The impact of residual and unmeasured confounding in epidemiologic studies: a simulation study

Measurement error in explanatory variables and unmeasured confounders can cause considerable problems in epidemiologic studies. It is well recognized that under certain conditions, nondifferential measurement error in the exposure variable produces bias towards the null. Measurement error in confounders will lead to residual confounding, but this is not a straightforward issue, and it is not clear in which direction the bias will point. Unmeasured confounders further complicate matters. There has been discussion about the amount of bias in exposure effect estimates that can plausibly occur due to residual or unmeasured confounding. In this paper, the authors use simulation studies and logistic regression analyses to investigate the size of the apparent exposure-outcome association that can occur when in truth the exposure has no causal effect on the outcome. The authors consider two cases with a normally distributed exposure and either two or four normally distributed confounders. When the confounders are uncorrelated, bias in the exposure effect estimate increases as the amount of residual and unmeasured confounding increases. Patterns are more complex for correlated confounders. With plausible assumptions, effect sizes of the magnitude frequently reported in observational epidemiologic studies can be generated by residual and/or unmeasured confounding alone.