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The Semiparametric Case‐Only Estimator
Author(s) -
Tchetgen Tchetgen Eric J.,
Robins James
Publication year - 2010
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.1541-0420.2010.01401.x
Subject(s) - estimator , semiparametric regression , mathematics , confounding , statistics , semiparametric model , conditional independence , econometrics , consistent estimator , multiplicative function , minimum variance unbiased estimator , mathematical analysis
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.