe 2 10
ldl 3 8 

stopifnot(
  # The 8 declared states occupy slots 1-8 and `ldl` (state 8) is unmoved.
  length(ui$state) == 8L,
  ui$predDf$cmt[ui$predDf$var == "ldl"] == which(ui$state == "ldl"),
  all(ui$predDf$cmt[ui$predDf$var != "ldl"] > length(ui$state)),
  all(ui$state %in% names(sim)),
  all(c("Cc_rosuvastatin", "Cc_ezetimibe", "ldl") %in% names(sim)),
  # The rosuvastatin arms receive drug in depot_rosuvastatin and none in the
  # ezetimibe depot; the ezetimibe arm is the mirror image.
  max(sim$depot_rosuvastatin[sim$arm == "Rosuvastatin 20 mg"]) > 0,
  max(sim$depot_ezetimibe[sim$arm == "Rosuvastatin 20 mg"]) == 0,
  max(sim$depot_ezetimibe[sim$arm == "Ezetimibe 10 mg"]) > 0,
  max(sim$depot_rosuvastatin[sim$arm == "Ezetimibe 10 mg"]) == 0
)

# `Cc_*` and `ldl` are individual predictions WITHOUT residual error; the column
# that carries residual error is `sim`. Confirm rather than assume, because the
# LDL-C comparison below depends on using the right one.
ldl_rows <- sim[sim$endpoint == "ldl", ]
stopifnot(nrow(ldl_rows) == 2L * 3L * n_arm)   # a zero-row filter would make every all.equal() below vacuous
stopifnot(isTRUE(all.equal(ldl_rows$ldl, ldl_rows$ipredSim)))
stopifnot(!isTRUE(all.equal(ldl_rows$ldl, ldl_rows$sim)))

Replicate published figures

Figure 1 – steady-state concentration-time profiles 

pk <- sim |>
  dplyr::filter(endpoint %in% c("Cc_rosuvastatin", "Cc_ezetimibe")) |>
  dplyr::mutate(
    tad     = time - 144,
    analyte = ifelse(endpoint == "Cc_rosuvastatin", "Rosuvastatin", "Total ezetimibe"),
    conc    = ifelse(endpoint == "Cc_rosuvastatin", Cc_rosuvastatin, Cc_ezetimibe)
  ) |>
  dplyr::filter(
    (analyte == "Rosuvastatin"    & arm %in% c("Rosuvastatin 20 mg", "Co-therapy")) |
    (analyte == "Total ezetimibe" & arm %in% c("Ezetimibe 10 mg",    "Co-therapy"))
  ) |>
  dplyr::mutate(therapy = ifelse(arm == "Co-therapy", "Co-therapy", "Monotherapy"))

pk |>
  dplyr::group_by(analyte, therapy, tad) |>
  dplyr::summarise(mean_conc = mean(conc), .groups = "drop") |>
  ggplot(aes(tad, mean_conc, colour = therapy, linetype = therapy)) +
  geom_line(linewidth = 0.7) +
  facet_wrap(~analyte, scales = "free_y") +
  scale_colour_manual(values = c("Monotherapy" = "black", "Co-therapy" = "grey50")) +
  labs(x = "Time after the day-7 dose (h)", y = "Mean plasma concentration (ng/mL)",
       colour = NULL, linetype = NULL,
       title = "Figure 1 -- mean steady-state profiles",
       caption = "Replicates Figure 1 of An 2025.")

The monotherapy and co-therapy curves overlie each other, which is the paper’s headline PK result: neither drug’s disposition parameters depend on the other, so the model carries no interaction term and the two arms are identical by construction.

An 2025 describes ezetimibe’s enterohepatic second peak as occurring “around 5 h post-dose”, but is explicit that in this study it was not visible: “the second peak at approximately 5 h was modest and not clearly observed in the present study” and “the secondary peak was less visually prominent in the mean profile (Figure 1)”. The packaged model reproduces exactly that. With kb,E = 0.013 1/h only 2.1% of the central compartment’s outflow is diverted to bile, so bile release does not create a local maximum – the profile declines monotonically – but it does lift the post-prandial concentrations measurably above what the same model gives with the recirculation loop removed.

The two chunks below check the mechanism directly rather than looking for a peak that the paper says is not there: first that the meal gate opens exactly where the protocol puts the meals, then that bile release raises the 5-6 h concentrations.

eze_grid <- seq(144, 169, by = 0.05)
eze_typ <- rxode2::rxSolve(
  rxode2::zeroRe(mod),
  rxode2::et(amt = 10, cmt = "depot_ezetimibe", time = dose_times) |>
    rxode2::et(eze_grid, cmt = "Cc_ezetimibe"),
  useLinCmt = FALSE, addDosing = FALSE, omega = NA, returnType = "data.frame"
) |>
  dplyr::filter(!is.na(Cc_ezetimibe)) |>
  dplyr::mutate(tad = time - 144)

# The gate is a deterministic function of tmeal1/2/3 and dge, so this is an
# exact test of the meal-window encoding, not a cohort-dependent one. It goes
# red on any change to the meal times or the 0.75 h release duration.
expected_open <- with(eze_typ,
  (tad >= 4  & tad < 4  + 0.75) |
  (tad >= 10 & tad < 10 + 0.75) |
  (tad >= 24 & tad < 24 + 0.75))
stopifnot(identical(as.logical(eze_typ$gbe == 1), expected_open))
range(eze_typ$tad[eze_typ$gbe == 1])
#> [1]  4.0 24.7
eze_no_ehc <- rxode2::rxSolve(
  rxode2::zeroRe(rxode2::ini(rxode2::rxode(mod), lkehc_ezetimibe = log(1e-8))),
  rxode2::et(amt = 10, cmt = "depot_ezetimibe", time = dose_times) |>
    rxode2::et(eze_grid, cmt = "Cc_ezetimibe"),
  useLinCmt = FALSE, addDosing = FALSE, omega = NA, returnType = "data.frame"
) |>
  dplyr::filter(!is.na(Cc_ezetimibe)) |>
  dplyr::mutate(tad = time - 144)
#> ℹ change initial estimate of `lkehc_ezetimibe` to `-18.4206807439524`

at <- function(df, tt) df$Cc_ezetimibe[which.min(abs(df$tad - tt))]
lift_times <- c(3, 5, 6, 12)
lift <- vapply(lift_times, function(tt) at(eze_typ, tt) / at(eze_no_ehc, tt),
               numeric(1))
names(lift) <- paste0(lift_times, " h")

# Deterministic (zeroRe) quantities, so these are not a cohort draw. At 3 h --
# before the day-7 meal -- the recirculating model is only 0.6% higher, and that
# residue is carry-over from the previous days' meals; the lift then rises to
# ~4% once the 4 h window has released bile. Setting kb,E to zero collapses
# every lift to exactly 1.000, and setting it to 0.13 (a decimal slip) pushes
# them past 1.3, so this band can go red in both directions.
stopifnot(
  all(lift > 1.000), all(lift < 1.15),
  lift[["3 h"]] < 1.02,                 # pre-meal: only prior-day carry-over
  lift[["5 h"]] > lift[["3 h"]],        # the 4 h bile release adds to it
  lift[["6 h"]] > 1.01,
  # No local maximum forms, matching the paper's own account of Figure 1.
  all(diff(eze_typ$Cc_ezetimibe[eze_typ$tad >= 2 & eze_typ$tad <= 20]) < 0)
)
round(lift, 4)
#>    3 h    5 h    6 h   12 h 
#> 1.0058 1.0380 1.0390 1.0458

Figure 4 – LDL-C lowering by treatment

This is the paper’s headline validation. An 2025 simulated 1,000 individuals from the final PK/PD model and reported the mean percentage change in LDL-C from the pre-dose baseline to 24 h after the last dose as -51.0 +/- 15.0% (rosuvastatin), -25.3 +/- 16.2% (ezetimibe) and -60.7 +/- 13.9% (co-therapy).

Those are simulated observations, so the comparison uses the sim column (individual prediction plus residual error), not ldl.

ldl_change <- sim |>
  dplyr::filter(endpoint == "ldl") |>
  dplyr::select(id, arm, time, sim) |>
  tidyr::pivot_wider(names_from = time, values_from = sim,
                     names_prefix = "t") |>
  dplyr::mutate(pct_change = 100 * (t168 - t0) / t0)

stopifnot(nrow(ldl_change) == 3L * n_arm, !anyNA(ldl_change$pct_change))

ldl_change |>
  ggplot(aes(arm, pct_change)) +
  geom_boxplot(fill = "grey85") +
  geom_hline(yintercept = 0, linetype = "dotted") +
  labs(x = NULL, y = "Change in LDL-C from baseline at 24 h post-dose (%)",
       title = "Figure 4 -- LDL-C lowering at steady state",
       caption = "Replicates Figure 4a of An 2025.")

published_ldl <- tibble::tribble(
  ~arm,                 ~ref_mean, ~ref_sd,
  "Rosuvastatin 20 mg",     -51.0,    15.0,
  "Ezetimibe 10 mg",        -25.3,    16.2,
  "Co-therapy",             -60.7,    13.9
)

ldl_cmp <- ldl_change |>
  dplyr::group_by(arm) |>
  dplyr::summarise(sim_mean = mean(pct_change), sim_sd = sd(pct_change),
                   .groups = "drop") |>
  dplyr::left_join(published_ldl, by = "arm") |>
  dplyr::mutate(diff_pp = sim_mean - ref_mean)

ldl_cmp |>
  dplyr::rename("Treatment"           = arm,
                "Simulated mean (%)"  = sim_mean,
                "Simulated SD (%)"    = sim_sd,
                "An 2025 mean (%)"    = ref_mean,
                "An 2025 SD (%)"      = ref_sd,
                "Difference (pp)"     = diff_pp) |>
  knitr::kable(digits = 1,
               caption = "Change in LDL-C from baseline to 24 h after the last dose, simulated vs An 2025.")
Change in LDL-C from baseline to 24 h after the last dose, simulated vs An 2025.
Treatment Simulated mean (%) Simulated SD (%) An 2025 mean (%) An 2025 SD (%) Difference (pp)
Co-therapy -60.9 12.0 -60.7 13.9 -0.2
Ezetimibe 10 mg -28.4 15.5 -25.3 16.2 -3.1
Rosuvastatin 20 mg -50.2 13.8 -51.0 15.0 0.8 
# Assert on the CENTRE of each arm, not on cohort extremes. A mis-transcribed
# IC50, kin, baseline, dose or concentration-unit scaling moves these means by
# tens of percentage points, so an 8 pp band still goes red on any of those
# while absorbing the Monte-Carlo spread of a 200-subject arm. Largest realised
# |difference| was 4.55 / 4.06 / 3.70 / 4.36 pp at 1 / 2 / 4 / 16 solver
# threads, so 8 leaves roughly a factor of two of headroom. An 2025's own three
# numbers are
# internally inconsistent by ~2.7 pp under Bliss independence
# (1 - (1 - 0.510)(1 - 0.253) = 63.4% against a reported 60.7%), which sets the
# floor on how tightly this can be reproduced at all.
stopifnot(all(abs(ldl_cmp$diff_pp) < 8))

# Direction and ordering are structural, not noise-limited: co-therapy must
# lower LDL-C more than either monotherapy, and every arm must lower it.
mean_by <- setNames(ldl_cmp$sim_mean, ldl_cmp$arm)
stopifnot(
  all(mean_by < -15),
  mean_by[["Co-therapy"]] < mean_by[["Rosuvastatin 20 mg"]],
  mean_by[["Co-therapy"]] < mean_by[["Ezetimibe 10 mg"]]
)
# The simulated drug-free baseline must reproduce Table 2's typical value of
# 92.2 mg/dL and sit inside the observed spread of An 2025 Table 1 (medians 91
# and 99 mg/dL, overall range 43-175).
baseline_median <- median(ldl_change$t0)
stopifnot(baseline_median > 80, baseline_median < 105)
c(simulated_baseline_median = baseline_median, published_typical = 92.2)
#> simulated_baseline_median         published_typical 
#>                  93.04169                  92.20000

PKNCA validation

An 2025 reports no NCA table of its own – it cites the companion clinical report for that – so the NCA below is used for the one quantitative PK claim the paper does state in text, the roughly 20 h mean half-life of total ezetimibe, and to document the steady-state exposures the model implies.

One PKNCA block is run per analyte, each restricted to the arms in which that drug was actually given, with a treatment grouping so the monotherapy and co-therapy arms can be compared.

nca_frame <- function(analyte_cmt, conc_col, keep_arms) {
  out <- sim |>
    dplyr::filter(endpoint == analyte_cmt, arm %in% keep_arms) |>
    dplyr::transmute(id, arm, time = time - 144, Cc = .data[[conc_col]]) |>
    dplyr::filter(!is.na(Cc))
  # Guarantee a time-zero record per (id, arm). Without it PKNCA warns
  # "Requesting an AUC range starting (0) before the first measurement" once
  # per subject. The 144 h grid already contains it; this is a defensive
  # no-op that keeps the gate honest if the grid ever changes.
  dplyr::bind_rows(
    out,
    out |> dplyr::distinct(id, arm) |> dplyr::mutate(time = 0, Cc = 0)
  ) |>
    dplyr::distinct(id, arm, time, .keep_all = TRUE) |>
    dplyr::arrange(id, arm, time)
}

dose_frame <- function(dose_cmt, keep_arms) {
  events |>
    dplyr::filter(evid == 1L, cmt == dose_cmt, arm %in% keep_arms, time == 144) |>
    dplyr::transmute(id, arm, time = 0, amt)
}

run_nca <- function(conc_df, dose_df) {
  conc_obj <- PKNCA::PKNCAconc(conc_df, Cc ~ time | arm + id)
  dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | arm + id)
  intervals <- data.frame(
    start = 0, end = c(24, 72),
    cmax = c(TRUE, FALSE), tmax = c(TRUE, FALSE),
    auclast = c(TRUE, FALSE), ctrough = c(TRUE, FALSE),
    half.life = c(FALSE, TRUE)
  )
  PKNCA::pk.nca(PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals))
}

nca_ros <- run_nca(
  nca_frame("Cc_rosuvastatin", "Cc_rosuvastatin", c("Rosuvastatin 20 mg", "Co-therapy")),
  dose_frame("depot_rosuvastatin", c("Rosuvastatin 20 mg", "Co-therapy"))
)
nca_eze <- run_nca(
  nca_frame("Cc_ezetimibe", "Cc_ezetimibe", c("Ezetimibe 10 mg", "Co-therapy")),
  dose_frame("depot_ezetimibe", c("Ezetimibe 10 mg", "Co-therapy"))
)
summarise_nca <- function(res, analyte) {
  as.data.frame(res$result) |>
    dplyr::filter(PPTESTCD %in% c("cmax", "tmax", "auclast", "ctrough", "half.life")) |>
    dplyr::group_by(analyte = analyte, arm, PPTESTCD) |>
    dplyr::summarise(median = median(PPORRES, na.rm = TRUE), .groups = "drop")
}

nca_tab <- dplyr::bind_rows(
  summarise_nca(nca_ros, "Rosuvastatin"),
  summarise_nca(nca_eze, "Total ezetimibe")
) |>
  tidyr::pivot_wider(names_from = PPTESTCD, values_from = median)

# Guard against a silently-empty table (a lookup that matches nothing makes
# every downstream all() vacuously TRUE).
stopifnot(nrow(nca_tab) == 4L, all(c("cmax", "auclast", "half.life") %in% names(nca_tab)))

nca_tab |>
  dplyr::select(analyte, arm, cmax, tmax, auclast, ctrough, half.life) |>
  dplyr::rename("Analyte"                = analyte,
                "Treatment"              = arm,
                "Cmax (ng/mL)"           = cmax,
                "Tmax (h)"               = tmax,
                "AUC0-24 (ng*h/mL)"      = auclast,
                "Ctrough at 24 h (ng/mL)" = ctrough,
                "t1/2 (h)"               = half.life) |>
  knitr::kable(digits = c(0, 0, 1, 2, 0, 2, 1),
               caption = "Median simulated steady-state NCA by analyte and treatment arm.")
Median simulated steady-state NCA by analyte and treatment arm.
Analyte Treatment Cmax (ng/mL) Tmax (h) AUC0-24 (ng*h/mL) Ctrough at 24 h (ng/mL) t1/2 (h)
Rosuvastatin Co-therapy 20.3 2.75 203 1.86 26.7
Rosuvastatin Rosuvastatin 20 mg 19.2 3.00 203 1.80 21.9
Total ezetimibe Co-therapy 68.5 1.00 494 9.53 18.6
Total ezetimibe Ezetimibe 10 mg 68.1 0.75 499 9.67 18.3 
med <- function(tab, an, param) {
  v <- tab[[param]][tab$analyte == an]
  if (length(v) < 1L) stop("no rows for ", an, " / ", param)
  median(v)
}

# 1. An 2025 Methods, p. 4778: sampling ran to 72 h "considering the longer mean
#    half-life of total ezetimibe with approximately 20 h". Deterministic
#    typical-value half-life is 18.6 h; the cohort median sits near it. The band
#    is wide enough to absorb the cohort draw and still red on a
#    mis-transcribed Cl,E or Vp,E, which move it by more than a factor of 1.5.
eze_thalf <- med(nca_tab, "Total ezetimibe", "half.life")
stopifnot(eze_thalf > 13, eze_thalf < 28)

# 2. No PK interaction: An 2025's central conclusion is that co-therapy leaves
#    both drugs' exposure unchanged. The model has no interaction term, so this
#    is a structural identity and can be asserted tightly -- the two arms share
#    parameters and differ only in the RNG draw.
ratio <- function(tab, an, param) {
  v <- tab[[param]][tab$analyte == an]
  a <- tab$arm[tab$analyte == an]
  v[a == "Co-therapy"] / v[a != "Co-therapy"]
}
stopifnot(
  abs(ratio(nca_tab, "Rosuvastatin",    "auclast") - 1) < 0.15,
  abs(ratio(nca_tab, "Total ezetimibe", "auclast") - 1) < 0.15
)

# 3. Rosuvastatin steady-state AUC0-24 must equal Dose / Cl to within the
#    accumulation the two-compartment tail carries past 24 h. Dose / Cl =
#    20 mg / 92.27 L/h = 0.2168 mg*h/L = 216.8 ng*h/mL. This is the closed-form
#    check that a mis-transcribed clearance or unit scaling cannot survive.
ros_auc <- med(nca_tab, "Rosuvastatin", "auclast")
stopifnot(abs(ros_auc / (1000 * 20 / 92.27) - 1) < 0.15)
c(rosuvastatin_auc0_24 = ros_auc, dose_over_cl = 1000 * 20 / 92.27,
  ezetimibe_half_life = eze_thalf)
#> rosuvastatin_auc0_24         dose_over_cl  ezetimibe_half_life 
#>            203.26253            216.75518             18.46045

Enterohepatic recirculation: effect on exposure

An 2025 quantifies the EHC contribution as an AUC ratio: “The AUC ratio in the absence of EHC was estimated assuming that reabsorption was incorporated into the elimination process. In the present study, the AUC ratio was estimated to be 0.94.” Removing EHC therefore lowers total ezetimibe exposure by about 6% in the paper’s own accounting.

That scenario is reproduced by driving kehc_ezetimibe to zero: biliary transfer at kb,E still removes drug from the central compartment, but nothing ever returns, which is exactly “reabsorption incorporated into the elimination process”. Everything here is a typical-value (zeroRe) solve, so the numbers are deterministic rather than a cohort draw.

auc_traps <- function(m, lo, hi) {
  d <- rxode2::rxSolve(
    rxode2::zeroRe(m),
    rxode2::et(amt = 10, cmt = "depot_ezetimibe", time = dose_times) |>
      rxode2::et(seq(144, 216, by = 0.05), cmt = "Cc_ezetimibe"),
    useLinCmt = FALSE, addDosing = FALSE, omega = NA, returnType = "data.frame"
  ) |>
    dplyr::filter(!is.na(Cc_ezetimibe), time >= lo, time <= hi)
  sum(diff(d$time) * (head(d$Cc_ezetimibe, -1) + tail(d$Cc_ezetimibe, -1)) / 2)
}

mod_no_ehc <- rxode2::rxode(mod) |> rxode2::ini(lkehc_ezetimibe = log(1e-8))
#> ℹ change initial estimate of `lkehc_ezetimibe` to `-18.4206807439524`

ehc_tab <- tibble::tibble(
  window     = c("AUC0-24 (dosing interval)", "AUC0-72 after the last dose"),
  with_ehc   = c(auc_traps(mod, 144, 168), auc_traps(mod, 144, 216)),
  without_ehc = c(auc_traps(mod_no_ehc, 144, 168), auc_traps(mod_no_ehc, 144, 216))
) |>
  dplyr::mutate(ratio = without_ehc / with_ehc)

ehc_tab |>
  dplyr::rename("Window"                     = window,
                "With EHC (ng*h/mL)"         = with_ehc,
                "Without EHC (ng*h/mL)"      = without_ehc,
                "Ratio (without / with)"     = ratio) |>
  knitr::kable(digits = c(0, 1, 1, 3),
               caption = "Effect of enterohepatic recirculation on total ezetimibe exposure. An 2025 reports 0.94.")
Effect of enterohepatic recirculation on total ezetimibe exposure. An 2025 reports 0.94.
Window With EHC (ng*h/mL) Without EHC (ng*h/mL) Ratio (without / with)
AUC0-24 (dosing interval) 498.1 488.1 0.980
AUC0-72 after the last dose 720.2 701.4 0.974 
# Reproduced qualitatively, not numerically -- see Assumptions and deviations.
# The gate holds the direction and the order of magnitude of the effect: EHC
# raises exposure, and by well under a factor of two. Raising kb,E by 10x
# (a plausible decimal-point transcription error) drives the ratio below 0.85
# and turns this red.
stopifnot(all(ehc_tab$ratio < 1), all(ehc_tab$ratio > 0.85))

Assumptions and deviations

  • IIV scale. An 2025 Table 2 heads the random-effect block “CV%” and the table’s own abbreviation footnote defines “CV, coefficient of variation”, so each entry is read as a coefficient of variation and converted with omega^2 = log(1 + CV^2). The competing reading – that the printed number is 100 * omega, the log-scale SD, which is how Monolix names the parameter omega_ka itself – cannot be excluded from the paper’s own numbers. It was tested and found not to matter: the two readings differ by under 5% for every parameter except omega Vp,R (0.776 as a CV against 1.083 as an SD), and the LDL-C simulation above is not sensitive enough to separate them. The literal reading of the column header is used; the alternative is recorded here.
  • Table 2 row labels. The fifth rosuvastatin IIV row and the fifth ezetimibe IIV row are both printed as “omega Vc” a second time. They are read as the peripheral-volume random effects: the central-volume rows appear immediately above them, the parameter blocks run Vc then Q then Vp in that order, and the ezetimibe correlation block names Vp,E as a correlated random effect, which requires an omega Vp,E to exist.
  • kout is derived, not published. Table 2 reports the baseline and kin but not kout. It is recovered per individual as kin / base from the drug-free steady state of Equation 1, giving a typical kout of 0.0206 1/h (LDL-C turnover half-life 33.6 h), which is consistent with published LDL fractional catabolic rates.
  • Ezetimibe residual error. Table 2 lists only a,E = 0.33, and the Results text states the model used “an additive error model with zero proportional error (b = 0)”. That literal reading is encoded. It is worth flagging that an additive-only SD of 0.33 ng/mL is very small for an analyte whose observed concentrations reach ~200 ng/mL; the Methods for the same model instead say residual variability was “described using an exponential model”, under which 0.33 would be a log-scale SD (about 33% CV) and far more plausible. The paper is self-contradictory here and nothing in it settles the question, so the explicitly stated form and the explicitly tabulated value are used.
  • EHC AUC ratio not reproduced numerically. An 2025 reports 0.94; the packaged model gives 0.97-0.99 depending on the window, under four different definitions of the ratio (steady-state AUC0-24, steady-state AUC0-72, single-dose AUC0-72, single-dose AUC0-inf). The published parameters imply that only kb,E / (Cl,E / Vc,E) = 0.013 / 0.627 = 2.1% of the central compartment’s outflow is diverted to bile, which cannot produce a 6% exposure effect. The paper’s qualitative conclusion – that EHC raised total ezetimibe exposure only slightly, and “less affected by EHC compared to previous studies” – is reproduced; the exact 0.94 is not. The gate above holds the direction and magnitude rather than the published number.
  • Meal-time origin. An 2025 places the three bile-release windows 4, 10 and 24 h after an administration. The model reads them against tad(), so a single-dose event table reproduces the paper’s literal Equations 3-6 indicator exactly, and a once-daily multiple-dose table repeats the 4 h and 10 h meals after every dose while opening the 24 h window only after the final one. The paper only ever specifies the pattern for the final dose, so the days-1-to-6 recurrence is an assumption; it changes total ezetimibe exposure by the same 2-3% the EHC check above quantifies.
  • Apparent parameters. The study has no intravenous arm, so every clearance and volume is apparent (relative to oral bioavailability). An 2025 writes them without an explicit /F; the model labels record the distinction.
  • No covariates. An 2025 screened age, weight, serum creatinine, albumin, ALP, ALT, AST and GGT on both the PK and PD parameters and retained none. They are recorded in covariatesDataExcluded for provenance, not in covariateData, because the final model does not reference them.
  • Cohort composition. The trial enrolled only young healthy Korean males, so the virtual cohort carries no demographic variation; the model has no covariates to vary. Extrapolation to women, older adults or patients with dyslipidaemia is outside what these data support, as the paper’s own Discussion states.