gms | German Medical Science

This manuscript investigates sample sizes for interim analyses in group sequential designs. Traditional group sequential designs (GSD) define interim sample sizes in terms of “information fractions”. Then, interim maximum likelihood estimators (MLEs) are used to decide whether to stop early or continue the data collection until the next interim analysis. The possibility of early stopping changes the distribution of interim and final MLEs bringing changes to Fisher information that are not commonly recognized. Possible interim decisions on stopping excludes some sample space elements. At each interim analysis, the distribution of an interim MLE is a mixture of truncated and untruncated distributions. The distributional form of an MLE becomes more and more complicated with each additional interim analysis. Test statistics that are asymptotically normal without a possibly of early stopping, become mixtures of truncated normal distributions under local alternatives. Stage-specific information ratios are equivalent to sample size ratios for independent and identically distributed data. This equivalence is used to determine interim sample sizes in GSDs. Because stage-specific information ratios derived from normally distributed data differ from those derived from non-normally distributed data, the former equivalence is invalid when there is a possibility of early stopping.

A new GSD was proposed [1] in which interim sample sizes are determined by a pre-defined sequence of ordered alternative hypotheses, and the calculation of information fractions is not needed. This innovation allows researchers to prescribe interim analyses based on desired power properties. This work compares interim power properties of a classical one-sided three stage Pocock design with a one-sided three stage design driven by three ordered alternatives.

The authors declare that they have no competing interests.

The authors declare that a positive ethics committee vote has been obtained.