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

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 (s) calculated from the minimum dataset from residents of 112 eterans ealth dministration nursing homes in fiscal years 2005–2008.

Study Design

We compared composite scores calculated from the 28 s using both observed rates and shrunken rates derived from a ayesian 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 s, 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 s are independent. Usually, shrunken‐rate composite scores in 1 year are better able to predict the observed total number of 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.