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Shrinkage Estimators for a Composite Measure of Quality Conceptualized as a Formative Construct
Author(s) -
Shwartz Michael,
Peköz Erol A.,
Christiansen Cindy L.,
Burgess James F.,
Berlowitz Dan
Publication year - 2013
Publication title -
health services research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.706
H-Index - 121
eISSN - 1475-6773
pISSN - 0017-9124
DOI - 10.1111/j.1475-6773.2012.01437.x
Subject(s) - estimator , statistics , composite number , shrinkage , shrinkage estimator , multivariate statistics , construct (python library) , medicine , mathematics , computer science , algorithm , bias of an estimator , programming language , minimum variance unbiased estimator
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 ( QI s) calculated from the minimum dataset from residents of 112 V eterans H ealth A dministration nursing homes in fiscal years 2005–2008. Study Design We compared composite scores calculated from the 28 QI s using both observed rates and shrunken rates derived from a B 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 QI 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 QI s 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.