Logistic Regression Analysis for Categorical Outcome

Logistic regression is a statistical technique used to model the relationship between a set of predictor variables and a binary outcome variable. This chapter explains the fundamentals of logistic regression analysis, focusing on its applications in predicting categorical outcomes and testing hypotheses. The logistic model transforms the linear combination of predictor variables into a log-odds scale, allowing the estimation of regression coefficients that represent the odds ratios. The chapter provides a step-by-step guide to performing univariate and multivariate logistic regression using a dataset from the Cleveland Heart Study, which investigates the risk factors for coronary artery narrowing. Variables such as age, sex, chest pain type, and other clinical parameters are analyzed to predict the presence of significant coronary artery disease. The chapter also explores model evaluation using metrics like accuracy, sensitivity, specificity, and the Area Under the Curve (AUC) of the Receiver Operating Characteristic (ROC) curve. The logistic regression model effectively discriminates between the levels of the binary outcome variable (in this example, patients with and without significant coronary artery narrowing), demonstrating its utility in clinical decision-making.