Cox versus Random Survival Forest for prostate Cancer mortality prediction: a retrospective competing risks analysis of 14,294 Patients
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Abstract
Machine learning survival models are increasingly applied to prostate cancer risk stratification, yet rigorous comparisons with traditional approaches accounting for competing mortality remain limited. We hypothesized that Random Survival Forest would demonstrate superior discrimination compared to Cox proportional hazards modelling. We analysed 14,294 prostate cancer patients (median follow-up 30 months). Cox and Random Survival Forest models were developed using grade, stage, and age. Proportional hazards were assessed via Schoenfeld residuals, with stage used as stratification where violated. Competing risks were modelled using Fine-Gray regression. Models were compared on an independent test set using C-index, time-dependent AUC, Integrated Brier Score, and calibration plots. Poor tumour grade was the strongest prognostic factor across all approaches (Cox HR = 4.15, p < 0.001; RSF importance = 0.374; Fine-Gray SHR = 3.91, p < 0.001). Age demonstrated a dose-response relationship, with patients aged 80+ years showing markedly elevated risk (Cox HR = 3.39; Fine-Gray SHR = 2.82; both p < 0.001). Both models demonstrated good discrimination (Cox C-index = 0.754, 95% CI: 0.731–0.777; RSF C-index = 0.734, 95% CI: 0.711–0.757) and excellent calibration (IBS: Cox = 0.063, RSF = 0.064; p = 0.215). Time-dependent AUC favoured RSF across all time points, though absolute differences were modest (ΔAUC = +0.005 to +0.019; all p = 0.05). Our hypothesis was not supported. RSF did not meaningfully outperform a well-specified Cox model. Both models provide excellent, nearly equivalent predictive performance. Traditional methods remain clinically appropriate; machine learning offers complementary value for time-dependent prediction but does not justify routine replacement.
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