Inferences in Binary Regression Models for Independent Data with Measurement Errors in Covariates

When responses along with covariates are collected from a group of independent individuals in a binary regression setup, in some practical situations the observed covariates may be subject to measurement errors differing from the true covariates values. These imprecise observed covariates, when used directly, the standard statistical methods such as naive likelihood and quasi-likelihood methods yield biased and hence inconsistent regression estimates. Because there does not exist a corrected score function for this binary measurement error model, a considerable attention is given in the literature to develop approximate unbiased estimating equation in order to obtain consistent regression estimate. In this paper, we review some of these widely used approaches and suggest a softer (approximate) quasi-likelihood approach for consistent regression parameters estimation.