Boylamsal ve Yaşam Verilerinin Parametrik Bileşik Modellemesinde Parametre Tahmin Yöntemleri

Abstract

Especially in biomedical and clinical research, longitudinal and survival data are often obtained together. Generally, when these two data are analyzed separately, while Cox regression model and parametric regression models are used for survival data, linear mixed effect model and generalized estimating equations are used for longitudinal data. However, in cases where longitudinal and survival data are related, non-random missing data occurs due to the inability to follow up the same unit during survival in longitudinal measurements obtained from units at different time points. For this reason, some researchers have suggested joint modeling that includes non - random missing data as an alternative to separate analysis of these two data. The main purpose of joint modelling is to estimate the relationship between longitudinal and survival data and to investigate the effect of independent variables on these two data. The joint model basically consists of a longitudinal sub-model and a survival sub-model. In the literature, many models have been developed for joint modelling of longitudinal and survival data with different structures. In addition to different model structures, different methods such as two - stage approach, likelihood approach and Bayesian approaches have been developed to obtain parameter estimates of the joint model. In the likelihood approach, since the integrals in the joint model likelihood function do not have a closed-form solution, different numerical approaches such as Laplace, Gauss Hermite and adapted Gauss Hermite have been proposed. In most of the studies on joint modeling and parameter estimation approaches, the joint model structure obtained by combining the linear mixed - effect model for longitudinal data and the Cox regression model for survival data with shared random effects is used. However, in cases where survival data does not satisfy the proportional hazards assumption and are suitable for a certain distribution, parametric joint models should be used to obtain more unbiased and reliable estimates. In this context, in this thesis, a Bayesian two - stage approach is proposed to calculate the parameter estimates of the parametric joint model used in cases where the survival data does not satisfy the proportional hazards assumption and is suitable for a certain distribution. The proposed approach was compared with the Gauss Hermite and adaptive Gauss Hermite approaches, which are frequently used in literature. Simulation scenarios were performed with different sample sizes, censoring rates and parameter values to examine the performance of the methods. According to the simulation results, it was seen that the proposed Bayesian two - stage approach gave better results compared to the Gauss Hermite and adapted Gauss Hermite approaches in all scenarios. In cases where the risk is high, it was determined that all methods gave more biased estimates compared to cases where the risk is low and medium. It was also observed that all methods gave less biased estimates as the sample size increased and the censoring rate decreased and estimated the group variable less biased compared to the association parameter. To demonstrate the applicability of the proposed approach, a random sample was selected from the aortic valve replacement surgery dataset and the AIDS dataset in the R program in accordance with the parametric joint model structure considered in the simulation study and the performances of the methods were compared. As a result of both applications, the best model estimations was obtained from the Bayesian two-stage approach, similar to the simulation results.