Conditions for Confounding of the Risk Ratio and of the Odds Ratio1

There are disagreements in the literature about the criteria to be used to ascertain whether or not a measure of association is confounded. The authors postulate the general principle that a crude unconfounded measure of association is structured as a weighted average of the stratum-specific values of the measure. They examine the relationships between stratum-specific measures of association, crude overall measures, and weighted averages of stratum-specific measures, and indicate how these relationships may be used to define criteria for the assessment of confounding in cohort studies in which the exposure, disease, and stratification variables are classified dichotomously. The criteria presented differ for the risk ratio and for the disease-odds ratio. In other words, one can reach different conclusions about the confounding effect of a given extraneous variable, depending on which measure of association is chosen. This view differs from that of Miettinen and Cook (Confounding: essence and detection. Am J Epidemiol 1981;114:593-603) who postulated one set of criteria for the assessment of confounding, which was applicable to both measures of association. These different approaches may lead to different conclusions about the presence or absence of confounding.