Regression analysis

Multivariable regression models estimate the relationship between a dependent variable (i.e., outcome) and more than one independent variable (i.e., predictor). In medical research, common applications of regression analysis include linear regression for continuous outcomes, logistic regression for binary outcomes, and Cox proportional hazards regression for time to event outcomes. Regression analysis allows for multiple predictors to be included in a model for a particular outcome and adjusts for the effects of confounding by these variables on the outcome of interest. Different strategies exist to determine which variables to include in the model and range from manually selecting clinically relevant factors to automated algorithms implemented in statistical software for model building. The effects of the independent variables on the outcome are summarized with a coefficient (linear regression), an odds ratio (logistic regression), or a hazard ratio (Cox regression). These should be reported along with the 95% confidence interval. As statistical software will generally analyze any model that is entered and provide output, it is critical to construct and interpret regression results appropriately. Considering factors such as appropriate events per variable ratio, variable selection, missing data, confounding, interactions, collinearity, and model fit are all important. Finally, regression analyses for observational data describe associations and not causal relationships, and should not be interpreted as such.