Measurement error affecting the independent variables in regression models is a common problem in many scientific areas. It is well known that the implications of ignoring measurement errors in inferential procedures may be substantial, often turning out in unreliable results. Many different measurement error correction techniques have been suggested in literature since the 80's. Most of them require many assumptions on the involved variables to be satisfied. However, it may be usually very hard to check whether these assumptions are satisfied, mainly because of the lack of information about the unobservable and mismeasured phenomenon. Thus, alternatives based on weaker assumptions on the variables may be preferable, in that they offer a gain in robustness of results. In this paper, we provide a review of robust techniques to correct for measurement errors affecting the covariates.
Attention is paid to methods which share properties of robustness against misspecifications of relationships between variables. Techniques are grouped according to the kind of underlying modeling assumptions and inferential methods.
Details about the techniques are given and their applicability is discussed. The basic framework is the epidemiological setting, where literature about the measurement error phenomenon is very substantial. The focus will be mainly on case-control studies
