Comparison of Exact, Mid-p, and Mantel-Haenszel Confidence Intervals for the Common Odds Ratio across Several 2 × 2 Contingency Tables

Mehta, Cyrus R.; Walsh, Stephen J.

doi:10.2307/2684185

Cited by 34 publications

(24 citation statements)

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“…4 Ninety-five percent confidence intervals on the odds ratios were computed using the mid-p technique. 5 The Breslow-Day test 6 was used to determine homogeneity of the individual odds ratios. Least squares regression was used to investigate possible linear relationships of odds ratio estimates to sample size, chronologic ordering, and observed risk in the groups of patients that did not undergo a transfusion.…”

Section: Discussionmentioning

confidence: 99%

Allogeneic Blood Transfusion Increases the Risk of Postoperative Bacterial Infection: A Meta-analysis

Hill

Frawley

Griffith

et al. 2003

The Journal of Trauma: Injury, Infection, and Critical Care

473

261

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Section: Discussionmentioning

confidence: 99%

Allogeneic Blood Transfusion Increases the Risk of Postoperative Bacterial Infection: A Meta-analysis

Hill

Frawley

Griffith

et al. 2003

The Journal of Trauma: Injury, Infection, and Critical Care

473

261

View full text Add to dashboard Cite

show abstract

“…The type I error rates of the mid- p test—as opposed to those of exact tests—are not bounded by the nominal level; however, in a wide range of designs and models, both mid- p tests and confidence intervals violate the nominal level rarely and with low degrees of infringement [11-13]. Because mid- p tests are based on exact distributions, they are sometimes called quasi-exact [14].…”

Section: Methodsmentioning

confidence: 99%

The McNemar test for binary matched-pairs data: mid-p and asymptotic are better than exact conditional

Fagerland

Lydersen

Laake

2013

BMC Med Res Methodol

285

208

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BackgroundStatistical methods that use the mid-p approach are useful tools to analyze categorical data, particularly for small and moderate sample sizes. Mid-p tests strike a balance between overly conservative exact methods and asymptotic methods that frequently violate the nominal level. Here, we examine a mid-p version of the McNemar exact conditional test for the analysis of paired binomial proportions.MethodsWe compare the type I error rates and power of the mid-p test with those of the asymptotic McNemar test (with and without continuity correction), the McNemar exact conditional test, and an exact unconditional test using complete enumeration. We show how the mid-p test can be calculated using eight standard software packages, including Excel.ResultsThe mid-p test performs well compared with the asymptotic, asymptotic with continuity correction, and exact conditional tests, and almost as good as the vastly more complex exact unconditional test. Even though the mid-p test does not guarantee preservation of the significance level, it did not violate the nominal level in any of the 9595 scenarios considered in this article. It was almost as powerful as the asymptotic test. The exact conditional test and the asymptotic test with continuity correction did not perform well for any of the considered scenarios.ConclusionsThe easy-to-calculate mid-p test is an excellent alternative to the complex exact unconditional test. Both can be recommended for use in any situation. We also recommend the asymptotic test if small but frequent violations of the nominal level is acceptable.

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“…In every case, the mid-p value approximation based on (10) is very close to the exact mid-p value computed by StatXact; the alternative method is modestly less conservative, and the extent to which the two disagree essentially reflects the degree to which the tail probability is decreasing nonlinearly at Wobs' A potential disadvantage of mid-p values is that unlike exact p values there is no guarantee of maintaining the nominal level (see, e.g., Kim and Agresti 1995). The extensive simulation study of Mehta and Walsh (1992) provides some evidence that the mid-p value approach preserves the nominal size in most cases while reducing conservativeness over the exact conditional approach (see also Agresti 1992a). This result is verified by an in-depth theoretical study of mid-p values undertaken by Hwang and Yang (1998), who also showed that the mid-p value has some heretofore unknown decision-theoretic optimality properties.…”

Section: Some Famous Examples Revisitedmentioning

confidence: 96%

“…This result is verified by an in-depth theoretical study of mid-p values undertaken by Hwang and Yang (1998), who also showed that the mid-p value has some heretofore unknown decision-theoretic optimality properties. It would be interesting to compare the respective performance of the usual mid-p value and the interpolated p value proposed here in a simulation study like that done by Mehta and Walsh (1992).…”

Section: Some Famous Examples Revisitedmentioning

confidence: 96%

Approximately Exact Inference for the Common Odds Ratio in Several 2 × 2 Tables

Strawderman

Wells

1998

Journal of the American Statistical Association

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The conditional maximum likelihood estimator (MLE) of the common odds ratio in a sequence of independent 2 x 2 tables is known to be superior to the Mantel-Haenszel estimator in terms of asymptotic efficiency and has the further advantage that its exact distribution is known. However, a long-standing barrier to the widespread use of this estimator has been computational intractability; in particular, the calculation of significance levels, confidence sets, and power based on the exact distribution requires fast and efficient algorithms. An important class of such algorithms form the basis of StatXact, a software package able to solve various aspects of the exact inference problem for a sequence of several 2 x 2 tables in real time. We provide an alternative methodology by developing several useful saddlepoint approximations to the exact distribution of the conditional MLE. The approximations are derived from an interesting representation for hypergeometric random variables as a sum of independent Bernoulli random variables and provide fast, accurate calculations of power functions, p values, and confidence sets. The primary computational burden is in determining the roots of a certain polynomial, which need be done numerically only once for each table. Consequently, the required computational effort is typically minimal; for example, all of the examples herein were done using code written by the authors entirely in S-PLUS.

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Comparison of Exact, Mid-p, and Mantel-Haenszel Confidence Intervals for the Common Odds Ratio across Several 2 × 2 Contingency Tables

Cited by 34 publications

References 0 publications

Allogeneic Blood Transfusion Increases the Risk of Postoperative Bacterial Infection: A Meta-analysis

Allogeneic Blood Transfusion Increases the Risk of Postoperative Bacterial Infection: A Meta-analysis

The McNemar test for binary matched-pairs data: mid-p and asymptotic are better than exact conditional

Approximately Exact Inference for the Common Odds Ratio in Several 2 × 2 Tables

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