A Joint Model for Exponential Survival Data and Poisson Count Data

Abstract

This research is motivated by the correlated outcomes of survival times and counts particularly in medical data. Analysis on individual patient data consisting of recurrent events of disease progression and survival times/death times give better results when a bivariate model/joint model of ‘survival’ and ‘count’ is used rather than fitting separate univariate models. For this purpose, a joint model for a proportional hazard survival response and a Poisson count responses is presented. The methodological aspects of the proposed model is outlined including parameter estimation. The proposed model was examined on a large scale simulation study and superior performance was demonstrated over the separate univariate models. The model was further showcased on an actual clinical trial data and found out to be capable of capturing the correlation between the survival and count variables found in the data.