Survival function model estimation for parkinson disease using independent metropolis-hastings algorithm with uniform proposal distribution in bayesian inference

Abstract

In medicine study, one of the things that is interesting enough to be studied is “time-to-event”. In general, time-to-event is used in doing survival analysis, such as analysis of Parkinson disease. Parkinson disease is one of the diseases which affects dopamine producer in brain area that is called by substantia nigra. The symptom of Parkinson disease is measured specifically by stages that are called by Hoehn and Yahr stages. This stages are distributed on integers between 0 to 5 with stage 0 is stage that does not have big impact and stage 5 is the most severe level. In this study, the survival function will be constructed from the time that the patient has the Hoehn and Yahr stages at A until increase to stage B with A < B. With A = 1, 2 and B = 3, 4, 5, overall it will be estimated six graphs of survival function. The process of construction survival function is using the Independent Metropolis-Hastings algorithm in Markov Chain Monte Carlo Methods on Bayesian Inference with uniform proposal distribution and the results are compared with Kaplan-Meier estimator for survival function. The result that is obtained through this algorithm is more represents the actual survival function if it is compared with Kaplan-Meier estimator, although there are so many censored data in the dataset.