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We consider generalized linear regression analysis with left-censoredcovariate due to the lower limit of detection. Complete case analysis byeliminating observations with values below limit of detection yields validestimates for regression coefficients, but loses efficiency; substitutionmethods are biased; maximum likelihood method relies on parametric models forthe unobservable tail probability distribution of such covariate, thus maysuffer from model misspecification. To obtain robust and more efficientresults, we propose a semiparametric likelihood-based approach for theestimation of regression parameters using an accelerated failure time model forthe covariate subject to limit of detection. A two-stage estimation procedureis considered, where the conditional distribution of the covariate with limitof detection given other variables is estimated prior to maximizing thelikelihood function. The proposed method outperforms the complete case analysisand the substitution methods as well in simulation studies. Technicalconditions for desirable asymptotic properties are provided.

Semiparametric Approach for Regression with Covariate Subject to Limit of Detection