Background and Context: In 2016, our team designed and implemented a cluster-randomized trial of a school-based empowerment training program, targeting adolescent girls in Nairobi, Kenya (Baiocchi et al., 2019; Rosenman et al., 2020). In that study, the primary outcome was the experience of sexual violence in the prior year. Participants disclosed their data via self-report in surveys. Despite the considerable size of the study (4,000 girls across nearly 100 schools over two years), we obtained a null result. When discussing our findings with stakeholders, a consistent point of contention was how to reason about the possibility of misreporting bias. Inaccurate reports provided by girls in the study -- e.g. due to hesitancy around disclosure of a traumatic experience -- were plausible (and understandable), but posed a challenge for causal inference. We lacked a coherent framework for characterizing the bias induced by misreporting, and for correcting experimental designs in future studies. Research Question: We consider statistical methods to address the problem of designing and analyzing a prospective randomized trial in which the outcome data will be self-reported and will involve sensitive topics. Our questions are twofold. First, if a (non-random) subset of participants in a study can be expected to misreport the outcome, how does that affect the bias and variance of the resulting causal estimate? Second, if we anticipate a certain amount of misreporting in the study, can we alter our experimental design to achieve a desired level of power, even in the presence of misreporting? Findings/Results: Our framework centers on two parallel characterizations of individuals in the super-population from which the study is drawn. For a given measurement instrument and intervention, we assume each individual is a member of one "reporting class": a True-reporter, False-reporter, Never-reporter, or Always-reporter. True-reporters always report their outcome accurately; false-reporters always report their outcome as 1 if it is truly 0, and vice versa. Never-reporters always report a 0 and Always-reporters always report a 1. Because the outcome is binary, each individual also falls into one of four "response classes" (Hernán and Robins, 2010), based on the value of their potential outcomes. These response classes are termed the "Increase" (Y(0) = 0, Y(1) = 1), "Decrease" (Y(0) = 1, Y(1) = 0), "Predisposed" (Y(0) = Y(1) = 1) and "Unsusceptible" (Y(0) = Y(1) = 0) classes. We show that it is the joint distribution of reporting classes and response classes in the super-population that precisely characterizes the bias and variance of a standard causal estimate. This result exposes some subtle challenges in analyzing studies with misreporting bias. Contrary to an oft-cited heuristic, non-differential measurement error does not necessarily induce bias toward the null. Moreover, researchers need to consider whether individuals who are responsive to the treatment (those in the Decrease or Increase class) may be disproportionately likely to be Never-reporters or Always-reporters. Such results could easily emerge when considering studies in vulnerable populations. For example, in our Kenya study, it may be that girls most likely to benefit from the empowerment training program may also be the most disinclined to report an experience of sexual violence if they do not receive the training, e.g. due to feelings of shame. We conclude by proposing a novel procedure for determining adequate sample sizes under the worst-case power corresponding to a given level of misreporting. Our procedure is based in convex optimization: we show that the worst-case power under a posited confounding structure reduces to a quadratic fractional programming problem. We suggest a two-stage process for designing experiments surveying sensitive topics. First, we suggest a pilot study be used to ascertain key parameters about the frequency of misreporting. Next, we recommend researchers use our optimization procedure to design a larger experiment that is sufficiently powered in the presence of misreporting bias.