Tests of noninferiority via rate difference for three-arm clinical trials with placebo

Man Lai TANG*, Nian Sheng Tang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

20 Citations (Scopus)


In assessing a noninferiority trial, the investigator intends to show efficacy by demonstrating that a new experimental drug/treatment is not worse than a known active control/reference by a small predefined margin. If it is ethically justifiable, it may be advisable to include an additional placebo group for internal validation purpose. This constitutes the well-known three-arm clinical trial with placebo. In this paper, we study two asymptotic statistical methods for testing of noninferiority in three-arm clinical trials with placebo for binary outcomes based on rate difference. They are sample-based estimation method and restricted maximum likelihood estimation method, respectively. We investigate the performance of the proposed test procedures under different sample size allocation settings via a simulation study. Both methods perform satisfactorily under moderate to large sample settings. However, the restricted maximum likelihood estimation method usually possesses slightly smaller actual type I error rates, which are relatively close to the prespecified nominal level, while the sample-based method can be expressed in a simple closed-form format. Real examples from a pharmacological study of patients with functional dyspepsia and a placebo-controlled trail of subjects with acute migraine are used to demonstrate our methodologies.

Original languageEnglish
Pages (from-to)337-347
Number of pages11
JournalJournal of Biopharmaceutical Statistics
Issue number2
Publication statusPublished - 2004

Scopus Subject Areas

  • Statistics and Probability
  • Pharmacology
  • Pharmacology (medical)

User-Defined Keywords

  • Noninferiority
  • Rate difference
  • Score test
  • Three-arm design


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