Maximally selected χ2 statistics for k x 2 tables

Rebecca Betensky, Daniel Rabinowitz

Research output: Contribution to journalArticle

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 - Jan 1 1999

Fingerprint

Asymptotic distribution
Tables
statistics
Statistics
Clinical Trials
Simulation Experiment
Test Statistic
Categorical or nominal
Table
Equality
Sample Size
Proportion
Maximise
Methodology
clinical trials
Acquired Immunodeficiency Syndrome
testing
Population
Trends
Experiments

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

Cite this

Maximally selected χ2 statistics for k x 2 tables. / Betensky, Rebecca; Rabinowitz, Daniel.

In: Biometrics, Vol. 55, No. 1, 01.01.1999, p. 317-320.

Research output: Contribution to journalArticle

Betensky, Rebecca ; Rabinowitz, Daniel. / Maximally selected χ2 statistics for k x 2 tables. In: Biometrics. 1999 ; Vol. 55, No. 1. pp. 317-320.
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