Comparing the Contributions of Groups of Predictors: Which Outcomes Vary with Hospital Rather than Patient Characteristics?

Abstract In a model, such as a logit regression model, we wish to compare the relative importance of two groups of predictors for various objectives. In the example that motivated this work, the model predicts patient outcomes during hospital stays, and we wish to measure the relative contribution of patient and hospital characteristics to the variation in outcomes among patients and among hospitals. This is done using the relative dispersion of patient and hospital contributions to the fitted outcomes. As is seen, this question is distinct from other common questions, including the quality of the overall fit, the degree to which the outcome is accurately predicted, the statistical significance of groups of predictors, and the correlations among and between groups of predictors. Relevant point estimates, confidence intervals, and hypothesis tests are developed. In the example, we examine three outcome measures and find that nearly all of the predictable variation in patient outcomes and most of the predictable variation in outcomes among hospitals reflects variation in patient characteristics rather than hospital characteristics; however, this is true in varying degrees for the three outcomes.