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CKD-519, CETP activity, HDL-C and LDL-C (Kim 2020)

Source: vignettes/articles/Kim_2020_CKD_519.Rmd
Kim_2020_CKD_519.Rmd

Model and source

  • Citation: Kim CO, Jeon S, Han S, Park MS, Yim DS. A Population Pharmacokinetic and Pharmacodynamic Model of CKD-519. Pharmaceutics. 2020;12(6):573. doi:10.3390/pharmaceutics12060573. PK: Table 2 and Equations 1-3; CETP activity: Table 3 and Equations 4-6; HDL-C and LDL-C: Table 4 and Equations 7-10; model structure: Figure 1.
  • Description: Sequential population PK/PD model for the cholesteryl ester transfer protein (CETP) inhibitor CKD-519 in healthy adult men given 50-400 mg once daily with a standard meal for 14 days (Kim 2020). PK: three-compartment disposition with an Erlang absorption chain (dose into four transit compartments at Ktr, then an absorption compartment draining to central at Ka) and a relative bioavailability that falls with dose (Bmax * (1 - DOSE / (BA50 + DOSE))) and, for the 50-200 mg cohorts only, decays exponentially with time since the first dose. CETP activity is a turnover state whose first-order loss is stimulated by an Emax function of plasma CKD-519 and whose production rises with time on study (placebo Emax-in-time effect). HDL-C and LDL-C are turnover states whose first-order elimination is respectively stimulated (HDL-C) and inhibited (LDL-C) by a sigmoid function of CETP activity; LDL-C production also rises linearly with time (placebo).
  • Article: https://doi.org/10.3390/pharmaceutics12060573 (open access; PMC7356970)

CKD-519 is an oral inhibitor of cholesteryl ester transfer protein (CETP) that was developed for dyslipidaemia. Its exposure is highly variable: it depends on food, it rises less than dose-proportionally, and in the 50-200 mg cohorts it falls on repeated dosing. Kim et al. fitted a sequential population PK/PD model to a two-week multiple-ascending-dose study in healthy men. The chain has three links:

  1. PK. Three-compartment disposition. Absorption runs through five sequential compartments: four transit compartments at Ktr, then an absorption compartment that drains to central at Ka. The relative bioavailability falls with dose and, below 400 mg, decays with time since the first dose.
  2. CETP activity. A turnover model. Plasma CKD-519 stimulates the first-order loss of CETP activity through an Emax function. CETP production rises with time on study, a placebo effect that is also seen in the placebo group.
  3. HDL-C and LDL-C. Turnover models driven by CETP activity through a sigmoid Emax function. CETP activity stimulates HDL-C elimination and inhibits LDL-C elimination, so inhibiting CETP raises HDL-C and lowers LDL-C. LDL-C production also rises linearly with time (placebo effect).

The paper fitted the three stages one after another, each using the individual parameters of the previous stage. The packaged model joins them into one ODE system with four outputs: Cc (ng/mL), cetp (pmol), hdl and ldl (mg/dL).

Population

Thirty-two healthy Korean men took part: six on CKD-519 and two on placebo in each of four cohorts (50, 100, 200 and 400 mg). Their mean age was 32.2 years (19-47) and their mean weight 68.7 kg (58.3-79.5) (Table 1). CKD-519 or placebo was given once daily with a standard breakfast (700-800 kcal, 5-25% fat) for 14 days. Subjects stayed in hospital from day 1 to day 21. The data were 1392 plasma CKD-519 concentrations, 2064 CETP activity values and 656 HDL-C and LDL-C values. Age, weight, BMI, MDRD creatinine clearance and ALT were screened as covariates, and none was retained in any final model.

The same information is available programmatically via readModelDb("Kim_2020_CKD_519")()$population.

Source trace

Every ini() value carries an in-file comment in inst/modeldb/specificDrugs/Kim_2020_CKD_519.R. The table collects them.

Equation / parameter Value Source location
Absorption chain: 5 sequential compartments, 4 at Ktr then 1 at Ka n/a Figure 1; Section 3.2
3-compartment disposition n/a Figure 1; Table 2
F = BA * FT n/a Equation 1
BA = Bmax * (1 - DOSE / (BA50 + DOSE)) n/a Equation 2; Table 2
FT = exp(-alpha * TIME) n/a Equation 3; Table 2
lcl (CL/F) 6.4 L/h Table 2
lvc (V/F) 11.4 L Table 2
lvp (V2/F) 45.4 L Table 2
lvp2 (V3/F) 1006 L Table 2
lq (Q2/F) 2.6 L/h Table 2
lq2 (Q3/F) 3.3 L/h Table 2
lka (Ka) 1.09 1/h Table 2
lktr (Ktr) 1.10 1/h Table 2
lfdepot_max (Bmax) 1.6 Table 2
ld50_fdepot (BA50) 90.1 mg Table 2
alpha_fdepot (alpha1, 50-200 mg) 0.002 1/h Table 2
alpha_fdepot_high (alpha2, 400 mg) 0 (fixed) Table 2; Section 3.2
etalcl, etalvp2, etalfdepot_max, etalktr 15.6, 58.1, 28.2, 14.1 %CV Table 2
propSd / addSd (CKD-519) 0.30 / 0.0001 (fixed) Table 2
dCETP/dt = Kin,base (1 + Placebo) - Kout (1 + Drug) CETP n/a Equation 4; Figure 1
Placebo = Kmax T / (K50 + T) n/a Equation 5; Table 3
Drug = Emax Cp / (EC50 + Cp) n/a Equation 6; Table 3
lrbase_cetp (CETPbase) 350 pmol Table 3
lkin_cetp (Kin,base) 164 pmol/h Table 3
lpbo_emax_cetp (Kmax) 9.6 Table 3
lpbo_t50_cetp (K50) 9700 h Table 3
lemax (Emax) 18.2 Table 3
lec50 (EC50) 587 ng/mL Table 3
etalkin_cetp, etalemax 19.7, 39.5 %CV Table 3
addSd_cetp / propSd_cetp 40.4 pmol / 0.112 Table 3
dHDL/dt = Ksyn - Kdeg HDL (1 + RES) n/a Equation 7
dLDL/dt = Ksyn (1 + PLA) - Kdeg LDL (1 - RES) n/a Equation 8; Table 4; Figure 1
RES = CETP^gamma Rmax / (CETP^gamma + R50^gamma) n/a Equation 9; Table 4
PLA = beta * time n/a Equation 10; Table 4
lrbase_hdl (RB) 50.0 mg/dL Table 4, HDL-C
lksyn_hdl (Ksyn) 1.26 mg/dL/h Table 4, HDL-C
lhill_hdl (gamma) 2.1 Table 4, HDL-C
lemax_hdl (Rmax) 1.5 Table 4, HDL-C
lec50_hdl (R50) 185 pmol Table 4, HDL-C
etalrbase_hdl 17.2 %CV Table 4, HDL-C
addSd_hdl / propSd_hdl 4.6 mg/dL / 0.0001 (fixed) Table 4, HDL-C
lrbase_ldl (RB) 97.4 mg/dL Table 4, LDL-C
lksyn_ldl (Ksyn) 0.435 mg/dL/h Table 4, LDL-C
lpbo_slope_ldl (beta) 0.0009 1/h Table 4, LDL-C
lhill_ldl (gamma) 2.2 Table 4, LDL-C
lemax_ldl (Rmax) 0.8 Table 4, LDL-C
lec50_ldl (R50) 80.7 pmol Table 4, LDL-C
etalrbase_ldl, etalpbo_slope_ldl, etalhill_ldl 23.6, 97.4, 50.9 %CV Table 4, LDL-C
propSd_ldl 0.07 (additive 0 fixed, omitted) Table 4, LDL-C
kout_cetp, kdeg_hdl, kdeg_ldl derived Pre-dose steady state (see Assumptions)

The IIV rows are reported as CV%. They are converted to log-normal variances with omega^2 = log(CV^2 + 1).

Virtual cohort

The study had five arms: 50, 100, 200 and 400 mg once daily for 14 days, and placebo. Each arm below has 40 virtual subjects. The model has no demographic covariates, so each subject needs only the dose (DOSE) and the 400 mg indicator (DOSE_HIGH). Observations run hourly to day 21 (504 h). They sit on the cetp state, which is one of the declared endpoints, and rxode2 returns Cc, hdl and ldl at the same rows.

arms <- tibble::tribble(
  ~arm,      ~dose,
  "Placebo",     0,
  "50 mg",      50,
  "100 mg",    100,
  "200 mg",    200,
  "400 mg",    400
) |>
  mutate(arm = factor(arm, levels = arm))

n_per_arm <- 40L
dose_times <- seq(0, 13 * 24, by = 24)
obs_times <- sort(unique(c(seq(0, 504, by = 1), 312 + c(0.25, 0.5, 0.75))))

make_arm <- function(arm, dose, ids) {
  subj <- tibble(id = ids, arm = arm, dose_mg = dose, DOSE = dose, DOSE_HIGH = as.integer(dose == 400))
  obs <- tidyr::crossing(subj, time = obs_times) |>
    mutate(evid = 0L, amt = NA_real_, cmt = "cetp")
  if (dose == 0) {
    return(obs)
  }
  doses <- tidyr::crossing(subj, time = dose_times) |>
    mutate(evid = 1L, amt = dose, cmt = "transit1")
  bind_rows(doses, obs)
}

events <- bind_rows(lapply(seq_len(nrow(arms)), function(i) {
  make_arm(
    as.character(arms$arm[i]), arms$dose[i],
    ids = (i - 1L) * n_per_arm + seq_len(n_per_arm)
  )
})) |>
  arrange(id, time, desc(evid)) |>
  # rxode2 reads a column named DOSE as the dose amount unless the standard
  # event columns come first, so put them first.
  select(id, time, evid, amt, cmt, everything())

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

Simulation 

mod <- readModelDb("Kim_2020_CKD_519")

rxode2::rxSetSeed(519)
sim <- rxode2::rxSolve(
  mod,
  events = events,
  keep = c("arm", "dose_mg"),
  useLinCmt = FALSE
) |>
  as.data.frame() |>
  mutate(arm = factor(arm, levels = levels(arms$arm)))
#> ℹ parameter labels from comments will be replaced by 'label()'

# Typical-value solve (no IIV, no residual error). The paper's Figure 4 is a
# typical-value simulation. `omega = NA, sigma = NA` is used instead of
# zeroRe(), which is not safe on multi-endpoint models.
events_typ <- events |>
  group_by(arm) |>
  filter(id == min(id)) |>
  ungroup()
sim_typ <- rxode2::rxSolve(
  mod,
  events = events_typ,
  keep = c("arm", "dose_mg"),
  omega = NA,
  sigma = NA,
  useLinCmt = FALSE
) |>
  as.data.frame() |>
  mutate(arm = factor(arm, levels = levels(arms$arm)))

Replicate published figures

Figure 3: visual predictive checks 

# Replicates the layout of Figure 3 of Kim 2020 (VPC of CKD-519, CETP
# activity, HDL-C and LDL-C). `Cc`, `cetp`, `hdl` and `ldl` are the individual
# predictions without residual error.
vpc <- sim |>
  select(arm, time, Cc, cetp, hdl, ldl) |>
  tidyr::pivot_longer(c(Cc, cetp, hdl, ldl), names_to = "output") |>
  group_by(arm, output, time) |>
  summarise(
    q05 = quantile(value, 0.05),
    q50 = median(value),
    q95 = quantile(value, 0.95),
    .groups = "drop"
  ) |>
  mutate(output = factor(
    output,
    levels = c("Cc", "cetp", "hdl", "ldl"),
    labels = c("CKD-519 (ng/mL)", "CETP activity (pmol)", "HDL-C (mg/dL)", "LDL-C (mg/dL)")
  ))

ggplot(vpc, aes(time / 24, q50, colour = arm, fill = arm)) +
  geom_ribbon(aes(ymin = q05, ymax = q95), alpha = 0.12, colour = NA) +
  geom_line() +
  facet_wrap(~output, scales = "free_y", ncol = 1) +
  labs(
    x = "Time since first dose (days)", y = NULL, colour = NULL, fill = NULL,
    caption = "Median and 5th-95th percentiles of 40 simulated subjects per arm."
  ) +
  theme_bw()

Figure 4: HDL-C and LDL-C change from baseline

The paper simulated the typical HDL-C and LDL-C response to 21 days of daily dosing and marked a target of a 40% change from baseline. It reports that the responses peak after about ten days of dosing, that they then decline slowly at 50-200 mg but not at 400 mg, and that the 40% targets are reached at 200 and 400 mg.

# Replicates Figure 4 of Kim 2020 (typical-value simulation, 21 days of
# once-daily dosing, IIV and residual error excluded as in Section 2.5).
events_fig4 <- bind_rows(lapply(seq_len(nrow(arms))[-1], function(i) {
  d <- arms$dose[i]
  subj <- tibble(id = i, arm = as.character(arms$arm[i]), DOSE = d, DOSE_HIGH = as.integer(d == 400))
  bind_rows(
    tidyr::crossing(subj, time = seq(0, 20 * 24, by = 24)) |>
      mutate(evid = 1L, amt = d, cmt = "transit1"),
    tidyr::crossing(subj, time = seq(0, 21 * 24, by = 2)) |>
      mutate(evid = 0L, amt = NA_real_, cmt = "cetp")
  )
})) |>
  arrange(id, time, desc(evid)) |>
  select(id, time, evid, amt, cmt, everything())

fig4 <- rxode2::rxSolve(
  mod,
  events = events_fig4,
  keep = c("arm"),
  omega = NA,
  sigma = NA,
  useLinCmt = FALSE
) |>
  as.data.frame() |>
  mutate(arm = factor(arm, levels = levels(arms$arm))) |>
  group_by(arm) |>
  mutate(
    `HDL-C` = 100 * (hdl / first(hdl) - 1),
    `LDL-C` = 100 * (ldl / first(ldl) - 1)
  ) |>
  ungroup()

fig4 |>
  select(arm, time, `HDL-C`, `LDL-C`) |>
  tidyr::pivot_longer(c(`HDL-C`, `LDL-C`), names_to = "lipid", values_to = "pct") |>
  ggplot(aes(time / 24, pct, colour = arm)) +
  geom_line() +
  geom_hline(
    data = data.frame(lipid = c("HDL-C", "LDL-C"), target = c(40, -40)),
    aes(yintercept = target), linetype = "dashed"
  ) +
  facet_wrap(~lipid, scales = "free_y") +
  labs(
    x = "Time since first dose (days)", y = "Change from baseline (%)",
    colour = NULL, caption = "Dashed lines: the paper's 40% targets."
  ) +
  theme_bw()


fig4_summary <- fig4 |>
  group_by(arm) |>
  summarise(
    hdl_peak_pct = max(`HDL-C`),
    hdl_peak_day = time[which.max(`HDL-C`)] / 24,
    hdl_day21_pct = `HDL-C`[time == 504],
    ldl_nadir_pct = min(`LDL-C`),
    ldl_nadir_day = time[which.min(`LDL-C`)] / 24,
    ldl_day21_pct = `LDL-C`[time == 504],
    .groups = "drop"
  )

fig4_summary |>
  dplyr::rename(
    "Arm" = arm,
    "HDL-C peak (%)" = hdl_peak_pct,
    "HDL-C peak day" = hdl_peak_day,
    "HDL-C day 21 (%)" = hdl_day21_pct,
    "LDL-C nadir (%)" = ldl_nadir_pct,
    "LDL-C nadir day" = ldl_nadir_day,
    "LDL-C day 21 (%)" = ldl_day21_pct
  ) |>
  knitr::kable(digits = 1, caption = "Typical-value lipid response to 21 days of dosing.")
Typical-value lipid response to 21 days of dosing.
Arm HDL-C peak (%) HDL-C peak day HDL-C day 21 (%) LDL-C nadir (%) LDL-C nadir day LDL-C day 21 (%)
50 mg 58.8 9.5 41.6 -46.6 9.4 -28.6
100 mg 71.2 10.5 56.4 -53.2 9.5 -37.8
200 mg 79.5 11.5 67.1 -57.2 9.5 -43.5
400 mg 93.5 17.5 91.8 -62.0 10.5 -55.6

The maintainers digitised the Figure 4 curves at their peak (HDL-C) and nadir (LDL-C). The HDL-C panel is reproduced. The Discussion also states the maximal responses: HDL-C rises to 160-190% of baseline and LDL-C falls by 47-66%.

fig4_digitised <- tibble::tribble(
  ~arm,     ~hdl_peak_fig4, ~ldl_nadir_fig4,
  "50 mg",              80,              72,
  "100 mg",             86,              64,
  "200 mg",             90,              58,
  "400 mg",             97,              51
)

fig4_cmp <- fig4_summary |>
  mutate(arm = as.character(arm)) |>
  inner_join(fig4_digitised, by = "arm") |>
  mutate(
    hdl_peak_sim = 50 * (1 + hdl_peak_pct / 100),
    ldl_nadir_sim = 97.4 * (1 + ldl_nadir_pct / 100),
    hdl_pct_diff = 100 * (hdl_peak_sim / hdl_peak_fig4 - 1),
    ldl_pct_diff = 100 * (ldl_nadir_sim / ldl_nadir_fig4 - 1)
  )

fig4_cmp |>
  select(arm, hdl_peak_sim, hdl_peak_fig4, hdl_pct_diff, ldl_nadir_sim, ldl_nadir_fig4, ldl_pct_diff) |>
  dplyr::rename(
    "Arm" = arm,
    "HDL-C peak, model (mg/dL)" = hdl_peak_sim,
    "HDL-C peak, Figure 4 (mg/dL)" = hdl_peak_fig4,
    "HDL-C difference (%)" = hdl_pct_diff,
    "LDL-C nadir, model (mg/dL)" = ldl_nadir_sim,
    "LDL-C nadir, Figure 4 (mg/dL)" = ldl_nadir_fig4,
    "LDL-C difference (%)" = ldl_pct_diff
  ) |>
  knitr::kable(digits = 1, caption = "Typical-value peaks and nadirs against Figure 4 (digitised).")
Typical-value peaks and nadirs against Figure 4 (digitised).
Arm HDL-C peak, model (mg/dL) HDL-C peak, Figure 4 (mg/dL) HDL-C difference (%) LDL-C nadir, model (mg/dL) LDL-C nadir, Figure 4 (mg/dL) LDL-C difference (%)
50 mg 79.4 80 -0.7 52.0 72 -27.8
100 mg 85.6 86 -0.5 45.6 64 -28.7
200 mg 89.7 90 -0.3 41.7 58 -28.1
400 mg 96.7 97 -0.3 37.0 51 -27.5 

stopifnot(
  # HDL-C peak reproduces Figure 4 (digitised to about +/-2 mg/dL); realised
  # differences are within 1-5%.
  all(abs(fig4_cmp$hdl_pct_diff) < 10),
  # Discussion: maximal HDL-C increase 160-190% of baseline (realised 159-194%).
  all(fig4_cmp$hdl_peak_sim / 50 > 1.50 & fig4_cmp$hdl_peak_sim / 50 < 2.05),
  # Discussion: maximal LDL-C decrease 47-66% (realised 47-62%).
  all(-fig4_cmp$ldl_nadir_pct > 40 & -fig4_cmp$ldl_nadir_pct < 70),
  # Section 3.5: 40% HDL-C increase and 40% LDL-C decrease reached at 200 and 400 mg.
  all(fig4_summary$hdl_peak_pct[fig4_summary$arm %in% c("200 mg", "400 mg")] > 40),
  all(fig4_summary$ldl_nadir_pct[fig4_summary$arm %in% c("200 mg", "400 mg")] < -40),
  # Section 3.5: responses peak after about ten days of dosing at 50-200 mg and
  # then decline, while the 400 mg response is sustained to day 21.
  all(fig4_summary$hdl_peak_day[fig4_summary$arm %in% c("50 mg", "100 mg", "200 mg")] > 6),
  all(fig4_summary$hdl_peak_day[fig4_summary$arm %in% c("50 mg", "100 mg", "200 mg")] < 15),
  with(fig4_summary[fig4_summary$arm == "400 mg", ], hdl_peak_pct - hdl_day21_pct < 2)
)

The LDL-C panel of Figure 4 is not reproduced: its curves sit about 38% above the model’s in every arm, from the nadir to day 20, while starting at the same baseline. The discrepancy is in the source, not the implementation. Figure 4’s LDL-C curves (a 26-47% maximal decrease) contradict the paper’s own Discussion (47-66%), which the model matches. They also contradict the observed LDL-C medians in the Figure 3 VPC (next section), which the model also matches. The HDL-C panel of Figure 4 is driven by the same CETP trajectory and is reproduced. The maintainers tested two alternative readings, and neither recovers the LDL-C panel. Applying the time term (1 + beta T) twice (Table 4 and Equation 8 read literally together) raises the late curve but not the nadir. Replacing the final estimates with the bootstrap medians changes the curves by less than 3 mg/dL.

Figure 3: observed medians

The Figure 3 VPC plots the observed data. The maintainers read the median line of each panel at three landmarks: the HDL-C peak, the LDL-C nadir, and CETP activity at 480 h, a week after the last dose. The typical-value solve of the 14-day study design is compared against them.

fig3_digitised <- tibble::tribble(
  ~arm,     ~hdl_peak, ~ldl_nadir, ~cetp_480,
  "50 mg",         80,         55,       270,
  "100 mg",        82,         55,       230,
  "200 mg",        92,         42,       190,
  "400 mg",        95,         42,       150
)

fig3_sim <- sim_typ |>
  filter(dose_mg > 0) |>
  group_by(arm) |>
  summarise(
    hdl_peak = max(hdl),
    ldl_nadir = min(ldl),
    cetp_480 = cetp[time == 480],
    .groups = "drop"
  ) |>
  mutate(arm = as.character(arm))

fig3_cmp <- fig3_sim |>
  tidyr::pivot_longer(-arm, names_to = "landmark", values_to = "model") |>
  inner_join(
    fig3_digitised |> tidyr::pivot_longer(-arm, names_to = "landmark", values_to = "figure_3"),
    by = c("arm", "landmark")
  ) |>
  mutate(pct_diff = 100 * (model / figure_3 - 1))

fig3_cmp |>
  dplyr::rename(
    "Arm" = arm, "Landmark" = landmark, "Model" = model,
    "Figure 3 median" = figure_3, "Difference (%)" = pct_diff
  ) |>
  knitr::kable(digits = 1, caption = "Typical-value landmarks against the observed medians of Figure 3 (digitised).")
Typical-value landmarks against the observed medians of Figure 3 (digitised).
Arm Landmark Model Figure 3 median Difference (%)
50 mg hdl_peak 79.4 80 -0.7
50 mg ldl_nadir 52.0 55 -5.5
50 mg cetp_480 264.8 270 -1.9
100 mg hdl_peak 85.6 82 4.4
100 mg ldl_nadir 45.6 55 -17.1
100 mg cetp_480 218.8 230 -4.9
200 mg hdl_peak 89.7 92 -2.5
200 mg ldl_nadir 41.7 42 -0.7
200 mg cetp_480 188.6 190 -0.7
400 mg hdl_peak 96.3 95 1.4
400 mg ldl_nadir 37.0 42 -11.9
400 mg cetp_480 139.7 150 -6.9 

stopifnot(
  # Figure 3 medians are read off a small panel (about +/-5 units); realised
  # differences are within 17%. A mis-transcribed EC50, R50 or Kin moves
  # these landmarks by far more.
  all(abs(fig3_cmp$pct_diff) < 25),
  abs(median(fig3_cmp$pct_diff)) < 10
)

PKNCA validation

The paper reports no NCA table for this study. Its Discussion quotes the observed apparent clearance by dose group (11.98 L/h at 50 mg, 30.04 L/h at 200 mg and 23.98 L/h at 400 mg) and a terminal half-life of 145.4-166.2 h. It also states that at 400 mg the AUC after repeated dosing was three times the AUC after the first dose. The NCA below computes the day-1 and day-14 dosing intervals and the terminal half-life after the last dose.

sim_nca <- sim |>
  filter(!is.na(Cc), dose_mg > 0) |>
  select(id, time, Cc, arm) |>
  mutate(arm = droplevels(arm))

dose_df <- events |>
  filter(evid == 1) |>
  select(id, time, amt, arm) |>
  mutate(arm = factor(arm, levels = levels(sim_nca$arm)))

conc_obj <- PKNCA::PKNCAconc(sim_nca, Cc ~ time | arm + id)
dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | arm + id)

intervals <- data.frame(
  start = c(0, 312, 312),
  end = c(24, 336, 504),
  cmax = c(TRUE, TRUE, FALSE),
  tmax = c(TRUE, TRUE, FALSE),
  auclast = c(TRUE, TRUE, FALSE),
  cl.last = c(FALSE, TRUE, FALSE),
  half.life = c(FALSE, FALSE, TRUE)
)

nca_res <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals))

nca_tab <- as.data.frame(nca_res) |>
  filter(PPTESTCD %in% c("cmax", "tmax", "auclast", "cl.last", "half.life")) |>
  mutate(period = case_when(
    start == 0 ~ "day 1",
    end == 336 ~ "day 14",
    TRUE ~ "after last dose"
  )) |>
  # cl.last is Dose / AUC in mg / (ng*h/mL); x 1000 gives L/h.
  mutate(PPORRES = ifelse(PPTESTCD == "cl.last", 1000 * PPORRES, PPORRES)) |>
  group_by(arm, period, PPTESTCD) |>
  summarise(median = median(PPORRES, na.rm = TRUE), .groups = "drop")

nca_tab |>
  mutate(parameter = paste(PPTESTCD, period, sep = ", ")) |>
  select(arm, parameter, median) |>
  tidyr::pivot_wider(names_from = parameter, values_from = median) |>
  dplyr::rename("Arm" = arm) |>
  knitr::kable(digits = 1, caption = "Median simulated NCA parameters (Cc in ng/mL, time in h, AUC in ng*h/mL, CL in L/h).")
Median simulated NCA parameters (Cc in ng/mL, time in h, AUC in ng*h/mL, CL in L/h).
Arm half.life, after last dose tmax, after last dose auclast, day 1 cmax, day 1 tmax, day 1 auclast, day 14 cl.last, day 14 cmax, day 14 tmax, day 14
50 mg 331.3 5 4420.0 729.4 5 3510.5 14.2 438.4 5
100 mg 371.1 5 7903.7 1323.0 5 5750.7 17.4 775.3 5
200 mg 332.1 5 9299.1 1515.7 5 7328.6 27.3 918.3 5
400 mg 288.5 5 11466.8 1992.3 5 15989.6 25.0 2143.6 5

Comparison against published values 

day14 <- as.data.frame(nca_res) |>
  filter(start == 312, end == 336, PPTESTCD == "cl.last")
hl <- as.data.frame(nca_res) |>
  filter(start == 312, end == 504, PPTESTCD == "half.life")

# PKNCA's cl.last uses the day-14 AUC over the dosing interval, so it is the
# steady-state apparent clearance Dose / AUCtau (reported in L/h after the
# unit conversion below: mg / (ng*h/mL) = 1000 L/h).
day14 <- day14 |> mutate(PPORRES = PPORRES * 1000)

published <- tibble::tribble(
  ~arm,     ~cl.last,
  "50 mg",     11.98,
  "200 mg",    30.04,
  "400 mg",    23.98
)

cmp <- nlmixr2lib::ncaComparisonTable(
  simulated = day14 |> filter(arm %in% published$arm),
  reference = published,
  by = "arm",
  units = c(cl.last = "L/h"),
  tolerance_pct = 20
)
#> Warning: ncaParamLabel(): unknown PKNCA code(s) returned as-is: 'cl.last'
knitr::kable(cmp, caption = "Day-14 apparent clearance, simulated vs. Kim 2020 Discussion. * differs by >20%.")
Day-14 apparent clearance, simulated vs. Kim 2020 Discussion. * differs by >20%.
NCA parameter arm Reference Simulated % diff
cl.last (L/h) 50 mg 12 14.2 +18.9%
cl.last (L/h) 200 mg 30 27.3 -9.1%
cl.last (L/h) 400 mg 24 25 +4.3% 
# Typical-value day-1 AUC0-24 and day-14 AUCtau by the trapezoidal rule on the
# hourly grid, and the steady-state CL/F = Dose / AUCtau (L/h).
auc_typ <- function(time, conc, from) {
  i <- time >= from & time <= from + 24
  sum(diff(time[i]) * (head(conc[i], -1) + tail(conc[i], -1)) / 2)
}
typ <- sim_typ |>
  filter(dose_mg > 0) |>
  group_by(arm) |>
  summarise(
    dose = first(dose_mg),
    auc_d1 = auc_typ(time, Cc, 0),
    auc_d14 = auc_typ(time, Cc, 312),
    .groups = "drop"
  ) |>
  mutate(
    arm = as.character(arm),
    cl_ss = 1000 * dose / auc_d14,
    ratio = auc_d14 / auc_d1
  )

cl_typ <- typ |>
  inner_join(published, by = "arm") |>
  mutate(pct_diff = 100 * (cl_ss / cl.last - 1))

typ |>
  select(arm, cl_ss, ratio) |>
  dplyr::rename(
    "Arm" = arm,
    "Day-14 CL/F, typical (L/h)" = cl_ss,
    "AUC ratio, day 14 / day 1" = ratio
  ) |>
  knitr::kable(digits = 2, caption = "Typical-value steady-state CL/F and accumulation ratio.")
Typical-value steady-state CL/F and accumulation ratio.
Arm Day-14 CL/F, typical (L/h) AUC ratio, day 14 / day 1
50 mg 12.99 0.79
100 mg 17.62 0.79
200 mg 26.89 0.79
400 mg 26.28 1.37 

stopifnot(
  # Day-14 CL/F by dose group (typical value, deterministic); realised
  # -10% to +10%. A mis-transcribed CL/F, Bmax, BA50 or alpha1 moves it by far
  # more.
  all(abs(cl_typ$pct_diff) < 25),
  # Section 3.2: exposure falls on repeated dosing at 50-200 mg (realised
  # ratio 0.79) but not at 400 mg (realised 1.37).
  all(typ$ratio[typ$arm != "400 mg"] < 0.9),
  typ$ratio[typ$arm == "400 mg"] > 1.2
)

hl |>
  group_by(arm) |>
  summarise(half_life_h = median(PPORRES, na.rm = TRUE)) |>
  dplyr::rename("Arm" = arm, "Median terminal half-life (h)" = half_life_h) |>
  knitr::kable(digits = 0, caption = "Terminal half-life after the last dose (Discussion: 145.4-166.2 h).")
Terminal half-life after the last dose (Discussion: 145.4-166.2 h).
Arm Median terminal half-life (h)
50 mg 331
100 mg 371
200 mg 332
400 mg 288

Day-14 apparent clearance reproduces the Discussion values. Three exposure figures do not, and the maintainers did not find a reading of the model that explains them:

  • Accumulation at 400 mg. Section 3.2 states that the 400 mg AUC after repeated dosing was three times the first-dose AUC. The final model gives a typical ratio of about 1.4. It does reproduce the direction: exposure falls on repeated dosing at 50-200 mg and rises at 400 mg.
  • Half-life. The simulated terminal half-life after the last dose is about 290-370 h, twice the observed 145.4-166.2 h, over a similar 192 h window. It is set by the slow third compartment (V3/F = 1006 L, Q3/F = 3.3 L/h). The paper does not say how its half-life was estimated.
  • Tmax. The Discussion describes absorption as delayed, with a Tmax of about 1 h. Five sequential compartments at Ktr = 1.10 and Ka = 1.09 1/h give a mean absorption time of about 4.6 h, and the simulated Tmax is 5 h.

Assumptions and deviations

  • Kout, Kdeg(HDL-C) and Kdeg(LDL-C) are derived. The paper does not tabulate the first-order loss constants. They are set so that each turnover state starts at steady state at its tabulated baseline: Kout = Kin,base / CETPbase, Kdeg,HDL = Ksyn / (RB (1 + RES0)) and Kdeg,LDL = Ksyn / (RB (1 - RES0)), where RES0 is the CETP-activity effect (Equation 9) at the baseline CETP activity of 350 pmol. The effect is not zero at baseline, so it has to enter the steady-state balance.
  • The CETP loss term includes the state. Printed Equation 4 writes the loss as Kout x (1 + Drug) without the CETP activity. The text defines Kout as a first-order rate constant and Figure 1 draws it as a loss from the CETP state, so the loss is Kout x (1 + Drug) x CETP.
  • The LDL-C time effect enters once. Table 4 writes Ksy = Ksyn x (1 + beta T) and Equation 8 writes Ksy x (1 + PLA) with PLA = beta x time. Read literally together, the time term would enter twice. Figure 1 labels the LDL-C input Ksyn,base x (1 + beta x T), so the model applies (1 + beta t) once to the tabulated Ksyn.
  • Ksyn units. Table 4 prints the unit of both Ksyn values as ‘h-1’. Both enter Equations 7 and 8 as zero-order production rates, so the model treats them as mg/dL/h.
  • HDL-C proportional error. Table 4 prints the HDL-C proportional residual error as ‘0.0.0001 FIX’. It is read as 0.0001 fixed, the same placeholder as the fixed CKD-519 additive error in Table 2. The LDL-C additive error is 0 fixed and is omitted.
  • Residual error as standard deviations. The sigma rows are read as standard deviations. The paper does not state whether they are variances or SDs. The values (30% proportional for CKD-519, 40.4 pmol additive for CETP activity against a baseline of 350 pmol) are plausible as SDs.
  • Time. TIME in Equation 3 and T in the placebo terms are time since the first dose, so the simulation starts dosing at t = 0. The 400 mg indicator DOSE_HIGH switches alpha to its fixed value of 0, as in Table 2. The paper defines the switch by dose group, so the model is not defined for doses between 200 and 400 mg.
  • Placebo subjects receive no dose. Their DOSE value does not matter because bioavailability never acts; 0 is used.
  • No correction notice for this article was found on the journal page as of 2026-09-26.