Consider the simple compliance randomized trial, in which patients randomly assigned to the experimental treatment may switch to receive the standard treatment, while patients randomly assigned to the standard treatment are all assumed to receive their assigned treatment. Six asymptotic interval estimators for the risk difference in probabilities of response among patients who would accept the experimental treatment were developed. Monte Carlo methods were employed to evaluate and compare the finite-sample performance of these estimators. An example studying the effect of vitamin A supplementation on reducing mortality in preschool children was included to illustrate their practical use.