Maximally selected χ2 statistics for k x 2 tables

Rebecca A. Betensky, Daniel Rabinowitz

Research output: Contribution to journalArticlepeer-review

Abstract

It is common in epidemiologic analyses to summarize continuous outcomes as falling above or below a threshold. With such a dichotomized outcome, the usual χ2 statistics for association or trend can be used to test for equality of proportions across strata of the study population. However, if the threshold is chosen to maximize the test statistic, the nominal χ2 reference distributions are incorrect. In this paper, the asymptotic distributions of maximally selected χ2 statistics for association and for trend for the k x 2 table are derived. The methodology is illustrated with data from an AIDS clinical trial. The results of simulation experiments that assess the accuracy of the asymptotic distributions in moderate sample sizes are also reported.

Original languageEnglish (US)
Pages (from-to)317-320
Number of pages4
JournalBiometrics
Volume55
Issue number1
DOIs
StatePublished - Mar 1999

Keywords

  • Association
  • Brownian bridge
  • Categorical data
  • Independence
  • Multivariate diffusion
  • Trend

ASJC Scopus subject areas

  • Statistics and Probability
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics

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