gms | German Medical Science

Introduction: The two-way factorial design is used in many different research areas such as agriculture, medicine and psychology. It allows to evaluate two exposures or interventions simultaneously in an efficient manner, in both independent and repeated measurement settings. Moreover, the interaction between these exposures can also be assessed. Different sample size calculation methods for two-way factorial experiments analyzed by analysis of variance (ANOVA) have been implemented. Although ANOVA is robust, strong deviations from normality in the outcome can render it unreliable. On the other hand, ANOVA, rank and permutation tests assume homoscedasticity. Sample size calculation for ANOVA alternatives in this framework is an area of active research.

Methods: Simulation based sample size calculation for two-way factorial designs for normal, skewed-normal, truncated normal or beta distributed outcomes is performed. If the levels of Factor A are i=1, 2, Â…, a and the levels of Factor B are j = 1, 2, ..., b and each ij group has k subjects, k values are sampled from the corresponding distribution with mean μij and standard deviation σij. For repeated measurement designs, a covariance matrix is constructed and multivariate distributions are sampled. At each simulation iteration hypothesis testing if performed for main effects and interaction with the selected method. Power for sample size ijk is the proportion of tests in which p<ɑ.

Results: We present a new R-package called extraSuperpower, which performs simulation based sample size calculation for two-way factorial designs. The outcome can be modeled as normal, skewed-normal, truncated normal or beta distributed. Measurements can be independent or repeated with a user defined correlation structure within individuals. The sample size required to obtain a specified power using ANOVA, rank or permutation tests can be calculated and plotted.

The package will be applied to compare empirical power for main and interaction effects based on the different tests under the different outcome distributions in the independent and repeated measurement settings.

Conclusion: Simulation is a good alternative for sample size calculation when data do not fulfill the requirements of ANOVA.

The authors declare that they have no competing interests.

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