Boylamsal ve Yaşam Verilerinin Parametrik Bileşik Modellemesi

Abstract

Longitudinal data consist of repeated measurements obtained from the same units at certain time intervals, while survival data consists of time until the occurrence of any event under consideration. There are different methods in the literature for separate analysis of longitudinal and survival data. Nevertheless, these two data, particularly collected together in clinical studies, should be analyzed together to obtain unbiased and effective results when there is a relationship between each other. The joint model is obtained by combining these two data with the shared parameter model, and consists of longitudinal sub models and survival sub models.

The standard joint model structure frequently used in the literature is obtained by combining the linear mixed effect model for longitudinal data and shared parameter models of Cox regression model for survival data. However, in order to apply Cox regression model the proportional hazard assumption must be satisfied. Parametric regression methods should be used in cases where the assumption is not provided, and when the survival data has a known distribution. In cases where the assumption of proportional hazard is not provided in joint modelling, the survival analysis sub model should be made with parametric survival analysis models.

In this study, standard joint model, separate analysis of longitudinal and survival data and joint model obtained with Exponential, Weibull, Log-logistic, Log-normal and Gamma parametric sub models have been applied to data set of Primary Biliary Cirrhosis in the literature. Firstly, the assumption of proportional hazard has been checked and found that the assumption is not provided. Because the assumption is not satisfied, parametric joint models have been examined and the joint modeling of the linear mixed effect model with parametric sub model is determined as the best model. When the standard joint model and Weibull parametric joint model results have been compared, statistically significant differences have been found. For separate analysis of longitudinal and survival data, the results of the linear mixed effect model and the Weibull parametric model have also been investigated and compared with the results of Weibull parametric joint model. Accordingly, the parameters of Weibull parametric model are determined to have higher hazard ratios than the parameters of Weibull parametric joint model. In addition, while Weibull parametric model is established, longitudinal observation have been considered as the independent variable but dependent on time and its effect on survival time has been investigated. At the end of the analysis, it has been observed that the effect of Weibull parametric model on the survival times of longitudinal observation is smaller than the Weibull parametric joint model.