Notes on interval estimation of risk difference in stratified noncompliance randomized trials: A Monte Carlo evaluation

When comparing an experimental treatment with a standard treatment in a randomized clinical trial (RCT), we often use the risk difference (RD) to measure the efficacy of an experimental treatment. In this paper, we have developed four asymptotic interval estimators for the RD in a stratified RCT with noncompliance. These include an asymptotic interval estimator based on the weighted-least-squares (WLS) estimator of the RD, an asymptotic interval estimator using tanh−1(x) transformation with the WLS optimal weight, an asymptotic interval estimator derived from Fieller's Theorem, and an asymptotic interval estimator using a randomization-based approach. Based on Monte Carlo simulations, we have compared these four asymptotic interval estimators with the asymptotic interval estimator recently proposed elsewhere. We have found that when the probability of compliance is high, the interval estimator using a randomization-based approach is probably more accurate than the others, especially when the stratum size is not large. When the probability of compliance is moderate, the interval estimator using tanh−1(x) transformation is likely to be the best among all interval estimators considered here. We note that the interval estimator proposed elsewhere can be of use when the underlying RD is small, but lose accuracy when the RD is large. We also note that when the number of patients per assigned treatment is large, the four asymptotic interval estimators developed here are essentially equivalent; they are all appropriate for use. Finally, to illustrate the use of these interval estimators, we consider the data taken from a large field trial studying the effect of a multifactor intervention program on reducing the mortality of coronary heart disease in middle-aged men.