TY - JOUR

T1 - Semiparametric estimation in the secondary analysis of case–control studies

AU - Ma, Yanyuan

AU - Carroll, Raymond J.

N1 - Funding Information:
Ma's research was supported by National Science Foundation grant DMS-1206693 and National Institute of Neurological Disorders and Stroke grant R01-NS073671. Carroll's research was supported by National Cancer Institute grant R37-CA057030 and by National Institute of Neurological Disorders and Stroke grant R01-NS073671.
Publisher Copyright:
© 2015 Royal Statistical Society

PY - 2016

Y1 - 2016

N2 - We study the regression relationship between covariates in case–control data: an area known as the secondary analysis of case–control studies. The context is such that only the form of the regression mean is specified, so that we allow an arbitrary regression error distribution, which can depend on the covariates and thus can be heteroscedastic. Under mild regularity conditions we establish the theoretical identifiability of such models. Previous work in this context has either specified a fully parametric distribution for the regression errors, specified a homoscedastic distribution for the regression errors, has specified the rate of disease in the population (we refer to this as the true population) or has made a rare disease approximation. We construct a class of semiparametric estimation procedures that rely on none of these. The estimators differ from the usual semiparametric estimators in that they draw conclusions about the true population, while technically operating in a hypothetical superpopulation. We also construct estimators with a unique feature, in that they are robust against the misspecification of the regression error distribution in terms of variance structure, whereas all other non-parametric effects are estimated despite the biased samples. We establish the asymptotic properties of the estimators and illustrate their finite sample performance through simulation studies, as well as through an empirical example on the relationship between red meat consumption and hetero-cyclic amines. Our analysis verified the positive relationship between red meat consumption and two forms of hetro-cyclic amines, indicating that increased red meat consumption leads to increased levels of MeIQx and PhIP, both being risk factors for colorectal cancer. Computer software as well as data to illustrate the methodology are available from http://www.stat.tamu.edu/~carroll/matlab__programs/software.php.

AB - We study the regression relationship between covariates in case–control data: an area known as the secondary analysis of case–control studies. The context is such that only the form of the regression mean is specified, so that we allow an arbitrary regression error distribution, which can depend on the covariates and thus can be heteroscedastic. Under mild regularity conditions we establish the theoretical identifiability of such models. Previous work in this context has either specified a fully parametric distribution for the regression errors, specified a homoscedastic distribution for the regression errors, has specified the rate of disease in the population (we refer to this as the true population) or has made a rare disease approximation. We construct a class of semiparametric estimation procedures that rely on none of these. The estimators differ from the usual semiparametric estimators in that they draw conclusions about the true population, while technically operating in a hypothetical superpopulation. We also construct estimators with a unique feature, in that they are robust against the misspecification of the regression error distribution in terms of variance structure, whereas all other non-parametric effects are estimated despite the biased samples. We establish the asymptotic properties of the estimators and illustrate their finite sample performance through simulation studies, as well as through an empirical example on the relationship between red meat consumption and hetero-cyclic amines. Our analysis verified the positive relationship between red meat consumption and two forms of hetro-cyclic amines, indicating that increased red meat consumption leads to increased levels of MeIQx and PhIP, both being risk factors for colorectal cancer. Computer software as well as data to illustrate the methodology are available from http://www.stat.tamu.edu/~carroll/matlab__programs/software.php.

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U2 - 10.1111/rssb.12107

DO - 10.1111/rssb.12107

M3 - Article

C2 - 26834506

AN - SCOPUS:84923166732

VL - 78

SP - 127

EP - 151

JO - Journal of the Royal Statistical Society. Series B: Statistical Methodology

JF - Journal of the Royal Statistical Society. Series B: Statistical Methodology

SN - 1369-7412

IS - 1

ER -