Design and analytic considerations for single-armed studies with misclassification of a repeated binary outcome

Due to logistics or prohibitive costs, clinical studies often rely upon a potentially misclassified binary outcome variable for assessing an intervention effect. We consider noncomparative single-armed studies that are sometimes necessary for ethical reasons, and we focus on the situation in which subjects are selected to receive the intervention contingent upon a positive screening test. Both initial misclassification at screening and a regression phenomenon impacting the error-prone follow-up outcome measure contribute to bias in the typical treatment effect estimate. We propose a study design involving the collection of internal validation data assuming the availability of a more demanding gold standard outcome measure. We pursue likelihood-based analysis and describe efficiency considerations relevant to two different treatment effect definitions. We identify four possible types of validation study observations, and discuss finding the optimal allocation into these four types in order to minimize the variance of the estimated treatment effect. The optimal allocation can be highly dependent upon whether a ratio or a difference measure is adopted to evaluate the intervention. The methods are illustrated numerically, and a real-life example motivating the proposed optimal design is provided.