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VOLUME 48 | NUMBER 1 | FEBRUARY 2013


Shrinkage Estimators for a Composite Measure of Quality Conceptualized as a Formative Construct

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Keywords: Composite measures; Bayesian models; quality indicators

Objective: To demonstrate the value of shrinkage estimators when calculating a composite quality measure as the weighted average of a set of individual quality indicators.

Data Sources: Rates of 28 quality indicators (QIs) calculated from the minimum dataset from residents of 112 Veterans Health Administration nursing homes in fiscal years 2005–2008.

Study Design: We compared composite scores calculated from the 28 QIs using both observed rates and shrunken rates derived from a Bayesian multivariate normal-binomial model.

Principal Findings: Shrunken-rate composite scores, because they take into account unreliability of estimates from small samples and the correlation among QIs, have more intuitive appeal than observed-rate composite scores. Facilities can be profiled based on more policy-relevant measures than point estimates of composite scores, and interval estimates can be calculated without assuming the QIs are independent. Usually, shrunken-rate composite scores in 1 year are better able to predict the observed total number of QI events or the observed-rate composite scores in the following year than the initial year observed-rate composite scores.

Conclusion: Shrinkage estimators can be useful when a composite measure is conceptualized as a formative construct.

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