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Robust Tests for Trend in Binomial Proportions

In: Probability and Bayesian Statistics

Author

Listed:
  • R. T. Smythe

    (George Washington University, Department of Statistics)

  • D. Krewski

    (Health and Welfare Canada, Health Protection Branch
    Carleton University, Department of Mathematics and Statistics)

  • A. Dewanji

    (Health and Welfare Canada, Health Protection Branch)

Abstract

Recent modifications to the Cochran-Armitage statistic used to test for trend in binomial proportions in carcinogenicity bioassays for which a series of historical control data is available employ a beta distribution for the between study variation in the binomial response rate in the control group. In this paper, the use of robust distributions with heavier tails than the beta is proposed as a means of accommodating the uncertainty as to the actual historical distribution of the binomial response rate. The robust distributions are selected from within a class of mixed distributions using a r-minimax criterion to select the most appropriate value of the mixing proportion. These tests are shown to be more robust than the existing tests with respect to inclusion or exclusion of individual historical control data points.

Suggested Citation

  • R. T. Smythe & D. Krewski & A. Dewanji, 1987. "Robust Tests for Trend in Binomial Proportions," Springer Books, in: R. Viertl (ed.), Probability and Bayesian Statistics, pages 443-454, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-1885-9_45
    DOI: 10.1007/978-1-4613-1885-9_45
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