Confidence intervals for exposure-adjusted rate differences in randomized trials

Exposure-adjusted event rate is a quantity often used in clinical trials to describe average event count per unit of person-time. The event count may represent the number of patients experiencing first (incident) event episode, or the total number of event episodes, including recurring events. For inference about difference in the exposure-adjusted rates between interventions, many methods of interval estimation rely on the assumption of Poisson distribution for the event counts. These intervals may suffer from substantial undercoverage both, asymptotically due to extra-Poisson variation, and in the settings with rare events even when the Poisson assumption is satisfied. We review asymptotically robust methods of interval estimation for the rate difference that do not depend on distributional assumptions for the event counts, and propose a modification of one of these methods. The new interval estimator has asymptotically nominal coverage for the rate difference with an arbitrary distribution of event counts, and good finite sample properties, avoiding substantial undercoverage with small samples, rare events, or over-dispersed data. The proposed method can handle covariate adjustment and can be implemented with commonly available software. The method is illustrated using real data on adverse events in a clinical trial.