Multiplicity and Multiple Testing
Sample-size planning for a prespecified sequence of treatment-versus-control hypotheses. Each hypothesis is tested at the full study-wide alpha level, and the next hypothesis is tested only when the preceding hypothesis is rejected. Supports conjunctive, disjunctive, and marginal power definitions used in fixed-sequence multiple-comparison framework.
A hierarchical or fixed-sequence procedure tests hypotheses in a prespecified order. The first hypothesis is tested at the full study-wide significance level. The second hypothesis is formally tested only if the first is rejected, the third only if the first two are rejected, and so on. Because the testing hierarchy itself restricts when later hypotheses can be tested, the full study-wide α can be passed through the sequence rather than divided among the hypotheses.
This calculator implements the continuous-endpoint, equal-allocation treatment-versus-common-control setting represented by the fixed-sequence multiple-comparison framework in. identifies Fixed Sequence Testing as a stepwise multiple-comparison procedure and provides conjunctive, disjunctive, and marginal definitions of power.
With equal sample size in every treatment arm and a common control, treatment-versus-control Z statistics share the control observations. Their pairwise correlation is therefore 1/2. The calculator evaluates the resulting joint rejection probability numerically using the corresponding equicorrelated multivariate-normal representation.
The sample size is the smallest even integer per arm whose calculated power reaches the requested target. The even-integer search is used because the normal-approximation formula expresses the information in terms of equal treatment and control sample sizes; the displayed total sample size is the resulting number of subjects across all arms.
A constructed numerical validation case uses two treatment-versus-control comparisons in a fixed sequence, a common SD of 1, treatment-control mean differences of 0.60 and 0.40, two-sided α = 0.05, and 80% conjunctive power. The calculation gives a minimum of 100 subjects per arm, or 300 subjects total. At 98 subjects per arm, calculated conjunctive power is approximately 79.57%; at 100 subjects per arm it is approximately 80.40%, confirming that 100 is the first even sample size meeting the target.
Statsols. 9.7 — Multiple Comparisons. Official documentation/release information. The documentation describes Fixed Sequence Testing as a stepwise procedure and specifies conjunctive, disjunctive, and marginal power definitions for multiple-comparison sample-size calculations.
Bretz, F., Maurer, W., Brannath, W., & Posch, M. (2009). A graphical approach to sequentially rejective multiple test procedures. Statistics in Medicine, 28(4), 586–604. doi:10.1002/sim.3495.
Maurer, W., Glimm, E., & Bretz, F. (2011). Multiple and Repeated Testing of Primary, Coprimary, and Secondary Hypotheses. Statistics in Biopharmaceutical Research, 3(2), 336–352.