Valuation Structures of Health States Revealed with Singular Value Decomposition

Abstract

Objective. A basic mathematical routine called singular value decomposition (SVD) is introduced and applied to explore the applicability of this methodology in the context of health state valuations. Methods. SVD dissects a data matrix into 3 separatematrices that contain all the information present in the original data. Eachmatrix comprises a specific type of information. One matrix comprises arrays of weights that show the different valuation structures (i.e., similar ways among respondents to quantify specific sets of health states). A 2nd matrix with weights expresses how strongly each respondent's ratings are related to each of the valuation structures, and a 3rd matrix contains the percentages of variance associated with the valuation structures. SVD was applied to data from a group of 340 respondents who each gave a value to 16 health states using the time tradeoff (TTO) method and the visual analog scale (VAS). Results. SVD of the VAS data showed 1 distinct response pattern that accounted for 91.6% of the total variance. The contribution of the 1st component in the TTO data wasmuch lower (57.4%), and a 2nd component (15.6%) could be identified that reflected a distinct preference structure opposed to the 1st and principal component. Conclusions. Application of SVD to the TTO data revealed that respondents fell into 2 different groups in their TTO evaluations, but respondents weremore similar to each other in their VAS responses. The author discusses other applications of SVD to clinical research.

Keywords

health states valuations values utilities preferences valuation techniques time tradeoff visual analog scale EQ-5D

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