Abstract

In cross-sectional retrospective studies, the subjects are monitored at any time, and the status of the event of interest is noted. Furthermore, if they had witnessed the event, they were asked to recall it. Among all subjects, some are able to recall the time of an event exactly, and some of them recall it at month level or at year level, and some of them are unable to recall it at all. Thus, the observed data is noted at multiple levels. In the competing risks scenario, the time of the event as well as the associated causes of the event are of interest. In our current study, we consider the multi-level recall-based data under competing risk scenarios. We assume that when the subject is able to recall the time of the event, associated causes are also recalled. In case the time of the event is not recalled exactly, we have only partial information on the time, and the associated causes are not recalled at all. The fact that memory fades with time makes censoring informative and is incorporated in modeling. We model recall probabilities as a function of time between monitoring and an event of interest. The time to the event is assumed to follow the Weibull distribution, with different shapes and scales associated with different causes. For point estimation, an expectation-maximization algorithm is used. For interval estimation, the observed Fisher information matrix is calculated using the missing information principle. For varying sample sizes, an extensive simulation study is conducted to assess the effect of different levels of non-recall and censoring. Finally, we illustrate the applicability of the proposed methods with the help of real data.