Recommended tests for association in 2×2 tables

Unit for Applied Clinical Research, Department of Cancer Research and Molecular Medicine, Norwegian University of Science and Technology, Trondheim, Norway.
Statistics in Medicine (Impact Factor: 1.83). 03/2009; 28(7):1159-75. DOI: 10.1002/sim.3531
Source: PubMed


The asymptotic Pearson's chi-squared test and Fisher's exact test have long been the most used for testing association in 2x2 tables. Unconditional tests preserve the significance level and generally are more powerful than Fisher's exact test for moderate to small samples, but previously were disadvantaged by being computationally demanding. This disadvantage is now moot, as software to facilitate unconditional tests has been available for years. Moreover, Fisher's exact test with mid-p adjustment gives about the same results as an unconditional test. Consequently, several better tests are available, and the choice of a test should depend only on its merits for the application involved. Unconditional tests and the mid-p approach ought to be used more than they now are. The traditional Fisher's exact test should practically never be used.

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Available from: Morten Wang Fagerland, Sep 30, 2015
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    • "Clearly, there are other (asymptotic or non-asymptotic) frequentist test approaches which are under certain assumptions on the expected cell counts more robust than chi-square tests; see, e.g. Lydersen et al. (2009) for a biostatistics tutorial with practical guidelines for choosing a marginal testing strategy in the case of a (2 × 2)-table. However, an automated application of such guidelines for a large number of contingency tables simultaneously, where parameters like the expected minor allele frequency are prone to change considerably from one genomic position to the other, appears extremely challenging. "
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    ABSTRACT: Genetic association studies lead to simultaneous categorical data analysis. The sample for every genetic locus consists of a contingency table containing the numbers of observed genotype-phenotype combinations. Under case-control design, the row counts of every table are identical and fixed, while column counts are random. The aim of the statistical analysis is to test independence of the phenotype and the genotype at every locus. We present an objective Bayesian methodology for these association tests, which relies on the conjugacy of Dirichlet and multinomial distributions. Being based on the likelihood principle, the Bayesian tests avoid looping over all tables with given marginals. Making use of data generated by The Wellcome Trust Case Control Consortium (WTCCC), we illustrate that the ordering of the Bayes factors shows a good agreement with that of frequentist p-values. Furthermore, we deal with specifying prior probabilities for the validity of the null hypotheses, by taking linkage disequilibrium structure into account and exploiting the concept of effective numbers of tests. Application of a Bayesian decision theoretic multiple test procedure to the WTCCC data illustrates the proposed methodology. Finally, we discuss two methods for reconciling frequentist and Bayesian approaches to the multiple association test problem.
    Statistical Applications in Genetics and Molecular Biology 07/2015; 14(4). DOI:10.1515/sagmb-2014-0052 · 1.13 Impact Factor
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    • "Continuous variables were compared between groups with the two-sample t-test (if approximately normally distributed) or the Mann–Whitney U-test (if markedly skewed). Categorical variables were compared using the Fisher mid-P-test [33]. Spearman rank correlation was used to assess simple (univariate) associations of continuous variables with MRP-8/14 or CRP. "
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    Sleep Medicine 07/2014; 15(7). DOI:10.1016/j.sleep.2014.03.008 · 3.15 Impact Factor
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    • "However , for testing the equality of two proportions, or the risk difference, there are multiple formulae, which can yield very different results. More than 60 asymptotic tests and many exact tests have been considered for 2 Â 2 tables [4]. Many researchers may not be aware that there are multiple ways to calculate sample size for 2 Â 2 table designs, and even with this awareness, they may not know which approach and assumptions their software uses. "
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