Bootstrap and second-order tests of risk difference

Biometrics

Volumn 66, Issue 3, 2010, Pages 975-982

  Lloyd, Chris J ^a  

^a UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

Equivalence test; Exact test; Noninferiority study; Nuisance parameters; R star statistic

Indexed keywords

HIGHER ORDER STATISTICS; STATISTICAL TESTS;

CLINICAL TRIAL; EQUIVALENCE TESTS; EXACT TESTS; NON-INFERIORITY; NONINFERIORITY STUDY; NUISANCE PARAMETER; R-STAR STATISTIC; RISK DIFFERENCE; SECOND ORDERS; STARS: STATISTICS;

STATISTICS;

ACCURACY ASSESSMENT; BOOTSTRAPPING; COMPUTER SIMULATION; DATA SET; ERROR ANALYSIS; NUMERICAL METHOD; RISK FACTOR;

EID: 77956792983     PISSN: 0006341X     EISSN: 15410420     Source Type: Journal    
DOI: 10.1111/j.1541-0420.2009.01354.x     Document Type: Article

References (26)

1. Barndorff, O. and Cox, D. R. (1994). Inferences and Asymptotics. London : Chapman and Hall.
2. Bickel, P. J. and Doksum, K. A. (1977). Mathematical Statistics. Oakland, California : Holden-Day.
3. Brazzale, A., Davison, A. C., and Reid, N. (2007). Applied Asymptotics: Case Studies in Small-sample Statistics. New York : Cambridge University Press.
4. Buehler, R. J. (1957). Confidence intervals for the product of two binomial probabilities. Journal of the American Statistical Association 52, 482 493.
5. Chan, I. S. F. (1998). Exact tests of equivalence and efficacy with a non-zero lower bound for comparative studies. Statistics in Medicine 17, 1403 1413.
6. Chan, I. S. F. and Zhang, Z. (1999). Test based exact confidence intervals for the difference of two binomial proportions. Biometrics 55, 1202 1209.
7. Davison, A. C., Fraser, D. A. S., and Reid, N. (2006). Improved likelihood inference for discrete data. Journal of the Royal Statistical Society, Series 68, 495 508.
8. DiCiccio, T. J. and Young, G. A. (2008). Conditional properties of unconditional parametric bootstrap procedures for inference in exponential families. Biometrika 95, 1 12.
9. Dunnett, C. W. and Gent, M. (1977). Significance testing to establish equivalence between treatments with special reference to data in the form of 2 × 2 tables. Biometrics 33, 593 602.
10. Farrington, C. P. and Manning, G. (1990). Test statistics and sample size formulae for comparative binomial trials with null hypothesis of non-zero risk difference or non-unity relative risk. Statistics in Medicine 9, 1447 1454.
11. Lee, S. M. S. and Young, G. A. (2005). Parametric bootstrapping with nuisance parameters. Statistics and Probability Letters 71, 143 153.
12. Liu, J.-P., Hsueh, H.-M., Hsieh, E., and Chen, J. J. (2002). Test for equivalence or non-inferiority for paired binary data. Statistics in Medicine 21, 231 245.
13. Lloyd, C. J. (2008a). Exact P-values for discrete models obtained by estimation and maximisation. Australian and New Zealand Journal of Statistics 50, 329 346.
14. Lloyd, C. J. (2008b). Exact tests based on pre-estimation and second order pivotals: non-inferiority trials. To appear in Journal of Statistical Computation and Simulation 15.
15. Lloyd, C. J. (2008c). A new exact and more powerful unconditional test of no treatment effect from binary matched pairs. Biometrics 64, 716 723.
16. Lloyd, C. J. (2008d). Bootstrap and second order tests of risk difference. MBS Working Paper.
17. Lloyd, C. J. (2010). Estimated P-values in discrete models: Asymptotic and non-asymptotic effects. To appear in Journal of Statistical Computation and Simulation.
18. Lloyd, C. J. and Moldovan, M. V. (2008). More powerful exact test of noninferiority from binary matched pairs data. Statistics in Medicine 27, 3540 3549.
19. Lugannani, R. and Rice, S. (1980). Saddle point approximation for the distribution of the sum of independent variables. Advances in Applied Probability 12, 475 490.
20. Mehrotra, D. V., Chan, I. S. F., and Berger, R. L. (2003). A cautionary note on exact unconditional inference for a difference between two independent binomial proportions. Biometrics 59, 441 450.
21. Munk, A., Skipka, G., and Stratmann, B. (2005). Testing general hypotheses under binomial sampling; The two sample case - asymptotic theory and exact procedures. Computational Statistics and Data Analysis 49, 723 739.
22. Pierce, D. A. and Peters, D. (1992). Practical use of higher order asymptotics for multiparameter exponential families (with discussion). Journal of the Royal Statistical Society, Series B 54, 701 737.
23. Reid, N. (2003). Asymptotics and the theory of inference. Annals of Statistics 31, 1695 1731.
24. Röhmel, J. (2005). Problems with existing procedures to calculate exact unconditional P-values for non-inferiority/superiority and confidence intervals for two binomials and who to resolve them. Biometrical Journal 47, 37 47.
25. Röhmel, J. and Mansmann, U. (1999). Unconditional non-asymptotic one-sided tests for independent binomial proportions when the interest lies in showing non-inferiority and/or superiority. Biometrical Journal 41, 149 170.
26. Spitzer, W. O., Sackett, D. L., Sibley, J. C., Roberts, R. S., Gent, M., Kergin, D. J., Hackett, B. C., and Olynich, A. (1974). The Burlington randomised trial of the nurse practitioner. New England Journal of Medicine 290, 251 256.