Journal
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
Volume 112, Issue 520, Pages 1648-1662Publisher
AMER STATISTICAL ASSOC
DOI: 10.1080/01621459.2016.1222944
Keywords
B-splines; Combining datasets; Healthy Eating Index; Partially linear single-index models; Semiparametric models; Single-index models
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Funding
- NSF [DMS-1306972, DMS-1206693]
- NIH [R01-NS073671]
- National Cancer Institute [U01-CA057030]
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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-indexmodel 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.
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