Variable selection for discrete competing risks models

Abstract

In competing risks models one distinguishes between several distinct target events that end duration. Since the effects of covariates are specific to the target events, the model contains a large number of parameters even when the number of predictors is not very large. Therefore, reduction of the complexity of the model, in particular by deletion of all irrelevant predictors, is of major importance. A selection procedure is proposed that aims at selection of variables rather than parameters. It is based on penalization techniques and reduces the complexity of the model more efficiently than techniques that penalize parameters separately. An algorithm is proposed that yields stable estimates. We consider reduction of complexity by variable selection in two applications, the evolution of congressional careers of members of the US congress and the duration of unemployment.

Modeling Discrete Time-to-Event Data

“…The tuning parameters themselves have to be chosen, for example, by cross-validation. For details, see Möst et al (2015).…”

“…The hazard rate for losing either a primary or a general election is rather constant in the considered group. For more details, in particular on the selection of effects, see Möst (2014) and Möst et al (2015). u t…”

Dynamic clinical prediction models for discrete time‐to‐event data with competing risks—A case study on the OUTCOMEREA database

“…The likelihood contribution of patient i is then (Möst, Pößnecker, & Tutz, ): Under the assumption of noninformative censoring, the censoring mechanism does not depend on the time‐dependent covariate vector , , and the factor in can be omitted: …”

Competing risks analysis for discrete time‐to‐event data

“…Narendranathan and Stewart (1993) specified a parametric function for the baseline coefficients that was motivated by the discretization of a Weibull distribution in continuous time. Möst, Pößnecker, and Tutz (2016) extended these approaches by developing a penalized estimation technique for smoothing the baseline coefficients that also incorporates variable selection (implemented in the R package MRSP). The penalty, which is subtracted from (4) for penalized maximum likelihood estimation, consists of a sum of the squared differences between neighboring baseline coefficients (or, alternatively, coefficients of neighboring spline basis functions) plus an L 1 penalty that enforces simultaneous inclusion or exclusion of a covariate from all cause‐specific predictors.…”

“…Details on the interpretation of random‐effects terms in time‐to‐event models, which has to be undertaken with some care, have been given in Austin (2017). Time‐dependent covariates, which can be incorporated into Model (2) with relative ease due to the binary structure in (3), have been considered, among others, in Luo et al (2016), Möst et al (2016), and Heyard et al (2019). Models with time‐varying covariate effects have been considered in McCall (1996).…”