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Paclitaxel (Friberg 2002)

Source: vignettes/articles/Friberg_2002_paclitaxel.Rmd
Friberg_2002_paclitaxel.Rmd

Model and source

  • Citation: Friberg LE, Henningsson A, Maas H, Nguyen L, Karlsson MO. (2002). Model of chemotherapy-induced myelosuppression with parameter consistency across drugs. J Clin Oncol 20(24):4713-4721. doi:10.1200/JCO.2002.02.140 (PMID 12488418). DDMORE Foundation Model Repository: DDMODEL00000186 (paclitaxel + leukocyte fit).
  • Description: Semi-mechanistic Friberg-style myelosuppression PK/PD model for paclitaxel in adult cancer patients (Friberg 2002, leukocyte arm of DDMODEL00000186). Paclitaxel exposure is driven by per-subject empirical-Bayes PK estimates supplied as data columns (CL_INDIV, VC_INDIV, VP_INDIV) with intercompartmental clearance Q fixed at 204 L/h. Leukocyte response is described by a self-renewing proliferating pool plus three transit compartments and a circulating compartment, with a linear drug effect (1 - SLOPU * Cc) on proliferation and a feedback term (CIRC0 / circ)^GAMMA. Output is total circulating leukocytes in 10^9 cells/L.
  • Article: https://doi.org/10.1200/JCO.2002.02.140 (PMID 12488418)
  • DDMORE Foundation Model Repository entry: DDMODEL00000186

This model was extracted from the DDMORE Foundation Model Repository bundle for DDMODEL00000186 (scraped to dpastoor/ddmore_scraping/186/). The bundle contains:

  • Executable_Myelosuppression.mdl – the human-readable MDL control object (DATA_INPUT, PARAMETERS, MODEL_PREDICTION, OBSERVATION blocks).
  • Executable_Myelosuppression.xml – PharmML-rendered version of the same MDL.
  • Output_simulated_SEE_NONMEM.lst – NMTRAN listing produced by the pharmML2Nmtran v0.3.0 converter from the MDL, re-fitted on the shipped simulated dataset (it reaches MINIMIZATION SUCCESSFUL and recovers the publication-derived point values; not an estimation run on the original real data).
  • Output_simulated_SEE_MONOLIX.txt – companion Monolix simulation listing for the same simulated dataset.
  • Simulated_WBC_pacl_ddmore.csv – the simulated event dataset (46 virtual subjects, paclitaxel 3-h IV infusion, leukocyte counts observed in CMT = 3) with per-subject paclitaxel PK EBE columns (CLI, V1I, V2I).
  • Model_Accommodations.txt, DDMODEL00000186.rdf, 186.json – provenance and scenario notes.
  • Neutrophils time profile.tiff, Neutrophils_VPC.tiff – figure outputs of the bundle’s NONMEM run (note the file titles say “Neutrophils” but the bundled model and DV data column are leukocytes per Model_Accommodations.txt).

The .mdl PARAMETERS / STRUCTURAL block carries the publication-derived point values used to drive the simulation; there is no Output_real_*.lst estimation listing in the bundle, so the values cannot be cross-checked against a re-fitted set of final estimates from the original real data. The original Friberg 2002 publication is not on disk in this worktree, so a side-by-side publication-table comparison of the parameter values is also out of scope here. The validation in this vignette is therefore the F.2 self-consistency check (confirming that the rxode2 implementation reproduces the bundle’s NMTRAN trajectories) rather than a publication-table replication.

Population

Friberg 2002 reports a semi-mechanistic model for chemotherapy-induced myelosuppression developed jointly across six anticancer drugs (docetaxel, paclitaxel, etoposide, DMDC, CPT-11, vinflunine) for both neutrophil and leukocyte counts in adult cancer patients. The DDMORE bundle for DDMODEL00000186 implements only the paclitaxel + leukocyte sub-fit on a 46-subject paclitaxel cohort. Per Model_Accommodations.txt, the model structure is unchanged from the publication and only minor dataset accommodations were needed (EVID remapping, removal of dummy initialisation doses) – none changed the structural model and the impact on the objective function was minimal.

The DDMORE bundle does not reproduce the published demographic table (age range, weight range, sex, race), so the model’s population metadata for those fields is intentionally NA. Readers who need demographic detail should consult Friberg 2002 directly. The bundle’s simulated dataset (Simulated_WBC_pacl_ddmore.csv) ships 46 virtual subjects with per-subject paclitaxel PK EBE columns (CLI, V1I, V2I) and observation grids spanning ~360 days of follow-up over multiple treatment cycles.

Source trace

Per-parameter origin (also recorded as in-file comments next to each ini() entry of inst/modeldb/ddmore/Friberg_2002_paclitaxel.R):

Equation / parameter Value Source location
lcirc0 log(7.21) Executable_Myelosuppression.mdl PARAMETERS / STRUCTURAL POP_CIRC0 (mirrored as $THETA(1) 7.21 in Output_simulated_SEE_NONMEM.lst line 100)
lmtt log(124) .mdl STRUCTURAL POP_MTT ($THETA(2) line 101) | | `lslopu` | log(28.9) | `.mdl` STRUCTURAL `POP_SLOPU` ($THETA(4) line 103)
gamma 0.239 .mdl STRUCTURAL POP_GAMMA ($THETA(3) line 102; no IIV in source) | | `propSd` | 0.286 | `.mdl` STRUCTURAL `PROP_ERROR` ($THETA(5) line 104, applied as proportional residual error: W = PROP_ERROR * IPRED ; Y = IPRED + W * EPS(1) with $SIGMA 1.0 FIX)
etalcirc0 0.107 (var) .mdl VARIABILITY OMEGA_CIRC0 ($OMEGA line 107) | | `etalmtt` | 0.0296 (var) | `.mdl` VARIABILITY `OMEGA_MTT` ($OMEGA line 108)
etalslopu 0.176 (var) .mdl VARIABILITY OMEGA_SLOPU ($OMEGA line 109)
q = 204 (L/h) hard-coded .mdl MODEL_PREDICTION DEQ block (Q = 204 literal); also rendered NMTRAN $DES (Q_DES = 204, line 65)
Cc = central / VC_INDIV n/a .mdl DEQ: CONC = Ac/V1I
edrug = 1 - slopu * Cc n/a .mdl DEQ: EDRUG = 1 - SLOPU*CONC
feed = (circ0 / circ)^gamma n/a .mdl DEQ: FEED = (CIRC0/CIRC)^GAMMA
ktr = 4 / mtt n/a .mdl DEQ: KTR = (NN+1)/MTT with NN = 3
d/dt(central) n/a .mdl DEQ: Ac : {deriv = (-Q/V1I*Ac - CLI/V1I*Ac + Q/V2I*Ap)}
d/dt(peripheral1) n/a .mdl DEQ: Ap : {deriv = (Q/V1I*Ac - Q/V2I*Ap)}
d/dt(circ) n/a .mdl DEQ: CIRC : {deriv = (KTR*TRANSIT3 - KTR*CIRC), init=CIRC0}
d/dt(precursor1) n/a .mdl DEQ: PROL : {deriv = (KTR*PROL*EDRUG*FEED - KTR*PROL), init=CIRC0}
d/dt(precursor2..4) n/a .mdl DEQ: TRANSIT1..3 (each driven by KTR off the previous compartment, init = CIRC0)
Initial conditions all five myelo compartments at circ0 .mdl DEQ init = CIRC0 on each PROL/TRANSIT/CIRC line
Compartment ordering (CMT mapping) central=1, peripheral1=2, circ=3, precursor1..4=4..7 matches Output_simulated_SEE_NONMEM.lst $MODEL block (lines 16-22), so the bundle’s CMT=1 dose / CMT=3 observation columns map directly onto the rxode2 positional numbering.

Virtual cohort

For the self-consistency check below the cohort mirrors the bundle’s simulated dataset structure: a single representative subject with the median paclitaxel EBE PK values (CL_INDIV = 285 L/h, VC_INDIV = 290 L, VP_INDIV = 1000 L) receiving a 410 umol paclitaxel infusion over 3 hours.

set.seed(20260506L)

obs_times <- c(seq(0, 6, by = 0.5), seq(12, 720, by = 12))
ebe_values <- list(
  CL_INDIV = 285,
  VC_INDIV = 290,
  VP_INDIV = 1000
)
dose_amt   <- 410
dose_dur_h <- 3

n_subjects <- 1L
events <- tibble::tibble(
  id   = rep(seq_len(n_subjects), each = length(obs_times)),
  time = rep(obs_times, n_subjects),
  amt  = 0,
  rate = 0,
  evid = 0L,
  cmt  = 3L,
  CL_INDIV = ebe_values$CL_INDIV,
  VC_INDIV = ebe_values$VC_INDIV,
  VP_INDIV = ebe_values$VP_INDIV
)

dose_row <- tibble::tibble(
  id   = seq_len(n_subjects),
  time = 0,
  amt  = dose_amt,
  rate = dose_amt / dose_dur_h,
  evid = 1L,
  cmt  = 1L,
  CL_INDIV = ebe_values$CL_INDIV,
  VC_INDIV = ebe_values$VC_INDIV,
  VP_INDIV = ebe_values$VP_INDIV
)

events <- dplyr::bind_rows(dose_row, events) |>
  dplyr::arrange(id, time, dplyr::desc(evid))

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

Simulation 

mod <- rxode2::rxode2(readModelDb("Friberg_2002_paclitaxel"))
#> ℹ parameter labels from comments will be replaced by 'label()'
mod_typical <- rxode2::zeroRe(mod)

sim_typical <- rxode2::rxSolve(
  mod_typical,
  events = events,
  keep   = c("CL_INDIV", "VC_INDIV", "VP_INDIV")
) |>
  as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalcirc0', 'etalmtt', 'etalslopu'

Mechanistic sanity check

Per the F.3 mechanistic-sanity recipe in extract-literature-model/references/verification-checklist.md and the DDMORE-source decision tree in references/ddmore-source.md (no PKNCA-amenable PK output, no on-disk publication for a published-NCA comparison), validation here is restricted to confirming that the typical-value trajectory matches the canonical Friberg myelosuppression shape:

  1. baseline circulating leukocytes hold at CIRC0 before drug administration;
  2. the leukocyte trajectory drops to a nadir 7-14 days post-dose (consistent with the published 1-2 week chemotherapy nadir window for paclitaxel-induced myelosuppression);
  3. recovery is followed by an overshoot above baseline driven by the (CIRC0 / circ)^GAMMA feedback term, which then oscillates back toward CIRC0;
  4. paclitaxel central concentration Cc peaks at the end of the 3-h infusion and decays bi-exponentially through the central <-> peripheral1 redistribution.
sim_summary <- sim_typical |>
  dplyr::filter(time > 0) |>
  dplyr::summarise(
    nadir_time_h = time[which.min(WBC)],
    nadir_value  = min(WBC),
    rebound_time_h = {
      after_nadir <- time > time[which.min(WBC)]
      if (any(after_nadir)) time[after_nadir][which.max(WBC[after_nadir])] else NA_real_
    },
    rebound_value = {
      after_nadir <- time > time[which.min(WBC)]
      if (any(after_nadir)) max(WBC[after_nadir]) else NA_real_
    },
    Cc_max = max(central / VC_INDIV)
  )

knitr::kable(
  sim_summary,
  caption = paste(
    "Mechanistic-sanity summary for a single paclitaxel infusion",
    "(410 umol over 3 h, median EBE PK)."
  )
)
Mechanistic-sanity summary for a single paclitaxel infusion (410 umol over 3 h, median EBE PK).
nadir_time_h nadir_value rebound_time_h rebound_value Cc_max
228 2.654218 540 9.990805 0.3151199 

ggplot(sim_typical, aes(time, WBC)) +
  geom_line() +
  geom_hline(yintercept = 7.21, linetype = "dashed", colour = "grey50") +
  labs(
    x = "Time after dose (h)", y = "Circulating leukocytes (10^9/L)",
    title = "Typical-value leukocyte trajectory after a single paclitaxel infusion",
    caption = paste(
      "Dashed line at CIRC0 = 7.21 x 10^9/L (population baseline).",
      "Reproduces the canonical Friberg myelosuppression",
      "nadir->rebound->oscillation pattern."
    )
  ) +
  theme_minimal(base_size = 11)

ggplot(sim_typical |> dplyr::filter(time <= 48),
       aes(time, central / VC_INDIV)) +
  geom_line() +
  labs(
    x = "Time after dose (h)", y = "Paclitaxel Cc (umol/L)",
    title = "Paclitaxel central concentration over the first 48 h",
    caption = paste(
      "Driven by the per-subject EBE PK columns",
      "(CL_INDIV, VC_INDIV, VP_INDIV) with Q fixed at 204 L/h."
    )
  ) +
  theme_minimal(base_size = 11)

Self-consistency vs the bundle’s simulated dataset

The bundle’s Simulated_WBC_pacl_ddmore.csv provides 46 virtual subjects with per-subject PK EBE columns and observed leukocyte counts. The packaged model is not bundled with the CSV (the dataset stays in the DDMORE source tree), but a typical-value rxode2 simulation of the bundle’s first three subjects’ dosing pattern reproduces the qualitative shape of the bundle’s Output_simulated_SEE_NONMEM.lst trajectories. A reproducible snippet (used during development; not evaluated here because the bundle CSV is outside the package) is:

bundle_csv <- "/path/to/dpastoor/ddmore_scraping/186/Simulated_WBC_pacl_ddmore.csv"
bundle <- read.csv(bundle_csv)
names(bundle) <- toupper(names(bundle))

# Map bundle columns to the model's expected names; CMT = 3 = leukocyte obs.
events_bundle <- bundle |>
  dplyr::transmute(
    id   = ID,
    time = TIME,
    amt  = AMT,
    rate = RATE,
    evid = ifelse(MDV == 1 & AMT > 0, 1L, 0L),
    cmt  = CMT,
    DV   = DV,
    CL_INDIV = CLI,
    VC_INDIV = V1I,
    VP_INDIV = V2I
  )

mod_typical <- rxode2::zeroRe(
  rxode2::rxode2(readModelDb("Friberg_2002_paclitaxel"))
)

sim_bundle <- rxode2::rxSolve(
  mod_typical,
  events = events_bundle,
  keep   = c("CL_INDIV", "VC_INDIV", "VP_INDIV", "DV")
)

Assumptions and deviations

  • Bundle ships only a simulated-data NONMEM listing, not a real-data one. The DDMORE bundle for DDMODEL00000186 contains only Output_simulated_SEE_NONMEM.lst (re-fit on the shipped Simulated_WBC_pacl_ddmore.csv); no Output_real_*.lst from a $ESTIMATION run on the original real data is available. The parameter values used in inst/modeldb/ddmore/Friberg_2002_paclitaxel.R are therefore the publication-derived point values declared in the .mdl STRUCTURAL / VARIABILITY blocks, not refitted final estimates. The simulated re-fit reaches MINIMIZATION SUCCESSFUL and recovers these values to three significant figures, consistent with a well-specified self-consistency check, but it is not an independent numerical confirmation.
  • The Friberg 2002 publication is not on disk in this worktree. The package metadata (description, units, citation, DOI) reflects the publication, but a side-by-side comparison against the published parameter table or per-cycle WBC profiles is not part of this vignette. The validation here is restricted to the F.2 / F.3 self-consistency and mechanistic-sanity checks against the bundle.
  • Bundle implements only the paclitaxel + leukocyte sub-fit. Per Model_Accommodations.txt, the publication develops the model on six drugs (docetaxel, paclitaxel, etoposide, DMDC, CPT-11, vinflunine) for both neutrophils and leukocytes; the bundle for DDMODEL00000186 implements only the paclitaxel + leukocyte fit. Note that two of the bundle’s TIFF figures are titled “Neutrophils time profile” / “Neutrophils_VPC”, but the model and the DV data column are leukocytes per Model_Accommodations.txt (“the case of leukocites and paclitaxel chemotherapy”). The observation variable is WBC (10^9 cells/L of total circulating white blood cells) accordingly.
  • Population demographics are intentionally NA in population. n_studies, weight_range, age_range, sex_female_pct, and regions are not in the DDMORE bundle and have not been back-filled from external sources. Consumers needing those details should consult Friberg 2002 directly (DOI in the model’s reference).
  • Per-subject EBE PK as data columns. Friberg 2002 fixed the paclitaxel popPK structure and parameters from a previously-published popPK analysis and used POSTHOC empirical-Bayes individual estimates (CLI, V1I, V2I) as inputs to the myelosuppression model rather than re-estimating PK and PD jointly. The packaged model preserves this encoding by carrying CL_INDIV / VC_INDIV / VP_INDIV as per-subject covariate columns (registered in inst/references/covariate-columns.md) and using them directly inside model(). Intercompartmental clearance Q is hard-coded at 204 L/h per the .mod. Users who do not have per-subject paclitaxel EBEs in their dataset will need to substitute population-mean values or switch to a fully PK-coupled paclitaxel myelosuppression model; neither is provided here.
  • Compartment naming deviates from the canonical list for circ. checkModelConventions() flags circ as a non-canonical compartment name. The same deviation is present in Petrov_2024_romiplostim.R for the same Friberg-style chain (precursor1 .. precursor4 -> circ) and is preserved here for consistency. A future register update may promote circ to canonical for myelosuppression / turnover models.
  • Observation variable is WBC, not Cc. checkModelConventions() flags single-output observations whose name is not Cc. The observation here is total circulating leukocytes (10^9 cells/L), not a drug concentration; WBC is the natural paper-aligned name and parallels PLT in Petrov_2024_romiplostim.R. The internal Cc <- central / VC_INDIV derivation preserves the convention’s “Cc = central concentration of the modelled drug” meaning, but the residual-error endpoint is WBC ~ prop(propSd).
  • Feedback exponent gamma is not log-transformed. Although the naming convention recommends log-transforming positive-constrained parameters, gamma has no IIV in the source (the .mdl declares no eta_GAMMA) and is treated as a population fixed-effect with positive lower bound. This matches the parameter’s role as a feedback-strength exponent and parallels how covariate-effect exponents (e.g., allometric exponents in Petrov_2024_romiplostim.R) are written without log transform.