A Bayesian Bernoulli-Exponential Joint Model for Binary Longitudinal Outcomes and Informative Time with Applications to Bladder Cancer Recurrence Data

Background: A variety of methods exist for the analysis of longitudinal data, many of which are characterized with the assumption of fixed visit time points for study individuals. This, however is not always a tenable assumption. Phenomenon that alter subject visit patterns such as adverse events due to investigative treatment administered, travel or any other emergencies may result in unbalanced data and varying individual visit time points. Visit times can be considered informative, because subsequent or current subject outcomes can change or be adapted due to previous subject outcomes. Methods: In this paper, a Bayesian Bernoulli-Exponential model for analyzing joint binary outcomes and exponentially distributed informative visit times is developed. Via statistical simulations, the influence of controlled variations in visit patterns, prior and sample size schemes on model performance is assessed. As an application example, the proposed model is applied to a Bladder Cancer Recurrence data. Results and Conclusions: Results from the simulation analysis indicated that the Bayesian Bernoulli-Exponential joint model converged in stationarity, and performed relatively better for small to medium sample size scenarios with less varying time sequences regardless of the choice of prior. In larger samples, the model performed better for less varying time sequences. This model's application to the bladder cancer data showed a statistically significant effect of prior tumor recurrence on the probability of subsequent recurrences.