Statistical properties of continuous composite scales and implications for drug development.

Little research has been conducted on the statistical properties of composite measures comprising linear combinations of continuous component scales. We assessed the quantitative relationship between the composites and their individual components regarding their abilities to detect treatment effects. In particular, we developed the mathematical derivation of the treatment effect size of a continuous composite in relation to the treatment effect sizes of its components and proved multiple properties of the composite. We demonstrated that the treatment effect size of a composite is greater than the minimum treatment effect size of its components and that above certain thresholds of correlations of components and ratios of component effect sizes, the composite may outperform its components. Examples from Alzheimer's disease (AD) clinical studies of solanezumab and donepezil using the composite Integrated AD Rating Scale (iADRS) and its components, the AD Assessment Scale-Cognitive subscale (ADAS-Cog) and AD Cooperative Study-Activities of Daily Living inventory, instrumental items (ADCS-iADL) were consistent with the theoretical statistical properties. The understanding of the quantitative relationships between continuous composites and their components will be useful in clinical trial design and the development of new scales and composites across therapeutic areas.