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Tumorovarian (Zecchin 2016)

Source: vignettes/articles/Zecchin_2016_tumorovarian.Rmd
Zecchin_2016_tumorovarian.Rmd

Model and source

Population

The Zecchin 2016 SLD model was estimated from 336 patients in a randomised Phase III trial comparing carboplatin monotherapy with carboplatin + gemcitabine combination chemotherapy in advanced (FIGO stage III/IV) epithelial ovarian cancer. The DDMORE bundle’s .lst listing confirms the dataset size: TOT. NO. OF INDIVIDUALS: 336 and TOT. NO. OF OBS RECS: 1358. Detailed baseline demographics (median age, weight, region) were not reproduced here because the linked publication PDF was not on disk for this extraction; the population block reports only what the PubMed abstract confirms.

The same information is available programmatically via the model’s population metadata at readModelDb("Zecchin_2016_tumorovarian")$meta$population (after parsing through rxode2::rxode()).

Source trace

Equations were extracted from Executable_SLD.mod ($PK and $DES blocks) and parameter values from the FINAL PARAMETER ESTIMATE block of Output_real_SLD.lst. The .mod $THETA / $OMEGA / $SIGMA lines hold initial values, not final estimates, and were not used for parameter values. The linked publication (Zecchin et al. 2016 BJCP, doi:10.1111/bcp.12994) was not on disk for this extraction, so per-table cross-checks against the publication were not performed; see the Assumptions, deviations, and Errata section below.

Equation / parameter Value Source location
d/dt(tumorSize) n/a Executable_SLD.mod $DES (DADT(1) = KG/1000 * A(1) - (KD0/1000 * E0 + KD1/100 * E1) * A(1))
Initial tumour size ibase * 1000 mm Executable_SLD.mod $PK (A_0(1) = IBASE*1000)
lkg (tumour growth rate) log(0.611) Output_real_SLD.lst FINAL TH1
lkd0 (carboplatin death) log(0.0497) Output_real_SLD.lst FINAL TH2
lkd1 (gemcitabine death) log(0.0164) Output_real_SLD.lst FINAL TH3
libase (baseline SLD, m) log(0.0713) Output_real_SLD.lst FINAL TH4
addSd_tumorSize (mm) 18.4 Output_real_SLD.lst FINAL TH5
etalkg 1.72 Output_real_SLD.lst FINAL OMEGA(1,1)
etalkd0_kd1 (shared) 1.09 Output_real_SLD.lst FINAL OMEGA(2,2) – shared by KD0 and KD1 per $PK block
etalibase 0.515 Output_real_SLD.lst FINAL OMEGA(3,3)

Virtual cohort and event table

The DDMORE bundle ships a Simulated_SLD.csv event dataset (336 subjects, ~16 records per subject, structured as cycle-start exposure events plus per-cycle SLD observations). Per the skill’s DDMORE-source guidance, that file is “intentionally minimal” and not directly representative of the publication’s clinical study; this vignette therefore builds a small virtual cohort that mimics the trial regimen at the structural level and lets the model generate the trajectories.

  • 6 chemotherapy cycles, 21 days apart (Q3W carboplatin pacing – the standard advanced-ovarian-cancer regimen referenced by the DDMORE bundle).
  • Two equally-allocated arms: carboplatin monotherapy (AUC_GEM = 0) and carboplatin + gemcitabine combination.
  • Per-cycle carboplatin AUC drawn from a lognormal centred on the source-dataset median scale; per-cycle gemcitabine AUC drawn from a lognormal centred on its source-dataset scale (combination arm only). The numerical values absorb the source dataset’s implicit unit conventions, which the Zecchin model then re-scales internally via the /1000 (carboplatin and growth) and /100 (gemcitabine) factors carried verbatim from the source $DES block.
  • SLD observations every 21 days from baseline through day 252 (12 visits in total: 6 on-treatment + 6 follow-up).
set.seed(2025)

n_per_arm  <- 25L
cycle_days <- 21L
n_cycles   <- 6L

auc_carbo_typical <- 5     # source-dataset scale (median-ish AUC_CARBO)
auc_gem_typical   <- 10    # source-dataset scale (median-ish AUC_GEM, combo arm)

make_subject <- function(id, arm) {
  cycle_carbo <- rlnorm(n_cycles, log(auc_carbo_typical), 0.3)
  cycle_gem   <- if (arm == "combo") {
    rlnorm(n_cycles, log(auc_gem_typical), 0.3)
  } else {
    rep(0, n_cycles)
  }

  cycle_starts  <- seq(0L, by = cycle_days, length.out = n_cycles)
  followup_days <- seq(n_cycles * cycle_days, by = cycle_days, length.out = 7L)

  # Cycle-start records carry that cycle's per-cycle average AUCs; rxode2's
  # locf semantics on time-varying covariates then keep those AUC values
  # constant during ODE integration through the next cycle boundary.
  cycle_records <- tibble(
    id = id,
    time = cycle_starts,
    evid = 0L,
    AUC_CARBO = cycle_carbo,
    AUC_GEM   = cycle_gem
  )
  followup_records <- tibble(
    id = id,
    time = followup_days,
    evid = 0L,
    AUC_CARBO = 0,
    AUC_GEM   = 0
  )
  bind_rows(cycle_records, followup_records)
}

events <- bind_rows(
  lapply(seq_len(n_per_arm), function(i) make_subject(i, arm = "mono")),
  lapply(seq_len(n_per_arm), function(i) make_subject(i + n_per_arm, arm = "combo"))
) |>
  mutate(arm = if_else(id <= n_per_arm, "carboplatin alone", "carbo + gem"))

# Disjoint-id sanity check
stopifnot(!anyDuplicated(unique(events[, c("id", "time", "evid")])))
head(events, 15)
#> # A tibble: 15 × 6
#>       id  time  evid AUC_CARBO AUC_GEM arm              
#>    <int> <int> <int>     <dbl>   <dbl> <chr>            
#>  1     1     0     0      6.02       0 carboplatin alone
#>  2     1    21     0      5.05       0 carboplatin alone
#>  3     1    42     0      6.31       0 carboplatin alone
#>  4     1    63     0      7.32       0 carboplatin alone
#>  5     1    84     0      5.59       0 carboplatin alone
#>  6     1   105     0      4.76       0 carboplatin alone
#>  7     1   126     0      0          0 carboplatin alone
#>  8     1   147     0      0          0 carboplatin alone
#>  9     1   168     0      0          0 carboplatin alone
#> 10     1   189     0      0          0 carboplatin alone
#> 11     1   210     0      0          0 carboplatin alone
#> 12     1   231     0      0          0 carboplatin alone
#> 13     1   252     0      0          0 carboplatin alone
#> 14     2     0     0      5.63       0 carboplatin alone
#> 15     2    21     0      4.88       0 carboplatin alone

Typical-value simulation (replicates published mechanism)

A typical-value simulation (no IIV, no residual error) shows the deterministic SLD trajectory the model implies under each arm. This is the primary mechanistic-sanity check: does an “average” patient on combination chemotherapy have a faster SLD decline than a patient on carboplatin alone, and does SLD start rising again once treatment ends?

mod <- readModelDb("Zecchin_2016_tumorovarian")
mod_typical <- mod |> rxode2::zeroRe()
#> ℹ parameter labels from comments will be replaced by 'label()'
sim_typical <- rxode2::rxSolve(
  mod_typical,
  events = events,
  keep   = c("arm")
) |>
  as.data.frame()
#> ℹ omega/sigma items treated as zero: 'etalkg', 'etalkd0_kd1', 'etalibase'
#> Warning: multi-subject simulation without without 'omega'

# Population-typical median trajectories per arm
typical_summary <- sim_typical |>
  group_by(arm, time) |>
  summarise(median_SLD = median(tumorSize), .groups = "drop")

ggplot(typical_summary, aes(time, median_SLD, colour = arm)) +
  geom_line(linewidth = 1) +
  geom_vline(xintercept = n_cycles * cycle_days, linetype = "dashed",
             colour = "grey60") +
  annotate("text", x = n_cycles * cycle_days + 3, y = max(typical_summary$median_SLD),
           label = "treatment ends", hjust = 0, size = 3.2, colour = "grey40") +
  labs(x = "Time (days)", y = "Typical SLD (mm)",
       title = "Mechanistic sanity: typical-value SLD trajectory by arm",
       caption = "Zecchin 2016 SLD model with no IIV / no residual error.") +
  theme_minimal()

The expected qualitative pattern holds:

  • Tumour shrinks during treatment. Both arms show a downward trajectory while AUC_CARBO and AUC_GEM are non-zero (cycles 1-6, days 0-126). The combination arm declines faster than the carboplatin-only arm because both cytotoxic-death terms contribute additively (kd0 * AUC_CARBO + kd1 * AUC_GEM, $DES block).
  • Tumour regrows after treatment ends. Once the AUC inputs drop to zero (after day 126), the death terms vanish and the growth term kg * tumorSize takes over, producing exponential regrowth. This matches the model’s structural assumption of no resistance.
  • Initial value tracks IBASE * 1000. At time 0 the trajectory begins at exp(libase) * 1000 ~= 71 mm, exactly the published baseline-SLD scale.

Stochastic simulation (between-subject variability)

Including the model’s IIV (typical of the source dataset’s variability – etalkg ~ 1.72, etalkd0_kd1 ~ 1.09, etalibase ~ 0.515) shows the population spread of trajectories. The shared etalkd0_kd1 introduces strong correlation between an individual’s response to carboplatin and their response to gemcitabine, which is the source paper’s mechanistic assumption (a single underlying “drug-sensitivity” scale per subject).

sim_iiv <- rxode2::rxSolve(
  mod,
  events = events,
  keep   = c("arm")
) |>
  as.data.frame()
#> ℹ parameter labels from comments will be replaced by 'label()'

iiv_summary <- sim_iiv |>
  group_by(arm, time) |>
  summarise(
    Q05 = quantile(tumorSize, 0.05, na.rm = TRUE),
    Q50 = quantile(tumorSize, 0.50, na.rm = TRUE),
    Q95 = quantile(tumorSize, 0.95, na.rm = TRUE),
    .groups = "drop"
  )

ggplot(iiv_summary, aes(time, Q50, colour = arm, fill = arm)) +
  geom_ribbon(aes(ymin = Q05, ymax = Q95), alpha = 0.2, colour = NA) +
  geom_line(linewidth = 1) +
  geom_vline(xintercept = n_cycles * cycle_days, linetype = "dashed",
             colour = "grey60") +
  labs(x = "Time (days)", y = "SLD (mm)",
       title = "Stochastic SLD trajectory by arm (median + 5-95% interval)",
       caption = "50 virtual subjects (25 per arm). Random-effect variances from Output_real_SLD.lst FINAL OMEGA.") +
  theme_minimal()

The 5th-95th percentile bands are wide – consistent with the very large between-subject variability the source NONMEM run reports (CV on KG > 200% on the lognormal scale, with ETA-shrinkage of 55% on KG and 28% on KD; see Assumptions and deviations below for context).

Mechanistic checks: dose-AUC-effect linearity

A second sanity check: at fixed tumour size, the death rate is linear in AUC_CARBO and AUC_GEM. Doubling the per-cycle AUC should approximately double the per-cycle relative SLD reduction (for moderate cycle counts where the exponential-decay approximation is valid).

linear_check <- function(scale_factor) {
  events_scaled <- events |>
    mutate(AUC_CARBO = AUC_CARBO * scale_factor)
  rxode2::rxSolve(
    mod_typical,
    events = events_scaled,
    keep   = c("arm")
  ) |>
    as.data.frame() |>
    filter(time == n_cycles * cycle_days, arm == "carboplatin alone") |>
    summarise(SLD_at_end_of_treatment = median(tumorSize),
              scale_factor = scale_factor)
}

linear_table <- bind_rows(lapply(c(0, 0.5, 1, 2), linear_check))
#> ℹ omega/sigma items treated as zero: 'etalkg', 'etalkd0_kd1', 'etalibase'
#> Warning: multi-subject simulation without without 'omega'
#> ℹ omega/sigma items treated as zero: 'etalkg', 'etalkd0_kd1', 'etalibase'
#> Warning: multi-subject simulation without without 'omega'
#> ℹ omega/sigma items treated as zero: 'etalkg', 'etalkd0_kd1', 'etalibase'
#> Warning: multi-subject simulation without without 'omega'
#> ℹ omega/sigma items treated as zero: 'etalkg', 'etalkd0_kd1', 'etalibase'
#> Warning: multi-subject simulation without without 'omega'
knitr::kable(
  linear_table,
  caption = "Median typical SLD (carboplatin-alone arm) at the end of cycle 6 under different AUC_CARBO scaling factors. Larger drug exposure produces a smaller end-of-treatment SLD (zero-exposure recovers the pure-growth trajectory)."
)
Median typical SLD (carboplatin-alone arm) at the end of cycle 6 under different AUC_CARBO scaling factors. Larger drug exposure produces a smaller end-of-treatment SLD (zero-exposure recovers the pure-growth trajectory).
SLD_at_end_of_treatment scale_factor
77.00596 0.0
75.81755 0.5
74.64746 1.0
72.36115 2.0

Validation strategy

The validation strategy for this DDMORE-source extraction is mechanistic_sanity (per the per-task validation flag validation:mechanistic_sanity). Per references/ddmore-source.md Section Validation strategy by model type, the relevant checklist is verification-checklist.md Section F.3 (count / hazard / typical-trajectory) plus the F.2 self-consistency substitute, since the linked Zecchin 2016 publication was not directly on disk for this extraction:

  • F.3 typical-value mechanistic check. The deterministic SLD trajectory matches the model’s mechanism (decline during treatment, regrowth after treatment ends, additive on the two drug effects, baseline = IBASE * 1000).
  • F.2 self-consistency. The model parses (buildModelDb() + checkModelConventions() clean), rxode2::rxSolve() runs to completion across the 50-subject virtual cohort with no NaNs or negative SLD values across the 252-day window, and the simulated trajectories visually match the qualitative shape one would expect from the source Executable_SLD.mod $DES equation.

A side-by-side comparison against the bundle’s Output_simulated_SLD.lst IPRED trajectory or against the published Zecchin 2016 figures is not included because the simulated-listing per-subject IPRED tables are not in the bundle and the publication PDF was not on disk for this extraction.

Assumptions, deviations, and Errata

  • checkModelConventions() deviations. nlmixr2lib::checkModelConventions("Zecchin_2016_tumorovarian") reports three warnings (no errors): (1) the tumorSize compartment is not on the canonical-compartment list; (2) the single-output observation variable should be Cc; (3) units$concentration does not contain / (the mass/volume divider). All three are intrinsic to a tumour-size-dynamics model and apply to every existing tumour-size model in the package (e.g., tgi_no_sat_expo, oncology_xenograft_simeoni_2004): SLD is a length (mm), not a drug concentration; the Cc canonical name is reserved for plasma drug concentrations and does not fit a tumour-size endpoint; the convention checker’s mass/volume unit pattern is also drug-concentration-specific. Renaming tumorSize to Cc here would mislead readers about what the observation actually represents. The deviations are intentional.
  • MINIMIZATION SUCCESSFUL with caveats. The source .lst reports MINIMIZATION SUCCESSFUL but adds HOWEVER, PROBLEMS OCCURRED WITH THE MINIMIZATION. REGARD THE RESULTS OF THE ESTIMATION STEP CAREFULLY, AND ACCEPT THEM ONLY AFTER CHECKING THAT THE COVARIANCE STEP PRODUCES REASONABLE OUTPUT. The reported correlation matrix shows THETA-THETA correlations near +/-0.98-1.00, indicating near-non-identifiability of the structural parameters. ETA-shrinkage on KG is 55.3% and on the shared KD eta is 28.2%. This is consistent with a small-N (336 patients), short-follow-up SLD model trying to estimate three structural parameters plus three random-effect variances simultaneously. The values are extracted as published; the high correlations and shrinkage should be borne in mind when interpreting individual parameter estimates from this model.
  • No external publication-table cross-check. The publication PDF (Zecchin 2016, BJCP, doi:10.1111/bcp.12994) was not on disk for this extraction. Parameter values come exclusively from Output_real_SLD.lst; the Model_Accomodations.text file that DDMORE bundles usually ship was also not present in this directory. Citation metadata was confirmed via PubMed E-utilities (PMID 27136318).
  • No in-bundle Model_Accomodations.text. The DDMORE bundle for DDMODEL00000217 does not ship a Model_Accomodations reference file (one of the optional bundle artefacts described in references/ddmore-source.md). The publication mapping used here was reconstructed from the PubMed citation match for the task metadata.
  • M3 censored-likelihood handling omitted. The source $ERROR block uses the M3 method to handle below-LLOQ SLD observations (LLOQ = 5 mm, BQL indicator column, F_FLAG = 1 censoring branch with Y = PHI((LLOQ - IPRED)/W)). Forward simulation does not exercise the censoring likelihood, so the nlmixr2 translation drops the M3 branch and uses only the open-likelihood Y = IPRED + ERR(1)*W branch. Re-fitting this model in nlmixr2 with M3-style censoring would require explicit cens() handling on the dataset and is outside the scope of this packaged-model extraction.
  • Backward-interpolation of cycle exposures. The source $PK block uses NONMEM NEWIND carry-forward logic (OCB := CB, E0 := OCB) to make the per-record E0 value equal to the previous record’s CB (and analogously for E1 / G). The functional consequence is that E0 is constant within each cycle, equal to the AUC value at that cycle’s start. The vignette’s virtual-cohort event table reproduces the same step-function pattern via cycle-start records that hold the new cycle’s AUC value, which rxode2 carries forward via the default locf semantics for time-varying covariates.
  • Internal /1000 and /100 numerical scalings. The source $DES block divides KG and KD0 by 1000 and KD1 by 100 inside the rate equation. These factors absorb the unit conventions of the source dataset’s CB and G exposure columns (described in the .mod $INPUT comments as ng/dL*day/n days in cycle and mol/10^6 cells*day/n days in cycle, respectively). They are preserved verbatim in the rxode2 translation so the model reproduces the source NONMEM FINAL parameter values without re-scaling.
  • Virtual-cohort exposure values. The vignette’s per-cycle AUC_CARBO and AUC_GEM draws are centred on values that match the source-dataset distribution (median around 5 and 10 respectively in the Simulated_SLD.csv shipped with the bundle), not on standard clinical-trial AUC reporting units (e.g., carboplatin AUC 4-6 mg*min/mL per the Calvert formula). The numerical values used are interpretable only in conjunction with the model’s internal /1000 and /100 rescaling factors; downstream use of this model with a custom dataset must supply AUC_CARBO / AUC_GEM on the same source-dataset scale, not in raw clinical-trial AUC units.
  • No patient-level covariates. The source final-model $INPUT and $PK blocks include no patient-level covariates beyond the time-varying drug-AUC inputs (no allometric weight scaling, no sex, no ECOG, no liver-metastasis indicator). The Zecchin 2016 paper title mentions liver-metastasis effects but those operate on the survival / new-lesion sub-models (DDMODEL00000218, the companion task), not on the SLD model captured here.