Optimal Statistical Decisions for Hospital Report Cards

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Abstract
Purpose. Hospital report cards provide information designed to help patients and providers to make decisions. The purpose of this study was to place the design of hospital report cards into a decision-theoretic framework. The authors’ objectives were 2-fold: 1st, to determine what the choice of significance level implies about the relative value of the different types of misclassifications that can arise. Second, to determine optimal significance levels for specific cost functions describing the relative costs associated with different types of misclassifications. Methods. Using a previously published theoretical model for hospital mortality, the authors computed false positive (i.e., falsely classified as providing poor-quality care) and false negative (falsely classified as providing good-quality care) rates. First, they determined the cost functions for false negatives and false positives that are implicitly associated with the use of significance levels of 0.05 and 0.01 for identifying hospitals with higher than average mortality. Second, they determined the levels of statistical significance that should be chosen to minimize predefined cost functions, thus minimizing costs associated with misclassifying hospitals. Results. The lower the statistical significance level required for identifying hospitals with higher than average mortality, the lower the implicit cost of false negatives compared to false positives. For a given significance level, the greater the number of patients treated at each hospital or the greater the proportion of truly poorly performing hospitals, the lower the value of the implicit cost incurred by a false negative compared to that for a false positive. For cost functions that put a high relative penalty on false negatives compared to false positives, the use of significance levels of 0.05 or 0.01 does not result in optimal decisions across expected number of patients treated at each hospital or proportions of truly poor-quality care. Conclusions. Hospital report cards that use significance levels of either 0.05 or 0.01 to identify hospitals that have statistically significantly higher than average mortality make implicit assumptions about cost functions, and the values of the optimal cost function vary across scenarios.