Sample size calculation for non-compliance randomized trials with repeated measurements in binary data

When we have difficulty in recruiting patients into a randomized clinical trial (RCT), we may consider taking more than one measurement per patient to reduce the number of patients needed to achieve a desired power. In this paper, we consider a double blind RCT with two courses of treatment per patient. At each course, a patient assigned to the experimental treatment could switch to receive the placebo if the patient declined his/her assigned (experimental) treatment, and a patient assigned to the placebo could switch to receive the experimental treatment if the patient refused his/her assigned (placebo) treatment as well. Sample size calculation without accounting for this non-compliance can be inadequate when we apply the standard procedure of intention-to-treat analysis for non-compliance trials to test no treatment effect. Based on the simple additive risk model proposed elsewhere, we have incorporated the initial probability of compliance, the dependence of patient's selection of a treatment on his/her previous response, and the variation of probabilities of response between patients into sample size determination. We have included a quantitative discussion that provides an insight into the effect of various parameters on the minimum required sample size. We have also noted the situation in which taking repeated measurements per patient can be most effective to reduce the number of patients needed to maintain a given power.