Primer on binary logistic regression

Abstract

Family medicine has traditionally prioritised patient care over research. However, recent recommendations to strengthen family medicine include calls to focus more on research including improving research methods used in the field. Binary logistic regression is one method frequently used in family medicine research to classify, explain or predict the values of some characteristic, behaviour or outcome. The binary logistic regression model relies on assumptions including independent observations, no perfect multicollinearity and linearity. The model produces ORs, which suggest increased, decreased or no change in odds of being in one category of the outcome with an increase in the value of the predictor. Model significance quantifies whether the model is better than the baseline value (ie, the percentage of people with the outcome) at explaining or predicting whether the observed cases in the data set have the outcome. One model fit measure is the count- $R^2$ , which is the percentage of observations where the model correctly predicted the outcome variable value. Related to the count- $R^2$ are model sensitivity—the percentage of those with the outcome who were correctly predicted to have the outcome—and specificity—the percentage of those without the outcome who were correctly predicted to not have the outcome. Complete model reporting for binary logistic regression includes descriptive statistics, a statement on whether assumptions were checked and met, ORs and CIs for each predictor, overall model significance and overall model fit.