Fuzzy logistic regression based on the least squares approach with application in clinical studies

Authors:
Saeedeh Pourahmad;Seyyed Mohammad Taghi Ayatollahi;S. Mahmoud Taheri;Zahra Habib Agahi
Affiliations:
Department of Biostatistics, School of Medicine, Shiraz University of Medical Sciences, Shiraz 71345-1874, Iran;Department of Biostatistics, School of Medicine, Shiraz University of Medical Sciences, Shiraz 71345-1874, Iran;Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran;Department of Rheumatology, School of Medicine, Shiraz University of Medical Sciences, Shiraz 71345-1874, Iran
Venue:
Computers & Mathematics with Applications
Year:
2011

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Abstract

To model fuzzy binary observations, a new model named ''Fuzzy Logistic Regression'' is proposed and discussed in this study. In fact, due to the vague nature of binary observations, no probability distribution can be considered for these data. Therefore, the ordinary logistic regression may not be appropriate. This study attempts to construct a fuzzy model based on possibility of success. These possibilities are defined by some linguistic terms such as ..., low, medium, high.... Then, by use of the Extension principle, the logarithm transformation of ''possibilistic odds'' is modeled based on a set of crisp explanatory variables observations. Also, to estimate parameters in the proposed model, the least squares method in fuzzy linear regression is used. For evaluating the model, a criterion named the ''capability index'' is calculated. At the end, because of widespread applications of logistic regression in clinical studies and also, the abundance of vague observations in clinical diagnosis, the suspected cases to Systematic Lupus Erythematosus (SLE) disease is modeled based on some significant risk factors to detect the application of the model. The results showed that the proposed model could be a rational substituted model of an ordinary one in modeling the clinical vague status.