On the practice of ignoring center-patient interactions in evaluating hospital performance

We evaluate the performance of medical centers based on a continuous or binary patient outcome (e.g., 30-day mortality). Common practice adjusts for differences in patient mix through outcome regression models, which include patient-specific baseline covariates (e.g., age and disease stage) besides center effects. Because a large number of centers may need to be evaluated, the typical model postulates that the effect of a center on outcome is constant over patient characteristics. This may be violated, for example, when some centers are specialized in children or geriatric patients. Including interactions between certain patient characteristics and the many fixed center effects in the model increases the risk for overfitting, however, and could imply a loss of power for detecting centers with deviating mortality. Therefore, we assess how the common practice of ignoring such interactions impacts the bias and precision of directly and indirectly standardized risks. The reassuring conclusion is that the common practice of working with the main effects of a center has minor impact on hospital evaluation, unless some centers actually perform substantially better on a specific group of patients and there is strong confounding through the corresponding patient characteristic. The bias is then driven by an interplay of the relative center size, the overlap between covariate distributions, and the magnitude of the interaction effect. Interestingly, the bias on indirectly standardized risks is smaller than on directly standardized risks. We illustrate our findings by simulation and in an analysis of 30-day mortality on Riksstroke.