Robust estimation for homoscedastic regression in the secondary analysis of case-control data

Jiawei Wei, Raymond J. Carroll, Ursula U. Müller, Ingrid Van Keilegom, Nilanjan Chatterjee

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


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, which is often invoked in modern genetic epidemiologic association studies, is to investigate the interrelationship between the covariates themselves. The task is complicated owing to the case-control sampling, where the regression of Y on X is different from what it is in the population. Previous work has assumed a parametric distribution for Y given X and derived semiparametric efficient estimation and inference without any distributional assumptions about X. We take up the issue of estimation of a regression function when Y given X follows a homoscedastic regression model, but otherwise the distribution of Y is unspecified. The semiparametric efficient approaches can be used to construct semiparametric efficient estimates, but they suffer from a lack of robustness to the assumed model for Y given X. We take an entirely different approach. We show how to estimate the regression parameters consistently even if the assumed model for Y given X is incorrect, and thus the estimates are model robust. For this we make the assumption that the disease rate is known or well estimated. The assumption can be dropped when the disease is rare, which is typically so for most case-control studies, and the estimation algorithm simplifies. Simulations and empirical examples are used to illustrate the approach.
Original languageEnglish (US)
Pages (from-to)185-206
Number of pages22
JournalJournal of the Royal Statistical Society: Series B (Statistical Methodology)
Issue number1
StatePublished - Dec 4 2012
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-CI-016-04
Acknowledgements: This paper represents part of the first author's doctoral dissertation at Texas A&M University. Wei and Carroll's research was supported by a grant from the National Cancer Institute (R37-CA057030). Carroll was also supported by award KUS-CI-016-04, made by King Abdullah University of Science and Technology. Chatterjee's research was supported by a gene–environment initiative grant from the National Heart, Lung and Blood Institute (RO1-HL091172-01) and by the Intramural Research Program of the National Cancer Institute. Müller was supported by a National Science Foundation grant (DMS-0907014). Van Keilegom gratefully acknowledges financial support from Interuniversity Attraction Pole research network P6/03 of the Belgian Government (Belgian science policy), and from the European Research Council under the European Community's seventh framework programme (FP7/2007-2013), European Research Council grant agreement 203650.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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