Clinical trials: odds ratios and multiple regression models--why and how to assess them

Odds ratios (ORs), unlike chi2 tests, provide direct insight into the strength of the relationship between treatment modalities and treatment effects. Multiple regression models can reduce the data spread due to certain patient characteristics and thus improve the precision of the treatment comparison. Despite these advantages, the use of these methods in clinical trials is relatively uncommon. Our objectives were (1) to emphasize the great potential of ORs and multiple regression models as a basis of modern methods; (2) to illustrate their ease of use; and (3) to familiarize nonmathematical readers with these important methods. Advantages of ORs are multiple. (1) They describe the probability that people with a certain treatment will have an event, versus those without the treatment, and are therefore a welcome alternative to the widely used chi2 tests for analyzing binary data in clinical trials. (2) statistical software of ORs is widely available. (3) Computations using risk ratios (RRs) are less sensitive than those using ORs. (4) ORs are the basis for modern methods such as meta-analyses, propensity scores, logistic regression, and Cox regression. For analysis, logarithms of the ORs have to be used; results are obtained by calculating antilogarithms. A limitation of the ORs is that they present relative benefits but not absolute benefits. ORs, despite a fairly complex mathematical background, are easy to use, even for nonmathematicians. Both linear and logistic regression models can be adequately applied for the purpose of improving precision of parameter estimates such as treatment effects. We caution that, although application of these models is very easy with computer programs widely available, the fit of the regression models should always be carefully checked, and the covariate selection should be carefully considered and sparse. We do hope that this article will stimulate clinical investigators to use ORs and multiple regression models more often.