Incorporating temporal features of repeatedly measured covariates into tree-structured survival models

Tree-structured survival methods empirically identify a series of covariate-based binary split points, resulting in an algorithm that can be used to classify new patients into risk groups and subsequently guide clinical treatment decisions. Traditionally, only fixed-time (e.g. baseline) values are used in tree-structured models. However, this manuscript considers the scenario where temporal features of a repeated measures polynomial model, such as the slope and/or curvature, are useful for distinguishing risk groups to predict future outcomes. Both fixed- and random-effects methods for estimating individual temporal features are discussed, and methods for including these features in a tree model and classifying new cases are proposed. A simulation study is performed to empirically compare the predictive accuracies of the proposed methods in a wide variety of model settings. For illustration, a tree-structured survival model incorporating the linear rate of change of depressive symptomatology during the first four weeks of treatment for late-life depression is used to identify subgroups of older adults who may benefit from an early change in treatment strategy.