An anatomy of the way composite scores work.

Recently, epidemiologists tend to focus on the association of health outcomes with combinations of exposures (composites), defined a-priori or a-posteriori. Such composites appear often in nutritional (dietary patterns) and genetic (genetic scores) epidemiology. The estimated associations, however, have not been linked to those of the components of the composite, at least in a systematic way. We considered composites (X) which are linear combinations of more than one exposures (components of the composite) and explored the association of X with a linear heath outcome (Y) in terms of the associations of its individual components with Y. We showed that: (1) the association of X with Y is a weighted average of the associations of the components of X with Y; (2) the weights depend on the estimated covariance matrix of the components, and on the scalar used for the linear combination, and; (3) when components are binary variables and X is a simple sum of its components, the weights depend solely on the proportion of "1"s that are present in each component and are common with the others. Using data from a cohort study in Greece we illustrated these properties for: (1) the a-priori Mediterranean diet score; (2) an a-priori genetic predisposition score, and; (3) an a-posteriori dietary pattern. Our findings may be important in interpreting estimated associations of composites with health outcomes, or, in designing composites that are expected to capture most of the associations of their components with health outcomes (new genetic scores, or composites of biomarkers).