Sample size estimation for the averted events ratio.

BACKGROUND: The averted events ratio (AER) is a recently developed estimand for non-inferiority active-control prevention trials with a time-to-event outcome. In contrast to the traditional rate ratio or rate difference, the AER is based on the number of events averted by each of the two treatments rather than the observed events. The AER requires an assumption about either the background event rate (the counterfactual placebo incidence) or the counterfactual effectiveness of the control treatment. We develop and present sample size formulae for trials in which the AER is defined as the primary estimand, and draw comparisons with the conventional 95-95 method based on the rate ratio. METHODS: We express sample size in terms of the expected number of events and required person-years follow-up in the control and experimental arms. Sample size formulae were based on Wald confidence intervals on a logarithmic scale, assuming the active and control treatments to be equally effective. Using the AER, sample size depends on whether the analysis will be based on the counterfactual placebo incidence or the counterfactual treatment effectiveness. For both approaches, and the 95-95 method, sample size is a function of the background event rate, the effectiveness of the control treatment, the preservation-of-effect size (non-inferiority margin), the confidence limit for inferring non-inferiority, and the desired statistical power to demonstrate non-inferiority. RESULTS: The smallest sample size is obtained using the AER based on the counterfactual placebo incidence. The advantage is greater the higher the value of the control treatment effectiveness. For example, compared with the 95-95 method, it allows between a 2.6-fold and 4.0-fold reduction in sample size for 50% treatment effectiveness (depending of the non-inferiority margin), and between a 7.7-fold and 11.9-fold reduction for 80% treatment effectiveness. The AER based on the control treatment effectiveness is less efficient but still requires smaller sample sizes than the 95-95 method: between a 1.5-fold and 2.9-fold reduction for 50% treatment effectiveness, and between a 2.3-fold and 6.4-fold reduction for 80% treatment effectiveness. Sample size is highly sensitive to the non-inferiority margin: increasing the preservation-of-effect size from 50% to 60% implies a 1.84-fold increase in the sample size; from 60% to 70%, an increase of 2.15-fold; and from 70% to 80%, an increase of 2.55-fold. CONCLUSION: As well as having important advantages of interpretation, using the AER as the primary estimand in active-control non-inferiority trials permits smaller and more cost-effective studies. Ideally, the AER should be derived via the counterfactual placebo incidence when this is practicable.