### Abstract

This paper investigates an approximate unconditional test for non-inferiority between two independent binomial proportions. The P-value of the approximate unconditional test is evaluated using the maximum likelihood estimate of the nuisance parameter. In this paper, we clarify some differences in defining the rejection regions between the approximate unconditional and conventional conditional or unconditional exact test. We compare the approximate unconditional test with the asymptotic test and unconditional exact test by Chan (Statistics in Medicine, 17, 1403-1413, 1998) with respect to the type I error and power. In general, the type I errors and powers are in the decreasing order of the asymptotic, approximate unconditional and unconditional exact tests. In many cases, the type I errors are above the nominal level from the asymptotic test, and are below the nominal level from the unconditional exact test. In summary, when the non-inferiority test is formulated in terms of the difference between two proportions, the approximate unconditional test is the most desirable, because it is easier to implement and generally more powerful than the unconditional exact test and its size rarely exceeds the nominal size. However, when a test between two proportions is formulated in terms of the ratio of two proportions, such as a test of efficacy, more caution should be made in selecting a test procedure. The performance of the tests depends on the sample size and the range of plausible values of the nuisance parameter.

Original language | English |
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Pages (from-to) | 2089-2100 |

Number of pages | 12 |

Journal | Statistics in Medicine |

Volume | 19 |

Issue number | 16 |

DOIs | |

Publication status | Published - 2000 Aug 30 |

### All Science Journal Classification (ASJC) codes

- Epidemiology
- Statistics and Probability

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## Cite this

*Statistics in Medicine*,

*19*(16), 2089-2100. https://doi.org/10.1002/1097-0258(20000830)19:16<2089::AID-SIM537>3.0.CO;2-B