| The unbiased estimating function method is a flexible approach to estimate and make inferences on the parameters of interest. However, special problems arise when covariates are measured with error.;Measurement errors arise in public health studies when some covariates are not measured precisely. We focus on the important case where the outcome is a binary variable and the interest is in coefficients from a logistic regression model. Two widely used estimating function methods for logistic regression with errors-in-covariates are the conditional score (Stefanski & Carroll 1987) and the parametric-correction estimation procedure (Huang & Wang 2001). The conditional score can have multiple-roots and not all of them are consistent, whereas the parametric-correction estimation only generate consistent roots. On the other hand, the conditional score in theory has an efficiency advantage in that its consistent estimator is asymptotically locally efficient. Despite the multiple-roots problem, the conditional approach is regarded as the standard method.;In this dissertation research, we aim to resolve the multiple-roots problem of the conditional score in logistic regression with errors-in-covariates. We investigate the root behaviors of the conditional score in finite samples and demonstrate the existence and seriousness of the problem posed by multiple roots, which have not been studied adequately in literature.;We propose two methods to achieve our research goal. In the first approach, we develop a weighted-correction estimating function that only yields consistent estimators and combine it with the conditional score using empirical likelihood. We prove that, asymptotically, the proposed approach admits only consistent estimators and is locally efficient.;In the second approach, we construct objective functions based on the weighted-correction estimating function and use them to distinguish among multiple roots from the conditional score.;In addition to developing the large sample theories of the proposed methods, we investigate their finite-sample properties through an extensive simulation. The simulation studies show that the proposed methods work well in finite samples and outperform existing methods in many situations. Finally, the proposed methods are applied to data presented in Hammer et al. (1996) and Pan et al. (1990). |
