Follow-up Design for Comparing Two Binary Diagnostic Tests

Most conventional methods of comparing two diagnostic tests require patients whose true disease statuses are known. We deal with in this paper a problem of comparing two binary diagnostic tests (referred to as new and standard tests) in a follow-up design, where there are no gold standards. Assume that each patient is examined twice by new and standard tests, respectively. We employed a comparison measure ψ, which is compared on the basis of the odds ratio of the new and standard test. It is not possible to estimate ψ from the full likelihood function based on the design, even if two independent multinomial distributions are assumed to the data. Therefore, we focus only on data from discordant pairs between new and standard tests. We construct conditional likelihood conditioned on those pairs and estimate parameters involved in the conditional likelihood. An estimate of ψ is obtained by plugging those estimates in ψ. The asymptotic normality of the estimator of ψ is shown based on delta method and a confidence interval of ψ is developed. A method of sample size determination for this design is also proposed. Simulation is conducted to study the behavior of the proposed method by considering several scenarios.