Determining sample size to evaluate and compare the accuracy of binary diagnostic tests in the presence of partial disease verification

Sample size calculation for comparing two screening tests when the gold standard is missing at random

Sample size formulas have been proposed for comparing two sensitivities (specificities) in the presence of verification bias under a paired design. However, the existing sample size formulas involve lengthy calculations of derivatives and are too complicated to implement. In this paper, we propose alternative sample size formulas for each of three existing tests, two Wald tests and one weighted McNemar's test. The proposed sample size formulas are more intuitive and simpler to implement than their existing counterparts. Furthermore, by comparing the sample sizes calculated based on the three tests, we can show that the three tests have similar sample sizes even though the weighted McNemar's test only use the data from discordant pairs whereas the two Wald tests also use the additional data from accordant pairs.

Determining sample size for a binary diagnostic test in the presence of verification bias

To compare a new binary diagnostic test with the gold standard, sensitivity and specificity are the two common measurements used to evaluate the new test. When not all the patients are verified by the gold standard due to time, budget, or cost considerations, several approaches have been proposed to compute sample size for such studies under the assumption of missing completely at random. However, the majority of them are based on asymptotic approaches that generally do not guarantee the type I and II error rates, and the remaining approaches use exact binomial distributions in sample size calculation but only the verified samples are used. In this article, for a study with verification bias, we propose computing exact sample sizes by using all the samples. The proposed approach is compared with the existing exact approach that compute sample size by using verified samples only, and the results show that the proposed approach requires fewer participants than the competitor.