Original Article| Volume 57, ISSUE 12, P1253-1261, December 2004

Likelihood ratio and a Bayesian approach were superior to standard noninferiority analysis when the noninferiority margin varied with the control event rate

  • Mimi Y. Kim
    Corresponding author. Tel.: 718-430-2017; fax: 718-430-8780.
    Division of Biostatistics Department of Epidemiology and Population Health Albert Einstein College of Medicine, 1300 Morris Park Avenue, Belfer Building, Room 1303B, Bronx, NY 10461, USA
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  • Xiaonan Xue
    Division of Biostatistics Department of Epidemiology and Population Health Albert Einstein College of Medicine, 1300 Morris Park Avenue, Belfer Building, Room 1303B, Bronx, NY 10461, USA
    Search for articles by this author



      To present and compare three statistical approaches for analyzing a noninferiority trial when the noninferiority margin depends on the control event rate.

      Study design and setting

      In noninferiority trials with a binary outcome, the noninferiority margin is often defined as a fixed δ, the largest clinically acceptable difference in event rates between treatment groups. An alternative and more flexible approach is to allow δ to vary according to the true event rate in the control group. The appropriate statistical method for evaluating noninferiority with a variable noninferiority margin is not apparent. Three statistical approaches are proposed and compared: an observed event rate (OER) approach based on equating the true control rate to the observed rate, a Bayesian approach, and a likelihood ratio test.

      Results and conclusions

      Simulations studies indicate that the proportion of trials in which noninferiority was erroneously demonstrated was higher for the OER approach than with the Bayesian and likelihood ratio approaches. In some cases, the Type I error rate exceeded 10% for the OER approach. The OER approach is not recommended for the analysis of noninferiority trials with a variable margin of equivalence. The Bayesian and likelihood ratio methods yielded better operating characteristics.


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