A general class of function-indexed nonparametric tests for survival analysis

Annals of Statistics

Volumn 27, Issue 5, 1999, Pages 1722-1744

  Lin, Chin Yu ^a   Kosorok, Michael R ^a  

^a NONE

Author keywords

Censored data; Contiguous alternatives; Counting process; Function indexed stochastic process; Martingale; Monte Carlo method; Nonparametric; Survival analysis; Weak convergence

Indexed keywords

EID: 0033212296     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (26)

1. ANDERSON, P. K., BORGAN, O., GILL, R. D. and KEIDING, N. (1993). Statistical Models Based on Counting Processes. Springer, New York.
2. β-BLOCKER HEART ATTACK TRIAL RESEARCH GROUP (1982). A randomized trial of propranolol in patients with acute myocardial infarction. J. Amer. Medical Assoc. 247 1707-1714.
3. BOSE, S. and SLUD, E. (1995). Maximin efficiency-robust tests and some extensions. J. Statist. Plann. Inference 46 105-121.
4. BROWN, B. W., JR., HOLLANDER, M. and KORWAR, R. M. (1974). Nonparametric tests of independence of censored data, with applications to heart transplant studies. In Reliability and Biometry, Statistical Analysis of Lifelength (F. Proschan and R. J. Serfling, eds.) 327-354. SIAM, Philadelphia.
5. COX, D. R. (1972). Regression models and life-tables (with discussion). J. Roy. Statist. Soc. Ser. B 34 187-220.
6. DOLIVO, F. (1974). Counting processes and integrated conditional rates: a martingale approach with application to detection. Technical report, College of Engineering, Univ. Michigan.
7. ETHIER, S. N. and KURTZ, T. G. (1986). Markov Processes. Wiley, New York.
8. FLEMING, T. R. and HARRINGTON, D. P. (1991). Counting Processes and Survival Analysis. Wiley, New York.
9. FLEMING, T. R., HARRINGTON, D. P. and O'SULLIVAN, M. (1987). Supremum versions of the log-rank and generalized Wilcoxon statistics. J. Amer. Statist. Assoc. 82 312-320.
10. GASTWIRTH, J. L. (1985). The use of maximin efficiency robust tests in combining contingency tables and survival analysis. J. Amer. Statist. Assoc. 80 380-384.
11. GEHAN, E. A. (1965). A generalized Wilcoxon test for comparing arbitrarily singly censored samples. Biometrika 52 203-223.
12. GILL, R. D. (1980). Censoring and Stochastic Integrals. Math. Centrum, Amsterdam.
13. HARRINGTON, D. P. and FLEMING, T. R. (1982). A class of rank test procedures for censored survival data. Biometrika 69 133-143.
14. JONES, M. P. and CROWLEY, J. (1989). A general class of nonparametric tests for survival analysis. Biometrics 45 157-170.
15. JONES, M. P. and CROWLEY, J. (1990). Asymptotic properties of a general class of nonparametric tests for survival analysis. Ann. Statist. 18 1203-1220.
16. KOSOROK, M. R. (1998). Families of weighted log-rank statistics as function-indexed stochastic processes (version 1e). Technical Report 98, Dept. Biostatistics, Univ. Wisconsin.
17. KOSOROK, M. R. and LIN, C. (1999). The versatility of function-indexed weighted log-rank statistics. J. Amer. Statist. Assoc. 94 320-332.
18. LIN, C. (1998). A general class of function-indexed nonparametric tests for survival analysis. Ph.D. dissertation, Dept. Statistics, Univ. Wisconsin.
19. O'BRIEN, P. C. (1978). A nonparametric test for association with censored data. Biometrics 34 243-250.
20. PEPE, M. S. and FLEMING, T. R. (1989). Weighted Kaplan-Meier statistics: a class of distance tests for censored survival data. Biometrics 45 497-507.
21. PETO, R. and PETO, J. (1972). Asymptotic efficient rank-invariant test procedures (with discussion). J. Roy. Statist. Soc. Ser. A 135 185-206.
22. PRENTICE, R. L. (1978). Linear rank tests with right-censored data. Biometrika 65 167-170.
23. TAHONE, R. E. (1975). Tests for trend in life table analysis. Biometrika 62 679-682.
24. TARONE, R. E. (1981). On the distribution of the maximum of the log-rank statistic and the modified Wilcoxon statistic. Biometrics 37 79-85.
25. TAKONE, R. E. and WARE, J. (1977). On distribution-free test for equality of survival distributions. Biometrika 64 156-160.
26. VAN DER VAART, A. W. and WELLNER, J. A. (1996). Weak Convergence and Empirical Processes. Springer, New York.