Logistic Regression for Fuzzy Covariates: Modeling, Inference, and Applications

Logistic regression is an important tool to evaluate the functional relationship between a binary response variable and a set of predictors. However, in clinical studies, often there is insufficient precision or indefiniteness of state. Therefore, we need to explore some soft methods for inference when the variables are reported as imprecise quantities. In this regard, we propose a fuzzy regression model with fuzzy covariates for imprecise binary-based response. We apply a least-squares method to estimate the model parameters and a bootstrap method for both computing confidence intervals and testing the hypotheses for the model parameters. The proposed model is then applied for verification to a numerical example based on a real clinical study of the effect of beloved person's voice on reducing patient pain during the chest tube removal after an open heart surgery. Finally, the proposed model is evaluated by a well-known goodness-of-fit index.