A novel approach for jointly modeling survival times and recurrent episodes of disease progression

Abstract

Accurate modelling of the effect of endogeneous time-varying covariates on the relative Recurrent episodes of disease progression (tumors, seizures etc) have an impact on their survival times, which requires analysis of recurrent events and survival in practice. Such analysis is mainly done either fitting models separately for recurrent events and survival or by fitting standard survival models where recurrent events are included as co variates in the survival model. However, literature gives evidences that treating both of these outcomes as responses in ajoint model is more efficient[l]. Multivariate survival models could have been used for this purpose if the timings of the recurring events are available. In contrast, this study proposes amodel which only requires the cumulative count of the recurring event treating the count variable as a Poisson or Negative Binomial and survival data can assume any parametric distribution or semi-parametric Cox model. The only constraint viable is the assumption of proportional hazards in survival times, which facilitates estimating the survival model through a Poisson regression model. Hence. the survival model is represented by aPoisson model and another Poisson model is assumed for the count variable enabling joint modeling of survival and count to be accomplished by joint modeling of two Poissons.The method is applied to a clinical trial dataset with survival time and event counts. Being able to assume any parametric or non-parametric model for survival data and not imposing any restrictions between the distributions of count and survival data in contrast to [1] formulates the main significance. The method can be applied for any data scenario which requires joint modeling of count and survival and extending the model for hierarchical!clustered data constitutes future work.