Asymmetrical reliability of the Alda Score favours a dichotomous representation of lithium responsiveness
The Alda score is commonly used to quantify lithium responsiveness in bipolar disorder. Most often, this score is dichotomized into "responder" and "non-responder" categories, respectively. This practice is often criticized as inappropriate, since continuous variables are thought to invariably be "more informative" than their dichotomizations. We therefore investigated the degree of informativeness across raw and dichotomized versions of the Alda score, using data from a published study of the scales inter-rater reliability (n=59 raters of 12 standardized vignettes each). After learning a generative model for the relationship between observed and ground truth scores (the latter defined by a consensus rating of the 12 vignettes), we show that the dichotomized scale is more robust to inter-rater disagreement than the raw 0-10 scale. Further theoretical analysis shows that when a measures reliability is stronger at one extreme of the continuum--a scenario which has received little-to-no statistical attention, but which likely occurs for the Alda score [≥] 7--dichotomization of a continuous variable may be more informative concerning its ground truth value, particularly in the presence of noise. Our study suggests that research employing the Alda score of lithium responsiveness should continue using the dichotomous definition, particularly when data are sampled across multiple raters.