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

Abstract

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.

Keywords: McNemar's test; Wald tests; sample size calculation; verification bias; weighted McNemar's test.