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Vinflunine (Schmitt 2018)

Source: vignettes/articles/Schmitt_2018_vinflunine.Rmd
Schmitt_2018_vinflunine.Rmd

Model and source

  • Citation: Schmitt A, Nguyen L, Zorza G, Ferre P, Petain A (2018). Better characterization of vinflunine pharmacokinetics variability and exposure/toxicity relationship to improve its use: Analyses from 18 trials. Br J Clin Pharmacol 84(7):1506-1517. doi:10.1111/bcp.13518.
  • Description: Combined population PK / PD model for IV vinflunine in adult cancer patients (Schmitt 2018, 18 phase I/II trials, n=372). Four-compartment IV-infusion popPK with creatinine clearance, body surface area, body weight, and PEGylated liposomal doxorubicin co-administration covariates, plus a five-compartment Friberg-style semi-mechanistic myelosuppression PD model for absolute neutrophil count (proliferation + 3 transit + circulation; linear drug effect 1 - slope*Cc on proliferation; (circ0/circ)^gamma feedback).
  • Article: https://doi.org/10.1111/bcp.13518

Schmitt et al. 2018 (Br J Clin Pharmacol 84(7):1506-1517) pooled data from 18 phase I / phase II vinflunine trials (372 patients, 4154 retained plasma concentrations) and fit two coupled models in NONMEM: a four-compartment popPK model for IV vinflunine and a semi-mechanistic Friberg-style myelosuppression PK/PD model for absolute neutrophil count (ANC) after vinflunine administration. This vignette reproduces both layers in nlmixr2lib / rxode2.

Population

The PK analysis pooled 372 adult cancer patients (44.4% female; median age 59 years, range 19-82; median weight 69 kg, range 42-114; median body surface area 1.8 m^2, range 1.3-2.4) across 18 phase I and phase II studies (8 phase I, 2 phase I/II, 6 phase II, 2 phase I special-population studies in renal and liver impairment). Median Cockcroft-Gault creatinine clearance was 82 mL/min (range 29-199). The cohort spanned multiple solid-tumour indications (bladder cancer being the marketed indication) and 43% of patients received vinflunine in combination with one of cisplatin, gemcitabine, carboplatin, PEGylated liposomal doxorubicin (PLDH), capecitabine, epirubicin or doxorubicin. See Schmitt 2018 Table 1 for the full baseline covariate distribution. The PK/PD analysis used the subset of 210 vinflunine-monotherapy patients (423 administrations, 1871 ANC observations).

The same information is available programmatically via the model’s population metadata (readModelDb("Schmitt_2018_vinflunine")$population).

Source trace

The per-parameter origin is recorded as an in-file comment next to each ini() entry in inst/modeldb/specificDrugs/Schmitt_2018_vinflunine.R. The table below collects them in one place for review.

Equation / parameter Value Source location
lcl (CL) log(40.5) L/h Schmitt 2018 Table 2 final covariate model column
lvc (V central) log(20.7) L Table 2 final covariate model
lvp (V2) log(115) L Table 2 final covariate model
lvp2 (V3) log(384) L Table 2 final covariate model
lvp3 (V4) log(593) L Table 2 final covariate model
lq (Q = K21*V2) log(108.79) L/h Computed from K21 = 0.946, V2 = 115 (Table 2)
lq2 (Q2 = K31*V3) log(54.144) L/h Computed from K31 = 0.141, V3 = 384 (Table 2)
lq3 (Q3 = K41*V4) log(13.580) L/h Computed from K41 = 0.0229, V4 = 593 (Table 2)
e_crcl_cl 0.134 Table 2 (CLCR on CL) and explicit CL formula p.1610
e_bsa_cl 0.542 Table 2 (BSA on CL) and explicit CL formula p.1610
e_pldh_cl 0.865 Table 2 (PLDH on CL) and explicit CL formula p.1610
e_wt_vp2 0.498 Table 2 (WT on V3)
e_wt_vp3 0.650 Table 2 (WT on V4)
IIV variances log(CV^2 + 1) Table 2 CV% values via the standard log-normal mapping
IIV corr(CL,V4) 0.726 Table 2 (correlation block)
IIV corr(V,V2) 0.644 Table 2 (correlation block)
propSd 0.203 (fraction) Table 2 (residual variability 20.3%)
lcirc0 (Circ0) log(4.53) x 10^9/L Table 3 (Base / Circ0)
lmtt (MTT) log(124) h Table 3 (MTT)
lslope (Slope) log(0.425) (ng/mL)^-1 Table 3 (Slope)
gamma 0.170 (fixed) Table 3 (gamma, no IIV in source)
IIV Circ0 omega^2 = 0.1957 Table 3 (IIV Circ0 = 46.5% CV)
IIV Slope omega^2 = 0.1213 Table 3 (IIV Slope = 35.9% CV)
expSd_ANC 0.424 (log SD) Table 3 (Residual additive on log-transformed ANC 42.4% CV)
4-compartment ODE n/a Schmitt 2018 Methods p.1607 (“linear four-compartment model”)
Friberg PD ODE n/a Schmitt 2018 Methods p.1607 (five-compartment Friberg structure)
CL covariate formula n/a Explicit formula on p.1610: CLi = 40.5 * (CLcr/82)^0.134 * (BSA/1.8)^0.542 * 0.865^PLDH

Virtual cohort and simulation

For PK validation we build a typical-PK (zero between-subject variability) event table for the median patient (CRCL = 82 mL/min, BSA = 1.8 m^2, WT = 69 kg, no PLDH co-administration) receiving the recommended single-agent dose of 320 mg/m^2 IV vinflunine as a 30-minute infusion, observed over a 21-day cycle.

set.seed(20260525L)

mod_full <- rxode2::rxode(readModelDb("Schmitt_2018_vinflunine"))
mod_typ  <- rxode2::zeroRe(mod_full)

# Dose: 320 mg/m^2 with BSA = 1.8 -> 576 mg per cycle (30-min infusion)
dose_mg     <- 320 * 1.8
infusion_h  <- 0.5
cycle_h     <- 21 * 24

obs_times <- sort(unique(c(
  seq(0, 1, by = 0.05),
  seq(1, 24, by = 0.5),
  seq(24, cycle_h, by = 4)
)))

make_subject <- function(id, crcl, bsa, wt, pldh) {
  obs <- tibble::tibble(
    id = id, time = obs_times, amt = 0, rate = 0, evid = 0L,
    cmt = NA_integer_, dvid = 1L,
    CRCL = crcl, BSA = bsa, WT = wt, CONMED_PLDH = pldh,
    cohort = "Normal renal (CRCL=82)"
  )
  obs_anc <- dplyr::mutate(obs, dvid = 2L)
  dose <- tibble::tibble(
    id = id, time = 0, amt = dose_mg, rate = dose_mg / infusion_h, evid = 1L,
    cmt = 1L, dvid = NA_integer_,
    CRCL = crcl, BSA = bsa, WT = wt, CONMED_PLDH = pldh,
    cohort = "Normal renal (CRCL=82)"
  )
  dplyr::bind_rows(dose, obs, obs_anc) |>
    dplyr::arrange(id, time, dplyr::desc(evid))
}

events_typ <- make_subject(1L, crcl = 82, bsa = 1.8, wt = 69, pldh = 0)
sim_typ    <- rxode2::rxSolve(mod_typ, events_typ, keep = "cohort") |>
  as.data.frame() |>
  # rxSolve drops `id` when a single subject is solved; restore it for
  # downstream PKNCA grouping.
  dplyr::mutate(id = 1L)

Replicate published values 

sim_typ |>
  dplyr::filter(time > 0, !is.na(Cc)) |>
  ggplot(aes(time, Cc)) +
  geom_line(colour = "steelblue", linewidth = 0.7) +
  scale_y_log10() +
  labs(x = "Time after dose (h)",
       y = "Vinflunine plasma concentration (ng/mL)",
       title = "Typical-PK vinflunine concentration time course (320 mg/m^2 IV)",
       caption = "Reproduces the four-compartment popPK profile from Schmitt 2018 (Table 2).")

sim_typ |>
  dplyr::filter(!is.na(ANC)) |>
  ggplot(aes(time / 24, ANC)) +
  geom_line(colour = "firebrick", linewidth = 0.7) +
  geom_hline(yintercept = 4.53, linetype = "dashed", colour = "grey50") +
  labs(x = "Time after dose (days)",
       y = "Absolute neutrophil count (10^9/L)",
       title = "Typical-PK Friberg ANC time course (320 mg/m^2 q3w)",
       caption = "Reproduces the five-compartment myelosuppression structure from Schmitt 2018 (Table 3). See Assumptions for the slope / nadir discrepancy.")

PKNCA validation

PKNCA is used to compute Cmax, Tmax, AUC0-inf, and terminal half-life on the typical-PK profile. The paper reports a typical AUC over the 21-day cycle of approximately 14000-15000 ng.h/mL at 320 mg/m^2 q3w for normal renal function (Schmitt 2018 p.1611: “Mean AUC for patient with a normal renal function was about 10% higher than for patient with a moderate or a severe impaired renal function (i.e. 15189 (14 884 -15494) ng h ml -1 …)”).

sim_nca <- sim_typ |>
  dplyr::filter(!is.na(Cc)) |>
  dplyr::distinct(id, time, cohort, .keep_all = TRUE) |>
  dplyr::select(id, time, Cc, cohort)

dose_df <- events_typ |>
  dplyr::filter(evid == 1) |>
  dplyr::select(id, time, amt, cohort)

conc_obj <- PKNCA::PKNCAconc(sim_nca, Cc ~ time | cohort + id,
                             concu = "ng/mL", timeu = "h")
dose_obj <- PKNCA::PKNCAdose(dose_df, amt ~ time | cohort + id,
                             doseu = "mg")

intervals <- data.frame(
  start       = 0,
  end         = Inf,
  cmax        = TRUE,
  tmax        = TRUE,
  aucinf.obs  = TRUE,
  half.life   = TRUE
)

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

knitr::kable(
  as.data.frame(nca_res$result) |>
    dplyr::select(cohort, PPTESTCD, PPORRES),
  caption = "Simulated NCA parameters for a typical patient receiving 320 mg/m^2 IV vinflunine."
)
Simulated NCA parameters for a typical patient receiving 320 mg/m^2 IV vinflunine.
cohort PPTESTCD PPORRES
Normal renal (CRCL=82) cmax 6.048443e+03
Normal renal (CRCL=82) tmax 5.000000e-01
Normal renal (CRCL=82) tlast 5.040000e+02
Normal renal (CRCL=82) clast.obs 2.575050e-02
Normal renal (CRCL=82) lambda.z 1.606440e-02
Normal renal (CRCL=82) r.squared 9.999198e-01
Normal renal (CRCL=82) adj.r.squared 9.999191e-01
Normal renal (CRCL=82) lambda.z.time.first 6.400000e+01
Normal renal (CRCL=82) lambda.z.time.last 5.040000e+02
Normal renal (CRCL=82) lambda.z.n.points 1.110000e+02
Normal renal (CRCL=82) clast.pred 2.546140e-02
Normal renal (CRCL=82) half.life 4.314809e+01
Normal renal (CRCL=82) span.ratio 1.019744e+01
Normal renal (CRCL=82) aucinf.obs 1.422355e+04

Comparison against published AUC 

auc_sim <- as.data.frame(nca_res$result) |>
  dplyr::filter(PPTESTCD == "aucinf.obs") |>
  dplyr::pull(PPORRES)

knitr::kable(
  tibble::tibble(
    Metric  = "AUC0-inf (ng.h/mL)",
    `Schmitt 2018 (normal renal, 320 mg/m^2)` = "~15189 (14884-15494)",
    `nlmixr2lib typical-PK simulation`        = sprintf("%.0f", auc_sim),
    `Relative difference`                     = sprintf("%.1f%%", 100 * (auc_sim - 15189) / 15189)
  ),
  caption = "Comparison of simulated typical-PK AUC against Schmitt 2018 p.1611 published mean AUC for normal renal function."
)
Comparison of simulated typical-PK AUC against Schmitt 2018 p.1611 published mean AUC for normal renal function.
Metric Schmitt 2018 (normal renal, 320 mg/m^2) nlmixr2lib typical-PK simulation Relative difference
AUC0-inf (ng.h/mL) ~15189 (14884-15494) 14224 -6.4%

Assumptions and deviations

  • Reference weight 69 kg for the WT effect on V3 / V4. Schmitt 2018 does not print an explicit (WT / ref)^exp formula for the volume covariates the way it does for CL (p.1610). The 69 kg reference is the paper-consistent population median (Table 1: median WT 69 kg), matching the reference values used in the explicit CL formula for CRCL (median 82 mL/min) and BSA (median 1.8 m^2). A user wishing to evaluate the model on a different reference weight (e.g. 70 kg) may rescale by passing WT adjusted by the ratio of references, since the power form is scale-invariant up to a constant multiplier on the typical V3 / V4.

  • Concentration units inside model(). Vinflunine PK observations and the Friberg slope parameter are reported in ng/mL. The internal central compartment carries amount in mg (matching the mg dosing convention) and vc is in L; the model computes the plasma concentration as Cc = 1000 * central / vc so that slope * Cc is dimensionless and Cc matches the paper’s ng/mL convention.

  • IOV not represented. Schmitt 2018 reports interoccasion variability of 8.34% on CL (Table 2) and 24.0% on MTT and 23.8% on Slope (Table 3). nlmixr2lib model files do not carry an OCC data column or per-occasion random effects; the user can introduce IOV by adding an OCC column and an inter-occasion eta_occ_<param> term outside the packaged model file.

  • Friberg-style PD layer reproduces published parameters but predicts a deeper nadir than the paper’s typical-value forecast. Direct simulation of the Friberg ODE with the published slope = 0.425 (ng/mL)^-1 (Schmitt 2018 Table 3) and the median-PK Cmax produces a much deeper ANC nadir than the paper’s published prediction of 1.40 x 10^9/L at day 11.3 for 320 mg/m^2 q3w (Schmitt 2018 p.1611-1612). The structural model and every parameter value match the publication; the discrepancy is an inherent feature of the reported slope when applied to the typical PK profile via the canonical linear-drug-effect Friberg formulation. Users who want to reproduce the paper’s published nadir prediction may need to (a) calibrate slope against the paper’s stated 47% grade 3-4 neutropenia incidence at 320 mg/m^2 q3w via re-fit, (b) clamp the proliferation drug effect (`edrug <- max(0, 1 - slope

    • Cc)`) as a non-canonical Friberg variant, or (c) interpret the published slope as applying to a different concentration unit (e.g. (mg/L)^-1) and re-scale. The packaged model is faithful to the paper’s reported text; the deviation in simulated nadir is documented here rather than tuned away.

  • Slope is encoded as a linear cell-loss term on the proliferation compartment (the canonical Friberg form): d/dt(precursor1) = ktr * precursor1 * (1 - slope * Cc) * (circ0 / circ)^gamma - ktr * precursor1. No floor is applied to edrug = 1 - slope * Cc; when slope * Cc > 1 the proliferation rate is negative, consistent with Friberg 2002’s original formulation and the Schmitt 2018 Methods text (“reduce proliferation rate or induce cell loss in a linear fashion”).

  • Infusion duration is supplied by the data, not the model. Vinflunine is administered IV per the SPC as a short infusion (typical 20-30 minutes). The model code does not impose a structural infusion duration; the simulation supplies rate or dur on the dosing record. The vignette uses 30 minutes for the typical profile.