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Finerenone (van den Berg 2021)

Source: vignettes/articles/vandenBerg_2021_finerenone.Rmd
vandenBerg_2021_finerenone.Rmd

Model and source

  • Citation: van den Berg P, Ruppert M, Mesic E, Snelder N, Seelmann A, Heinig R, Joseph A, Garmann D, Lippert J, Eissing T (2022). Finerenone Dose-Exposure-Response for the Primary Kidney Outcome in FIDELIO-DKD Phase III: Population Pharmacokinetic and Time-to-Event Analysis. Clin Pharmacokinet 61(7):943-955. doi:10.1007/s40262-021-01082-2
  • Article: https://doi.org/10.1007/s40262-021-01082-2

Population

van den Berg et al. 2021 developed the population PK model of oral finerenone on data from the FIDELIO-DKD Phase III trial (NCT02540993): a randomised, double-blind, placebo-controlled, international study of finerenone (10 or 20 mg once daily, titrated by potassium and eGFR) versus placebo on top of maximally tolerated renin-angiotensin system inhibitor in patients with chronic kidney disease and type 2 diabetes. The popPK analysis cohort contained 2284 subjects contributing 5057 valid sparse PK observations (trough at month 4, post-dose at any time on yearly visits). The cohort median (5th-95th percentile) baseline eGFR was 43.0 (26.7-66.9) mL/min/1.73 m^2 and median UACR was 852 (140-3366) mg/g.

The structural model is two-compartment with the peripheral volume fixed equal to the central volume (Vp/F = Vc/F, ratio fixed at 1, per ESM ‘Volume of Distribution’ subsection), preceded by an absorption chain of four sequential first-order steps (the depot plus three buffer compartments) all at the common rate Ka = 22.5 1/h and a fixed 0.215 h absorption lag time. The ARTS-DN Phase IIb model [Snelder 2020] was used as the starting point; the FIDELIO-DKD analysis re-estimated the structural parameters and dropped the inter-individual variability on Ka (Results paragraph 2: “the inter-individual variability parameter on the absorption rate was dropped as data were not sufficiently informative”).

The same information is available programmatically:

rxode2::rxode2(readModelDb("vandenBerg_2021_finerenone"))$population
#> ℹ parameter labels from comments will be replaced by 'label()'
#> $species
#> [1] "human"
#> 
#> $n_subjects
#> [1] 2284
#> 
#> $n_studies
#> [1] 1
#> 
#> $n_observations
#> [1] 5057
#> 
#> $disease_state
#> [1] "chronic kidney disease and type 2 diabetes mellitus (FIDELIO-DKD eligibility: eGFR 25 to <75 mL/min/1.73 m^2 with persistent moderately or severely elevated albuminuria, on maximally tolerated renin-angiotensin system inhibitor)"
#> 
#> $dose_range
#> [1] "10 or 20 mg finerenone QD oral (starting dose 10 mg if eGFR <60, 20 mg if eGFR >=60; up- or down-titrated by potassium / eGFR), average 15.1 mg/day across follow-up"
#> 
#> $follow_up
#> [1] "median 2.6 years"
#> 
#> $egfr_range
#> [1] "median (5th-95th) 43.0 (26.7-66.9) mL/min/1.73 m^2 at baseline (FIDELIO-DKD population)"
#> 
#> $uacr_range
#> [1] "median (5th-95th) 852 (140-3366) mg/g at baseline (FIDELIO-DKD population)"
#> 
#> $reference_weight
#> [1] "85 kg (cohort median, used as ref for WT power-form on Vc/F)"
#> 
#> $reference_height
#> [1] "167 cm (cohort median, used as ref for HT power-form on CL/F and F)"
#> 
#> $reference_creatinine
#> [1] "1.51 mg/dL (cohort median, used as ref for CREAT power-form on CL/F and F)"
#> 
#> $reference_egfr
#> [1] "39.1 mL/min/1.73 m^2 (cohort median time-varying value, used as ref for CRCL power-form on CL/F and F)"
#> 
#> $reference_ggt
#> [1] "25 U/L (cohort median, used as ref for GGT power-form on CL/F)"
#> 
#> $sampling_design
#> [1] "sparse: trough at month 4, post-dose at any time on yearly visit days"
#> 
#> $regions
#> [1] "international (FIDELIO-DKD enrolled in North America, EU, Latin America, and Asia-Pacific)"
#> 
#> $notes
#> [1] "Population is the FIDELIO-DKD per-protocol Phase III analysis set (5734 randomized total, 5674 valid for analysis, 2833 on finerenone of whom 2284 had at least one valid PK sample after outlier exclusions; see Results 'Clinical Study' and 'Population PK Modeling and Simulation' paragraphs). Demographic ranges (age, sex, race percentages) not separately reported in the popPK section; see Bakris et al. 2020 NEJM 383:2219-2229 (the main FIDELIO-DKD efficacy publication) for full Table 1 baseline demographics."

Source trace

Per-parameter origin (also recorded as in-file comments next to each ini() value):

Parameter Value Source location
Ka 22.5 1/h Table 2 “Ka (1/h) = 22.5 (RSE 16.2%)”
CL/F 29.9 L/h Table 2 “CL/F (L/h) = 29.9 (RSE 3.62%)”
Vc/F 113 L Table 2 “Vc/F (L) = 113 (RSE 2.79%)”
Q/F 0.335 L/h Table 2 “Q/F (L/h) = 0.335 (RSE 9.28%)”
Vp/F : Vc/F 1 fixed Table 2 “Ratio Vp/F and Vc/F = 1 (fixed)”
ALAG1 0.215 h fixed Table 2 “Absorption lag time (h) = 0.215 (fixed)”
F1 (rel. bio) 1 fixed Table 2 “Relative bioavailability = 1 (fixed)”
e_wt_vc 0.501 Table 2 row 8
e_egfr_clf 0.155 Table 2 row 9
e_ht_clf 0.720 Table 2 row 10
e_creat_clf 0.118 Table 2 row 11
e_korean_vc log(1.29) Table 2 row 12
e_sglt_clf log(1.10) Table 2 row 13
e_smoke_clf log(1.04) Table 2 row 14
e_ggt_clf -0.0694 Table 2 row 15 (CL/F only)
e_cypinhi_clf log(0.951) Table 2 row 16
e_cypinlo_clf log(0.996) Table 2 row 17
omega^2 CL/F 0.0961 Table 2 IIV “omega^2 CL/F = 0.0961”
omega^2 Vc/F 0.104 Table 2 IIV “omega^2 Vc/F = 0.104”
cov(CL/F, Vc/F) 0.0442 Table 2 “Covariance CL/F x Vc/F = 0.0442”
sigma^2 (prop) 0.313 Table 2 residual “sigma^2 = 0.313”; propSd = sqrt()
ref WT 85 kg ESM NONMEM “CV1 = (BW0/85)**THETA(9)”
ref CRCL 39.1 mL/min/1.73 m^2 ESM NONMEM “CV2 = (EGFREP/39.1)**THETA(10)”
ref HT 167 cm ESM NONMEM “CV3 = (HGHT/167)**THETA(11)”
ref CREAT 1.51 mg/dL ESM NONMEM “CV4 = (CREA/1.51)**THETA(12)”
ref GGT 25 U/L ESM NONMEM “CV5 = (GGT/25)**THETA(16)”

Load and inspect the model 

mod <- rxode2::rxode2(readModelDb("vandenBerg_2021_finerenone"))
#> ℹ parameter labels from comments will be replaced by 'label()'
mod_typical <- rxode2::zeroRe(mod)

Typical-value simulation: 10 mg and 20 mg QD to steady state

Simulate a reference adult subject at cohort-median covariates: WT 85 kg, HT 167 cm, CRCL 39.1 mL/min/1.73 m^2, CREAT 1.51 mg/dL, GGT 25 U/L, never-smoker (SMOKE_NEVER = 1), no concomitant SGLT2i and no CYP3A4 inhibitors, non-Korean. Compare 10 mg QD and 20 mg QD oral, 24 h dosing interval, to day 8 (steady state is effectively reached after the second dose given the 2.7 h half-life).

sim_one_dose <- function(dose_mg) {
  ev <- rxode2::et(amt = dose_mg, time = 0:6 * 24, cmt = "depot") |>
    rxode2::et(seq(0, 8 * 24, by = 0.25))
  ev_df <- as.data.frame(ev)
  ev_df$WT <- 85
  ev_df$HT <- 167
  ev_df$CRCL <- 39.1
  ev_df$CREAT <- 1.51
  ev_df$GGT <- 25
  ev_df$SMOKE_NEVER <- 1
  ev_df$CONMED_SGLT2I <- 0
  ev_df$CONMED_CYP3A4_INH_HI <- 0
  ev_df$CONMED_CYP3A4_INH_LO <- 0
  ev_df$RACE_KOREAN <- 0
  out <- rxode2::rxSolve(mod_typical, events = ev_df)
  as.data.frame(out) |>
    dplyr::mutate(dose_mg = dose_mg)
}

sim_typical <- dplyr::bind_rows(sim_one_dose(10), sim_one_dose(20))
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc'
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc'
ggplot(sim_typical, aes(x = time / 24, y = Cc, colour = factor(dose_mg))) +
  geom_line() +
  scale_x_continuous(breaks = 0:8) +
  scale_y_continuous(expand = expansion(mult = c(0, 0.05))) +
  labs(
    x      = "Time (days)",
    y      = expression(paste("Finerenone plasma concentration (", mu, "g/L)")),
    colour = "Dose (mg QD)",
    title  = "Typical-value concentration-time profile, 10 mg vs 20 mg QD"
  ) +
  theme_bw()

The 2.7 h dominant half-life (paper Results: “the relevant half-life for steady-state exposure and accumulation t1/2_alpha was estimated at 2.7 h”) causes deep troughs and supports the paper’s statement that “near steady-state conditions are reached after the second dose of finerenone.”

Virtual stochastic cohort and prediction-corrected check

Build a small virtual cohort of N = 100 subjects with covariates drawn to approximate the FIDELIO-DKD cohort and simulate full inter-individual variability for a sense of the prediction interval.

set.seed(2021)
n_subj <- 100
pop <- tibble::tibble(
  id    = seq_len(n_subj),
  WT    = pmax(45, rnorm(n_subj, mean = 85,   sd = 17)),
  HT    = pmax(140, rnorm(n_subj, mean = 167, sd = 9)),
  CRCL  = pmax(15, rnorm(n_subj, mean = 43.0, sd = 12.5)),
  CREAT = pmax(0.7, rnorm(n_subj, mean = 1.51, sd = 0.4)),
  GGT   = pmax(8,  exp(rnorm(n_subj, mean = log(25), sd = 0.5))),
  SMOKE_NEVER         = rbinom(n_subj, 1, 0.55),
  CONMED_SGLT2I       = rbinom(n_subj, 1, 0.05),
  CONMED_CYP3A4_INH_HI = rbinom(n_subj, 1, 0.06),
  CONMED_CYP3A4_INH_LO = rbinom(n_subj, 1, 0.10),
  RACE_KOREAN          = rbinom(n_subj, 1, 0.024)
)
# Mutually exclusive CYP3A4 inhibitor categories
pop$CONMED_CYP3A4_INH_LO[pop$CONMED_CYP3A4_INH_HI == 1] <- 0L

dose_mg <- 20
ev_pop_template <- as.data.frame(
  rxode2::et(amt = dose_mg, time = 0:6 * 24, cmt = "depot") |>
    rxode2::et(seq(0, 8 * 24, by = 1))
)

build_events <- function(p) {
  e <- ev_pop_template
  e$id   <- p$id
  e$WT   <- p$WT
  e$HT   <- p$HT
  e$CRCL <- p$CRCL
  e$CREAT <- p$CREAT
  e$GGT  <- p$GGT
  e$SMOKE_NEVER         <- p$SMOKE_NEVER
  e$CONMED_SGLT2I       <- p$CONMED_SGLT2I
  e$CONMED_CYP3A4_INH_HI <- p$CONMED_CYP3A4_INH_HI
  e$CONMED_CYP3A4_INH_LO <- p$CONMED_CYP3A4_INH_LO
  e$RACE_KOREAN          <- p$RACE_KOREAN
  e
}

ev_all <- dplyr::bind_rows(lapply(seq_len(n_subj), function(i) build_events(pop[i, ])))
sim_cohort <- rxode2::rxSolve(mod, events = ev_all) |>
  as.data.frame()
sim_summ <- sim_cohort |>
  dplyr::filter(time > 0) |>
  dplyr::group_by(time) |>
  dplyr::summarise(
    p05 = quantile(Cc, 0.05, na.rm = TRUE),
    p50 = quantile(Cc, 0.50, na.rm = TRUE),
    p95 = quantile(Cc, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(sim_summ, aes(x = time / 24)) +
  geom_ribbon(aes(ymin = p05, ymax = p95), alpha = 0.2, fill = "steelblue") +
  geom_line(aes(y = p50), colour = "steelblue", linewidth = 0.6) +
  scale_x_continuous(breaks = 0:8) +
  labs(
    x      = "Time (days)",
    y      = expression(paste("Finerenone (", mu, "g/L)")),
    title  = "Virtual cohort: median and 90% prediction interval, 20 mg QD"
  ) +
  theme_bw()

PKNCA validation against the AUC = F * Dose / CL identity

The source paper does not report an NCA table; the natural anchor for PKNCA-vs-model comparison is the algebraic steady-state identity AUC0-tau,ss = F * Dose / CL = Dose / CL (because F = 1 fixed). At typical-value reference covariates with CL/F = 29.9 L/h, the expected AUCs are:

  • 10 mg QD: AUC0-tau,ss = 10 mg / 29.9 L/h = 0.3344 mgh/L = 334.4 ugh/L; Cavg,ss = 334.4 / 24 = 13.9 ug/L
  • 20 mg QD: AUC0-tau,ss = 20 mg / 29.9 L/h = 0.6689 mgh/L = 668.9 ugh/L; Cavg,ss = 668.9 / 24 = 27.9 ug/L

Run PKNCA on the steady-state day-7 dosing interval (t = 144-168 h) of the typical-value simulation, for both 10 mg and 20 mg, and compare to the expectations above.

ss_start <- 144  # day 6 start (the dose interval is 144 -> 168)
ss_end   <- 168  # day 7 start

ss_obs <- sim_typical |>
  dplyr::mutate(id = 1L) |>  # one virtual subject per dose level (typical value)
  dplyr::filter(!is.na(Cc), time >= ss_start, time <= ss_end) |>
  dplyr::mutate(
    tad       = time - ss_start,
    treatment = paste0(dose_mg, " mg QD")
  ) |>
  dplyr::select(id, time = tad, Cc, treatment)

# Defensive time-zero per (id, treatment) so PKNCA does not warn about
# "AUC range starting (0) before the first measurement". The typical-value
# simulation grid hits t = 144 h exactly, so this is usually a no-op, but
# the safety net keeps things robust if the grid changes.
ss_nca <- dplyr::bind_rows(
  ss_obs,
  ss_obs |> dplyr::distinct(id, treatment) |>
    dplyr::mutate(time = 0, Cc = 0)
) |>
  dplyr::distinct(id, treatment, time, .keep_all = TRUE) |>
  dplyr::arrange(id, treatment, time)

ss_dose <- dplyr::tibble(
  id        = 1L,
  time      = 0,
  amt       = c(10, 20),
  treatment = c("10 mg QD", "20 mg QD")
)

conc_obj <- PKNCA::PKNCAconc(
  ss_nca, Cc ~ time | treatment + id,
  concu = "ug/L", timeu = "h"
)
dose_obj <- PKNCA::PKNCAdose(
  ss_dose, amt ~ time | treatment + id,
  doseu = "mg", route = "extravascular"
)

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

nca_data <- PKNCA::PKNCAdata(conc_obj, dose_obj, intervals = intervals)
nca_res  <- suppressWarnings(PKNCA::pk.nca(nca_data))
published <- tibble::tribble(
  ~treatment,    ~auclast, ~cav,
  "10 mg QD",      334.4,  13.94,
  "20 mg QD",      668.9,  27.87
)

cmp <- nlmixr2lib::ncaComparisonTable(
  simulated = nca_res,
  reference = published,
  by        = "treatment",
  units     = c(auclast = "ug*h/L", cav = "ug/L"),
  tolerance_pct = 5
)

knitr::kable(
  cmp,
  caption = paste(
    "Simulated PKNCA (steady-state, day-7 dosing interval) vs analytic",
    "F * Dose / CL identity, typical-value reference covariates. The",
    "model's exposure scales linearly with dose, and the simulated AUC",
    "and Cavg should match the F * Dose / CL identity within rxode2",
    "numerical-integration tolerance (the PKNCA log-trapezoidal AUC adds",
    "a small bias relative to the analytic value)."
  ),
  align = c("l", "l", "r", "r", "r")
)
Simulated PKNCA (steady-state, day-7 dosing interval) vs analytic F * Dose / CL identity, typical-value reference covariates. The model’s exposure scales linearly with dose, and the simulated AUC and Cavg should match the F * Dose / CL identity within rxode2 numerical-integration tolerance (the PKNCA log-trapezoidal AUC adds a small bias relative to the analytic value).
NCA parameter treatment Reference Simulated % diff
AUClast (ug*h/L) 10 mg QD 334 331 -1.0%
AUClast (ug*h/L) 20 mg QD 669 662 -1.0%
Cavg (ug/L) 10 mg QD 13.9 13.8 -1.0%
Cavg (ug/L) 20 mg QD 27.9 27.6 -1.0%

Covariate effect on steady-state AUC: comparison against paper forest plot

Each shared covariate in the paper’s NONMEM parameterisation acts on both CL/F (multiplicatively) and F1 (inversely), so the net effect on steady-state AUC scales as 1 / cov_factor^2. Reproduce a subset of the paper’s Fig. 3 forest plot rows by simulating typical-value AUC ratios relative to the reference subject.

ref_state <- list(WT = 85, HT = 167, CRCL = 39.1, CREAT = 1.51, GGT = 25,
                  SMOKE_NEVER = 1, CONMED_SGLT2I = 0,
                  CONMED_CYP3A4_INH_HI = 0, CONMED_CYP3A4_INH_LO = 0,
                  RACE_KOREAN = 0)

scenarios <- list(
  list(label = "Reference (median covariates, never smoker)", overrides = list()),
  list(label = "WT 5th pctile (62 kg)",   overrides = list(WT = 62)),
  list(label = "WT 95th pctile (115 kg)", overrides = list(WT = 115)),
  list(label = "CRCL 5th pctile (26.7)",  overrides = list(CRCL = 26.7)),
  list(label = "CRCL 95th pctile (66.9)", overrides = list(CRCL = 66.9)),
  list(label = "Korean",                  overrides = list(RACE_KOREAN = 1)),
  list(label = "Long-term SGLT2i",        overrides = list(CONMED_SGLT2I = 1)),
  list(label = "Ever smoker",             overrides = list(SMOKE_NEVER = 0)),
  list(label = "CYP3A4 inh HI",           overrides = list(CONMED_CYP3A4_INH_HI = 1))
)

auc_for <- function(state) {
  ev <- as.data.frame(
    rxode2::et(amt = 20, time = 0:6 * 24, cmt = "depot") |>
      rxode2::et(seq(0, 8 * 24, by = 0.5))
  )
  for (nm in names(state)) ev[[nm]] <- state[[nm]]
  out <- as.data.frame(rxode2::rxSolve(mod_typical, events = ev))
  ss <- out[out$time >= 144 & out$time <= 168, ]
  sum(diff(ss$time) * (utils::head(ss$Cc, -1) + utils::tail(ss$Cc, -1)) / 2,
      na.rm = TRUE)
}

ref_auc <- auc_for(ref_state)
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc'
results <- dplyr::bind_rows(lapply(scenarios, function(s) {
  state <- ref_state
  for (nm in names(s$overrides)) state[[nm]] <- s$overrides[[nm]]
  data.frame(scenario = s$label, auc = auc_for(state))
}))
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc'
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc'
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc'
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc'
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc'
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc'
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc'
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc'
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalvc'
results$auc_ratio <- results$auc / ref_auc

knitr::kable(
  results,
  digits = c(0, 1, 3),
  col.names = c("Scenario", "AUC0-tau,ss (ug*h/L)", "Ratio vs reference"),
  caption = paste(
    "Steady-state AUC by covariate scenario, 20 mg QD, typical-value",
    "simulation. Compare ratios qualitatively against the paper's",
    "Figure 3 forest plot (all covariate effects in the published",
    "model fell within or close to the 0.8-1.25 equivalence range)."
  )
)
Steady-state AUC by covariate scenario, 20 mg QD, typical-value simulation. Compare ratios qualitatively against the paper’s Figure 3 forest plot (all covariate effects in the published model fell within or close to the 0.8-1.25 equivalence range).
Scenario AUC0-tau,ss (ug*h/L) Ratio vs reference
Reference (median covariates, never smoker) 679.1 1.000
WT 5th pctile (62 kg) 682.0 1.004
WT 95th pctile (115 kg) 676.7 0.996
CRCL 5th pctile (26.7) 763.0 1.124
CRCL 95th pctile (66.9) 576.3 0.849
Korean 675.2 0.994
Long-term SGLT2i 562.8 0.829
Ever smoker 628.6 0.926
CYP3A4 inh HI 749.8 1.104

Assumptions and deviations

  • Demographic ranges of FIDELIO-DKD subjects not separately reported in the popPK section. The virtual-cohort covariate distributions used for illustration in this vignette (WT mean 85 kg, HT mean 167 cm, CRCL mean 43.0 mL/min/1.73 m^2) are anchored on the paper’s reported cohort medians and the FIDELIO-DKD eGFR/UACR ranges in Results paragraph 1. The full Table 1 demographics live in the main efficacy publication (Bakris et al. 2020, N Engl J Med 383:2219-2229), not in this paper.

  • PEAK / TROUGH sampling-window quality-control exclusions, M3 LLOQ handling, and outlier flags described in the ESM ‘PK outlier identification’ subsection are NOT replicated here. The vignette uses a dense regular simulation grid for illustration, not the FIDELIO-DKD sparse sampling design.

  • Time-varying eGFR-CKD-EPI is treated as constant within the 8-day vignette simulation window. In FIDELIO-DKD the model’s CRCL covariate is updated visit-by-visit over the 2.6-year follow-up; an 8-day window is too short for clinically meaningful eGFR drift, so the vignette uses a single time-fixed value per subject.

  • PKNCA reference values are derived from the analytic F * Dose / CL identity, not from a published NCA table because the source paper does not report numerical Cmax / AUC values for finerenone (only graphical forest plots in Figs. 3-4 and the relative-ratio steady-state simulations of ESM Figs. S2-S5). A future patient-level NCA validation could be added if a regulatory review publishes raw Cmax / AUC summary statistics for the FIDELIO-DKD cohort.

  • Erratum search. A PubMed and journal-landing-page search for errata or corrigenda for doi:10.1007/s40262-021-01082-2 returned no hits as of the extraction date; all values in this model file are the original paper Table 2 / ESM NONMEM control-stream estimates.

  • Time-to-event layer (kidney composite endpoint, Weibull hazard + Emax exposure-response) NOT included. The source paper develops both a popPK model (Section 3.2 / Table 2) and a parametric time-to-event model (Section 3.3 / Table 3). This nlmixr2lib extraction implements only the popPK layer; the TTE / hazard layer would need a separate _kidney_tte extraction using a hazard ODE, and is not yet implemented because the TTE simulation infrastructure in nlmixr2lib is not aligned with the canonical popPK conventions that drive modellib() / readModelDb() listings.