Identification of interactions of binary variables associated with survival time using survivalFS

Many medical studies aim to identify factors associated with a time to an event such as survival time or time to relapse. Often, in particular, when binary variables are considered in such studies, interactions of these variables might be the actual relevant factors for predicting, e.g., the time to recurrence of a disease. Testing all possible interactions is often not possible, so that procedures such as logic regression are required that avoid such an exhaustive search. In this article, we present an ensemble method based on logic regression that can cope with the instability of the regression models generated by logic regression. This procedure called survivalFS also provides measures for quantifying the importance of the interactions forming the logic regression models on the time to an event and for the assessment of the individual variables that take the multivariate data structure into account. In this context, we introduce a new performance measure, which is an adaptation of Harrel's concordance index. The performance of survivalFS and the proposed importance measures is evaluated in a simulation study as well as in an application to genotype data from a urinary bladder cancer study. Furthermore, we compare the performance of survivalFS and its importance measures for the individual variables with the variable importance measure used in random survival forests, a popular procedure for the analysis of survival data. These applications show that survivalFS is able to identify interactions associated with time to an event and to outperform random survival forests.