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Sequential nonparametrics and semiparametrics: Theory, implementation and applications to clinical trials
One of Pranab K. Sen’s major research areas is sequential nonparametrics and semiparametrics and their applications to clinical trials, to which he has made many important contributions. Herein we review a number of these contributions and related developments. We also describe some recent work on nonparametric and semiparametric inference and the associated computational methods in time-sequential clinical trials with survival endpoints.
First available in Project Euclid: 1 April 2008
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Copyright © 2008, Institute of Mathematical Statistics
Lai, Tze Leung; Su, Zheng. Sequential nonparametrics and semiparametrics: Theory, implementation and applications to clinical trials. Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen, 332--349, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2008. doi:10.1214/193940307000000257. https://projecteuclid.org/euclid.imsc/1207058284
-  Andersen, P. K., Borgan, O., Gill, R. D. and Keiding, N. (1993). Statistical Models for Counting Processes. Springer, New York.
-  Anscombe, F. J. (1952). Large sample theory of sequential estimation. Proc. Camb. Phil. Soc. 48 600–607.
-  Armitage, P., McPherson C. K. and Bowe, B. C. (1969). Repeated significance tests on accumulating data. J. Roy. Statist. Soc. Ser. A 132 235–244.
-  Barber, S. and Jennison, C. (2002). Optimal asymmetric one-sided group sequential tests. Biometrika 89 49–60.
-  Bilias, Y., Gu, M. G. and Ying, Z. (1997). Towards a general asymptotic theory for Cox model with staggered entry. Ann. Statist. 25 662–682.
-  Breslow, N. E. (1974). Covariance analysis of censored survival data. Biometrika 30 89–99.
-  Chang, M. N. (1989). Confidence intervals for a normal mean following a group sequential test. Biometrics 45 247–254.
-  Chang, M. N. and O’Brien, P. C. (1986). Confidence intervals following group sequential tests. Contr. Clin. Trials 7 18–26.
-  Chatterjee, S. K. and Sen, P. K. (1973). Nonparametric testing under progressive censoring. Calcutta Statist. Assoc. Bull. 23 13–50.
-  Chuang, C. S. and Lai, T. L. (1998). Resampling methods for confidence intervals in group sequential trials. Biometrika 85 317–332.
-  Chuang, C. S. and Lai, T. L. (2000). Hybrid resampling methods for confidence intervals (with discussion). Statist. Sinica 10 1–50.
-  Cox, D. R. (1972). Regression models and life-tables (with discussion). J. Roy. Statist. Soc. Ser. B 34 187–220.
-  Davison, A. C. and Hinkley, D. V. (1988). Saddlepoint approximations in resampling methods. Biometrika 75 417–431.
-  Do, K. A. and Hall, P. (1991). On importance resampling for the bootstrap. Biometrika 78 161–167.
-  Eales, J. D. and Jennison, C. (1992). An improved method for deriving optimal group sequential tests. Biometrika 79 13–24.
-  Efron, B. (1987). Better bootstrap confidence intervals (with discussion). J. Amer. Statist. Assoc. 82 171–200.
-  Emerson, S. S. and Fleming, T. R. (1990). Parameter estimation following group sequential hypothesis testing. Biometrika 77 875–892.
-  Ghosh, M. and Sen, P. K. (1977). Sequential rank tests for regression. Sankhyā Ser. A 39 45–62.
-  Gu, M. G. and Lai, T. L. (1991). Weak convergence of time-sequential rank statistics with applications to sequential testing in clinical trials. Ann. Statist. 19 1403–1433.
-  Gu, M. G. and Lai, T. L. (1998). Repeated significance testing with censored rank statistics in interim analysis of clinical trials. Statist. Sinica 8 411–423.
-  Gu, M. G. and Lai, T. L. (1999). Determination of power and sample size in the design of clinical trials with failure-time endpoints and interim analyses. Contr. Clin. Trials 20 423–438.
-  Gu, M. G., Lai, T. L. and Lan, K. K. G. (1991). Rank tests based on censored data and their sequential analogues. Amer. J. Math. Management Sci. 11 147–176.
-  Gu, M. G. and Ying, Z. (1995). Group sequential methods for survival data using partial likelihood score processes with covariate adjustment. Statist. Sinica 5 793–804.
-  Hall, W. J. and Loynes, R. M. (1977). Weak convergence of processes related to likelihood ratios. Ann. Statist. 5 330–341.
-  Harrington, D. F. and Fleming, T. R. (1982). A class of rank test procedures for censored survival data. Biometrika 69 553–566.
-  Haybittle, J. L. (1971). Repeated assessments of results in clinical trials of cancer treatment. Brit. J. Radiol. 44 793–797.
-  Hoeffding, W. (1960). Lower bounds for the expected sample size and average risk of a sequential procedure. Ann. Math. Statist. 31 352–368.
-  Hu, J. Q. and Su, Z. (2007). Adaptive resampling algorithms for bootstrap distributions. J. Statist. Plann. Inference. To appear.
-  Jin, Z., Lin, D. Y., Wei, L. J. and Ying, Z. (2003). Rank-based inference for the accelerated failure-time model. Biometrika 90 341–353.
-  Johns, M. V. Jr. (1988). Importance sampling for bootstrap confidence intervals. J. Amer. Statist. Assoc. 83 709–714.
-  Jones, D. and Whitehead, J. (1979). Sequential forms of the log rank and modified Wilcoxon tests for censored data. Biometrika 66 105–113.
-  Kim, K. and DeMets, D. L. (1987). Design and analysis of group sequential tests based on the type I error spending rate function. Biometrika 74 149–154.
-  Kim, C. K. and Lai, T. L. (1999). Robust regression with censored and truncated data. In Multivariate Analysis, Design of Experiments and Survey Sampling (S. Ghosh, ed.) 231–263. Dekker, New York.
-  Lai, T. L. (1975). On Chernoff-Savage statistics and sequential rank tests. Ann. Statist. 3 825–845.
-  Lai, T. L. (1978). Pitman efficiencies of sequential tests and uniform limit theorems in nonparametric statistics. Ann. Statist. 5 1027–1047.
-  Lai, T. L. and Li, W. (2006). Confidence intervals in group sequential trials with random group sizes and applications to survival analysis. Biometrika 93 641–654.
-  Lai, T. L. and Shih, M. C. (2004). Power, sample size and adaptation considerations in the design of group sequential trials. Biometrika 91 507–528.
-  Lan, K. K.G. and DeMets, D. L. (1983). Discrete sequential boundaries for clinical trials. Biometrika 70 659–663.
-  Lan, K. K.G. and DeMets, D. L. (1989). Group sequential procedures: calendar versus information time. Statist. Med. 8 1191–1198.
-  Lan, K. K.G., DeMets, D. L. and Halperin, M. (1984). More flexible sequential and nonsequential designs in long-term clinical trials. Comm. Statist. Theory Methods 13 2339–2353.
-  Lin, D. Y. (1992). Sequential logrank tests adjusting for covariates with accelerated life model. Biometrika 79 523–529.
-  Mantel, N. (1966). Evaluation of survival data and two new rank order statistics arising in their consideration. Cancer Chemo. Rep. 94 510–521.
-  O’Brien, P. C. and Fleming, T. R. (1979). A multiple testing procedure for clinical trials. Biometrics 35 549–556.
-  Peto R. and Peto, J. (1972). Asymptotically efficient rank invariant test procedures (with discussion). J. Roy. Statist. Soc. Ser. A 135 185–207.
-  Peto R., Pike, M. C., Armitage, P., Breslow, N. E., Cox, D. R., Howard, S. V., Mantel, N., McPherson, K., Peto, J. and Smith, P. G. (1976). Design and analysis of randomized clinical trials requiring prolonged observation of each patient. I. Introduction and design. Brit. J. Cancer 34 585–612.
-  Pocock, S. J. (1977). Group sequential methods in the design and analysis of clinical trials. Biometrika 64 191–199.
-  Pocock, S. J. (1982). Interim analysis for randomised clinical trials: The group sequential approach. Biometrics 38 153–162.
-  Prentice, R. L. (1978). Linear rank statistics with right censored data. Biometrika 65 167–179.
-  Rosner, G. L. and Tsiatis, A. A. (1988). Exact confidence intervals following a group sequential trial: A comparison of methods. Biometrika 75 723–729.
-  Savage, I. R. and Sethuraman, J. (1966). Stopping time of a rank-order sequential probability ratio test on Lehmann alternatives. Ann. Math. Statist. 37 1154–1160.
-  Scharfstein, D. O. and Tsiatis, A. A. (1998). The use of simulation and bootstrap in information-based group sequential studies. Statist. Med. 17 75–87.
-  Sellke, T. and Siegmund, D. (1983). Sequential analysis of the proportional hazards model. Biometrika 70 315–326.
-  Sen, P. K. (1976). Asymptotically optimal rank order tests for progressive censoring. Calcutta Statist. Assoc. Bull. 25 65–78.
-  Sen, P. K. (1978). Nonparametric repeated significance tests. In Developments in Statistics 1 (P. R. Krishnaiah, ed.) 227–264. Academic Press, New York.
-  Sen, P. K. (1979). Weak convergence of some quantile processes arising in progressively censored tests. Ann. Statist. 7 414–431.
-  Sen, P. K. (1981). Sequential Nonparametrics. Wiley, New York.
-  Sen, P. K. and Ghosh, M. (1974). On sequential rank tests for location. Ann. Statist. 2 540–552.
-  Siegmund, D. (1978). Estimation following sequential tests. Biometrika 65 341–349.
-  Siegmund, D. (1985). Sequential Analysis: Tests and Confidence Intervals. Springer, New York.
-  Slud, E. V. (1984). Sequential linear rank tests for two-sample censored survival data. Ann. Statist. 12 551–571.
-  Slud, E. V. and Wei, L. J. (1982). Two-sample repeated significance tests based on the modified Wilcoxon statistics. J. Amer. Statist. Assoc. 77 862–868.
-  Tsiatis, A. A. (1981). The asymptotic joint distribution of the efficient scores test for the proportional hazards model calculated over time. Biometrika 68 311–315.
-  Tsiatis, A. A. (1982). Repeated significance testing for a general class of statistics used in censored survival analysis. J. Amer. Statist. Assoc. 77 855–861.
-  Tsiatis, A. A., Rosner, G. L. and Mehta, C. R. (1984). Exact confidence intervals following a group sequential test. Biometrics 40 797–803.
-  Tsiatis, A. A., Rosner, G. L. and Tritchler, D. L. (1985). Group sequential tests with censored survival data adjusting for covariates. Biometrika 72 365–373.
-  Wald, A. (1945). Sequential tests of statistical hypotheses. Ann. Math. Statist. 15 283–296.
-  Wang, S. K. and Tsiatis, A. A. (1987). Approximately optimal one-parameter boundaries for group sequential trials. Biometrics 43 193–200.
-  Wilcoxon, F., Rhodes, L. J. and Bradley, R. A. (1963). Two sequential two-sample grouped rank tests with applications to screening experiments. Biometrics 19 58–84.