The Semiparametric Case-Only Estimator
Article first published online: 11 MAR 2010
© 2010, The International Biometric Society
Volume 66, Issue 4, pages 1138–1144, December 2010
How to Cite
Tchetgen Tchetgen, E. J. and Robins, J. (2010), The Semiparametric Case-Only Estimator. Biometrics, 66: 1138–1144. doi: 10.1111/j.1541-0420.2010.01401.x
- Issue published online: 11 MAR 2010
- Article first published online: 11 MAR 2010
- Received February 2009. Revised December 2009. Accepted December 2009.
- Gene–environment independence;
- Gene–environment interaction;
- Generalized odds ratio;
- Double robustness;
- Local efficiency
Summary We propose a semiparametric case-only estimator of multiplicative gene–environment or gene–gene interactions, under the assumption of conditional independence of the two factors given a vector of potential confounding variables. Our estimator yields valid inferences on the interaction function if either but not necessarily both of two unknown baseline functions of the confounders is correctly modeled. Furthermore, when both models are correct, our estimator has the smallest possible asymptotic variance for estimating the interaction parameter in a semiparametric model that assumes that at least one but not necessarily both baseline models are correct.