Wald-Type Testing and Estimation Methods for Asymmetric Comparisons of Poisson Rates

Brianna C. Bright, Julia N. Soulakova

Research output: Contribution to journalArticle

Abstract

This article considers the problem of asymmetric comparisons, that is, instances where one treatment serves as the compelling standard treatment for a certain disease or health condition, where the asymmetric comparisons are performed in terms of the Poisson rates. We propose asymptotic Wald-type tests and confidence intervals suitable for demonstrating superiority and noninferiority for a given margin. The testing methods for the difference and ratio are based on the unconstrained (MLE) and constrained (CMLE) maximum likelihood estimator. The resulting CMLE-based tests for asymmetric comparisons are equivalent to the standard (i.e., those for symmetric comparisons) CMLE-based tests. The asymmetric tests as well as the standard MLE-based tests are evaluated via simulations. The CMLE-based asymmetric tests are shown to adequately control the Type I error in most settings, while the MLE-based asymmetric tests are shown to have this property only in settings with relatively large sample sizes and means. In all settings, the MLE-based asymmetric tests are more powerful than both the asymmetric CMLE-based and the standard MLE-based tests. We also propose asymptotic confidence intervals that can be used to estimate the difference or ratio of the two rates (the presentation of this content includes supplementary material that is available online), and discuss how power and sample size estimation can be done to aid in study planning. Supplementary materials for this article are available online.

Original languageEnglish (US)
JournalStatistics in Biopharmaceutical Research
Volume7
Issue number1
DOIs
StatePublished - Jan 2 2015

Fingerprint

Siméon Denis Poisson
Testing
Sample Size
Confidence Intervals
Confidence interval
Non-inferiority
Health
Type I error
Sample mean
Maximum Likelihood Estimator
Margin
Planning
Standards
Estimate
Simulation

Keywords

  • Confidence intervals
  • Hypothesis testing
  • Poisson distribution
  • Variance estimation

ASJC Scopus subject areas

  • Statistics and Probability
  • Pharmaceutical Science

Cite this

Wald-Type Testing and Estimation Methods for Asymmetric Comparisons of Poisson Rates. / Bright, Brianna C.; Soulakova, Julia N.

In: Statistics in Biopharmaceutical Research, Vol. 7, No. 1, 02.01.2015.

Research output: Contribution to journalArticle

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