A Bayesian Proportional Mean Model Using Panel Binary Data-An Application to Health and Retirement Study

Abstract: In recurrent event studies, panel binary data arise when subjects are observed at discrete time points and only the recurrent event status within each observation window is recorded. Such data frequently occur in longitudinal studies due to recall difficulties or participants' privacy concerns during follow-ups, necessitating rigorous statistical analysis. While frequentist methods exist for handling such data, Bayesian approaches remain largely unexplored. This article proposes an efficient Bayesian proportional mean model for analysing recurrent events using panel binary data. In addition to the estimation procedure, the article introduces techniques for model validation, selection, and Bayesian influence diagnostics. Simulation studies demonstrate the method's effectiveness and robustness in different practical scenarios. The proposed approach is then applied to analyse the latest version of the Health and Retirement Study dataset, identifying key risk factors influencing doctor visits among the elderly. The analysis is therefore capable of providing valuable insights into healthcare utilisation patterns in ageing populations.