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Stat Biosci. 2013 Nov 1;5(2):250-260.

A Note on Penalized Regression Spline Estimation in the Secondary Analysis of Case-Control Data.

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Department of Mathematical Sciences, Montana Tech of the University of Montana, Butte MT 59701.
Beijing Novartis Pharma Co. Ltd., Integrated Information Sciences (IIS), Building 3 Floor 3, No. 3728 Jinke Road, Pudong New District, Shanghai, 201203, China.
Department of Statistics, Texas A&M University, 3143 TAMU, College Station, TX 77843-3143.


Primary analysis of case-control studies focuses on the relationship between disease (D) and a set of covariates of interest (Y, X). A secondary application of the case-control study, often invoked in modern genetic epidemiologic association studies, is to investigate the interrelationship between the covariates themselves. The task is complicated due to the case-control sampling, and to avoid the biased sampling that arises from the design, it is typical to use the control data only. In this paper, we develop penalized regression spline methodology that uses all the data, and improves precision of estimation compared to using only the controls. A simulation study and an empirical example are used to illustrate the methodology.


B-splines; Biased samples; Homoscedastic regression; Nonparametric regression; Regression splines; Secondary data; Secondary phenotypes; Two-stage samples

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