Abstract
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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 127-151 |
| Number of pages | 25 |
| Journal | Journal of the Royal Statistical Society. Series B: Statistical Methodology |
| Volume | 78 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 1 2016 |
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All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
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Semiparametric estimation in the secondary analysis of case–control studies. / Ma, Yanyuan; Carroll, Raymond J.
In: Journal of the Royal Statistical Society. Series B: Statistical Methodology, Vol. 78, No. 1, 01.01.2016, p. 127-151.Research output: Contribution to journal › Article
TY - JOUR
T1 - Semiparametric estimation in the secondary analysis of case–control studies
AU - Ma, Yanyuan
AU - Carroll, Raymond J.
PY - 2016/1/1
Y1 - 2016/1/1
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.
UR - http://www.scopus.com/inward/record.url?scp=84923166732&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84923166732&partnerID=8YFLogxK
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 -