Comparing multiple treatments to both positive and negative controls

Nairanjana Dasgupta*, Eleanne Solorzano, Tiejun TONG

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In the past, most comparison to control problems have dealt with comparing k test treatments to either positive or negative controls. Dasgupta et al. [2006. Using numerical methods to find the least favorable configuration when comparing k test treatments to both positive and negative controls. Journal of Statistical Computation and Simulation 76, 251-265] enumerate situations where it is imperative to compare several test treatments to both a negative as well as a positive control simultaneously. Specifically, the aim is to see if the test treatments are worse than the negative control, or if they are better than the positive control when the two controls are sufficiently apart. To find critical regions for this problem, one needs to find the least favorable configuration (LFC) under the composite null. In their paper, Dasgupta et al. [2006. Using numerical methods to find the least favorable configuration when comparing k test treatments to both positive and negative controls. Journal of Statistical Computation and Simulation 76, 251-265] came up with a numerical technique to find the LFC. In this paper we verify their result analytically. Via Monte Carlo simulation we compare the proposed method to the logical single step alternatives: Dunnett's [1955. A multiple comparison procedure for comparing several treatments with a control. Journal of the American Statistical Association 50, 1096-1121] or the Bonferroni correction. The proposed method is superior in terms of both the Type I error and the marginal power.

Original languageEnglish
Pages (from-to)180-188
Number of pages9
JournalJournal of Statistical Planning and Inference
Volume140
Issue number1
DOIs
Publication statusPublished - 1 Jan 2010

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

User-Defined Keywords

  • Least favorable configuration
  • Log concavity
  • Multiple comparison
  • Negative control
  • Positive control

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