Estimation from Recall-Based Competing Risk Data: A Multilevel Framework

Abstract This study aims to analyze recall-based data on multiple causes of an event, hypothesizing that the likelihood of recall depends on the elapsed time between monitoring and the time-to-event. The recall probability is modeled using this elapsed time. Addressing the challenge posed by non-recalled observations, which yield interval-censored time-to-event data often with missing causes, the equivalent quantity approach with expectation-maximization and Gibbs sampling are employed. This method handles censored time-to-event data while simultaneously addressing missing causes. Weibull distributions for time-to-event under different causes are considered. In the frequentist approach, parameter estimates are obtained via the expectation-maximization method, with asymptotic confidence intervals calculated using the Fisher information matrix. In the Bayesian setting, a data augmentation algorithm approach is proposed for handling missingness, and nested Gibbs sampling is employed to extract posterior samples. The validation of our methods is conducted through numerical simulations and the analysis of a women's health survey dataset to estimate the age at menopause.