×

A new exact and more powerful unconditional test of no treatment effect from binary matched pairs. (English) Zbl 1267.62107

Summary: We consider the problem of testing for a difference in the probability of success from matched binary pairs. Starting with three standard inexact tests, the nuisance parameter is first estimated and then the residual dependence is eliminated by maximization, producing what I call an E+M P-value. The E+M P-value based on Q. McNemar’s statistic [Psychometrika 12, 153–157 (1947)] is shown numerically to dominate previous suggestions, including partially maximized P-values as described by R.L. Berger and K. Sidik [Stat. Methods Med. Res. 12, 91–108 (2003)]. The latter method, however, may have computational advantages for large samples.

MSC:

62P10 Applications of statistics to biology and medical sciences; meta analysis
92C50 Medical applications (general)
65C60 Computational problems in statistics (MSC2010)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Agresti, Simple improved confidence intervals for comparing matched proportions, Statistics in Medicine 24 pp 729– (2005a) · doi:10.1002/sim.1781
[2] Agresti, Frequentist performance of Bayesian confidence intervals for comparing proportions in 2 {\(\times\)} 2 contingency tables, Biometrics 61 pp 515– (2005b) · Zbl 1077.62015 · doi:10.1111/j.1541-0420.2005.031228.x
[3] Barndoff-Nielsen, On M-ancillarity, Biometrika 60 pp 447– (1973) · doi:10.2307/2334993
[4] Berger, P values maximised over a confidence set for the nuisance parameter, Journal of the American Statistical Association 89 pp 1012– (1994) · Zbl 0804.62018 · doi:10.2307/2290928
[5] Berger, Exact unconditional tests for a 2 {\(\times\)} 2 matched pairs design, Statistical Methods in Medical Research 12 pp 91– (2003) · Zbl 1121.62573 · doi:10.1191/0962280203sm312ra
[6] Bickel, Mathematical Statistics (1977)
[7] Brix, High frequency of skewed X-chromosome inactivation in females with autoimmune thyroid disease: A possible explanation for the female predisposition to thyroid autoimmunity, Journal of Clinical Endocrinology and Metabolism 90 pp 5949– (2005) · doi:10.1210/jc.2005-1366
[8] Chan, Statistical analysis of noninferiority trials with a rate ratio in small-sample matched-pair designs, Biometrics 59 pp 1170– (2003) · Zbl 1274.62741 · doi:10.1111/j.0006-341X.2003.00134.x
[9] Frisen, Consequences of the use of conditional inference in the analysis of a correlated contingency table, Biometrika 67 pp 23– (1980) · Zbl 0427.62034 · doi:10.1093/biomet/67.1.23
[10] Kalbfleisch, Sufficiency and conditionality, Biometrika 62 pp 251– (1975) · Zbl 0313.62004 · doi:10.1093/biomet/62.2.251
[11] Lloyd , C. J. 2005 More powerful unconditional tests of no treatment effect from binary matched pairs http://www.mbs.edu/go/faculty-and-research/faculty-publications
[12] Lloyd, Exact P-values for discrete models obtained by estimation and maximisation, Australian and New Zealand Journal of Statistics (2008) · Zbl 1337.62033 · doi:10.1111/j.1467-842X.2008.00520.x
[13] Lloyd, Exact one-sided confidence limits for the difference between two correlated proportions, Statistics in Medicine 26 pp 3369– (2007) · doi:10.1002/sim.2708
[14] McNemar, Note on the sampling error of the differences between correlated proportions or percentages, Psychometrika 12 pp 153– (1947) · doi:10.1007/BF02295996
[15] Mehrotra, A cautionary note on exact unconditional inference for a difference between two independent binomial proportions, Biometrics 59 pp 441– (2003) · Zbl 1210.62012 · doi:10.1111/1541-0420.00051
[16] Sandved, A principle for conditioning on an ancillary statistic, Scandinavian Actuarial 50 pp 23– (1967)
[17] Sprott, Marginal and conditional sufficiency, Biometrika 62 pp 599– (1975) · Zbl 0317.62003 · doi:10.1093/biomet/62.3.599
[18] Suissa, The 2 {\(\times\)} 2 matched pairs trial: Exact unconditional design and analysis, Biometrics 47 pp 361– (1991) · doi:10.2307/2532131
[19] Tang, Confidence interval for rate ratio in a 2 {\(\times\)} 2 table with structural zero: An application in assessing false-negative rate ratio when combining two diagnostic tests, Biometrics 60 pp 550– (2004) · Zbl 1274.62882 · doi:10.1111/j.0006-341X.2004.203_1.x
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.