Sample size calculations with compliance information

In randomized clinical trials, non-compliance will lead to the loss of power in the standard intention-to-treat analysis and one should account for this in sample size calculations. In this paper a new sample size formula for a binary outcome is proposed in which compliance information is considered. The proposed method is based purely on the treatment randomization. We compare it to the conventional sample size calculation method based on the two independent binomial distributions assumption. We examine 3100 combinations of risks of control group (baseline risks), treatment effects (risk differences), compliances in the test treatment group and the control treatment group, test sizes and powers. We found that, compared to the conventional method, the proposed method gives similar sample sizes for baseline risks 0.4-0.6, larger sample sizes for baseline risks less than 0.4, and smaller sample sizes for baseline risks greater than 0.6 when the true risk difference is negative.