Refining the Analysis of Multidimensional Psychometric Data: A Geometric Distance Approach

Validated instruments such as questionnaires, patient-reported outcome measures and clinician-rated psychopathology scales, are indispensable for measuring symptom burden and mental state, and for defining outcomes in both psychiatric practice and clinical trials. Most often, the values on the instruments multiple items (dimensions) are added to derive a single, univariate (scalar) sum-score. Although this approach simplifies interpretation, there are always many possible combinations of individual items that can yield the same sum-score. Two patients can therefore obtain identical scores on a given instrument, despite having very different combinations of underlying item scores corresponding to different patterns of clinical symptoms. The same is also true when a single patient is measured at two different time points, where the resulting sum-scores can obscure changes that may be clinically meaningful. We present an alternative analytic framework, which leverages geometric concepts to represent measurements as points in a vector space. Using this framework, we show why sum-scores obscure information present in measurements of clinical state, and also provide a straightforward algorithm to mitigate against this problem. Clinically-relevant outcomes, such as remission or patient-centered treatment goals, can be represented intuitively, as reference points or anchors within this space. Using real-world data, we then demonstrate how measuring the relative distance between points and anchors preserves more information, allowing outcomes such as proximity to remission, to be defined and measured.