Conditional and Corrected Score Methods

Abstract

This chapter presents an overview of the conditional score and corrected score approaches for measurement error correction. The conditional score approach was introduced by Stefanski and Carroll (1987, Biometrika). The corrected score approach was introduced by Stefanski (1989, Communications in Statistics – Theory and Methods) and Nakamura (1990, Biometrika). These are functional methods that do not involve modeling the distribution of the true covariate. They are based on the likelihood score function (log-likelihood derivative) or its counterpart for estimation methods based on a likelihood-like function (such as the Cox partial likelihood for survival data). The chapter begins with a review of the concept of the likelihood score function, focusing on the setting of generalized linear models (GLM's). The chapter then presents the conditional score method for GLM's under the classical measurement error model. Following this, the chapter presents an overview of various methods using the corrected score approach in various settings.