Using Log-linear and Logistic Regression for Inferences on Adjusted Estimates of Relative Risk in Randomized Comparative Trials

Randomized comparative trials are often used to assess the relative merits of two or more interventions aimed at having beneficial effects on the incidence of categorical outcomes. In simple applications chisquare tests can be used to analyze contrasts among proportions of incident events or risk ratios (relative risks). However, assessment of intervention differences may be obscured by outcome variations attributable to covariates. There are advantages to using logistic regression analysis to assess intervention effects in terms of odds ratios (OR) adjusted for covariates. The limitation of using OR rather than relative risk (RR) estimates in making statistical inferences about incidence rates is well documented. Subjectspecific estimates of probabilities for a specified covariate profile are readily obtained by logistic and loglinear regression models. Functions of the marginal probabilities provide estimates of incident risk and RR for each intervention. We illustrate novel applications of the inferential methods in this paper.