Relative Risks, Odds Ratios and Cluster Randomised Trials

It is well known in cluster randomised trials with a binary outcome and a logistic link that the population average model and cluster specific model estimate different population parameters for the odds ratio. However, it is less well appreciated that for a log link, the population parameters are the same and a log link leads to a relative risk. This suggests that for a prospective cluster randomised trial the relative risk is easier to interpret. Commonly the odds ratio and the relative risk have similar values and are interpreted similarly. However, when the incidence of events is high they can differ quite markedly, and it is unclear which is the better parameter . We explore these issues in a cluster randomised trial, the Paramedic Practitioner Older People’s Support Trial 3 .