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Since the early work of RA Fisher, exact methods have been recognized as important tools in data analysis because they provide valid statistical inference even with small sample sizes, or with sparse or skewed data. With the recent advance of computational power and the availability of commercial software packages, exact methods have gained substantial popularity over the past two decades. However, most of these exact methods have been devoted to testing classical null hypotheses of no differences, and until recently little was known about exact methods dealing with non-inferiority or equivalence hypotheses. The presence of nuisance parameters in testing non-inferiority/equivalence hypotheses presents a special challenge for exact methods because of the intense computational requirement. In this paper, we review exact methods available for proving non-inferiority or equivalence of two treatments with a dichotomous endpoint. First, we present the general methodology for conducting exact tests for non-inferiority or equivalence; we then discuss several unconditional and conditional methods available for constructing hypothesis tests and confidence intervals based on three commonly used measures, namely, the difference, relative risk, and odds ratio of two independent proportions or rates. Finally, we illustrate with several examples the application of these exact methods in analysing and planning non-inferiority or equivalence trials. [ABSTRACT FROM AUTHOR]