Use of Additional Information for Current Status Data with Two Competing Risks and Missing Failure Types

In practice, the failure type for some subjects may be missing or uncertain in competing risks data. Analysis of such uncertain failure type in current status data with two competing risks suffers from issues of model identifiability and requires some model assumptions to deal with that (Koley and Dewanji. Journal of Applied Statistics 49(7), (2022)). In this work, we attempt to alleviate this identifiability problem using some additional information and without any such model assumption. In particular, we consider additional information in the form of some prior knowledge on the missing probabilities. Next, we briefly discuss another type of additional information from a validation sample which ascertains failure type. We consider parametric estimation of the model parameters and non-parametric estimation of the sub-distribution functions. We investigate the associated large sample properties theoretically and the finite sample properties through simulation. We also consider analysis of a real data set for the purpose of illustration.