Individual risk prediction: Comparing random forests with Cox proportional-hazards model by a simulation study

Area of Science:

• Biostatistics
• Machine Learning in Healthcare
• Survival Analysis

Background:

• Big data in healthcare necessitates advanced risk prediction models.
• Machine learning algorithms like Random Forest (RF) and Random Survival Forest (RSF) are alternatives to the Cox Proportional Hazards (Cox-PH) model.
• RF ignores time-to-event data, while RSF handles right-censored data.

Purpose of the Study:

• To systematically compare the performance of RF and RSF against Cox-PH for individual risk prediction.
• To evaluate various RSF split criteria (log-rank, log-rank score, maximally selected rank statistics) and Cox-PH with splines (Cox-S).

Main Methods:

• A simulation study based on real data was conducted across 180 scenarios.
• Scenarios varied predictor-outcome associations, training sample sizes, censoring rates, hazard functions, and number of predictors (including noise variables).
• Performance was assessed using time-dependent area under the curve and integrated Brier score.

Main Results:

• Random Forest (RF) consistently showed the worst performance across all scenarios.
• Cox-PH was non-inferior or superior to RSF in low-event scenarios and under linearity assumptions.
• RSF demonstrated better performance than Cox-PH with increasing events and interactions; Cox-S performed similarly to RSF under nonlinear effects.
• RSF algorithms incorporating survival time outperformed others when applied to real data.

Conclusions:

• Random Survival Forest (RSF) algorithms are promising alternatives to Cox-PH, especially with increasing data complexity.
• RSF models require a higher number of events for effective training compared to Cox-PH.
• For time-to-event analysis, utilizing algorithms that explicitly consider survival time is recommended.