Penalized Estimation of Cumulative Effects

Abstract

Modeling effects of time dependent covariates (TDC) introduces additional complexity to time-to-event analysis, especially when these effects are assumed to depend on the complete or partial history of the TDC. Such effects are often referred to as cumulative effects. We present a general framework for penalized estimation of such effects, that potentially vary non-linearly with respect to timing and amount of the TDC as well as over time. Moreover, the time-window of past exposures that may affect the hazard at time $t$ can be specified flexibly. As we embed our approach in the framework of Generalized Additive Mixed Models,robust algorithms for estimation, as well as powerful inference procedures are readily available. We illustrate the proposed method, by investigating the association between daily caloric intake on the intensive care unit and acute survival in critically ill patients.