The performance of the log rank test for different relationships between the hazards: the case of the triangular test in comparison with some other sequential tests

References

• Beltangady, M. S., and R. F. Frankowski, 1989. Effect of unequal censoring on the size and power of the logrank and Wilcoxon types of tests for survival data. Statistics in Medicine 8 (8):937–45. doi:10.1002/sim.4780080805.
   PubMed Web of Science ®Google Scholar
• Benichou, J., and C. Chastang. 1986. A simulation study of three sequential methods for the comparison of two treatment groups when the response criterion is censored. Statistics in Medicine 5 (4):375–85.
   PubMed Web of Science ®Google Scholar
• Cox, D. R. 1972. Regression models and life‐tables. Journal of the Royal Statistical Society: Series B (Methodological) 34 (2):187–202.
   Web of Science ®Google Scholar
• Cox, D. R., and D. V. Hinkley. 1974. Theoretical statistics. London, UK: Chapman and Hall.
   Google Scholar
• Chow, S. C., and J. P. Liu. 2008. Design and analysis of clinical trials: Concepts and methodologies, vol. 507. Hoboken, NJ: John Wiley & Sons.
   Google Scholar
• DeMets, D. L., and M. H. Gail. 1985. Use of logrank tests and group sequential methods at fixed calendar times. Biometrics 41 (4):1039–44.
   PubMed Web of Science ®Google Scholar
• Gail, M. H., D. L. DeMets, and E. V. Slud. 1982. Simulation studies on increments of the two-sample logrank score test for survival time data, with application to group sequential boundaries. Lecture Notes-Monograph Series 2:287–301.
   Google Scholar
• Gehan, E. A. 1965. A generalized two-sample Wilcoxon test for doubly censored data. Biometrika 52 (3):650–53. doi:10.1093/biomet/52.3-4.650.
   PubMed Web of Science ®Google Scholar
• Gordon Lan, K. K., and D. L. DeMets. 1983. Discrete sequential boundaries for clinical trials. Biometrika 70 (3):659–63. doi:10.1093/biomet/70.3.659.
   Web of Science ®Google Scholar
• Hackett, G. H., M. N. E. Harris, O. M. Plantevin, H. M. Pringle, D. B. Garrioch, and A. J. Avery. 1982. Anaesthesia for outpatient termination of pregnancy: A comparison of two anaesthetic techniques. British Journal of Anaesthesia 54 (8):865–70.
   PubMed Web of Science ®Google Scholar
• Haybittle, J. L. 1971. Repeated assessment of results in clinical trials of cancer treatment. The British Journal of Radiology 44 (526):793–97. doi:10.1259/0007-1285-44-526-793.
   PubMed Web of Science ®Google Scholar
• Hulot, J.-S., M. Cucherat, A. Charlesworth, D. J. Van Veldhuisen, J.-C. Corvol, A. Mallet, J.-P. Boissel, J. Hampton, and P. Lechat. 2003. Planning and monitoring of placebo‐controlled survival trials: Comparison of the triangular test with usual interim analyses methods. British Journal of Clinical Pharmacology 55 (3):299–306.
   PubMed Web of Science ®Google Scholar
• Jones, D. R., C. E. Newman, and J. Whitehead. 1982. The design of a sequential clinical trial for the comparison of two lung cancer treatments. Statistics in Medicine 1 (1):73–82.
   PubMedGoogle Scholar
• Jones, D., and J. Whitehead. 1979. Sequential forms of the log rank and modified Wilcoxon tests for censored data. Biometrika 66 (1):105–13. doi:10.1093/biomet/66.1.105.
   Web of Science ®Google Scholar
• Ltntnger, L., M. H. Gail, S. B. Green, and D. P. Byar. 1979. Comparison of four tests for equality of survival curves in the presence of stratification and censoring. Biometrika 66 (3):419–28. doi:10.1093/biomet/66.3.419.
   Web of Science ®Google Scholar
• Moreno, V., I. Martín, F. Torres, M. Horas, J. Ríos, and J. R. González. 2002. Inverse sampling and triangular sequential designs to compare a small proportion with a reference value. Qüestiió: Quaderns D'estadística i Investigació Operativa 26 (1):259–71.
   Google Scholar
• O'Brien, P. C., and T. R. Fleming. 1979. A multiple testing procedure for clinical trials. Biometrics (3)35:549–56. doi:10.2307/2530245.
   PubMed Web of Science ®Google Scholar
• Perera, A. A. P. N. M., M. R. Sooriyarachchi, and S. L. Wickramasuriya. 2016. A goodness of fit test for the multilevel logistic model. Communications in Statistics - Simulation and Computation 45 (2):643–59. doi:10.1080/03610918.2013.868906.
   Web of Science ®Google Scholar
• Pocock, S. J. 1977. Group sequential methods in the design and analysis of clinical trials. Biometrika 64 (2):191–99. doi:10.1093/biomet/64.2.191.
   Web of Science ®Google Scholar
• Pocock, S. J. 1983. Statistical methods for determining trial size in clinical trials. Clinical trials: A practical approach. Chichester: John Wiley and Sons, 123–33.
   Google Scholar
• Sebille, V., and E. Bellissant. 2000. Comparison of four sequential methods allowing for early stopping of comparative clinical trials. Clinical Science (London, England: 1979) 98 (5):569–78.
   PubMed Web of Science ®Google Scholar
• Sooriyarachchi, M. R., and J. Whitehead. 1998. A method for sequential analysis of survival data with nonproportional hazards. Biometrics 54 (3):1072–84. doi:10.2307/2533858.
   PubMed Web of Science ®Google Scholar
• Storb, R., H. J. Deeg, J. Whitehead, F. Appelbaum, P. Beatty, W. Bensinger, C. D. Buckner, R. Clift, K. Doney, V. Farewell, et al. 1986. Methotrexate and cyclosporine compared with cyclosporine alone for prophylaxis of acute graft versus host disease after marrow transplantation for leukemia. New England Journal of Medicine 314 (12):729–35. doi:10.1056/NEJM198603203141201.
   PubMed Web of Science ®Google Scholar
• Todd, S., A. Whitehead, N. Stallard, and J. Whitehead. 2001. Interim analyses and sequential designs in phase III studies. British Journal of Clinical Pharmacology 51 (5):394–99.
   PubMed Web of Science ®Google Scholar
• Wald, A. 1947. Sequential analysis. New York, NY: John Wiley & Sons.
   Google Scholar
• Whitehead, J. 1986. On the bias of maximum likelihood estimation following a sequential test. Biometrika 73 (3):573–81. doi:10.1093/biomet/73.3.573.
   Web of Science ®Google Scholar
• Whitehead, J. 1997. The design and analysis of sequential clinical trials. Chichester, UK: John Wiley & Sons.
   Google Scholar
• Whitehead, J., and P. Marek. 1985. A FORTRAN program for the design and analysis of sequential clinical trials. Computers and Biomedical Research, an International Journal 18 (2):176–83. doi:10.1016/0010-4809(85)90043-6.
   Google Scholar
• Yanagida, T. 2017. seqtest: An R package for sequential triangular tests. Journal of Statistical Theory and Practice 11 (3):402–406. doi:10.1080/15598608.2016.1268549.
   Web of Science ®Google Scholar