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

Authors

  • Michael Shwartz Ph.D.,

    Corresponding author
    1. School of Management, Boston University, Boston, MA
    • School of Management , Boston University , Boston, MA
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  • Erol A. Peköz Ph.D.,

    1. School of Management , Boston University , Boston, MA
    2. Center for Organization, Leadership and Management Research, VA Boston Healthcare System (152M), Boston, MA
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  • Cindy L. Christiansen Ph.D.,

    1. School of Public Health, Boston University, Boston, MA
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  • James F. Burgess Jr. Ph.D.,

    1. Center for Organization, Leadership and Management Research, VA Boston Healthcare System (152M), Boston, MA
    2. School of Public Health, Boston University, Boston, MA
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  • Dan Berlowitz M.D., M.P.H.

    1. Center for Health Quality, Outcomes and Economic Research, Bedford VA Hospital, Boston, MA
    2. School of Public Health, Boston University, Boston, MA
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Address correspondence to Michael Shwartz, Ph.D., Center for Organization, Leadership and Management Research, VA Boston Healthcare System (152M), 150 South Huntington Avenue, Boston, MA 02130; e-mail: mshwartz@bu.edu

Abstract

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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