Adjusting a relative-risk estimate for study imperfections

A statistical analysis combines data with assumptions to yield a quantitative result that is a function of both. One goal of an epidemiological analysis, then, should be to combine data with good assumptions. Unfortunately, a typical quantitative epidemiological analysis combines data with an assumption for which there is neither theoretical nor empirical justification. The assumption is that study imperfections (eg residual confounding, subject losses, non-random subject sampling, subject non-response, exclusions because of missing data, measurement error, incorrect statistical assumptions) have no important impact on study results. The author explains how a typical epidemiological analysis implicitly makes this assumption. It is then shown how in a quantitative analysis the assumption can be replaced with a better one. A simple, everyday example to illustrate the fundamental concepts is used to begin with. The relationship between an observed relative risk, the true causal relative risk and error terms that describe the impact of study imperfections on study results is described mathematically. This mathematical description can be used to quantitatively adjust a relative-risk estimate for the combined effect of study imperfections.