Valuation structures of health states revealed with singular value decomposition

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.

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).

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.

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.