gms | German Medical Science

Background: Distribution theory of test statistics in the presence of sample size recalculation (SSR) is often considered under a fixed alternative hypothesis. At fixed alternatives, however, statistical power to reject the null hypothesis increases to one as sample size increases for any consistent test. This effectively eliminates the concept of statistical power from consideration whenever asymptotic distribution theory is used. To keep asymptotic power from diverging to one, statistical power against local alternative hypotheses is considered. An SSR changes the finite and large sample distributions of the test statistic.

Methods: Finite and large sample distributions in the presence of SSR are found. Alternative hypotheses converge to the null hypothesis at a SQRT(N) rate, where N is the sample size. Monte-Carlo simulation studies are used to evaluate distribution of test statistics under several hypothesized values of the treatment effect. Asymptotic distributions under blinded and unblinded sample size recalculation are considered.

Results: Using SSR changes the single-sample (without SSR) distribution of test statistics. The conditional and unconditional distributions become mixture distributions. With few exceptions, the mixtures persist even asymptotically at both null and local alternatives. Consequently, Fisher information changes as well. If a single-sample test statistic follows a normal distribution, then with an SSR its finite and large sample distributions differ from normal. Previous research showed that estimation of nuisance parameters (such as standard deviation) in blinded SSR leads to an upward bias in total (re-estimated) sample size and this bias continues to affect the re-calculated sample size even asymptotically. This impact, however, does go away asymptotically under the local asymptotic framework which, in contrast to previous research, justifies the use of blinded SSR for large sample studies.

Conclusion: Impact of SSR on the distributions of test statistics and on Fisher information should not be ignored and needs to be accommodated when studies are being designed. In the presence of SSR, investigators should consider local asymptotic framework when characterizing large sample properties.

The authors declare that they have no competing interests.

The authors declare that an ethics committee vote is not required.