A Semiparametric Single-Index Risk Score Across Populations

Shujie Ma, Yanyuan Ma, Yanqing Wang, Eli S. Kravitz and Raymond J. Carroll

Journal of the American Statistical Association, 2017, vol. 112, issue 520, 1648-1662

Abstract: We consider a problem motivated by issues in nutritional epidemiology, across diseases and populations. In this area, it is becoming increasingly common for diseases to be modeled by a single diet score, such as the Healthy Eating Index, the Mediterranean Diet Score, etc. For each disease and for each population, a partially linear single-index model is fit. The partially linear aspect of the problem is allowed to differ in each population and disease. However, and crucially, the single-index itself, having to do with the diet score, is common to all diseases and populations, and the nonparametrically estimated functions of the single-index are the same up to a scale parameter. Using B-splines with an increasing number of knots, we develop a method to solve the problem, and display its asymptotic theory. An application to the NIH-AARP Study of Diet and Health is described, where we show the advantages of using multiple diseases and populations simultaneously rather than one at a time in understanding the effect of increased Milk consumption. Simulations illustrate the properties of the methods. Supplementary materials for this article are available online.

Date: 2017
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DOI: 10.1080/01621459.2016.1222944

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