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Separable covariance models for health care quality measures across years and topics
Author(s) -
Hatfield Laura A.,
Zaslavsky Alan M.
Publication year - 2018
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.7656
Subject(s) - kronecker product , computer science , covariance matrix , covariance , quality (philosophy) , econometrics , varimax rotation , dimension (graph theory) , product (mathematics) , measure (data warehouse) , variance (accounting) , statistics , data mining , mathematics , kronecker delta , business , psychometrics , philosophy , physics , geometry , cronbach's alpha , accounting , epistemology , quantum mechanics , pure mathematics
Public quality reports for Medicare Advantage health plans include 11 measures of patient experiences reported in the annual Consumer Assessment of Healthcare Providers and Systems surveys. Computing summaries at the health plan level (of multiple measures in multiple years) yields an array‐structured random variable. To summarize associations among measures and years, we model the variance‐covariance matrix governing the plan‐level vectors of yearly quality measures as a Kronecker product of an across‐measure matrix and an across‐year matrix, or a sum of such Kronecker products. This approach extends separable covariance structure to Fay‐Herriot models. In addition, we develop linear combinations of Kronecker products similar to principal components for array random variables. To each Kronecker‐product term, we apply post hoc analyses suited to the corresponding dimension of the cross‐classification: 1‐way factor analysis for the across‐measure factor and time‐series analysis to the across‐year factor. These methods draw out key patterns of variation in the quality measures over time and suggest new strategies for reporting quality information to consumers.