Cause-Specific Cox and Fine-Gray Regression in Competing Risks: A Reproducible Synthetic Prostate Cancer Illustration

Abstract

Background: Competing mortality complicates estimation and interpretation of prostate cancer-specific death. Cause-specific Cox and Fine-Gray models answer related but different questions and should be selected according to the target estimand.
Objective: To demonstrate, using a fully reproducible fixed synthetic dataset, how cause-specific and subdistribution hazard estimands differ in risk-set construction, regression interpretation, and relation to cumulative incidence.
Methods: A single fixed dataset of 500 synthetic observations was generated using seed 123. Covariates, treatment indicators, follow-up time sampled from 1-60 months, and event status sampled with probabilities 0.20 for prostate cancer death, 0.20 for other-cause death, and 0.60 for censoring were mutually independent; therefore, no covariate or treatment effects were encoded. Multivariable cause-specific Cox and Fine-Gray models included 15 regression parameters. Cumulative incidence functions, proportionality diagnostics, event-per-parameter calculations, an exploratory other-cause Cox model, and comparison with the naive Kaplan-Meier complement were examined.
Results: Within this single realization, the fitted hormonal-therapy estimates were below unity in both models (CSHR 0.568, 95% CI 0.381-0.849; SHR 0.605, 95% CI 0.405-0.903). Stage III versus stage I had estimates in the same direction and of comparable magnitude (CSHR 2.227, 95% CI 1.045-4.746; SHR 2.006, 95% CI 0.948-4.245), and the difference in p-value thresholds was not interpreted as model disagreement. Global proportionality tests were not significant for the primary cause-specific Cox (p = 0.605) or Fine-Gray (p = 0.550) model. At 60 months, the naive Kaplan-Meier complement exceeded the cumulative incidence estimate by 12.2 percentage points, although only seven observations remained at risk.
Conclusions: This reproducible worked example demonstrates that cause-specific Cox and Fine-Gray models provide complementary, estimand-specific descriptions of competing-risks data. Because the generator encoded zero covariate effects, the fitted coefficients are illustrative sample estimates and do not establish treatment effects, clinical associations, or real-world prostate cancer prognosis.