Modeling Missing Covariate Data and Temporal Features of Time-Dependent Covariates in Tree-Structured Survival Analysis

Tree-structured survival analysis (TSSA) is used to recursively detect covariate values that best divide the sample into subsequent subsets with respect to a time to event outcome. The result is a set of empirical classification groups, each of which identifies individuals with more homogeneous risk than the original sample. We propose methods for managing missing covariate data and also for incorporating temporal features of repeatedly measured covariates into TSSA. First, for missing covariate data, we propose an algorithm that uses a stochastic process to add draws to an existing single tree-structured imputation method. Secondly, to incorporate temporal features of repeatedly measured covariates, we propose two different methods: (1) use a two-stage random effects polynomial model to estimate temporal features of repeatedly measured covariates to be used as TSSA predictor variables, and (2) incorporate other types of functions of repeatedly measured covariates into existing time-dependent TSSA methodology. We conduct simulation studies to assess the accuracy and predictive abilities of our proposed methodology. Our methodology has particular public health importance because we create, interpret and assess TSSA algorithms that can be used in a clinical setting to predict response to treatment for late-life depression.