| Statistical methods for cluster effects with grouped data have been developed for decades. During that time biostatisticians have investigated sample size estimation based upon those methods. The current literature focuses on parametric sample size formulas taking into account the effect of the intracluster correlation coefficient and the variability of cluster sizes. In our study we explore sample size estimation methods with nonparametric one-sample location tests for clustered data with a common intracluster correlation structure and variation in cluster size. For correlated binary outcomes, sample size formulas are derived with the nonparametric proportion test using three weighting schemes: equal weights to individuals, equal weights to clusters, and optimal weights that yield minimum variance of the estimator. For correlated continuous outcomes sample size formulas based upon the weighted sign test of Larocque et al. (2007), and a sample size estimation method based upon the weighted signed-rank test of Rosner et al. (2006a), which combines upper bound sample size formulas and a efficient bisectional simulation algorithm, are proposed. Simulation experiments are conducted to evaluate the performance of the proposed sample size calculation methods and the effect of the intracluster correlation coefficient and the cluster size distribution. Our proposed sample size estimation methods are compared with their corresponding parametric sample size formulas through simulations as well. From our experiment results we can conclude that our proposed sample size estimation methods perform better than their corresponding parametric sample size formulas under the normal model but worse than their corresponding parametric sample size formulas under the Laplace model. |
