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One-tailed asymptotic inferences for the relative risk: A comparison of 63 inference methods

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  • Antonio Martín Andrés
  • Maria Álvarez Hernández
  • Inmaculada Herranz Tejedor

Abstract

Two-tailed asymptotic inferences for the ratio R=p2/p1 of two independent proportions have been well covered in the published literature. However, not very much has been written about one-tailed asymptotic inferences. This paper evaluates 63 different methods for realizing such inferences (hypothesis tests and confidence intervals). In general it is noted that: (a) the one-tailed inferences require at least 80 observations per sample, compared to the 40 observations necessary for two-tailed inferences; (b) the traditional methods do not perform well; (c) the methods selected for each case are not always the same; and (d) the optimal method is the ‘approximate adjusted score’ method (ZA1 in this paper), which is not always reliable, or ‘Peskun´s score’ method (ZP0 in theis paper), which is always reliable but is very conservative. The two selected methods provide an confidence interval that is obtained through an explicit formula.

Suggested Citation

  • Antonio Martín Andrés & Maria Álvarez Hernández & Inmaculada Herranz Tejedor, 2022. "One-tailed asymptotic inferences for the relative risk: A comparison of 63 inference methods," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(5), pages 1330-1348, March.
    • Handle: RePEc:taf:lstaxx:v:51:y:2022:i:5:p:1330-1348
    DOI: 10.1080/03610926.2020.1760299
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