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A New Exact and More Powerful Unconditional Test of No Treatment Effect from Binary Matched Pairs

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  • Chris J. Lloyd

Abstract

Summary We consider the problem of testing for a difference in the probability of success from matched binary pairs. Starting with three standard inexact tests, the nuisance parameter is first estimated and then the residual dependence is eliminated by maximization, producing what I call an E+M P‐value. The E+M P‐value based on McNemar's statistic is shown numerically to dominate previous suggestions, including partially maximized P‐values as described in Berger and Sidik (2003, Statistical Methods in Medical Research12, 91–108). The latter method, however, may have computational advantages for large samples.

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  • Chris J. Lloyd, 2008. "A New Exact and More Powerful Unconditional Test of No Treatment Effect from Binary Matched Pairs," Biometrics, The International Biometric Society, vol. 64(3), pages 716-723, September.
    • Handle: RePEc:bla:biomet:v:64:y:2008:i:3:p:716-723
    DOI: 10.1111/j.1541-0420.2007.00936.x
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    References listed on IDEAS

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    1. Devan V. Mehrotra & Ivan S. F. Chan & Roger L. Berger, 2003. "A Cautionary Note on Exact Unconditional Inference for a Difference between Two Independent Binomial Proportions," Biometrics, The International Biometric Society, vol. 59(2), pages 441-450, June.
    2. Alan Agresti & Yongyi Min, 2005. "Frequentist Performance of Bayesian Confidence Intervals for Comparing Proportions in 2 × 2 Contingency Tables," Biometrics, The International Biometric Society, vol. 61(2), pages 515-523, June.
    3. Man-Lai Tang & Nian-Sheng Tang & Vincent J. Carey, 2004. "Confidence Interval for Rate Ratio in a 2 × 2 Table with Structural Zero: An Application in Assessing False-Negative Rate Ratio When Combining Two Diagnostic Tests," Biometrics, The International Biometric Society, vol. 60(2), pages 550-555, June.
    4. Quinn McNemar, 1947. "Note on the sampling error of the difference between correlated proportions or percentages," Psychometrika, Springer;The Psychometric Society, vol. 12(2), pages 153-157, June.
    5. Ivan S. F. Chan & Nian-Sheng Tang & Man-Lai Tang & Ping-Shing Chan, 2003. "Statistical Analysis of Noninferiority Trials with a Rate Ratio in Small-Sample Matched-Pair Designs," Biometrics, The International Biometric Society, vol. 59(4), pages 1170-1177, December.
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    Cited by:

    1. Guogen Shan & Gregory Wilding, 2015. "Unconditional tests for association in 2 × 2 contingency tables in the total sum fixed design," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(1), pages 67-83, February.
    2. Shan, Guogen, 2013. "More efficient unconditional tests for exchangeable binary data with equal cluster sizes," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 644-649.
    3. Xiaochun Li & Mengling Liu & Judith D. Goldberg, 2011. "A Note on Monotonicity Assumptions for Exact Unconditional Tests in Binary Matched-Pairs Designs," Biometrics, The International Biometric Society, vol. 67(4), pages 1666-1668, December.

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