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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]

All models of this paper involve R x C contingency tables in which the total frequency is fixed (full multinomial model), or in which the row totals are fixed (product multinomial model). For the most part, we assume that the column categories are ordered. For the full multinomial model the null hypothesis of interest is independence, i.e., the (ij)th cell probability is the product of the marginal probabilities of the ith row and jth column. In the product multinomial model the null hypothesis is that the R multinomial distributions have the same vector of cell probabilities. Our review includes (1) a careful listing of two-sided and one-sided alternatives, and (2) methodology to reduce the loss of efficiency of tests because of the discreteness of the model (The methodologies discussed are efficient in several senses. Tests are exact. Tests have very favorable and robust power properties. Tests make use of back-up statistics, thereby providing a finer grid of p-values. In some special cases, e.g., a 2 x C table and a one-sided alternative, conditional p-values are found, within seconds, simply by entering row frequencies into a given website. Thus, computational efficiency is exceptional.), and (3) a critique of some exact linear permutation tests (that are conditional on row and column margins) for both two-sided and some one-sided alternatives. Furthermore, recommendations as to which tests to use for specific alternatives are made. [ABSTRACT FROM AUTHOR]