Partially linear Bayesian modeling of longitudinal rank and time-to-event data using accelerated failure time model with application to brain tumor data

Joint modeling of longitudinal rank and time-to-event data with random effects model using a Bayesian approach is presented. Accelerated failure time (AFT) models can be used for the analysis of time-to-event data to estimate the effects of covariates on acceleration/deceleration of the survival time. The parametric AFT models require determining the event time distribution. So, we suppose that the time variable is modeled with Weibull AFT distribution. In many real-life applications, it is difficult to determine the appropriate distribution. To avoid this restriction, several semiparametric AFT models were proposed, containing spline-based model. So, we propose a flexible extension of the accelerated failure time model. Furthermore, the usual joint linear model, a joint partially linear model, is also considered containing the nonlinear effect of time on the longitudinal rank responses and nonlinear and time-dependent effects of covariates on the hazard. Also, a Bayesian approach that yields Bayesian estimates of the model's parameters is used. Some simulation studies are conducted to estimate parameters of the considered models. The model is applied to a real brain tumor patient's data set that underwent surgery. The results of analyzing data are presented to represent the method.