  We consider generalized linear regression analysis with left-censored
covariate due to the lower limit of detection. Complete case analysis by
eliminating observations with values below limit of detection yields valid
estimates for regression coefficients, but loses efficiency; substitution
methods are biased; maximum likelihood method relies on parametric models for
the unobservable tail probability distribution of such covariate, thus may
suffer from model misspecification. To obtain robust and more efficient
results, we propose a semiparametric likelihood-based approach for the
estimation of regression parameters using an accelerated failure time model for
the covariate subject to limit of detection. A two-stage estimation procedure
is considered, where the conditional distribution of the covariate with limit
of detection given other variables is estimated prior to maximizing the
likelihood function. The proposed method outperforms the complete case analysis
and the substitution methods as well in simulation studies. Technical
conditions for desirable asymptotic properties are provided.
