Generalized Competing Event Modeling with gcemod

What gcemod does

gcemod estimates covariate effects on omega+ — the ratio of the hazard for an event of interest to the hazard for a competing event — on either the cause-specific (Cox) or subdistribution (Fine-Gray) scale. Confidence intervals and p-values come from the Lunn-McNeil stacked-model construction. Per-subject omega = omega+/(1+omega+) is reported as a descriptive quantity so model-predicted values can be compared with observed ones.

The workflow: (1) fit the GCE model, (2) build a risk score, (3) find cutpoints that maximize the omega+ difference between groups, (4) draw alligator plots of cumulative incidence by group, and (5) check calibration of predicted vs. observed omega+.

Two contrasting cohorts

The package bundles two competing-risks example datasets that illustrate contrasting GCE applications. They are provided for illustration only and do not represent real patients. In hn (head and neck) the event of interest (cancer recurrence) is more frequent than the competing event (omega+ > 1). In prostate the event of interest (distant metastasis or prostate-cancer death) is less frequent than the competing event (other-cause death) (omega+ < 1). Both use status: 0 = censored, 1 = event of interest, 2 = competing event, with time in years.

data(hn)
Ind <- data.frame(event     = as.integer(hn$status == 1),   # recurrence
                  competing = as.integer(hn$status == 2))   # death w/o recurrence
Cov <- hn[, c("age", "smoker", "t_cat", "n_cat", "p16")]

fit <- gcecox(hn$time, Ind, Cov, M = 5, t = 5)
summary(fit)
#> Generalized competing event model [Cox (cause-specific)]
#> Call: gcecox(Time = hn$time, Ind = Ind, Cov = Cov, M = 5, t = 5)
#>   n = 1000;  events of interest = 391;  competing events = 243;  t = 5
#> 
#> --- omega+ ratio (event of interest vs. competing event) ---
#>        exp(coef) (omega+ ratio) lower .95 upper .95 P-value
#> age                     0.93295   0.91310   0.95323 0.00000
#> smoker                  0.71795   0.49232   1.04697 0.08516
#> t_cat2                  1.00580   0.40885   2.47437 0.98995
#> t_cat3                  0.80732   0.33493   1.94596 0.63349
#> t_cat4                  0.90705   0.37726   2.18085 0.82747
#> n_cat1                  1.26583   0.71349   2.24574 0.42031
#> n_cat2                  1.30179   0.84012   2.01715 0.23788
#> n_cat3                  0.91398   0.47167   1.77110 0.78987
#> p16                     0.64152   0.38994   1.05542 0.08053
#> 
#> Lunn-McNeil omnibus test: chi-sq = 49.215, df = 9, p = <1e-04

fit_fg <- gcefg(hn$time, Ind, Cov, M = 5, t = 5)
summary(fit_fg)

head(data.frame(riskscore = fit$riskscore,
                omegaplus = fit$omegaplus, omega = fit$omega))
#>    riskscore omegaplus     omega
#> 1  0.3111360 2.4611482 0.7110785
#> 2  1.6653168 9.5334700 0.9050645
#> 3  0.5548256 3.1402976 0.7584715
#> 4 -0.5955188 0.9939913 0.4984933
#> 5 -0.1996211 1.4767900 0.5962516
#> 6  0.4918702 2.9486935 0.7467517

cuts <- gce_cutpoints(fit, groups = 2, method = "optimal")
cuts$summary
#>   group   n events_of_interest competing_events mean_omegaplus mean_omega
#> 1   Low 484                181              167       1.105913  0.5070653
#> 2  High 516                210               76       3.396035  0.7458401
cuts$cutpoints
#> [1] -0.02022627

gce_alligator(fit, groups = cuts)

gce_calibration(fit, which = "omegaplus", groups = 5)

gce_performance(fit)
#> C-index (event of interest): 0.502 (95% CI 0.471-0.532)  [risk-score orientation flipped]

The competing-dominant contrast: prostate

Running the same workflow on prostate shows the opposite regime. Here the competing event (other-cause death) dominates, so omega+ ratios and the risk score point the other way, and the alligator jaws open with the competing-event CIF on top.

data(prostate)
Ind_p <- data.frame(event     = as.integer(prostate$status == 1),
                    competing = as.integer(prostate$status == 2))
Cov_p <- prostate[, c("age", "psa", "gleason", "t2b", "comorbidity")]

fit_p <- gcecox(prostate$time, Ind_p, Cov_p, M = 5, t = 5)
summary(fit_p)
gce_alligator(fit_p, groups = 2)

References

Lunn M, McNeil D (1995) Applying Cox regression to competing risks. Biometrics 51:524–32.

Carmona R, et al. (2014) Validated competing event model for the stage I-II endometrial cancer population. Int J Radiat Oncol Biol Phys 89:888–98.

Carmona R, et al. (2016) Improved method to stratify elderly patients with cancer at risk for competing events. J Clin Oncol 34:1270–77.

Mell LK, et al. (2019) Nomogram to predict the benefit of intensive treatment for locoregionally advanced head and neck cancer. Clin Cancer Res 25:7078–7088.

Zakeri K, et al. (2020) Predictive classifier for intensive treatment of head and neck cancer. Cancer 126:5263–5273.

Mell LK, et al. (2024) Effects of androgen deprivation therapy on prostate cancer outcomes according to competing event risk. Eur Urol 85:373–381.