Combining one-sample confidence procedures for inference in the two-sample case

Biometrics

Volumn 71, Issue 1, 2015, Pages 146-156

  Fay, Michael P ^a   Proschan, Michael A ^a   Brittain, Erica ^a  

^a NATIONAL INSTITUTE OF ALLERGY AND INFECTIOUS DISEASES   (United States)

Author keywords

Behrens Fisher problem; Confidence distributions; Difference in medians; Exact confidence interval; Fisher's exact test; Kaplan Meier estimator

Indexed keywords

ERROR ANALYSIS;

BEHRENS FISHER PROBLEMS; CONFIDENCE DISTRIBUTION; CONFIDENCE INTERVAL; DIFFERENCE IN MEDIAN; EXACT CONFIDENCE INTERVAL; FISHER EXACT TEST; GENERAL METHOD; KAPLAN-MEIER ESTIMATORS; SIMPLE++; TWO-SAMPLE PROBLEMS;

FINANCIAL DATA PROCESSING;

ACCURACY ASSESSMENT; CONFIDENCE INTERVAL; POISSON RATIO; SAMPLING;

ALGORITHM; BIOMETRY; COMPUTER SIMULATION; CONFIDENCE INTERVAL; EPIDEMIOLOGY; MATHEMATICAL COMPUTING; PROCEDURES; SAMPLE SIZE; STATISTICAL ANALYSIS; STATISTICAL DISTRIBUTION; STATISTICAL MODEL;

ALGORITHMS; BIOMETRY; COMPUTER SIMULATION; CONFIDENCE INTERVALS; DATA INTERPRETATION, STATISTICAL; EPIDEMIOLOGIC METHODS; MODELS, STATISTICAL; NUMERICAL ANALYSIS, COMPUTER-ASSISTED; SAMPLE SIZE; STATISTICAL DISTRIBUTIONS;

EID: 84961290330     PISSN: 0006341X     EISSN: 15410420     Source Type: Journal    
DOI: 10.1111/biom.12231     Document Type: Article

References (30)

1. Altham, P. M. (1969). Exact Bayesian analysis of a 2× 2 contingency table, and fisher's" exact" significance test. Journal of the Royal Statistical Society, Series B (Methodological) 31, 261-269.
2. Balch, M. (2012). Mathematical foundations for a theory of confidence structures. International Journal of Approximate Reasoning 53, 1003-1019.
3. Chan, I. S. and Wang, W. W. (2009). On analysis of the difference of two exposure-adjusted poisson rates with stratification: From asymptotic to exact approaches. Statistics in Biosciences 1, 65-79.
4. Chan, I. S. and Zhang, Z. (1999). Test-based exact confidence intervals for the difference of two binomial proportions. Biometrics 55, 1202-1209.
5. Clopper, C. and Pearson, E. S. (1934). The use of confidence or fiducial limits illustrated in the case of the binomial. Biometrika 26, 404-413.
6. Efron, B. and Tibshirani, R. (1993). An Introduction to the Bootstrap, Vol. 57. New York: CRC Press.
7. Fay, M. P., Brittain, E. H., and Proschan, M. A. (2013). Pointwise confidence intervals for a survival distribution with small samples or heavy censoring. Biostatistics 14, 723-736.
8. Fisher, R. A. (1935). The fiducial argument in statistical inference. Annals of Eugenics 6, 391-398.
9. Garwood, F. (1936). Fiducial limits for the poisson distribution. Biometrika 28, 437-442.
10. Hannig, J. (2009). On generalized fiducial inference. Statistica Sinica 19, 491.
11. Hannig, J. and Xie, M. (2012). A not on Dempster-Shafer recombination of confidence distributions. Electronic Journal of Statistics 6, 1943-1966.
12. Hodges, J. L. and Lehmann, E. L. (1963). Estimates of location based on rank tests. The Annals of Mathematical Statistics 34, 598-611.
13. Kalbfleisch, J. and Prentice, R. (2002). The Statistical Analysis of Failure Time Data, 2nd edition. New York: Wiley.
14. Klein, J., Logan, B., Harhoff, M., and Andersen, P. (2007). Analyzing survival curves at a fixed point in time. Statistics in Medicine 26, 4505-4519.
15. Kosorok, M. R. (1999). Two-sample quantile tests under general conditions. Biometrika 86, 909-921.
16. Lehmann, E. and Romano, J. (2005). Testing Statistical Hypotheses, 3rd edition. New York: Springer.
17. Little, R. J. (1989). Testing the equality of two independent binomial proportions. The American Statistician 43, 283-288.
18. Lydersen, S., Fagerland, M. W., and Laake, P. (2009). Recommended tests for association in 2× 2 tables. Statistics in Medicine 28, 1159-1175.
19. Martin, R. and Liu, C. (2013). Inferential models: A framework for prior-free posterior probabilistic inference. Journal of the American Statistical Association 108, 301-313 (correction 108(503):1138-1139).
20. Pedersen, J. (1978). Fiducial inference. International Statistical Review 46, 147-170.
21. Robinson, G. (1976). Properties of Students t and of the Behrens-Fisher solution to the two means problem. The Annals of Statistics 4, 963-971.
22. Slud, E. V., Byar, D. P., and Green, S. B. (1984). A comparison of reflected versus test-based confidence intervals for the median survival time, based on censored data. Biometrics 40, 587-600.
23. Stevens, W. (1950). Fiducial limits of the parameter of a discontinuous distribution. Biometrika 37, 117-129.
24. Su, J. Q. and Wei, L. (1993). Nonparametric estimation for the difference or ratio of median failure times. Biometrics 49, 603-607.
25. Upton, G. J. (1992). Fisher's exact test. Journal of the Royal Statistical Society, Series A (Statistics in Society) 155, 395-402.
26. Xie, M.-g. and Singh, K. (2013). Confidence distribution, the frequentist distribution estimator of a parameter: A review (with discussion). International Statistical Review 81, 3-77.
27. Yager, R. and Liu, L. e. (2008). Classic Works of the Dempster-Shafer Theory of Belief Functions, Vol. 219. New York: Springer.
28. Yang, G., Liu, D., Liu, R. Y., Xie, M., and Hoaglin, D. C. (2014). Efficient network meta-analysis: A confidence distribution approach. Statistical Methodology 20, 105-125.
29. Yates, F. (1984). Tests of significance for 2× 2 contingency tables. Journal of the Royal Statistical Society, Series A (General) 147, 426-463.
30. Zabell, S. (1992). R. a. fisher and the fiducial argument. Statistical Science 7, 369-387.