M.L. Estimator for Fuzzy Survival Function to the Kidney Failure Patients

Abstract

The dependence of traditional statistical methods in finding estimators and testing hypotheses depends on data that take specific values. However, uncertainty (Fuzzy) appears in most data, including survival time data, which requires researchers to apply Fuzzy methods in general when finding estimators, particularly the estimators of a survival function. In this research, the experimental method (simulation) was used to compare Fuzzy methods (definition of fuzzy logic, cut level -δ, Buckley) at three fuzzy degrees (0, 0.5, 1), for selected survival times (t = 2, 4, 6, 8, 10, 12) in days. To determine the best fuzzy method used to find the Maximum Likelihood Estimators of the fuzzy survival function depends on the Avery Mean Squares Error (AMES) for the lower and upper bound estimators of the fuzzy survival function for each method. From the experimental method, we came to an advantage of defining fuzzy logic for the maximum likelihood estimator for the survival function of Weibull distribution (distribution of survival times data in the research). The maximum likelihood estimator calculated according to the method of defining fuzzy logic for patients' survival times with kidney failure collected from sections of the dialysis department in educational hospitals (Baghdad, Al-Kindi, Al-Karama, Al-Kadhimiya). This research found that the probability of fuzzy survival for two days to the patients with kidney failure reaches 0.7504 and this probability decreases with an increase in the time of stay until it reaches 0.07704 the probability of staying for a month.