Advanced Statistics: Multiple Logistic Regression, Cox Proportional Hazards, and Propensity Scores

Abstract

Background: Randomized controlled trials (RCTs) are generally regarded as the gold standard for demonstrating causality because they effectively mitigate bias from both known and unknown confounders. However, conducting an RCT is not always feasible because of logistical and ethical considerations. This is especially true when evaluating surgical interventions, and non-randomized study designs must be utilized instead. Methods: Statistical methods that adjust for baseline differences in non-randomized studies were reviewed. Results: The three methods used most commonly to adjust for confounding factors are multiple logistic regression, Cox proportional hazard, and propensity scoring. Multiple logistic regression (MLR) is implemented to analyze the influence of categorical and/or continuous variables on a single dichotomous outcome. The model controls for multiple covariates while also quantifying the magnitude of each covariate's influence on the outcome. Selecting which variables to include in a model should be the most important consideration, and authors must report how and why variables were chosen. Cox proportional hazards modeling is conceptually similar to logistic regression and is used when analyzing survival data. When applied to survival curves, Cox proportional hazards can adjust for baseline group differences and provide a hazard ratio to quantify the effect that any single factor contributes to the survival curve. Propensity scores (PS) range from zero to one and are defined as the probability of receiving an intervention based on observed baseline characteristics. Propensity score matching (PSM) is especially useful when the outcome of interest is a rare event. Treated and untreated subjects with similar propensity scores are paired, forming balanced samples for further analysis. Conclusions: The method by which to address confounding should be selected according to the data format and sample size. Reporting of methods should provide justification for selected covariates, confirmation that data did not violate model assumptions, and measures of model performance.