Interval estimation of the risk difference in non-compliance randomized trials with repeated binary measurements

In a randomized clinical trial (RCT), we often encounter non-compliance with the treatment protocol for a subset of patients. The intention-to-treat (ITT) analysis is probably the most commonly used method in a RCT with non-compliance. However, the ITT analysis estimates 'the programmatic effectiveness' rather than 'the biological efficacy'. In this paper, we focus attention on the latter index and consider use of the risk difference (RD) to measure the effect of a treatment. Based on a simple additive risk model proposed elsewhere, we develop four asymptotic interval estimators of the RD for repeated binary measurements in a RCT with non-compliance. We apply Monte Carlo simulation to evaluate and compare the finite-sample performance of these interval estimators in a variety of situations. We find that all interval estimators considered here can perform well with respect to the coverage probability. We further find that the interval estimator using a tanh(-1)(x) transformation is probably more precise than the others, while the interval estimator derived from a randomization-based approach may cause a slight loss of precision. When the number of patients per treatment is large and the probability of compliance to an assigned treatment is high, we find that all interval estimators discussed here are essentially equivalent. Finally, we illustrate use of these interval estimators with data simulated from a trial of using macrophage colony-stimulating factor to reduce febrile neutropenia incidence in acute myeloid leukaemia patients.