A. Agresti and B. Caffo, “Simple and Effective Confidence Intervals for Proportions and Differences of Proportions Result from Adding Two Successes and Two Failures,” The American Statistician, Vol. 54, No. 4, 2000, pp. 280-288. doi:10.2307/2685779

has been cited by the following article:

• TITLE: Minimum MSE Weights of Adjusted Summary Estimator of Risk Difference in Multi-Center Studies

  AUTHORS: Chukiat Viwatwongkasem, Jirawan Jitthavech, Dankmar Bohning, Vichit Lorchirachoonkul

  KEYWORDS: Minimum MSE Weights; Optimal Weights; Cochran-Mantel-Haenszel Weights; Inverse Variance Weights; Multi-Center Studies; Risk Difference

  JOURNAL NAME: Open Journal of Statistics, Vol.2 No.1, January 6, 2012

  ABSTRACT: The simple adjusted estimator of risk difference in each center is easy constructed by adding a value c on the number of successes and on the number of failures in each arm of the proportion estimator. Assessing a treatment effect in multi-center studies, we propose minimum MSE (mean square error) weights of an adjusted summary estimate of risk difference under the assumption of a constant of common risk difference over all centers. To evaluate the performance of the proposed weights, we compare not only in terms of estimation based on bias, variance, and MSE with two other conventional weights, such as the Cochran-Mantel-Haenszel weights and the inverse variance (weighted least square) weights, but also we compare the potential tests based on the type I error probability and the power of test in a variety of situations. The results illustrate that the proposed weights in terms of point estimation and hypothesis testing perform well and should be recommended to use as an alternative choice. Finally, two applications are illustrated for the practical use.