The effect of misclassification on sample size for one and two-sample tests with binary endpoints

In recent years, an increasing number of publications on the analysis of binary data have applied methods that take misclassification into account. However, potential misclassification is often ignored in study design due to the lack of sample size formulas or software. This may lead to a considerable loss of power in studies that only account for misclassification at the analysis stage. We argue that analyses correcting for misclassification should be used in combination with appropriate sample size adjustment in the design phase of the studies. We illustrate the importance of this by comparing the required sample sizes with and without misclassification, and provide an appropriate sample size procedure implemented as an R function for the one-sample and two-sample tests for binary endpoints. The sample size is calculated from the presumed binomial parameters (p₀ and p_a for one-sample and p₁ and p₂ for two-sample tests), the required power, and the probabilities of correct classification, sensitivity (Se), and specificity (Sp). Our results show that misclassification may drastically affect the necessary sample size in both testing scenarios.