Re-evaluating composite scores: Adaptive Lasso variable selection for non-linear models

In nutrition, epidemiology, and other public health fields, composite scores are a common tool used to assess a health behaviour. These composite scores compare an individual's health behaviour to an idealized standard and provide a number, often between 0 and 100, to indicate their compliance to a health behaviour. Crucially, this measure of health behaviour is applied across populations (gender, smoking status, etc.) and health outcomes (colon cancer, breast cancer, etc.) to create a single interpretable score. One such composite score is the 2005 Healthy Eating Index that breaks diet into 12 components and evaluates nutritional intake by adherence to these components. We provide a general method that can be used to reassess the importance of these 12 components using flexible non-linear models, across populations and diseases, based on an asymptotic least squares approximation. We establish oracle properties of this variable selection technique in our context, which is different from the usual one population and one disease context. Although our methods are motivated by the Healthy Eating Index, they are broad enough to be applied to any composite score and a broad range of non-linear models.