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 misreporting behavior, and how respondents' tendency to under- or overreport a binary outcome might affect the power of the experiment. We model the problem by assuming each individual in our study is a member of one "reporting class": a truth-teller, underreporter, overreporter, or false-teller. We show that the joint distribution of reporting classes and "response classes" (characterizing individuals' response to the treatment) will exactly define the bias and variance of the causal estimate in our experiment. Then, we propose a novel procedure for deriving 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 Nairobi, Kenya.

翻译：我们考虑了设计预期随机审判的问题,结果数据将在其中自我报告,并将涉及敏感议题。我们感兴趣的是错误报告行为,以及被调查者低报或多报一个二进制结果的倾向会如何影响实验的力量。我们通过在我们的研究中假设每个人是“报告阶层”的成员来模拟这一问题:一个“报告阶层”的成员:一个真相学家、低报者、过度报告者或错误报告者。我们表明,联合分发报告班和“反应班”(描述个人对治疗的反应)将确切地界定我们实验中因果估计的偏差和差异。然后,我们提出一个新的程序,根据与特定程度的错误报告相对应的最坏情况来计算样本大小。我们的问题源于在肯尼亚内罗毕对少女实施随机控制性性暴力预防方案的经验。