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    This study addresses powering randomized trials with sensitive, self-reported outcomes. It introduces a method to calculate sample sizes accounting for misreporting, ensuring study power even with inaccurate data.

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    Area of Science:

    • Biostatistics
    • Clinical Trial Design
    • Public Health Research

    Background:

    • Designing prospective randomized trials with self-reported outcomes, especially those involving sensitive topics, presents challenges in accurately powering studies.
    • Misreporting of binary outcomes can significantly impact statistical power and introduce bias in causal estimates.
    • Previous experience with a sexual violence prevention program trial highlighted the need for methods to address data inaccuracies.

    Purpose of the Study:

    • To develop methods for calculating adequate sample sizes in randomized trials where outcome data is self-reported and potentially subject to misreporting.
    • To provide researchers with tools to maintain study power when dealing with sensitive data and respondent inaccuracies.
    • To quantify the bias and variance introduced by misreporting in binary outcomes.

    Main Methods:

    • Derived expressions for bias and variance caused by misreporting in binary outcomes.
    • Modeled respondents into distinct 'reporting classes' (true, false, never, always reporters).
    • Proposed a novel procedure for determining sample sizes based on worst-case power under specified misreporting levels.

    Main Results:

    • The joint distribution of reporting classes and response classes precisely defines error terms for causal estimates.
    • The proposed method allows for sample size determination that accounts for the impact of misreporting on statistical power.
    • The approach is validated through its application to a real-world trial.

    Conclusions:

    • Accurate power calculations in randomized trials with sensitive, self-reported data require explicit modeling of misreporting.
    • The developed procedure offers a robust approach to ensure adequate sample sizes, maintaining study power despite potential data inaccuracies.
    • This methodology is crucial for the successful design and execution of trials involving sensitive health and behavioral outcomes.