# Attempt to Raise the Predictive Accuracy in Binary Logistic Regression Analysis

Many reports have used Functional Independence Measure (FIM) gain (FIM at discharge minus FIM at admission) as the dependent variable in multiple linear regression analysis. Binary logistic regression analyses have also been carried out using 1 for FIM gains equal to or greater than the median value and 0 for FIM gains less than the median value. The deliberate conversion of quantitative FIM gains into 0/1 binary data is thought to be advantageous in that this does not require as much rigor in terms of the type or distribution of data.

While multiple regression analysis envisions a linear relationship between independent variables and dependent variable, there are in fact many cases where no such linear relationship exists. Especially, there is no linear relationship found between FIM at admission and FIM gain. Accordingly, it has been reported that, rather than relying on a single predictive formula, the predictive accuracy of motor FIM (mFIM) gain will be increased by creating two predictive formulae by stratifying mFIM scores at the time of admission (mFIMa) into two groups

In binary logistic regression analysis, as well, stratifying mFIMa to create two predictive formulae may improve the predictive accuracy of mFIM gain. In addition, because it is possible to categorize independent variables in binary logistic regression analysis, it may also be possible to heighten the predictive accuracy of mFIM gain by categorizing mFIMa.

This study conducted binary logistic regression analysis with mFIM gain as dependent variable among stroke patients admitted to convalescent rehabilitation wards in Japan. The aim of this study was to compare the predictive accuracy of mFIM gain (a 0/1 binary value) between “mFIMa used as quantitative data”, “categorized mFIMa into 4 groups, and “creation of two predictive formulae”.

We used patient data from the Japan Rehabilitation Database (JRD). The subjects were selected from 6,322 stroke patients hospitalized in convalescent rehabilitation wards and registered with the JRD in April 2015. To reduce the influence of exceptional cases that could be seen as outliers, the subjects were limited to patients who fulfilled the following inclusion criteria: age 15 to 99 years, duration from onset to hospital admission of 5 to 90 days, admitted to convalescent rehabilitation wards for 21 to 210 days, total score of 13 to 90 for mFIMa, FIM gain of 0 or higher, and having entries for all items to be examined. The remaining 2,542 patients were included in this study.