Robust Designs for Prospective Randomized Trials Surveying Sensitive Topics

We consider the problem of designing a prospective randomized trial in which the outcome data will be self-reported and will involve sensitive topics. Our interest is in how a researcher can adequately power her study when some respondents misreport the binary outcome of interest. To correct the power calculations, we first obtain expressions for the bias and variance induced by misreporting. We model the problem by assuming each individual in our study is a member of one "reporting class": a true-reporter, false-reporter, never-reporter, or always-reporter. We show that the joint distribution of reporting classes and "response classes" (characterizing individuals' response to the treatment) will exactly define the error terms for our causal estimate. We propose a novel procedure for determining adequate sample sizes under the worst-case power corresponding to a given level of misreporting. Our problem is motivated by prior experience implementing a randomized controlled trial of a sexual-violence prevention program among adolescent girls in Kenya.