Reconceptualizing the p-value from a likelihood ratio test: a probabilistic pairwise comparison of models based on Kullback-Leibler discrepancy measures

References

• H. Akaike, Information theory and an extension of the maximum likelihood principle, in 2nd International Symposium on Information Theory, B. N. Petrov and F. Csáki, eds., Akadémia Kiadó, Budapest, 1973, pp. 267–281.
   Google Scholar
• H. Akaike, A new look at the statistical model identification, IEEE Trans. Automat. Contr. 19 (1974), pp. 716–723. doi: 10.1109/TAC.1974.1100705
   Web of Science ®Google Scholar
• D.W. Andrews, Testing when a parameter is on the boundary of the maintained hypothesis, Econometrica 69 (2001), pp. 683–734. doi: 10.1111/1468-0262.00210
   Web of Science ®Google Scholar
• N. Balakrishnan and M. Stehlik, Likelihood testing with censored and missing duration data, J. Stat. Theory Pract. 9 (2015), pp. 2–22. doi: 10.1080/15598608.2014.927811
   Web of Science ®Google Scholar
• J.O. Berger, B. Liseo, and R.L. Wolpert, Integrated likelihood methods for eliminating nuisance parameters, Stat. Sci. 14 (1999), pp. 1–28. doi: 10.1214/ss/1009212518
   Web of Science ®Google Scholar
• M. Bland, Do baseline p-values follow a uniform distribution in randomized trials? PLoS ONE 8 (2013), p. e76010. doi: 10.1371/journal.pone.0076010
   PubMed Web of Science ®Google Scholar
• D. Boos and L. Stefanski, P-value precision and reproducibility, Am. Stat. 65 (2011), pp. 213–221. doi: 10.1198/tas.2011.10129
   PubMed Web of Science ®Google Scholar
• G.E. Box, Science and statistics, J. Am. Stat. Assoc. 71 (1976), pp. 791–799. doi: 10.1080/01621459.1976.10480949
   Web of Science ®Google Scholar
• K.P. Burnham and D.R. Anderson, Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach, Springer, New York, 2003.
   Google Scholar
• B. Efron, Estimating the error rate of a prediction rule: Improvement on cross-validation, J. Am. Stat. Assoc. 78 (1983), pp. 316–331. doi: 10.1080/01621459.1983.10477973
   Web of Science ®Google Scholar
• B. Efron, How biased is the apparent error rate of a prediction rule? J. Am. Stat. Assoc. 81 (1986), pp. 461–470. doi: 10.1080/01621459.1986.10478291
   Web of Science ®Google Scholar
• B. Efron and R.J. Tibshirani, An Introduction to the Bootstrap, CRC Press, Boca Raton, FL, 1994.
   Google Scholar
• B. Garel, Recent asymptotic results in testing for mixtures, Computational Statistics and Data Analysis 51 (2007), pp. 5295–5304. doi: 10.1016/j.csda.2006.09.033
   Web of Science ®Google Scholar
• R. Gould and C. Ryan, Introductory Statistics: Exploring the World through Data, Pearson Education, London, England, 2013.
   Google Scholar
• D.H. Johnson, Statistical sirens: The allure of nonparametrics, Ecology 76 (1995), pp. 1998–2000. doi: 10.2307/1940733
   Web of Science ®Google Scholar
• V. Johnson, Revised standards for statistical evidence, Proc. Natl. Acad. Sci. 110 (2013), pp. 19313–19317. doi: 10.1073/pnas.1313476110
   PubMed Web of Science ®Google Scholar
• S. Kullback and R.A. Leibler, On information and sufficiency, Ann. Math. Statist. 22 (1951), pp. 79–86. doi: 10.1214/aoms/1177729694
   Google Scholar
• I. Lawrence and K. Lin, A concordance correlation coefficient to evaluate reproducibility, Biometrics 45 (1989), pp. 255–268. doi: 10.2307/2532051
   PubMed Web of Science ®Google Scholar
• A.D. McQuarrie and C. Tsai, Regression and Time Series Model Selection, World Scientific, Hackensack, NJ, 1998.
   Google Scholar
• B. McShane, D. Gal, A. Gelman, C. Robert, and J. Tackett, Abandon statistical significance, Am. Stat. 73 (2019), pp. 235–245. doi: 10.1080/00031305.2018.1527253
   Web of Science ®Google Scholar
• A.A. Neath, J.E. Cavanaugh, and B. Riedle, A bootstrap method for assessing uncertainty in Kullback-Leibler discrepancy model selection problems, Math. Eng. Sci. Aerosp. 3 (2012), pp. 381–391.
   Google Scholar
• P. T. O'Gara, F. G. Kushner, D. D. Ascheim, D. E. Casey, M. K. Chung, J. A. de Lemos, S. M. Ettinger, J. C. Fang, F. M. Fesmire, B. A. Franklin, C. B. Granger, H. M. Krumholz, J. A. Linderbaum, D. A. Morrow, L. K. Newby, J. P. Ornato, N. Ou, M. J. Radford, J. E. Tamis-Holland, C. L. Tommaso, C. M. Tracy, Y. J. Woo, and D. X. Zhao, 2013 ACCF/AHA guideline for the management of ST-elevation myocardial infarction, J. Am. Coll. Cardiol. 61 (2013), pp. e78–e140. doi: 10.1016/j.jacc.2012.11.019
   PubMed Web of Science ®Google Scholar
• R. Peng, The reproducibility crisis in science: A statistical counterattack, Significance 12 (2015), pp. 30–32. doi: 10.1111/j.1740-9713.2015.00827.x
   Google Scholar
• M. A. Pfeffer, E. Braunwald, L. A. Moyé, L. Basta, E. J. Brown, T. E. Cuddy, B. R. Davis, E. M. Geltman, S. Goldman, G. C. Flaker, M. Klein, G. A. Lamas, M. Packer, J. Rouleau, J. L. Rouleau, J. Rutherford, J. H. Wertheimer, and C. M. Hawkins, Effect of captopril on mortality and morbidity in patients with left ventricular dysfunction after myocardial infarction: Results of the survival and ventricular enlargement trial, New Engl. J. Med. 327 (1992), pp. 669–677. doi: 10.1056/NEJM199209033271001
   PubMed Web of Science ®Google Scholar
• R Core Team, R: A language and environment for statistical computing. R Foundation for Statistical Computing, 2017. Available at http://www.R-project.org/.
   Google Scholar
• B.N. Riedle, Probabilistic Pairwise Model Comparisons Based on Discrepancy Measures and a Reconceptualization of the p-Value, Ph.D. thesis, Department of Biostatistics, University of Iowa, 2018. Available at https://ir.uiowa.edu/etd/6257/.
   Google Scholar
• RStudio Team, RStudio: Integrated development environment for R. RStudio, Inc, 2017. Available at http://www.rstudio.com/.
   Google Scholar
• S.G. Self and K.Y. Liang, Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions, J. Am. Stat. Assoc. 82 (1987), pp. 605–610. doi: 10.1080/01621459.1987.10478472
   Web of Science ®Google Scholar
• S. Setoguchi, R.J. Glynn, J. Avorn, M.A. Mittleman, R. Levin, and W.C. Winkelmayer, Improvements in long-term mortality after myocardial infarction and increased use of cardiovascular drugs after discharge: a 10-year trend analysis, J. Am. Coll. Cardiol. 51 (2008), pp. 1247–1254. doi: 10.1016/j.jacc.2007.10.063
   PubMed Web of Science ®Google Scholar
• S. C. Smith, E. J. Benjamin, R. O. Bonow, L. T. Braun, M. A. Creager, B. A. Franklin, R. J. Gibbons, S. M. Grundy, L. F. Hiratzka, D. W. Jones, D. M. Lloyd-Jones, M. Minissian, L. Mosca, E. D. Peterson, R. L. Sacco, J. Spertus, J. H. Stein, and K. A. Taubert, AHA/ACCF secondary prevention and risk reduction therapy for patients with coronary and other atherosclerotic vascular disease: 2011 update, Circulation 124 (2011), pp. 2458–2473. doi: 10.1161/CIR.0b013e318235eb4d
   PubMed Web of Science ®Google Scholar
• M. Stehlik and H. Wagner, Exact likelihood ratio testing for homogeneity of the exponential distribution, Comm. Statist. Simul. Comput. 40 (2011), pp. 663–684. doi: 10.1080/03610918.2010.551011
   Web of Science ®Google Scholar
• D. Trafimow and M. Marks, Editorial, Basic. Appl. Soc. Psych. 37 (2015), pp. 1–2. doi: 10.1080/01973533.2015.1012991
   Web of Science ®Google Scholar
• R.L. Wasserstein and N.A. Lazar, The ASA's statement on p-values: Context, process, and purpose, Am. Stat. 70 (2016), pp. 129–133. doi: 10.1080/00031305.2016.1154108
   Web of Science ®Google Scholar
• S.S. Wilks, The large-sample distribution of the likelihood ratio for testing composite hypotheses, Ann. Math. Statist. 9 (1938), pp. 60–62. doi: 10.1214/aoms/1177732360
   Google Scholar