Simultaneous score confidence bounds for risk differences in multiple comparisons to a control
Asymptotic simultaneous lower (upper) confidence bounds for risk differences arising from comparing several treatments to a common control are constructed by inverting the maximum (minimum) of score statistics. With a few exceptions, these bounds perform better in terms of simultaneous coverage probability than procedures based on adjusted Wald methods (e.g., adding pseudo-observations), especially over relevant parts of the parameter space in superiority or inferiority studies. A further improvement is realized by using an appropriate multiplicity adjusted critical value that takes advantage of the correlation information in the score statistics estimated under the null instead of a regular plug-in estimate. Simulation results and a worked example show a gain in terms of the precision of the lower bounds and their power; however, not too much is lost when using the straightforward Sidak multiplicity adjustment when the number of comparisons is small. All methods discussed are implemented and reproducible with general and publicly available R code.
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- Pan, Wei, 2002. "Approximate confidence intervals for one proportion and difference of two proportions," Computational Statistics & Data Analysis, Elsevier, vol. 40(1), pages 143-157, July.
- Zou, Guang Yong & Huang, Wenyi & Zhang, Xiaohe, 2009. "A note on confidence interval estimation for a linear function of binomial proportions," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1080-1085, February.
- Santner, Thomas J. & Pradhan, Vivek & Senchaudhuri, Pralay & Mehta, Cyrus R. & Tamhane, Ajit, 2007. "Small-sample comparisons of confidence intervals for the difference of two independent binomial proportions," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5791-5799, August.
- Andersson, Per GÃ¶sta, 2009. "A Simple Correlation Adjustment Procedure Applied to Confidence Interval Construction," The American Statistician, American Statistical Association, vol. 63(3), pages 258-262.
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