Causality, Measurement Error and Multicollinearity in Epidemiology

This paper demonstrates that measurement error can conspire with multicollinearity among explanatory variables to mislead an investigator. A causal variable measured with error may be overlooked and its significance transferred to a surrogate. The latter’s significance can then be entirely spurious, in that controlling it will not predictably change the response variable. In epidemiological research, such a response may be a health outcome. The phenomenon we study is demonstrated through simulation experiments involving nonlinear regression models. Also, the paper presents the measurement error problem in a theoretical setting. The paper concludes by echoing the familiar warning against making conclusions about causality from a multiple regression analysis, in this case because of the phenomenon presented in the paper.