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

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Abstract

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

Original languageEnglish (US)
Pages (from-to)1253-1261
Number of pages9
JournalJournal of Clinical Epidemiology
Volume57
Issue number12
DOIs
StatePublished - Dec 2004

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Bayes Theorem
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Keywords

  • Bayesian methods
  • Likelihood ratio test
  • Noninferiority margin
  • Noninferiority trial

ASJC Scopus subject areas

  • Medicine(all)
  • Public Health, Environmental and Occupational Health
  • Epidemiology

Cite this

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title = "Likelihood ratio and a Bayesian approach were superior to standard noninferiority analysis when the noninferiority margin varied with the control event rate",
abstract = "To present and compare three statistical approaches for analyzing a noninferiority trial when the noninferiority margin depends on the control event rate. 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. 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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AB - To present and compare three statistical approaches for analyzing a noninferiority trial when the noninferiority margin depends on the control event rate. 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. 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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