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Linagliptin (Tadayasu 2014)

Source: vignettes/articles/Tadayasu_2014_linagliptin.Rmd
Tadayasu_2014_linagliptin.Rmd

Model and source

  • Citation: Tadayasu Y, Sarashina A, Tsuda Y, Tatami S, Friedrich C, Retlich S, Staab A, Takano M. Population pharmacokinetic/pharmacodynamic analysis of the DPP-4 inhibitor linagliptin in Japanese patients with type 2 diabetes mellitus. J Pharm Pharm Sci. 2013;16(5):708-721. doi:10.18433/j3s304.
  • Description: Two-compartment target-mediated drug disposition population PK model for linagliptin with quasi-equilibrium concentration-dependent binding to DPP-4 in both the central and peripheral compartments, coupled with an occupancy-based DPP-4-inhibition pharmacodynamic model (DPP-4 inhibition = Emax * Cbound/BMAX in the central compartment), in Japanese patients with type 2 diabetes mellitus (Tadayasu 2014 Table 3).
  • Article: https://doi.org/10.18433/j3s304

Population

Tadayasu 2014 analysed a single Phase II trial in Japanese patients with type 2 diabetes mellitus (T2DM). 72 patients were randomised to placebo, 0.5 mg, 2.5 mg, or 10 mg linagliptin orally once daily for 28 days; the final population PK/PD model uses only the 2.5 mg and 10 mg arms (18 patients each, n = 36 total), because the 0.5 mg arm violated the quasi-equilibrium assumption (Tadayasu 2014 Methods, Patient population).

Demographics in the modelled cohort (Tadayasu 2014 Methods):

  • Age 40 - 69 years (mean 60.2 in 2.5 mg arm, 59.1 in 10 mg arm).
  • Body mass index 18.4 - 34.4 kg/m^2 (mean 26.0 in 2.5 mg arm, 23.8 in 10 mg arm).
  • 25 % female (only 9 of the 36 patients).
  • 100 % Japanese.
  • Baseline fasting plasma glucose 154.7 +/- 25.1 mg/dL (2.5 mg arm) and 158.4 +/- 28.6 mg/dL (10 mg arm); baseline HbA1c 7.1 +/- 0.5 % and 7.2 +/- 0.9 % respectively.
  • Individual antidiabetic treatment discontinued 14 days prior to the first drug administration.

The model is fit to 498 + 520 = 1018 plasma concentrations and 520 + 538 = 1058 DPP-4 inhibition observations after exclusion of 9 records with protocol violations (Tadayasu 2014 Table 2).

The same metadata are available programmatically via readModelDb("Tadayasu_2014_linagliptin")$population.

Source trace

Every ini() parameter in inst/modeldb/specificDrugs/Tadayasu_2014_linagliptin.R carries an inline source-trace comment. The table below collects them in one place for review; numeric values are reproduced verbatim from Tadayasu 2014 Table 3.

Equation / parameter Value Source location
2-cmt TMDD-QE structural ODE n/a Tadayasu 2014 Figure 1 (model schematic)
QE binding (central + peripheral) n/a Tadayasu 2014 Methods, Pharmacokinetic model
Occupancy PD: DPP-4 inh = Emax * Cb/BMAX n/a Tadayasu 2014 Methods, Pharmacokinetic/Pharmacodynamic model
lfdepot (F1 fixed = 1) 1 (fixed) Table 3 row F1
lka (KA) 1.63 1/h Table 3 row KA
lcl (CL/F1) 121 L/h Table 3 row CL/F1
lvc (V2/F1) 633 L Table 3 row V2/F1
lq (Q3/F1) 73.0 L/h Table 3 row Q3/F1
lvp (V3/F1) 683 L Table 3 row V3/F1
lbmax (BMAX, central) 6.07 nmol/L Table 3 row BMAX
lkd (KD) 0.108 nmol/L Table 3 row KD
lamax2 (AMAX2/F1, peripheral) 534 nmol Table 3 row AMAX2/F1
emax (Emax fraction) 0.925 Table 3 row EMAX (92.5 %)
IIV F1 (CV 46.7 %) omega^2 = 0.19727 Table 3 row ‘IIV in F1’
IIV KA (CV 73.6 %) omega^2 = 0.43288 Table 3 row ‘IIV in KA’
IIV CL (CV 68.8 %) omega^2 = 0.38754 Table 3 row ‘IIV in CL’
IIV BMAX (CV 14.2 %) omega^2 = 0.01996 Table 3 row ‘IIV in BMAX’
OMEGA matrix diagonal Tadayasu 2014 Results, Pharmacokinetic model (BMAX-CL block tested but not retained)
PK proportional residual (CV 27.0 %) propSd = 0.270 Table 3 row ‘Proportional residual variability PK’
PD residual Y = Y_hat + (100 - Y_hat) * eps propSd_Dpp4Act = 0.201 Table 3 row ‘Proportional residual variability PD’

Virtual cohort

Original observed concentrations were not released. The simulations below use small virtual cohorts whose dose levels match the published 5 mg, 2.5 mg, and 10 mg arms (the 5 mg arm is the simulation that supported the dose-selection conclusion of the paper).

set.seed(20260520)

n_per_arm <- 60L

make_arm <- function(arm_label, dose_mg, id_offset) {
  dose_times <- seq(0, by = 24, length.out = 28)              # 28-day QD regimen
  ss_obs <- 27 * 24 + c(0, 0.5, 1, 1.5, 2, 3, 4, 6, 8, 10, 12, 16, 20, 24)
  obs_times <- sort(unique(c(
    seq(0, 27 * 24, by = 6),                                  # coarse pre-SS sampling
    ss_obs                                                    # dense day-28 SS profile
  )))
  id_seq <- id_offset + seq_len(n_per_arm)
  dose_rows <- expand.grid(id = id_seq, time = dose_times) |>
    dplyr::mutate(evid = 1L, amt = dose_mg, cmt = "depot")
  obs_rows  <- expand.grid(id = id_seq, time = obs_times) |>
    dplyr::mutate(evid = 0L, amt = 0, cmt = "Cc")
  dplyr::bind_rows(dose_rows, obs_rows) |>
    dplyr::mutate(cohort = arm_label, DOSE = dose_mg) |>
    dplyr::arrange(id, time, dplyr::desc(evid))
}

events <- dplyr::bind_rows(
  make_arm("2.5 mg QD", dose_mg = 2.5, id_offset =   0L),
  make_arm("5 mg QD",   dose_mg = 5,   id_offset = 200L),
  make_arm("10 mg QD",  dose_mg = 10,  id_offset = 400L)
)

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

Simulation 

mod <- readModelDb("Tadayasu_2014_linagliptin")
sim <- rxode2::rxSolve(
  mod,
  events = events,
  keep   = c("cohort", "DOSE")
) |>
  as.data.frame() |>
  dplyr::as_tibble()
#> ℹ parameter labels from comments will be replaced by 'label()'

For deterministic typical-value replication of the per-arm steady-state profile (no between-subject variability), zero out the random effects:

mod_typical <- mod |> rxode2::zeroRe()
#> ℹ parameter labels from comments will be replaced by 'label()'
typical_events <- events |> dplyr::filter(id %in% c(1L, 201L, 401L))
sim_typical <- rxode2::rxSolve(
  mod_typical,
  events = typical_events,
  keep   = c("cohort", "DOSE")
) |>
  as.data.frame() |>
  dplyr::as_tibble()
#> ℹ omega/sigma items treated as zero: 'etalfdepot', 'etalka', 'etalcl', 'etalbmax'
#> Warning: multi-subject simulation without without 'omega'

Replicate published figures

Figure 4 – predicted steady-state DPP-4 inhibition

Figure 4 of Tadayasu 2014 shows the predicted steady-state DPP-4 inhibition time profile for 2.5 mg, 5 mg, and 10 mg linagliptin once daily, with the 80 % inhibition target marked in red. The simulation here replicates the median trajectory plus 90 % prediction interval over a single day-28 dosing interval.

fig4 <- sim |>
  dplyr::filter(time >= 27 * 24, time <= 28 * 24) |>
  dplyr::mutate(time_h = time - 27 * 24) |>
  dplyr::group_by(cohort, time_h) |>
  dplyr::summarise(
    Q05 = quantile(Dpp4Inh, 0.05, na.rm = TRUE),
    Q50 = quantile(Dpp4Inh, 0.50, na.rm = TRUE),
    Q95 = quantile(Dpp4Inh, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(fig4, aes(time_h, Q50, colour = cohort, fill = cohort)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.2, colour = NA) +
  geom_line(linewidth = 0.7) +
  geom_hline(yintercept = 80, colour = "red", linetype = "dashed") +
  coord_cartesian(ylim = c(0, 100)) +
  labs(
    x = "Time after last dose (h)",
    y = "DPP-4 inhibition (%)",
    title = "Figure 4 -- Predicted steady-state DPP-4 inhibition",
    caption = "Replicates Figure 4 of Tadayasu 2014. Solid line = median, ribbon = 90 % PI; red dashed line = 80 % target."
  )

Figure 3A – linagliptin steady-state concentration VPC

Figure 3A of the paper shows a VPC of linagliptin plasma concentrations on day 28; this chunk replicates the 2.5 mg and 10 mg arms (the two arms used in fitting).

fig3a <- sim |>
  dplyr::filter(time >= 27 * 24, time <= 28 * 24, cohort %in% c("2.5 mg QD", "10 mg QD")) |>
  dplyr::mutate(time_h = time - 27 * 24) |>
  dplyr::group_by(cohort, time_h) |>
  dplyr::summarise(
    Q05 = quantile(Cc, 0.05, na.rm = TRUE),
    Q50 = quantile(Cc, 0.50, na.rm = TRUE),
    Q95 = quantile(Cc, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(fig3a, aes(time_h, Q50, colour = cohort, fill = cohort)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.2, colour = NA) +
  geom_line(linewidth = 0.7) +
  scale_y_log10() +
  labs(
    x = "Time after last dose (h)",
    y = "Linagliptin Cc (ng/mL, log scale)",
    title = "Figure 3A -- Linagliptin Cc VPC at steady state",
    caption = "Replicates Figure 3A of Tadayasu 2014 (2.5 mg and 10 mg arms only). Solid line = median, ribbon = 90 % PI."
  )

Reproducing published E24,ss values

The simulation paper reports median predicted DPP-4 inhibition 24 h after the last steady-state dose (E24,ss): 79.2 % (2.5 mg), 84.2 % (5 mg), and 87.7 % (10 mg). The typical-value chunk below reproduces these directly.

e24 <- sim_typical |>
  dplyr::filter(round(time, 1) == 28 * 24) |>
  dplyr::select(cohort, DOSE, Cc_ng_mL = Cc, Dpp4Inh) |>
  dplyr::mutate(
    paper_E24ss = dplyr::case_when(
      DOSE == 2.5 ~ 79.2,
      DOSE == 5   ~ 84.2,
      DOSE == 10  ~ 87.7
    ),
    abs_diff_pct = round(Dpp4Inh - paper_E24ss, 2)
  )
knitr::kable(
  e24,
  digits   = 2,
  caption  = "Typical-value E24,ss vs Tadayasu 2014 Simulation Results."
)
Typical-value E24,ss vs Tadayasu 2014 Simulation Results.
cohort DOSE Cc_ng_mL Dpp4Inh paper_E24ss abs_diff_pct
2.5 mg QD 2.5 2.73 78.73 79.2 -0.47
5 mg QD 5.0 3.11 84.00 84.2 -0.20
10 mg QD 10.0 3.67 87.76 87.7 0.06

PKNCA validation

PKNCA-derived steady-state Cmax, Tmax, AUCtau, and half-life from the day-28 simulated dosing interval. The treatment grouping | cohort + id keeps per-dose-group rollups available for comparison.

# Day-28 (steady-state) interval: only the 24 h after the last dose are kept
sim_nca <- sim |>
  dplyr::filter(time >= 27 * 24, time <= 28 * 24, !is.na(Cc)) |>
  dplyr::mutate(time = time - 27 * 24) |>
  dplyr::select(id, time, Cc, cohort)

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

# Dose rows: only the steady-state dose at the start of the chosen interval
dose_df <- events |>
  dplyr::filter(evid == 1L, time == 27 * 24) |>
  dplyr::mutate(time = 0) |>
  dplyr::select(id, time, amt, cohort)

dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | cohort + id)

intervals <- data.frame(
  start          = 0,
  end            = 24,
  cmax           = TRUE,
  tmax           = TRUE,
  auclast        = TRUE,
  half.life      = TRUE
)

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

nca_summary <- summary(nca_res)
knitr::kable(
  nca_summary,
  caption = "Simulated steady-state NCA parameters by dose group (day 28 dosing interval)."
)
Simulated steady-state NCA parameters by dose group (day 28 dosing interval).
start end cohort N auclast cmax tmax half.life
0 24 10 mg QD 60 153 [43.8] 14.8 [45.6] 1.50 [0.500, 3.00] 35.1 [7.41]
0 24 2.5 mg QD 60 79.4 [28.9] 5.28 [27.1] 1.50 [0.500, 3.00] 55.1 [13.2]
0 24 5 mg QD 60 114 [39.0] 8.65 [37.7] 1.50 [0.500, 3.00] 47.7 [9.01]

PD-side validation – DPP-4 activity NCA

PKNCA is set up here on the DPP-4 activity output (= 100 - inhibition) as a sanity check that the per-arm activity profile remains low and is dose-ordered.

sim_pd <- sim |>
  dplyr::filter(time >= 27 * 24, time <= 28 * 24, !is.na(Dpp4Act)) |>
  dplyr::mutate(time = time - 27 * 24) |>
  dplyr::select(id, time, Dpp4Act, cohort)

conc_pd <- PKNCA::PKNCAconc(sim_pd, Dpp4Act ~ time | cohort + id)
nca_pd  <- PKNCA::PKNCAdata(conc_pd, dose_obj, intervals = data.frame(
  start = 0, end = 24, auclast = TRUE
))
suppressWarnings({
  nca_pd_res <- PKNCA::pk.nca(nca_pd)
})
knitr::kable(
  summary(nca_pd_res),
  caption = "Simulated AUC of DPP-4 activity over the day-28 dosing interval (lower AUC = more inhibition)."
)
Simulated AUC of DPP-4 activity over the day-28 dosing interval (lower AUC = more inhibition).
start end cohort N auclast
0 24 10 mg QD 60 264 [30.3]
0 24 2.5 mg QD 60 424 [40.8]
0 24 5 mg QD 60 305 [36.6]

Assumptions and deviations

  • Custom PD residual encoded as proportional error on DPP-4 activity. The paper’s residual model on DPP-4 inhibition is Y = Y_hat + (100 - Y_hat) * eps with eps ~ N(0, sigma^2). For a symmetric Gaussian residual this is algebraically identical to a proportional residual on DPP-4 activity (= 100 - inhibition), since 100 - Y = (100 - Y_hat) * (1 - eps). The model file therefore exposes Dpp4Act as the residual-bearing output with Dpp4Act ~ prop(propSd_Dpp4Act), and emits Dpp4Inh = 100 - Dpp4Act as a derived quantity. Users with DPP-4 inhibition data should convert to activity (activity = 100 - inhibition) before fitting.
  • Concentration unit conversion (nmol/L -> ng/mL). Tadayasu 2014 reports linagliptin concentrations, BMAX, KD, and AMAX2 in nmol/L (or nmol). Doses are clinical (2.5, 5, 10 mg). The model uses nmol/L internally so the published parameters can be used verbatim, but converts the Cc output to ng/mL via the linagliptin molecular weight 472.54 g/mol so the observation unit is dimensionally consistent with the mg dose. The conversion is Cc_ng_mL = Cc_nmolL * MW / 1000. The same pattern is used in the companion non-Japanese Retlich_2015_linagliptin model.
  • 0.5 mg arm excluded. The paper drops the 0.5 mg arm because the quasi-equilibrium assumption fails when free linagliptin concentrations drop below BMAX (Tadayasu 2014 Discussion, Pharmacokinetics). The packaged model inherits this scope. Simulating sub-2.5 mg doses with this model is outside the validated range; the predictions will be biased because the TMDD-QE assumption no longer holds.
  • OMEGA matrix is diagonal. The paper tested a BMAX-CL OMEGA block with R = 0.837 but did not retain it in the final model because it overestimated the variability (Tadayasu 2014 Results, Pharmacokinetic model). The packaged model follows the final-model choice.
  • No subject-level covariates. The paper does not report covariate effects on any structural parameter (the Japanese cohort was demographically narrow: 100 % Japanese, 75 % male, age 40 - 69, controlled T2DM). The packaged covariateData is therefore empty.
  • Simulation scope. The packaged model is suitable for simulating Japanese T2DM patients at doses 2.5 - 10 mg linagliptin PO once daily. Extrapolation to other ethnicities, doses < 2.5 mg, paediatric patients, or patients with renal or hepatic impairment is not supported by the source data; see Retlich_2015_linagliptin for the broader Caucasian / multi-region popPK/PD model with covariate effects.