Testing for Single Against Competing Risks Models in Survival Analysis

Abstract

In the competing risks model the type and time of the first event are observed and the other latent event is unobserved. This model is widely used in engineering, biology and, recently, social sciences. However, if types of an event are inessential, time to an event can be analyzed more accurately using a single risk model than a competing risks model. Specification testing for single and competing risks model would be of importance, since these two models are difficult to identify empirically. We then propose the Lagrange multiplier test for the null hypothesis of single risk against dependent competing risks model under the proportional hazard model assumption. The test utilizes the fact that single risk model is a limiting case of competing risks model where bivariate survival distributions are perfectly correlated.