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Asymptotic confidence interval construction for risk difference under inverse sampling

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  • Tang, Man-Lai
  • Tian, Maozai

Abstract

Risk difference (RD) has played an important role in a lot of biological and epidemiological investigations to compare the risks of developing certain disease or tumor for two drugs or treatments. When the disease is rare and acute, inverse sampling (rather than binomial sampling) is usually recommended to collect the binary outcomes. In this paper, we derive an asymptotic confidence interval estimator for RD based on the score statistic. To compare its performance with three existing confidence interval estimators, we employ Monte Carlo simulation to evaluate their coverage probabilities, expected confidence interval widths, and the mean difference of the coverage probabilities from the nominal confidence level. Our simulation results suggest that the score-test-based confidence interval estimator is generally more appealing than the Wald, uniformly minimum variance unbiased estimator and likelihood ratio confidence interval estimators for it maintains the coverage probability close to the desired confidence level and yields the shortest expected width in most cases. We illustrate these confidence interval construction methods with real data sets from a drug comparison study and a congenital heart disease study.

Suggested Citation

  • Tang, Man-Lai & Tian, Maozai, 2009. "Asymptotic confidence interval construction for risk difference under inverse sampling," Computational Statistics & Data Analysis, Elsevier, vol. 53(3), pages 621-631, January.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:3:p:621-631
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    References listed on IDEAS

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    1. Lui, Kung-Jong, 2000. "Asymptotic conditional test procedures for relative difference under inverse sampling," Computational Statistics & Data Analysis, Elsevier, vol. 34(3), pages 335-343, September.
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    Cited by:

    1. Zou, G.Y., 2010. "Confidence interval estimation under inverse sampling," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 55-64, January.
    2. Röhmel, Joachim, 2010. "Comparing two independent samples using the risk difference under inverse sampling," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 804-805, April.
    3. de Peretti, Christian & Siani, Carole, 2010. "Graphical methods for investigating the finite-sample properties of confidence regions," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 262-271, February.
    4. Piero Quatto & Antonella Zambon, 2012. "The uniformly minimum variance unbiased estimator of odds ratio in case–control studies under inverse sampling," Statistical Papers, Springer, vol. 53(2), pages 305-309, May.

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