The Errors-in-Variables Problem: Considerations Provided by Radiation Dose-Response Analyses of the A-Bomb Survivor Data

Abstract

Some basic issues in the errors-in-variables problem are discussed, in terms of considerations that arose in analyses of radiation effects on atomic bomb survivors. The setting essentially involves generalized linear models for the response variables, a very nonnormal distribution of the true covariable, and multiplicative errors in the observed covariable. Consideration is given to distinctions between structural and functional modeling. It is argued that careful attention to the apparent distribution of true covariables is critical in either case, and a quasi-structural approach to functional models is suggested. The focus is on the case in which the expected response is linear in the true covariable and strong assumptions are tentatively made about the model for covariate errors. For settings such as just described, which differ from that of much of the classical work in the area, it is emphasized that an attractive approach is based on weighted regression of the response on the expected values of the true covariable, given the observed values.

Key Words:

• Dose-response analysis
• Errors in variables
• Generalized linear models
• Measurement errors
• Radiation effects