Affiliations: Department of Biostatistics & Epidemiology, School of Public Health, Hamadan University of Medical Sciences, Hamadan, Iran | Division of Computing, McKendree University, Lebanon, IL, USA | Research Center for Health Sciences and Department of Biostatistics & Epidemiology, School of Public Health, Hamadan University of Medical Sciences, Hamadan, Iran
Note: [] Corresponding author. Hossein Mahjub, Research Center for Health Sciences and Department of Biostatistics & Epidemiology, School of Public Health, Hamadan University of Medical Sciences, Hamadan, Postal code: 65175-4171, Hamadan, Iran. Tel.: +98 811 8380090; Fax: +98 811 8380509; E-mail: [email protected]
Abstract: A common and critical issue in survival data analysis is the way in which censored data are handled. The Kaplan-Meier (KM) estimator is a frequently used statistical method in survival analysis that works well with censored data. In small sample sizes with heavy censoring the estimates of KM are not reliable, because the assumptions of KM estimator are violated. In this study, fuzzy logic is used to obtain more reliable estimates when standard statistical methods cannot be used. Data analyzed in this study were the survival times of six AIDS patients under ten years old. One of the patients died after 197 days and the others were censored, giving a censor rate of 83%. The fuzzy-product-limit estimator (FPLE) and a modified FPLE were used to analyze the data. Mean survival time was calculated and associated confidence interval was calculated along with a measure of the amount of “fuzzy information” used to obtain the estimates. In addition, one to ten year survival rates estimated by the KM, FPLE and proposed methods are presented. The result of the simulations showed that the fuzzy methods with few and highly censored data provide more reasonable results than the standard statistical method.
