A nonparametric vertical model: An application to discrete time competing risks data with missing failure causes

Discrete time competing risks data continue to arise in social sciences, education etc., where time to failure is usually measured in discrete units. This data may also come with unknown failure causes for some subjects. This occurs against a background of very limited discrete time analysis methods that were developed to handle such data. A number of continuous time missing failure causes models have been proposed over the years. We select one of these continuous time models, the vertical model (Nicolaie et al., 2015), and present it as a nonparametric model that can be applied to discrete time competing risks data with missing failure causes. The proposed model is applied to real data and compared to the MI. It was found that the proposed model compared favorably with the MI method

A mixture model with application to discrete competing risks data

In this paper, we modify the continuous time mixture competing risks model (Larson and Dinse, 1985) to handle discrete competing risks data. The main result of the model is an alternate regression expression for the cumulative incidence function. The structure of the regression expression for the cumulative incidence function under this model, and the proportional hazards assumption for the conditional hazard rates with piece-wise constant baseline conditional hazards, combine to allow for another means to assess the covariate effects on the cumulative incidence function. This benefit comes at some computational costs because the parameters are estimated via an EM algorithm. The proposed model is applied to real data and it is found that it improves the exercise of evaluating the covariate effects on the cumulative incidence function compared to other discrete competing risks models