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Using Flexibility-Based Weights to Calculate a Composite Measure of Quality
Dan Berlowitz, Center for Health Quality, Outcomes and Economic Research 
*James Francis Burgess, Center for Organization, Leadership and Management Research 
Michael Shwartz, Center for Organization, Leadership and Management Research 

Keywords: composite measures, health care quality, performance measurement, linear programming, data envelopment analysis

Standard approaches used by policy makers for determining weights when calculating a composite measure of quality from individual quality indicators (QIs) include equal weighting, prevalence-based weights, and judgment-based weights. Providers may have legitimate reasons for wanting to modify these weights. In this paper, we examine the effect of allowing providers some flexibility in adjusting baseline weights in order to optimize their composite score. We consider two approaches for determining what we call flexibility-based weights: 1) a linear programming model that constrains the sum of the weights to one; and 2) a data envelopment analysis model that constrains the composite score to be no larger than one. In both cases, constraints are added so that only moderate changes can be made from baseline weights. Using each of the approaches, composite scores are calculated from data on five QIs from a sample of 32 Department of Veterans Affairs nursing homes. For the most part, both of the flexibility-based approaches identify the same set of high performing facilities as the standard approaches (i.e., the top 6 or 7 ranked facilities). Across all facilities, the effect on facility ranks of using the weight-constrained approach is not much greater than the effect of switching between the standard approaches. Flexibility-based approaches, because they allow facilities to reflect local preferences and conditions, should be attractive to facilities and may allow policy makers to “buy” provider good will without having a major impact on which facilities are identified as high performers.