Comparing the Response Rates for Superiority, Noninferiority and Equivalence Testing with Multiple-to-One Matched Binary Data

Abstract

Paired and multiple-to-one matched data have often been collected in clinical trials and epidemiological safety studies. When the response is binary, the sample size and power are determined by the discordant pairs or matched sets. Fixed sample size determination in assessing response rate difference of superiority, noninferiority, and equivalence tests of paired binary data has been discussed by Lu and Bean (1995)Nam (1997), and Liu et al. (2002). We extend the results of Lu and Bean (1995)Nam (1997), and Liu et al. (2002) to more general cases of multiple-to-one matched binary data. We further examine two issues regarding such tests. First, we examine the issue of simultaneous test and two-stage test for both superiority and noninferiority/equivalence hypotheses. Although, as discussed in Nam (1997) and Liu et al. (2002), the standard errors restricted to null hypothesis are different between superiority and noninferiority test, the monotonic property of the two tests makes the simultaneous testing and switching between the hypotheses valid. Second, in practice, the joint distribution of matched responses is often unknown, and thus determining the sample size using only the background information of the control group could be inefficient. Furthermore, for noninferiority or equivalence tests, the sample sizes are often determined using the unrealistic alternative hypothesis that the response rates of both treatments are identical. We propose to use a two-stage adaptive design strategy for sample size reestimation that uses the interim information to improve the efficiency.