Rockwood N, Qin S, Yarr S. Estimating change score/responsiveness correlations among ordinal measures. Presented at the ISOQOL 30th Annual Conference; October 20, 2023. Calgary, Canada.

AIMS: Polychoric correlations are commonly used to estimate the associations among ordinal clinical outcome assessments (COAs). Such correlations are derived by viewing the ordinal measures as discretizations of underlying (i.e., latent) continuous variables. Correlations among change (or difference) scores are commonly used to assess the responsiveness of a target COA, as well as ensure change defined using global anchors are adequately associated with the target COA change scores prior to their use in anchor-based threshold analyses. Typically, change score correlations are computed by first computing the change scores for the variables of interest, and then computing the correlations among these newly computed change scores. Unfortunately, the difference between ordinal variables is not, in fact, ordinal (or continuous) which makes correlations among these change scores difficult to interpret. The aim of this presentation is to provide an alternative method for estimating the correlations between changes on ordinal variables.

METHODS: Analogous to polychoric correlations, the proposed method estimates the correlation among the change scores of the latent continuous variables X* and Y* underlying the observed, ordinal responses X and Y. Letting Xc* = X2* - X1* and Yc* = Y2* - Y1* denote the change scores from time 1 to time 2 on the latent continuous variables X* and Y*, respectively, the correlation between the latent change scores Xc* and Yc* can be derived as a function of the bivariate correlations between each pair of latent scores X1*, X2*, Y1*, and Y2*. Estimates of these correlations can be obtained using the bivariate polychoric correlations among the corresponding observed, ordinal variables. These estimates can then be used to obtain an estimate of the correlation between the latent change scores without explicit computation of the observed change scores or the correlations between the observed change scores.

RESULTS: Using a small-scale simulation study, the proposed estimation method is shown to adequately recover the true correlation between the latent change scores, whereas the correlation between the observed change scores does not properly reflect the strength of this relationship.

CONCLUSIONS: Estimating the correlation among latent change scores rather than observed change scores is recommended for assessing the responsiveness of ordinal COAs.

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