Odds per adjusted standard deviation: comparing strengths of associations for risk factors measured on different scales and across diseases and populations.

How can the "strengths" of risk factors, in the sense of how well they discriminate cases from controls, be compared when they are measured on different scales such as continuous, binary, and integer? Given that risk estimates take into account other fitted and design-related factors-and that is how risk gradients are interpreted-so should the presentation of risk gradients. Therefore, for each risk factor X0, I propose using appropriate regression techniques to derive from appropriate population data the best fitting relationship between the mean of X0 and all the other covariates fitted in the model or adjusted for by design (X1, X2, … , Xn). The odds per adjusted standard deviation (OPERA) presents the risk association for X0 in terms of the change in risk per s = standard deviation of X0 adjusted for X1, X2, … , Xn, rather than the unadjusted standard deviation of X0 itself. If the increased risk is relative risk (RR)-fold over A adjusted standard deviations, then OPERA = exp[ln(RR)/A] = RR(s). This unifying approach is illustrated by considering breast cancer and published risk estimates. OPERA estimates are by definition independent and can be used to compare the predictive strengths of risk factors across diseases and populations.