### Abstract

A large-sample problem of illustrating noninferiority of an experimental treatment over a referent treatment for binary outcomes is considered. The methods of illustrating noninferiority involve constructing the lower two-sided confidence bound for the difference between binomial proportions corresponding to the experimental and referent treatments and comparing it with the negative value of the noninferiority margin. The three considered methods, Anbar, Falk-Koch, and Reduced Falk-Koch, handle the comparison in an asymmetric way, that is, only the referent proportion out of the two, experimental and referent, is directly involved in the expression for the variance of the difference between two sample proportions. Five continuity corrections (including zero) are considered with respect to each approach. The key properties of the corresponding methods are evaluated via simulations. First, the uncorrected two-sided confidence intervals can, potentially, have smaller coverage probability than the nominal level even for moderately large sample sizes, for example, 150 per group. Next, the 15 testing methods are discussed in terms of their Type I error rate and power. In the settings with a relatively small referent proportion (about 0.4 or smaller), the Anbar approach with Yates' continuity correction is recommended for balanced designs and the Falk-Koch method with Yates' correction is recommended for unbalanced designs. For relatively moderate (about 0.6) and large (about 0.8 or greater) referent proportion, the uncorrected Reduced Falk-Koch method is recommended, although in this case, all methods tend to be over-conservative. These results are expected to be used in the design stage of a noninferiority study when asymmetric comparisons are envisioned.

Original language | English (US) |
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Pages (from-to) | 147-155 |

Number of pages | 9 |

Journal | Pharmaceutical Statistics |

Volume | 12 |

Issue number | 3 |

DOIs | |

State | Published - May 1 2013 |

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### Keywords

- binomial distribution
- coverage probability
- difference between proportions
- variance estimation

### ASJC Scopus subject areas

- Statistics and Probability
- Pharmacology
- Pharmacology (medical)

### Cite this

*Pharmaceutical Statistics*,

*12*(3), 147-155. https://doi.org/10.1002/pst.1566