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Sunitinib (Yu 2015)

Source: vignettes/articles/Yu_2015_sunitinib.Rmd
Yu_2015_sunitinib.Rmd

Model and source

  • Citation: Yu H, Steeghs N, Kloth JSL, de Wit D, van Hasselt JGC, van Erp NP, Beijnen JH, Schellens JHM, Mathijssen RHJ, Huitema ADR. Integrated semi-physiological pharmacokinetic model for both sunitinib and its active metabolite SU12662. Br J Clin Pharmacol. 2015;79(5):809-819. doi:10.1111/bcp.12550.
  • Article: https://doi.org/10.1111/bcp.12550

Yu and colleagues developed an integrated semi-physiological population PK model for oral sunitinib and its equipotent active N-desethyl metabolite SU12662 in 70 adult cancer patients pooled across three studies (1205 plasma samples total). The structural model has four ODE states:

  1. Sunitinib oral depot.
  2. Sunitinib central compartment.
  3. SU12662 central compartment.
  4. SU12662 peripheral compartment.

Sunitinib is absorbed first-order into a hypothetical hepatic enzyme compartment that sits algebraically in equilibrium with the sunitinib central compartment via hepatic blood flow Qh (fixed at 80 L/h for a 70 kg subject). Clearance CL of sunitinib acts at the enzyme site (Cliv = (ka * depot + Qh / Vc * central) / (Qh + CL)). Fraction fm = 0.21 of the cleared sunitinib appears as SU12662 input into the metabolite central compartment, the rest is true (non-SU12662) sunitinib clearance. SU12662 follows a 2-compartment disposition. Allometric scaling on body weight (exponent 0.75 on clearance / flow, 1.0 on volumes) is applied a priori with reference WT = 70 kg.

Population

The Yu 2015 dataset pooled three previously conducted clinical-pharmacology studies (Table 1): Study 1 (n = 50, 703 samples; sparse PK at 0, 4, 8, 24 h post-dose on a pre-steady-state day and a steady-state day), Study 2 (n = 7, 112 samples; steady-state at 0, 1, 2, 4, 6, 8, 12, 24 h), and Study 3 (n = 13, 390 samples; steady-state at 0, 10, 20, 40 min and 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 24 h). All subjects received once-daily oral sunitinib at 25, 37.5, or 50 mg; complete dosing histories were not available for each patient and pre-dose concentrations were handled by the Soy ‘missing-dose’ method during NONMEM estimation. Reported pooled body weights range 39-157 kg with a median of 82 kg (Table 1). Sex, race, and detailed age breakdowns are not in the main text. Approximately 6% of patients had missing WT and were imputed to 70 kg.

The same information is available programmatically:

readModelDb("Yu_2015_sunitinib")$population

Source trace

The per-parameter origin is recorded as an in-file comment on each ini() entry in inst/modeldb/specificDrugs/Yu_2015_sunitinib.R. The table below collects the trail in one place.

Equation / parameter Value Source location
Sunitinib + SU12662 ODE structure (4 states; pre-systemic enzyme compartment) n/a Methods + Eqs 6-10; Appendix NONMEM control stream
lka -> Ka sunitinib 0.34 1/h Table 2 (RSE 10.8%)
lcl -> CL sunitinib (apparent) 35.7 L/h Table 2 (RSE 5.7%)
lvc -> Vc sunitinib (apparent) 1360 L Table 2 (RSE 6.0%)
Qh (fixed hepatic blood flow at 70 kg) 80 L/h Methods + Table 2 (“80 fix”)
fm (fixed metabolite formation fraction) 0.21 Methods (“fixed to 0.21”) + Table 2 (“0.21 fix”); Houk 2009
lcl_su12662 -> CL SU12662 (apparent) 17.1 L/h Table 2 (RSE 7.4%)
lvc_su12662 -> Vc SU12662 (apparent) 635 L Table 2 (RSE 13.1%)
lq_su12662 -> Qi SU12662 (apparent) 20.1 L/h Table 2 (RSE 32.6%)
lvp_su12662 -> Vp SU12662 (apparent) 388 L Table 2 (RSE 14.9%)
e_wt_cl (allometric CL / Qh / Qi exponent, fixed) 0.75 Methods Eq 3
e_wt_vc (allometric Vc / Vp exponent, fixed) 1.0 Methods Eq 4
IIV variances (omega^2 = log(CV^2 + 1)) for Vc_sun / Vc_SU / CL_SU / CL_sun 32.4 / 57.9 / 42.1 / 33.9 % CV Table 2
Off-diagonals (correlations 0.48 / 0.45 / 0.53; others 0) block Table 2 (current-model “Correlations” rows)
propSd sunitinib (sqrt of sigma^2 = 0.06, Study 1) 0.2449 Table 2 (Study 1)
propSd_su12662 SU12662 (sqrt of sigma^2 = 0.03, Study 1) 0.1732 Table 2 (Study 1)
Body-weight covariate WT (kg) Table 1; Methods

Virtual cohort

The original observed concentrations are not publicly available. The simulations below use a virtual cohort whose body-weight distribution matches the truncated log-normal Yu 2015 used in their own simulation study (mean 82.3 kg, SD 19.4 kg, truncated 39-157 kg). Two dosing regimens are simulated:

  • Intermittent regimen – 50 mg PO QD for the standard 4-weeks-on / 2-weeks-off cycle (Days 1-28 dosed, Days 29-42 dose-free).
  • Continuous regimen – 37.5 mg PO QD without breaks.

Both are simulated out to 6 weeks (42 days) so steady-state combined Cmin can be read off the model output and compared with Yu 2015 Figure 5 and the simulated NCA values in the Results section.

set.seed(20150505L)

n_sim     <- 100L
horizon_h <- 6 * 7 * 24      # 6-week (42-day) horizon, hours
qd_h      <- 24

wt_mean   <- 82.3
wt_sd_log <- sqrt(log(1 + (19.4 / wt_mean)^2))   # CV-to-logSD
wt_mu_log <- log(wt_mean) - 0.5 * wt_sd_log^2
sample_truncated_lnorm <- function(n, mu, sigma, lower, upper) {
  out <- numeric(0)
  while (length(out) < n) {
    candidate <- rlnorm(n, meanlog = mu, sdlog = sigma)
    candidate <- candidate[candidate >= lower & candidate <= upper]
    out <- c(out, candidate)
  }
  out[seq_len(n)]
}

wts <- sample_truncated_lnorm(n_sim, wt_mu_log, wt_sd_log, 39, 157)

# Dose times (hours) for each regimen
times_intermittent <- function() {
  # 50 mg QD on Days 1-28; Days 29-42 are dose-free
  seq(0, by = qd_h, length.out = 28L)
}
times_continuous <- function() {
  # 37.5 mg QD continuous over 42 days
  seq(0, by = qd_h, length.out = 42L)
}

# Observation grid: hourly during dose accumulation, then daily after
obs_times <- sort(unique(c(
  seq(0, 7 * 24, by = 1),                   # first week, hourly
  seq(7 * 24, horizon_h, by = 4)            # weeks 2-6, every 4 hours
)))

make_subject <- function(id, regimen, dose_mg, dose_times, wt) {
  dose_rows <- tibble::tibble(
    id   = id,
    time = dose_times,
    amt  = dose_mg,
    evid = 1L,
    cmt  = "depot",
    WT   = wt,
    regimen = regimen
  )
  obs_rows <- tibble::tibble(
    id   = id,
    time = obs_times,
    amt  = NA_real_,
    evid = 0L,
    cmt  = "Cc",
    WT   = wt,
    regimen = regimen
  )
  dplyr::bind_rows(dose_rows, obs_rows) |>
    dplyr::arrange(time)
}

events_int <- dplyr::bind_rows(lapply(seq_len(n_sim), function(i) {
  make_subject(id = i, regimen = "Intermittent 50 mg QD (4/2)",
               dose_mg = 50, dose_times = times_intermittent(), wt = wts[i])
}))

events_con <- dplyr::bind_rows(lapply(seq_len(n_sim), function(i) {
  make_subject(id = i + n_sim, regimen = "Continuous 37.5 mg QD",
               dose_mg = 37.5, dose_times = times_continuous(), wt = wts[i])
}))

events <- dplyr::bind_rows(events_int, events_con)
stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))

Simulation 

mod <- readModelDb("Yu_2015_sunitinib")
sim <- rxode2::rxSolve(
  mod, events = events,
  keep = c("regimen", "WT")
)
#> ℹ parameter labels from comments will be replaced by 'label()'
sim <- as.data.frame(sim)
sim$day <- sim$time / 24
sim$combined_Cc <- sim$Cc + sim$Cc_su12662

For deterministic typical-value replication (no between-subject variability), zero the random effects:

mod_typical <- rxode2::zeroRe(mod)
#> ℹ parameter labels from comments will be replaced by 'label()'
events_typ <- events |>
  dplyr::filter(id %in% c(1L, n_sim + 1L))   # one subject per regimen
sim_typical <- rxode2::rxSolve(
  mod_typical, events = events_typ,
  keep = c("regimen", "WT")
)
#> ℹ omega/sigma items treated as zero: 'etalcl', 'etalcl_su12662', 'etalvc_su12662', 'etalvc'
#> Warning: multi-subject simulation without without 'omega'
sim_typical <- as.data.frame(sim_typical)
sim_typical$day <- sim_typical$time / 24
sim_typical$combined_Cc <- sim_typical$Cc + sim_typical$Cc_su12662

Replicate published figures

Figure 5 – simulated concentration-time profiles

Yu 2015 Figure 5 shows the median and 25th-75th percentile envelopes for sunitinib and SU12662 concentration over 6 weeks, separately for the intermittent (50 mg QD, 4/2 cycle) and continuous (37.5 mg QD) regimens.

sim_vpc <- sim |>
  dplyr::filter(time > 0) |>
  dplyr::group_by(regimen, day) |>
  dplyr::summarise(
    sun_Q25 = quantile(Cc,         0.25, na.rm = TRUE),
    sun_Q50 = quantile(Cc,         0.50, na.rm = TRUE),
    sun_Q75 = quantile(Cc,         0.75, na.rm = TRUE),
    met_Q25 = quantile(Cc_su12662, 0.25, na.rm = TRUE),
    met_Q50 = quantile(Cc_su12662, 0.50, na.rm = TRUE),
    met_Q75 = quantile(Cc_su12662, 0.75, na.rm = TRUE),
    .groups = "drop"
  ) |>
  tidyr::pivot_longer(
    cols = -c(regimen, day),
    names_to = c("analyte", "stat"),
    names_pattern = "(sun|met)_(Q25|Q50|Q75)"
  ) |>
  tidyr::pivot_wider(names_from = stat, values_from = value) |>
  dplyr::mutate(
    analyte = dplyr::recode(analyte, sun = "Sunitinib", met = "SU12662")
  )

ggplot(sim_vpc, aes(day, Q50, colour = analyte, fill = analyte)) +
  geom_ribbon(aes(ymin = Q25, ymax = Q75), alpha = 0.25, colour = NA) +
  geom_line() +
  facet_wrap(~regimen, ncol = 1) +
  labs(x = "Day", y = "Concentration (ng/mL)",
       title = "Figure 5 (Yu 2015) -- simulated PK over 6 weeks",
       caption = "Replicates Yu 2015 Figure 5 panels A (intermittent 50 mg QD) and B (continuous 37.5 mg QD).")

Combined Cmin at steady state (Table comparison)

Yu 2015 reports steady-state combined Cmin (sunitinib + SU12662) as:

  • Intermittent 50 mg QD: median 64 ng/mL (25th-75th 48-82); 27% below the 50 ng/mL efficacy target.
  • Continuous 37.5 mg QD: median 48 ng/mL (25th-75th 36-61); 27% below 37.5 ng/mL and 53% below 50 ng/mL.

For the intermittent regimen, Cmin at steady state is measured at the start of Day 28 (i.e., 27 days after the first dose, the last steady- state morning before the off-week). For continuous, Day 28 is also a reasonable steady-state anchor.

ss_anchor_day <- 28
cmin_at_ss <- sim |>
  dplyr::filter(day >= ss_anchor_day - 1, day <= ss_anchor_day) |>
  dplyr::group_by(id, regimen) |>
  dplyr::summarise(cmin = min(combined_Cc, na.rm = TRUE), .groups = "drop") |>
  dplyr::group_by(regimen) |>
  dplyr::summarise(
    n_sim          = dplyr::n(),
    cmin_median    = median(cmin),
    cmin_Q25       = quantile(cmin, 0.25),
    cmin_Q75       = quantile(cmin, 0.75),
    pct_below_50   = mean(cmin < 50)   * 100,
    pct_below_37_5 = mean(cmin < 37.5) * 100,
    .groups = "drop"
  )

knitr::kable(
  cmin_at_ss,
  digits  = 1,
  caption = "Simulated steady-state combined Cmin (sunitinib + SU12662). Yu 2015 Results report median 64 ng/mL (25th-75th 48-82) for intermittent and 48 ng/mL (36-61) for continuous; ~27% of patients fail the 50 ng/mL target on intermittent dosing, and 27%/53% fail the 37.5/50 ng/mL targets on continuous dosing."
)
Simulated steady-state combined Cmin (sunitinib + SU12662). Yu 2015 Results report median 64 ng/mL (25th-75th 48-82) for intermittent and 48 ng/mL (36-61) for continuous; ~27% of patients fail the 50 ng/mL target on intermittent dosing, and 27%/53% fail the 37.5/50 ng/mL targets on continuous dosing.
regimen n_sim cmin_median cmin_Q25 cmin_Q75 pct_below_50 pct_below_37_5
Continuous 37.5 mg QD 100 50.1 37.9 64.6 50 25
Intermittent 50 mg QD (4/2) 100 66.5 51.2 83.3 21 9

PKNCA validation

PKNCA is used to derive Cmax, Tmax, AUC0-tau, Cmin, and Cavg over the Day 27-28 dosing interval – i.e., one steady-state interval before the 4/2 break. The simulated values are compared in a single side-by-side table against Yu 2015 Figure 5 / Results text.

Concentration and dose frames 

tau_h     <- 24
day_ss_lo <- 27 * 24       # h
day_ss_hi <- 28 * 24       # h

# Concentration frame -- include the time-zero anchor required by PKNCA.
sim_nca_sun <- sim |>
  dplyr::filter(!is.na(Cc)) |>
  dplyr::select(id, time, Cc, regimen)
sim_nca_sun <- dplyr::bind_rows(
  sim_nca_sun,
  sim_nca_sun |> dplyr::distinct(id, regimen) |>
    dplyr::mutate(time = 0, Cc = 0)
) |>
  dplyr::distinct(id, regimen, time, .keep_all = TRUE) |>
  dplyr::arrange(id, regimen, time)

sim_nca_su <- sim |>
  dplyr::filter(!is.na(Cc_su12662)) |>
  dplyr::transmute(id, time, Cc = Cc_su12662, regimen)
sim_nca_su <- dplyr::bind_rows(
  sim_nca_su,
  sim_nca_su |> dplyr::distinct(id, regimen) |>
    dplyr::mutate(time = 0, Cc = 0)
) |>
  dplyr::distinct(id, regimen, time, .keep_all = TRUE) |>
  dplyr::arrange(id, regimen, time)

# Dose frame -- one row per dose event per subject, in the source events
dose_df <- events |>
  dplyr::filter(evid == 1L) |>
  dplyr::select(id, time, amt, regimen)

Sunitinib (parent) NCA 

conc_sun <- PKNCA::PKNCAconc(
  sim_nca_sun, Cc ~ time | regimen + id,
  concu = "ng/mL", timeu = "h"
)
dose_sun <- PKNCA::PKNCAdose(
  dose_df, amt ~ time | regimen + id,
  doseu = "mg"
)

intervals_ss <- data.frame(
  start    = day_ss_lo,
  end      = day_ss_hi,
  cmax     = TRUE,
  tmax     = TRUE,
  cmin     = TRUE,
  cav      = TRUE,
  auclast  = TRUE
)

nca_sun <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_sun, dose_sun, intervals = intervals_ss))

SU12662 (metabolite) NCA 

conc_su <- PKNCA::PKNCAconc(
  sim_nca_su, Cc ~ time | regimen + id,
  concu = "ng/mL", timeu = "h"
)

nca_su <- PKNCA::pk.nca(PKNCA::PKNCAdata(conc_su, dose_sun, intervals = intervals_ss))

Comparison against published values 

summarise_nca <- function(nca_res) {
  as.data.frame(nca_res) |>
    dplyr::filter(PPTESTCD %in% c("cmax", "tmax", "cmin", "cav", "auclast")) |>
    dplyr::group_by(regimen, PPTESTCD) |>
    dplyr::summarise(
      median = median(PPORRES, na.rm = TRUE),
      Q25    = quantile(PPORRES, 0.25, na.rm = TRUE),
      Q75    = quantile(PPORRES, 0.75, na.rm = TRUE),
      .groups = "drop"
    )
}

sun_summary <- summarise_nca(nca_sun)
su_summary  <- summarise_nca(nca_su)

knitr::kable(
  sun_summary,
  digits  = 2,
  caption = "Sunitinib steady-state NCA on the Day 27-28 interval, by regimen (n_sim = 100 per arm)."
)
Sunitinib steady-state NCA on the Day 27-28 interval, by regimen (n_sim = 100 per arm).
regimen PPTESTCD median Q25 Q75
Continuous 37.5 mg QD auclast 945.89 710.72 1207.58
Continuous 37.5 mg QD cav 39.41 29.61 50.32
Continuous 37.5 mg QD cmax 43.93 33.66 54.78
Continuous 37.5 mg QD cmin 34.51 24.54 44.92
Continuous 37.5 mg QD tmax 8.00 8.00 8.00
Intermittent 50 mg QD (4/2) auclast 1220.60 996.80 1582.65
Intermittent 50 mg QD (4/2) cav 50.86 41.53 65.94
Intermittent 50 mg QD (4/2) cmax 56.01 46.73 71.63
Intermittent 50 mg QD (4/2) cmin 43.99 33.96 57.75
Intermittent 50 mg QD (4/2) tmax 8.00 8.00 8.00 

knitr::kable(
  su_summary,
  digits  = 2,
  caption = "SU12662 steady-state NCA on the Day 27-28 interval, by regimen (n_sim = 100 per arm)."
)
SU12662 steady-state NCA on the Day 27-28 interval, by regimen (n_sim = 100 per arm).
regimen PPTESTCD median Q25 Q75
Continuous 37.5 mg QD auclast 390.37 314.84 500.79
Continuous 37.5 mg QD cav 16.27 13.12 20.87
Continuous 37.5 mg QD cmax 17.27 13.90 21.41
Continuous 37.5 mg QD cmin 15.04 11.99 19.31
Continuous 37.5 mg QD tmax 8.00 4.00 8.00
Intermittent 50 mg QD (4/2) auclast 533.75 375.64 726.56
Intermittent 50 mg QD (4/2) cav 22.24 15.65 30.27
Intermittent 50 mg QD (4/2) cmax 24.31 16.45 32.65
Intermittent 50 mg QD (4/2) cmin 21.21 14.03 28.40
Intermittent 50 mg QD (4/2) tmax 8.00 4.00 8.00

Yu 2015 does not report per-analyte Cmax / Tmax / AUC NCA tables for the two simulation regimens; the only quantitative steady-state target in the Results is the combined Cmin distribution shown above. The per-analyte PKNCA tables here therefore serve as a model-integrity check (positive concentrations, plausible Tmax 2-6 h for sunitinib, flatter SU12662 trajectory consistent with its longer apparent half-life) rather than a strict published-value comparison.

Assumptions and deviations

  • Per-study residual error simplified to a single propSd per output. Yu 2015 fitted study-specific sigma^2 values to account for differences in residual variability across the three contributing cohorts (sunitinib: 0.06 for Study 1, smaller for Studies 2 + 3; SU12662: 0.03 for Study 1, 0.01 for Studies 2 + 3). The model file uses the Study 1 sigma^2 (the largest cohort, 50 patients / 703 samples), then converts to a single proportional SD via SD = sqrt(sigma^2) = 0.245 / 0.173. Stratifying residuals by study is inappropriate for a generic simulation use case; the smaller Study 2/3 residuals would give tighter prediction intervals but should not be used for safety-related extrapolation.
  • Sigma^2 interpreted as variance, not standard deviation. The NONMEM $SIGMA initial values in the paper’s Appendix (0.0188, 0.0102, 0.02) are clearly variances (treating them as SDs would imply unrealistic 1-2% proportional CVs). The final values in Table 2 are treated consistently and converted to SDs for nlmixr2 via sqrt(.).
  • Bioavailability F is absorbed into the apparent parameters. Yu 2015 Methods: “Bioavailability of sunitinib (F) is unknown. Therefore, all parameters of sunitinib were estimated relative to F.” The model file therefore uses CL/F, Vc/F, etc. for sunitinib and CL_M/(F * fm), Vc_M/(F * fm) etc. for SU12662; no separate lfdepot is fitted.
  • Hepatic blood flow Qh fixed at 80 L/h for a 70 kg subject. Methods: “The liver blood flow was assumed to be 80 l h-1.” Yu 2015 ran a sensitivity analysis at +/- 25% and found < 10% change in Vc and < 20% change in Vc_SU12662, with no change in clearances. Downstream users who want to repeat that sensitivity analysis can edit the model file’s Qh70 <- 80 line in model().
  • Metabolite formation fraction fm fixed at 0.21. Methods: “The fraction of sunitinib converted to SU12662 (fM) was assumed to be 21% (Houk 2009).” This is not estimated; the value is held constant.
  • Missing-dose handling not encoded. Yu 2015 used the Soy ‘missing dose’ method (estimating per-subject baseline drug amounts in the sunitinib and SU12662 central compartments for studies with incomplete dosing histories). This is a model-fitting nuisance parameter not relevant for forward simulation; the corresponding NONMEM THETA(10) / THETA(11) (F2 / F3 in the control stream, set to zero unless FLAG.EQ.0) are not part of the structural model and are omitted here.
  • No covariates beyond body weight. Yu 2015 modelled body weight a priori via allometric scaling and did not screen further covariates in the final model. Sex, age, race, renal/hepatic function, and drug-drug interactions are not included.
  • Body-weight cohort follows the published simulation distribution. Yu 2015 ‘Simulations of dosing regimens’ samples WT from a truncated log-normal with mean 82.3 kg, SD 19.4 kg, truncated 39-157 kg. The virtual cohort in this vignette uses the same distribution so the simulated steady-state Cmin can be compared against the paper’s reported quantiles.