A comparative study of forest methods for time-to-event data: variable selection and predictive performance

Background As a hot method in machine learning field, the forests approach is an attractive alternative approach to Cox model. Random survival forests (RSF) methodology is the most popular survival forests method, whereas its drawbacks exist such as a selection bias towards covariates with many possible split points. Conditional inference forests (CIF) methodology is known to reduce the selection bias via a two-step split procedure implementing hypothesis tests as it separates the variable selection and splitting, but its computation costs too much time. Random forests with maximally selected rank statistics (MSR-RF) methodology proposed recently seems to be a great improvement on RSF and CIF. Methods In this paper we used simulation study and real data application to compare prediction performances and variable selection performances among three survival forests methods, including RSF, CIF and MSR-RF. To evaluate the performance of variable selection, we combined all simulations to calculate the frequency of ranking top of the variable importance measures of the correct variables, where higher frequency means better selection ability. We used Integrated Brier Score (IBS) and c-index to measure the prediction accuracy of all three methods. The smaller IBS value, the greater the prediction. Results Simulations show that three forests methods differ slightly in prediction performance. MSR-RF and RSF might perform better than CIF when there are only continuous or binary variables in the datasets. For variable selection performance, When there are multiple categorical variables in the datasets, the selection frequency of RSF seems to be lowest in most cases. MSR-RF and CIF have higher selection rates, and CIF perform well especially with the interaction term. The fact that correlation degree of the variables has little effect on the selection frequency indicates that three forest methods can handle data with correlation. When there are only continuous variables in the datasets, MSR-RF perform better. When there are only binary variables in the datasets, RSF and MSR-RF have more advantages than CIF. When the variable dimension increases, MSR-RF and RSF seem to be more robustthan CIF Conclusions All three methods show advantages in prediction performances and variable selection performances under different situations. The recent proposed methodology MSR-RF possess practical value and is well worth popularizing. It is important to identify the appropriate method in real use according to the research aim and the nature of covariates.