The paper is motivated by the problem of comparing the accuracy of two molecular tests in detecting genetic mutations in tumor samples when there is no gold standard test. Commonly used sequencing methods require a large number of tumor cells in the tumor sample and the proportion of tumor cells with mutation positivity to be above a threshold level whereas new tests aim to reduce the requirement for number of tumor cells and the threshold level. A new latent class model is proposed to compare these two tests in which a random variable is used to represent the unobserved proportion of mutation positivity so that these two tests are conditionally dependent; furthermore, an independent random variable is included to address measurement error associated with the reading from each test, while existing latent class models often assume conditional independence and do not allow measurement error. In addition, methods for calculating the sample size for a study that is sufficiently powered to compare the accuracy of two molecular tests are proposed and compared. The proposed methods are then applied to a study which aims to compare two molecular tests for detecting EGFR mutations in lung cancer patients.
Keywords: Gold standard; latent class model; measurement error; sample size calculation; sensitivity; specificity.