Responsiveness correlations involving ordinal clinical outcomes assessment scores

Objectives The longitudinal validity (i.e., responsiveness) of a target clinical outcomes assessment (COA) score is often assessed by correlating changes in the COA scores with changes in supporting scores assessing similar and dissimilar constructs. When the target score and/or supporting score is ordinal, standard approaches for assessing responsiveness are not appropriate because the observed change score is neither ordinal nor continuous. The aim of this paper is to provide a method for appropriately estimating change score correlations when one or both of the scores is ordinal. Methods Analogous to polychoric and polyserial correlations, the proposed method adopts a latent response formulation and uses covariance algebra to estimate the correlation among the change scores of the latent continuous variables underlying the observed, ordinal responses. The method can be implemented using general purpose statistical software such as SAS or R. Results Using a simulated example analysis and small-scale simulation study, the proposed method is shown to adequately recover the true correlation between the latent change scores. In contrast, the correlation between the observed change scores tends to underestimate the strength of this relationship, particularly when the true correlation is strong in magnitude, the target and/or supporting score has a small number of response categories, and the response category thresholds are unequally spaced. Conclusion Estimating the correlation among latent change scores rather than observed change scores is recommended for collecting longitudinal validity evidence for a COA score when the target and/or supporting score is ordinal. Impact statement This study proposes an alternative approach for estimating responsiveness correlations when the target and/or supporting COA score is ordinal. The proposed approach may lead to a more accurate assessment of longitudinal construct validity and could impact the determination of appropriate anchor variables for estimating meaningful within-person change thresholds.