Random survival forests for the analysis of recurrent events for right-censored data, with or without a terminal event

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BACKGROUND: Random survival forests (RSF) have emerged as valuable tools in medical research. They have shown their utility in modelling complex relationships between predictors and survival outcomes, overcoming linearity or low dimensionality assumptions. Nevertheless, RSF have not been adapted to right-censored data with recurrent events (RE). METHODS: This work introduces RecForest, an extension of RSF and tailored for RE data, leveraging principles from survival analysis and ensemble learning. RecForest adapts the splitting rule to account for RE, with or without a terminal event, by employing the pseudo-score test or the Wald test derived from the marginal Ghosh-Lin model. The ensemble estimate is constructed by aggregating the expected number of events from each tree. Performance metrics involve a concordance index (C-index) tailored for RE analysis, along with an extension of the mean squared error (MSE). A comprehensive evaluation was conducted on both simulated and open-source data. We compared RecForest against the non-parametric mean cumulative function and the Ghosh-Lin model. RESULTS: Across the simulations and application, RecForest consistently outperforms, exhibiting C-index values ranging from 0.60 to 0.82 and lowest MSE metrics. CONCLUSIONS: As analysing time-to-recurrence data is critical in medical research, the proposed method represents a valuable addition to the analytical toolbox in this domain. The RecForest implementation is publicly available as an R package on CRAN.

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