Seongho Song, PhD, Department of Mathematics, University of Cincinnati

"Bayesian Multivariate Gamma-Frailty Cox Model For Clustered Current Status Data"

Biomedical data analysis plays a key role in today's medicine. Multivariate current status data is a common type of Biomedical data which gives rise to two main challenges in data analysis. First, all event times are censored, making censoring times the only indicator of event occurrence. Second, an unobserved heterogeneity caused by clusters of units or individuals is probable. To address these issues, mixed Cox proportional hazard model with random block frailty has been used. Here, we consider a Bayesian multivariate Gamma-frailty Cox model and augment the likelihood with respect to random frailties and a set of Poisson latent variables. We also introduce a novel MCMC algorithm by employing two different cumulative baseline hazard function structures: a transformed mixture of incomplete Beta distributions and a linear combination of monotone integrated splines. Through several simulations, we show that our methodology achieves competitive results. We also compare the performance of the two baseline hazard functions using model selection criteria such as AIC and DIC. Finally, we apply the model to a bivariate current status cataract dataset and investigate the effect of various risk factors on the occurrence of cataracts.

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