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.
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Funding: Early work on this topic was supported by grant number NIH/1R29-ES07986 from the National Institute of Environmental Health Sciences (NIEHS), NIH. Its contents are solely the responsibility of the authors and do not necessarily represent the official views of the NIEHS, NIH.
Competing interests: None.
↵i For example, if Bi is the number of disease-free people at the beginning of the target time period, then Ri is an incidence proportion. If Bi is the number of disease-free people at the end of the target time period, then Ri is an incidence odds. If Bi is the person-time during the target time period, then Ri is a person-time incidence rate.
↵ii We use “exposure pattern 1” and “exposure pattern 0” to denote generally any two exposure patterns that a causal contrast compares. “Exposure pattern 1” is not meant to imply that everyone in the target or substitute is exposed and experiences the same exposure level. “Exposure pattern 0” is not meant to imply that everyone in the target or substitute is unexposed.