Improved joint modeling of longitudinal and survival data using a poisson regression approach

Data of repeated measurements (longitudinal) and time-to-events (survival) are commonly recorded in studies. The joint model (JM) of longitudinal and survival data, which allows simultaneously analysis of the two types of outcomes, has been extensively discussed recently. JMs are computationally intensive due to large number of parameters and the complexity of fitting the survival submodel. The centerpiece of the survival submodel is the piecewise constant proportional hazard (PCPH). An alternative to PCPH for analysing survival data is the auxiliary Poisson regression model. However, the use of this approach in JMs has not been discussed. In this study, we propose using the auxiliary Poisson model as the survival part in a JM within a Bayesian framework. We conducted comprehensive simulation studies to assess the performance of our proposed method under various conditions and compared it to a published R package for JMs called JMbayes. Additionally, we used data from the Manitoba Follow-Up Study to illustrate the advantages and feasibility of our proposed method. The findings have showed that using the auxiliary Poisson approach as the survival submodel is a very promising method for jointly modeling longitudinal and survival data, as it helps decrease the computing burden.