Indian Journal of Science and Technology

Abstract

Objectives: The subject of survival analysis mainly concentrated on the behavior of the survival times of specific organisms or objects, which is the time at which a specified event occurs from an initial epoch. The problem of censoring adds complexity to survival analysis, and specific types of tools have been developed to deal with censored observations, some of which are nonparametric and semi-parametric approaches. When the proportion of censored observations becomes higher, it is natural that the results obtained from any type of survival analysis are less reliable. In this article, an attempt has been made to meaningfully incorporate the censored observations in survival data using fuzzy theory. Method: Taking Kaplan-Meier's procedure as a base, the fuzzy numbers are used for censored observations. Findings: In the presence of censored observations, ascertaining the median survival time is always obscure; hence, fuzzy methodology has been adopted in this article. The corresponding survival curves are drawn, and the median survival time is estimated with reference to an example. Novelty: Incorporating fuzzy theory into Kaplan-Meier's procedure, particularly regarding censoring, is a novel methodology discussed here. So, the presence of impreciseness in statistical data with particular reference to survival analysis has not been considered much in the literature. The present work has addressed this issue and proposes a new type of Kaplan-Meier estimator for addressing censoring.

Keywords: Censoring, Survival Curve, Product Limit Estimator, Fuzzy sets, and Fuzzy Numbers