Use of odds ratio or relative risk to measure a treatment effect in clinical trials with multiple correlated binary outcomes: data from the NINDS t-PA stroke trial

In clinical trials, when a single outcome is not sufficient to describe the underlying concept of interest, it may be necessary to compare treatment groups on multiple correlated outcomes. A global test based on a logit link function provides an estimate of the odds ratio for assessing a common treatment effect among correlated binary outcomes. In this paper we extend the use of generalized estimating equations (GEE) to calculate a common relative risk from correlated binary outcomes based on a log link function. In the context of global tests, we discuss the equivalence and difference between logit and log links and their estimates. We also derive a formula for calculating a common risk difference between two treatment groups based on multiple correlated binary outcomes with categorical covariates, assuming the asymptotic equivalency between the logit and log-linear links. We discuss the statistical tools to be used in choosing between the logit and log links when models on different links yield contrasting results. Examples using data from the NINDS t-PA Stroke Trials are provided. We conclude, in a study of correlated binary outcomes, that the choice of the logit or log link could be based on a comparison of goodness-of-link.