Model Selection for the Competing-Risks Model With and Without Masking

The competing risks model is useful in settings in which individuals (or units) may die (or fail) due to a number of different causes. It can also be the case that for some of the items the failure cause is known only up to a subgroup of all causes in which case we say that the failure is group masked. A widely used approach for competing risks data with and without masking involves the specification of cause-specific hazard rates. Often, due to the availability of likelihood methods for estimation and testing, piecewise constant hazards are used. The piecewise constant rates also offer model flexibility and 1 computational convenience. However, for such piecewise constant hazard models the choice of the end points for each interval on which the hazards are constant is usually a subjective one. In this paper we discuss and propose the use of model selection methods that are data driven and automatic. We compare three model selection procedures, based on the Minimum Description Length (MDL) principle, the Bayes Information Criterion (BIC) and the Akaike Information Criterion (AIC). A fast splitting algorithm is the computational tool used to select among an enormous number of possible models. We test the effectiveness of the methods via numerical studies, including a real dataset with masked failure causes. key words: Akaike information criterion; Bayesian information criterion; Code length; Competing risks; EM algorithm; Group masked cause; Minimum description length principle; Missing data; Model selection; Piecewise constant hazard