Electronic Journal of Statistics
- Electron. J. Statist.
- Volume 12, Number 1 (2018), 1782-1821.
Dimension reduction and estimation in the secondary analysis of case-control studies
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.
Electron. J. Statist., Volume 12, Number 1 (2018), 1782-1821.
Received: February 2017
First available in Project Euclid: 12 June 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62G05: Estimation
Liang, Liang; Carroll, Raymond; Ma, Yanyuan. Dimension reduction and estimation in the secondary analysis of case-control studies. Electron. J. Statist. 12 (2018), no. 1, 1782--1821. doi:10.1214/18-EJS1446. https://projecteuclid.org/euclid.ejs/1528769120