A Semiparametric Single-Index Risk Score Across Populations

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

Research output: Contribution to journalArticle

1 Citation (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)1648-1662
Number of pages15
JournalJournal of the American Statistical Association
Volume112
Issue number520
DOIs
StatePublished - Oct 2 2017

Fingerprint

Single-index Model
Epidemiology
Asymptotic Theory
Scale Parameter
B-spline
Knot
Linear Model
Health
Diet
Simulation
Index model
Healthy eating
Milk
Asymptotic theory

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Ma, Shujie ; Ma, Yanyuan ; Wang, Yanqing ; Kravitz, Eli S. ; Carroll, Raymond J. / A Semiparametric Single-Index Risk Score Across Populations. In: Journal of the American Statistical Association. 2017 ; Vol. 112, No. 520. pp. 1648-1662.
@article{484ebca290e64df59e32f8d9ad4da1d2,
title = "A Semiparametric Single-Index Risk Score Across Populations",
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.",
author = "Shujie Ma and Yanyuan Ma and Yanqing Wang and Kravitz, {Eli S.} and Carroll, {Raymond J.}",
year = "2017",
month = "10",
day = "2",
doi = "10.1080/01621459.2016.1222944",
language = "English (US)",
volume = "112",
pages = "1648--1662",
journal = "Journal of the American Statistical Association",
issn = "0162-1459",
publisher = "Taylor and Francis Ltd.",
number = "520",

}

A Semiparametric Single-Index Risk Score Across Populations. / Ma, Shujie; Ma, Yanyuan; Wang, Yanqing; Kravitz, Eli S.; Carroll, Raymond J.

In: Journal of the American Statistical Association, Vol. 112, No. 520, 02.10.2017, p. 1648-1662.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A Semiparametric Single-Index Risk Score Across Populations

AU - Ma, Shujie

AU - Ma, Yanyuan

AU - Wang, Yanqing

AU - Kravitz, Eli S.

AU - Carroll, Raymond J.

PY - 2017/10/2

Y1 - 2017/10/2

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85024473270&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85024473270&partnerID=8YFLogxK

U2 - 10.1080/01621459.2016.1222944

DO - 10.1080/01621459.2016.1222944

M3 - Article

C2 - 29520120

AN - SCOPUS:85024473270

VL - 112

SP - 1648

EP - 1662

JO - Journal of the American Statistical Association

JF - Journal of the American Statistical Association

SN - 0162-1459

IS - 520

ER -