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2018 Dimension reduction and estimation in the secondary analysis of case-control studies
Liang Liang, Raymond Carroll, Yanyuan Ma
Electron. J. Statist. 12(1): 1782-1821 (2018). DOI: 10.1214/18-EJS1446


Studying the relationship between covariates based on retrospective data is the main purpose of secondary analysis, an area of increasing interest. We examine the secondary analysis problem when multiple covariates are available, while only a regression mean model is specified. Despite the completely parametric modeling of the regression mean function, the case-control nature of the data requires special treatment and semiparametric efficient estimation generates various nonparametric estimation problems with multivariate covariates. We devise a dimension reduction approach that fits with the specified primary and secondary models in the original problem setting, and use reweighting to adjust for the case-control nature of the data, even when the disease rate in the source population is unknown. The resulting estimator is both locally efficient and robust against the misspecification of the regression error distribution, which can be heteroscedastic as well as non-Gaussian. We demonstrate the advantage of our method over several existing methods, both analytically and numerically.


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Liang Liang. Raymond Carroll. Yanyuan Ma. "Dimension reduction and estimation in the secondary analysis of case-control studies." Electron. J. Statist. 12 (1) 1782 - 1821, 2018.


Received: 1 February 2017; Published: 2018
First available in Project Euclid: 12 June 2018

zbMATH: 06886385
MathSciNet: MR3813597
Digital Object Identifier: 10.1214/18-EJS1446

Primary: 62G05

Keywords: Biased samples , case-control study , Dimension reduction , heteroscedastic error , secondary analysis , Semiparametric estimation


Vol.12 • No. 1 • 2018
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