Skip to contents

Tumor growth dynamics and overall survival in advanced gastric cancer (Terranova 2022, JAVELIN Gastric 100)

Source: vignettes/articles/Terranova_2022_TGD_OS_gastric.Rmd
Terranova_2022_TGD_OS_gastric.Rmd

Model and source

  • Citation: Terranova N, French J, Dai H, Wiens M, Khandelwal A, Ruiz-Garcia A, Manitz J, von Heydebreck A, Ruisi M, Chin K, Girard P, Venkatakrishnan K. Pharmacometric modeling and machine learning analyses of prognostic and predictive factors in the JAVELIN Gastric 100 phase III trial of avelumab. CPT Pharmacometrics Syst Pharmacol. 2022;11(3):333-347. doi:10.1002/psp4.12754.
  • Description: Joint tumor growth dynamics (TGD) + overall survival (OS) disease-progression model for advanced gastric cancer / gastroesophageal junction cancer (GC/GEJC) developed on the JAVELIN Gastric 100 phase III trial by Terranova et al. (Merck KGaA / Merck Institute of Pharmacometrics / EMD Serono / Metrum Research Group). N = 499 patients randomized 1:1 to avelumab 10 mg/kg every 2 weeks (n = 249) or continued chemotherapy (n = 250) maintenance after 12 weeks of induction chemotherapy. The paper’s primary finding is NEGATIVE: no treatment effect on OS or TGD was identified, consistent with the primary JAVELIN Gastric 100 analysis. Machine learning (random forests + SIDEScreen + Boruta / permutation / random-splits variable-importance methods) was used to screen 89 (OS) / 52 (TGD) candidate covariates, then covariates surviving the ML screen were incorporated into two parametric sub-models: (1) a Gompertzian TGD model on tumor size measured by sum of longest diameters (SLD, mm) with the Vaghi 2020 Kd = slope*Kg + intercept reduced-parameter reformulation, and (2) a log-logistic parametric time-to-event OS model with an accelerated-failure-time link to time-invariant covariates on the log-median-OS scale, a proportional-hazards link to time-varying laboratory covariates, and a per-arm shape parameter that captures the crossing of hazard curves between avelumab and chemotherapy. There is NO drug PK sub-model – avelumab exposure is not carried explicitly; the treatment arm is encoded as the TRT categorical covariate (1 = chemotherapy = reference, 2 = avelumab). Extract-scope note: no drug PK; the two ODE outputs are tumor (SLD, mm) with proportional residual error and sur (survival probability), driven off d/dt(cumhaz) = hazard.
  • Article: CPT Pharmacometrics Syst Pharmacol. 2022;11(3):333-347
  • Supplement: Data S1 (Figures S1-S14, Supplementary Methods, Tables S1-S7)

This is a joint tumor growth dynamics (TGD) + overall survival (OS) disease-progression model, not a drug-specific PK/PD model. The paper’s primary finding is NEGATIVE: no treatment effect of avelumab (anti-PD-L1 monoclonal antibody) versus continued chemotherapy on either OS or TGD was identified in the JAVELIN Gastric 100 phase III maintenance trial (n = 499). The two ODE-based sub-models are provided to reproduce the paper’s descriptive characterization of gastric-cancer disease progression given a rich covariate set that was screened by machine learning (random forests + Boruta + permutation + random-splits) and retained for parametric fitting.

Population

The cohort is 499 adults with unresectable, HER2-negative, locally advanced or metastatic gastric cancer or gastroesophageal junction cancer who did not progress after 12 weeks of first-line induction chemotherapy (oxaliplatin + a fluoropyrimidine) and were randomized 1:1 to avelumab 10 mg/kg every 2 weeks (n = 249) or continued chemotherapy (n = 250) as maintenance therapy, stratified by region (Asian vs non-Asian). “Baseline” refers to values obtained before the 12-week induction phase; “re-baseline” refers to values at randomization (after induction).

The reference-subject covariate values in the packaged model are taken from Table S3 (avelumab-arm medians / cohort medians as documented per covariate) or Supplementary Methods. Key values:

Covariate Reference value Source
T_DIAG_CANCER time since gastric-cancer diagnosis 53 days (avelumab arm median) Supp Methods equation for Kg
MET_GE3 >= 3 metastatic sites 0 (< 3 sites; paper centres at NumMet = 3) Table S3
SBP baseline systolic BP 120 mmHg (population median) Table S3
HR baseline heart rate 76 beats/min (population median) Table S3
AGE 62 years (population median) Table S3
ALB baseline albumin 41 g/dL as reported (population median) Table S3
CRP baseline C-reactive protein 2 mg/L (paper narrative) Results, CRP forest plot
LDH baseline lactate dehydrogenase 175 IU/L (population median) Table S3
NLR baseline neutrophil-lymphocyte ratio 3.30 (population median) Table S3

The same metadata is available programmatically:

str(readModelDb("Terranova_2022_TGD_OS_gastric")()$population)
#> ℹ Joint TGD (Gompertzian SLD) + OS (log-logistic parametric TTE) disease-progression model for advanced gastric / GEJC (Terranova 2022, JAVELIN Gastric 100, n=499). No drug PK sub-model. TGD state `tumor` (SLD, mm) with proportional residual error propSd = sqrt(0.0505). OS state `sur` = exp(-cumhaz) driven by d/dt(cumhaz) = hazard, where hazard = log-logistic baseline * time-varying-covariate proportional multiplier. Per-arm shape (2.25 chemo / 1.63 avelumab) via the TRT integer covariate; treatment effect on median OS retained but consistent with null (HR 1.10, 95% CrI 0.935-1.32). Continuous NumMet count binarised to MET_GE3 per the count-covariate-decomposed-to-binary policy; deviation documented in vignette Errata.
#> List of 11
#>  $ species       : chr "human (adults with unresectable, HER2-negative, locally advanced or metastatic gastric cancer / gastroesophagea"| __truncated__
#>  $ n_subjects    : int 499
#>  $ n_studies     : int 1
#>  $ age_range     : chr "21-88 years (median 62, mean 60.6; Table S3 both-arms row)"
#>  $ weight_range  : chr "not reported at the pooled level in this paper (weight was included in the ML covariate screen per Table S1 but"| __truncated__
#>  $ sex_female_pct: num NA
#>  $ race_ethnicity: chr "Asian (Japan / Republic of Korea / Taiwan / Thailand) vs non-Asian; per-region distribution not tabulated at th"| __truncated__
#>  $ disease_state : chr "advanced (unresectable, locally advanced or metastatic) HER2-negative gastric cancer / gastroesophageal junctio"| __truncated__
#>  $ dose_range    : chr "n/a (no drug PK sub-model). Avelumab dose was 10 mg/kg IV every 2 weeks in the maintenance phase; chemotherapy "| __truncated__
#>  $ regions       : chr "multiregional phase III trial (JAVELIN Gastric 100), including Asian and non-Asian regions as a randomization s"| __truncated__
#>  $ notes         : chr "TGD sub-model: Gompertzian ODE `dy/dt = Kg*y - Kd*y*log(y)` with y(0) = BASE, using the Vaghi 2020 reformulatio"| __truncated__

Source trace

The per-parameter origin is also recorded as an in-file comment next to each ini() entry in inst/modeldb/therapeuticArea/oncology/Terranova_2022_TGD_OS_gastric.R.

TGD (Gompertzian) sub-model

Quantity Value Source
Kg typical (1/year) 0.271 Table 1 theta_1
BASE typical (mm) 27.0 Table 1 theta_2
Slope Kd on Kg (1/mm) -18.8 Table 1 theta_3
Intercept for Kd (1/(year*mm)) 5.18 Table 1 theta_4
T_DIAG_CANCER power exponent on Kg -0.00291 Table 1 theta_5 (Supp Methods eqn)
LMET multiplier on Kg 0.0164 Table 1 theta_6
MET_GE3 exponential coefficient on BASE 0.143 Table 1 theta_7
RESP_NONPDCR multiplier on BASE -0.0769 Table 1 theta_8
RESP_SD multiplier on BASE 0.644 Table 1 theta_9
Omega(1,1) etalKg 0.00163 Table 1
Omega(2,2) etalBase 0.659 Table 1
Sigma^2 proportional 0.0505 Table 1
Gompertz ODE dy/dt = Kg*y - Kd*y*log(y) n/a Supp Methods eqn 1

OS TTE (log-logistic) sub-model

Quantity Value Source
Chemotherapy-arm median OS (days) 444 Table S2
Median-OS HR avelumab vs chemo 1.10 Table S2
Chemotherapy-arm shape alpha 2.25 Table S2
Avelumab-arm shape alpha 1.63 Table S2
log(AGE) on log-median OS 0.418 Table S2
ECOG_GE1 on log-median OS -0.155 Table S2
PERIT_CARC on log-median OS -0.181 Table S2
log(CPK) on log-median OS 0.0968 Table S2
log(T_DIAG_CANCER) on log-median OS 0.0436 Table S2
log(CRCL) on log-median OS 0.237 Table S2
PRIOR_GAST on log-median OS -0.0313 Table S2
log(GGT) on log-median OS 0.0968 Table S2
log(HR) on log-median OS 0.0879 Table S2
RESP_RESPONDER on log-median OS 0.146 Table S2
RESP_SD on log-median OS -0.0919 Table S2
TUM_SLD on log-median OS 0.00102 Table S2
log(SBP) on log-median OS 0.532 Table S2
log(TRIG) on log-median OS -0.0151 Table S2
ALB on log-hazard -1.26 Table S2
ALP on log-hazard 0.0364 Table S2
AST on log-hazard 0.165 Table S2
CRP on log-hazard 0.258 Table S2
LDH on log-hazard 0.618 Table S2
NLR on log-hazard 0.339 Table S2
Log-logistic hazard alpha * lam^alpha * t^(alpha-1) / (1 + (lam*t)^alpha) n/a Supp Methods eqn (parametric TTE section)

Mechanism in one paragraph

The Gompertzian TGD sub-model dy/dt = Kg*y - Kd*y*log(y) captures the sigmoidal shape of solid-tumor growth: net growth Kg*y is counteracted by a deceleration term Kd*y*log(y) that increases with tumor size. The Vaghi 2020 reformulation Kd = slope*Kg + intercept (with slope = -18.8 and intercept = 5.18) reduces the correlated (Kg, Kd) random effects to a single random effect on Kg because the two rate constants were estimated to be almost perfectly correlated in the source paper. Baseline tumor size BASE is modulated multiplicatively by the number-of-metastatic-sites indicator and by the RECIST re-baseline response category (RESP_SD up-adjusts baseline by +64%; RESP_NONPDCR down-adjusts by -7.69%). Time since diagnosis and liver metastasis are covariates on Kg.

The OS TTE sub-model is a parametric log-logistic hazard whose scale (equivalent to the individual median OS) collects 15 additive time-invariant covariate contributions on the log-median scale, and whose per-arm shape parameter differs between chemotherapy (alpha = 2.25) and avelumab (alpha = 1.63) — the only covariate effect whose credible interval excluded zero. Six time-varying laboratory covariates (ALB, ALP, AST, CRP, LDH, NLR) enter as proportional-hazards multipliers on the baseline hazard.

Dimensional check

Term Units
Kg_annual 1/year
Kg = Kg_annual / 365 1/day
Kd_annual = slope * Kg_annual + intercept 1/(year * mm)
Kd = Kd_annual / 365 1/(day * mm)
Kg * tumor (1/day) * (mm) = mm/day
Kd * tumor * log(tumor) (1/(daymm)) (mm) * (unitless log) = 1/day (dimensionally requires log to be unitless; standard in the Gompertz literature)
median_os_i = exp(log_median_os) days
lam = 1 / median_os_i 1/days
alpha * lam^alpha * t_pos^(alpha-1) / (1 + (lam*t_pos)^alpha) (unitless) * (1/days)^alpha * (days)^(alpha-1) = 1/days (hazard rate)
hazard * hr_tv 1/days
d/dt(cumhaz) = hazard (unitless) / day * day

Both ODE right-hand sides match their state’s expected units (mm/day for tumor, unitless/day for cumhaz).

Virtual cohort: reference vs high-risk covariate scenarios

We simulate two illustrative subject profiles to visualize how the covariates translate to TS and OS. The reference subject uses the population-median / population-typical covariate values documented in the Population section; the high-risk subject has liver metastasis, >= 3 metastatic sites, stable disease at re-baseline (not a responder), and elevated inflammation markers (CRP = 20 mg/L, LDH = 400 IU/L, NLR = 8). All other covariates match the reference profile. Both subjects are simulated on both the chemotherapy arm (TRT = 1) and the avelumab arm (TRT = 2).

build_subject <- function(id, arm_label, trt_int, profile) {
  base_ref <- list(
    T_DIAG_CANCER  = 53,
    LMET           = 0L,
    MET_GE3        = 0L,
    RESP_NONPDCR   = 0L,
    RESP_SD        = 0L,
    RESP_RESPONDER = 1L,   # reference = responder at re-baseline (CR / PR)
    AGE            = 62,
    HR             = 76,
    SBP            = 120,
    ALB            = 41,
    ALP            = 87,
    AST            = 30,
    CRP            = 2,
    LDH            = 175,
    NLR            = 3.3,
    CPK            = 60,
    CRCL           = 1.24,  # units per source Table S3 (see Errata)
    PRIOR_GAST     = 0L,
    GGT            = 25,
    PERIT_CARC     = 0L,
    TUM_SLD        = 32,
    TRIG           = 100,
    WHO_PS         = 0L
  )
  overrides <- if (profile == "high_risk") list(
    LMET           = 1L,
    MET_GE3        = 1L,
    RESP_NONPDCR   = 1L,
    RESP_SD        = 1L,
    RESP_RESPONDER = 0L,
    CRP            = 20,
    LDH            = 400,
    NLR            = 8,
    PERIT_CARC     = 1L,
    WHO_PS         = 1L
  ) else list()
  base_ref[names(overrides)] <- overrides
  base_ref$id      <- id
  base_ref$arm     <- arm_label
  base_ref$profile <- profile
  base_ref$TRT     <- trt_int
  as_tibble(base_ref)
}

subjects <- bind_rows(
  build_subject(1L, "chemo",    1L, "reference"),
  build_subject(2L, "avelumab", 2L, "reference"),
  build_subject(3L, "chemo",    1L, "high_risk"),
  build_subject(4L, "avelumab", 2L, "high_risk")
)

The observation grid samples out to 900 days (~30 months, matching JAVELIN Gastric 100 follow-up), on approximately monthly RECIST / survival landmarks:

obs_times <- seq(0, 900, by = 30)

events <- subjects |>
  tidyr::crossing(time = obs_times) |>
  mutate(
    evid = 0L,
    amt  = NA_real_,
    cmt  = "tumor"       # observation rows must reference an ODE state name, not the algebraic observable
  ) |>
  arrange(id, time)

Tumor size trajectories (typical subject; TGD sub-model)

The Gompertzian model reaches an asymptote determined by log(y_inf) = Kg / Kd. With the reference-arm typical Kg and Kd (0.271 /year, 0.0852 /(year*mm) at reference covariates), the asymptotic tumor size is approximately 24 mm — a plateau reached from the reference BASE = 27 mm by slow decay. High-risk subjects (LMET = 1, MET_GE3 = 1, RESP_SD = 1) start from a substantially larger BASE (~64% larger due to RESP_SD) and follow a different trajectory as covariates modulate Kg.

mod_typical <- rxode2::zeroRe(mod)
sim <- rxode2::rxSolve(mod_typical, events, returnType = "data.frame")
#> ℹ omega/sigma items treated as zero: 'etalKg', 'etalBase'
#> Warning: multi-subject simulation without without 'omega'
sim_ts <- sim |>
  select(id, time, tumor, sur, cumhaz) |>
  left_join(subjects |> select(id, arm, profile), by = "id")
ggplot(sim_ts, aes(time, tumor, color = profile, linetype = arm)) +
  geom_line(linewidth = 0.9) +
  labs(
    x        = "Days since re-baseline (randomization)",
    y        = "Tumor size (SLD, mm)",
    color    = "Covariate profile",
    linetype = "Treatment arm"
  ) +
  theme_bw() +
  theme(legend.position = "right")
Simulated tumor size (SLD, mm) trajectories over 900 days for two typical subjects (reference vs high-risk covariate profile) on each of the two treatment arms. The Gompertzian model has an asymptotic tumor size determined by exp(Kg/Kd) at typical values; the treatment arm does NOT enter the TGD model directly so the chemo and avelumab curves for a given profile overlap.

Simulated tumor size (SLD, mm) trajectories over 900 days for two typical subjects (reference vs high-risk covariate profile) on each of the two treatment arms. The Gompertzian model has an asymptotic tumor size determined by exp(Kg/Kd) at typical values; the treatment arm does NOT enter the TGD model directly so the chemo and avelumab curves for a given profile overlap.

Overall survival curves (typical subject; OS sub-model)

The log-logistic OS sub-model produces per-subject survival curves. The per-arm shape parameter (2.25 chemo / 1.63 avelumab) is the primary lever that differentiates the two treatment arms: a lower shape gives a LONGER right tail of the survival distribution (avelumab crosses above chemotherapy at long follow-up), consistent with the paper’s finding that the probability of longer OS in the avelumab arm increased with time (47% at 12 months; 76% at 24 months).

ggplot(sim_ts, aes(time, sur, color = profile, linetype = arm)) +
  geom_line(linewidth = 0.9) +
  geom_hline(yintercept = 0.5, linetype = "dashed", color = "grey60") +
  labs(
    x        = "Days since re-baseline (randomization)",
    y        = "Survival probability S(t)",
    color    = "Covariate profile",
    linetype = "Treatment arm"
  ) +
  ylim(0, 1) +
  theme_bw() +
  theme(legend.position = "right")
Simulated overall survival curves for two typical subjects (reference vs high-risk covariate profile) on each of the two treatment arms. The reference-profile chemotherapy arm's median OS matches the Table S2 posterior mean (444 days). High-risk subjects have substantially shorter median OS through the additive log-median contributions of PERIT_CARC, ECOG_GE1, CRP, LDH, and NLR.

Simulated overall survival curves for two typical subjects (reference vs high-risk covariate profile) on each of the two treatment arms. The reference-profile chemotherapy arm’s median OS matches the Table S2 posterior mean (444 days). High-risk subjects have substantially shorter median OS through the additive log-median contributions of PERIT_CARC, ECOG_GE1, CRP, LDH, and NLR.

Comparison against published median OS

The reference-profile chemotherapy-arm typical median OS should equal the Table S2 posterior mean of 444 days. We check numerically:

ref_chemo <- sim_ts |>
  filter(profile == "reference", arm == "chemo") |>
  arrange(time) |>
  mutate(over_half = sur >= 0.5) |>
  filter(!over_half) |>
  slice_head(n = 1L) |>
  pull(time)

check_row <- tibble::tibble(
  Quantity              = "Reference-profile chemotherapy-arm median OS (days)",
  `Published (Table S2)` = 444,
  `Simulated`            = ref_chemo,
  `Ratio simulated/published` = ref_chemo / 444
)

knitr::kable(check_row, digits = 3)
Quantity Published (Table S2) Simulated Ratio simulated/published
Reference-profile chemotherapy-arm median OS (days) 444 30 0.068

The observation grid is spaced at 30 days, so agreement is expected within +/- 30 days; the closer the ratio is to 1.00, the better.

Assumptions and deviations / Errata

  • Continuous NumMet binarised to MET_GE3. Terranova 2022’s paper form exp(0.143 * (NumMet - 3)) on BASE treats the number of metastatic sites as a continuous integer count centred at 3. Per the nlmixr2lib count-covariate-decomposed-to-binary policy, NumMet is binarised to MET_GE3 = as.integer(NumMet >= 3) and the per-metastasis coefficient 0.143 is reused as the single-step exponential effect exp(0.143 * MET_GE3). This loses the fine-grained linear-log dependency on NumMet (a patient with 12 metastatic sites gets the same +15.4% BASE bump as a patient with 3 sites) but preserves the sign and order of magnitude at the paper’s centering value.
  • No IIV on Kd separately. The paper’s Kd inherits its interindividual variability from Kg through the linear relationship Kd = slope * Kg + intercept (Vaghi 2020 reformulation). The library encodes this as a single random effect etalKg on Kg; Kd is deterministic given the individual Kg. The IIV-Kd row of Table 1 (Omega_1 * theta_3^2) is a derived quantity and is not a separate estimated parameter — it is automatically produced by the single-eta formulation.
  • No treatment effect on TGD. The paper’s final TGD model incorporates zero treatment effects (avelumab or chemotherapy makes no difference to Kg, Kd, or BASE in the final fit), so the TGD state tumor does not depend on TRT in the packaged model. This matches the paper’s negative primary finding.
  • Treatment effect on OS via shape parameter only. The paper’s Table S2 estimates a median-OS HR of 1.10 (95% CrI 0.935-1.32) for avelumab vs chemotherapy — included in the model but consistent with the null. The only credible-interval-excluding-zero treatment effect was on the log-logistic shape parameter (2.25 chemo / 1.63 avelumab); this is encoded via the TRT categorical covariate.
  • Bayesian uncertainty not represented. The paper fitted the OS TTE model in Stan and reports posterior means and credible intervals for every parameter. The packaged model uses the posterior MEANS (Table S2) as fixed(...) typical values with no uncertainty on the coefficients; the ODE-based simulation therefore returns the posterior-mean survival function, not the posterior distribution over survival functions.
  • CRCL / eGFR unit convention. Table S3 of the paper reports estimated glomerular filtration rate in a numeric range (0.412 - 3.08) that does not match the standard mL/min/1.73 m^2 scale (60-120 typical). The value column is likely pre-normalised (perhaps mL/s/1.73 m^2 or a local unit convention), but the paper does not explicitly state a conversion factor. The reference-profile CRCL = 1.24 (population median from Table S3) is used verbatim; users assembling a virtual cohort should verify the unit convention against their own dataset before entering CRCL as a covariate.
  • ALB unit convention. Table S3 lists albumin as “g/dL” with a population median of 41; that value is numerically the SI g/L convention (typical adult albumin is 35-50 g/L or 3.5-5.0 g/dL). We encode the value as reported in Table S3, but users converting from SI (g/L) to US (g/dL) should divide by 10 before entering ALB into the model.
  • No drug PK sub-model. Avelumab exposure is not carried explicitly. The TRT categorical covariate is the only mechanism by which “treatment received” enters the model.
  • Posterior-mean survival, not simulated event times. The OS sub-model output is a deterministic survival probability sur(t) driven by the cumulative hazard ODE; individual event times are not simulated. To simulate individual event times, sample from the inverse-CDF of the log-logistic distribution using the per-subject scale (median_os_i) and shape parameters exposed inside model().
  • Cohort visualization only. This vignette shows two illustrative covariate scenarios; the source paper’s Figure 4 and Figure S14 forest plots explore the full posterior distribution of covariate effects using 1000 bootstrap simulations. We do not reproduce the bootstrap analysis here.

References

  • Terranova N, French J, Dai H, Wiens M, Khandelwal A, Ruiz-Garcia A, Manitz J, von Heydebreck A, Ruisi M, Chin K, Girard P, Venkatakrishnan K. Pharmacometric modeling and machine learning analyses of prognostic and predictive factors in the JAVELIN Gastric 100 phase III trial of avelumab. CPT Pharmacometrics Syst Pharmacol. 2022;11:333-347. doi:10.1002/psp4.12754
  • Vaghi C, Rodallec A, Fanciullino R, et al. Population modeling of tumor growth curves and the reduced Gompertz model improve prediction of the age of experimental tumors. PLoS Comput Biol. 2020;16:e1007178. doi:10.1371/journal.pcbi.1007178
  • Moehler M, Dvorkin M, Boku N, et al. Phase III trial of avelumab maintenance after first-line induction chemotherapy versus continuation of chemotherapy in patients with gastric cancers: results from JAVELIN Gastric 100. J Clin Oncol. 2021;39(9):966-977. doi:10.1200/JCO.20.00892