A Goodness of Fit Test for a Survival and Count Bayesian Joint Model: In the Presence of Clusters

Abstract

Bayesian statistical model fitting was an uncommon approach until recently, causing a lack of assessment techniques for these models. However, with the enhancement of computational facilities and advanced estimation techniques, Bayesian models have become popular. Though there are developed goodness of fit (GOF) tests available for classical multilevel models including joint modelling of mixed responses, there is no suitable model based GOF test to be applied on such a model which is fitted under a Bayesian framework. Therefore, this study focused on developing a suitable GOF test for multilevel Bayesian joint models having survival and count responses which are two frequently occurring data types in many fields. The novel test is developed mainly based on four classical GOF tests, including the well-known Hosmer-Lemeshow test and, the Bayesian concepts such as Bayesian credible intervals and regions. In addition, a simulation study has been used to examine the properties of the GOF test together with an application to a real-life example. The novel test performed well in terms of power and acceptable in terms of Type I error rates. Overall, the test performed well with small sample sizes.