Abstract
This article gives an overview of sequential analysis and its applications to data and safety monitoring of clinical trials, determination of median effective dose and maximum tolerated dose, fixed-width confidence intervals, and adaptive design of biomedical studies.
References
- 1
Anscombe, F. J.
(1992).
Large sample theory of sequential estimation,
Proceedings of the Cambridge Philosophical Society
48,
600–607.
10.1017/S0305004100076386 Google Scholar
- 2 Armitage, P. (1958). Numerical studies in the sequential estimation of a binomial parameter Biometrika 45, 1–15.
- 3 Armitage, P. (1975). Sequential Medical Trials, 2nd Ed. Blackwell, Oxford.
- 4 Armitage, P., McPherson, C. K. & Rowe, B. C. (1969). Repeated significance tests on accumulating data, Journal of the Royal Statistical Society, Series A 132, 235–244.
- 5 Berry, D. A. & Ho, C. H. (1988). One-sided sequential stopping boundaries for clinical trials: a decision-theoretic approach, Biometrics 44, 219–227.
- 6
Chernoff, H.
(1972).
Sequential Analysis and Optimal Design.
SIAM,
Philadelphia.
10.1137/1.9781611970593 Google Scholar
- 7 Chow, Y. S. & Robbins, H. (1965). On the asymptotic theory of fixed width sequential confidence intervals for the mean, Annals of Mathematical Statistics 36, 457–462.
- 8 Cochran, W. G. & Davis, M. (1965). The Robbins–Monro method for estimating the median lethal dose, Journal of the Royal Statistical Society, Series B 27, 28–44.
- 9 Dixon, W. J. (1965). The up-and-down method for small samples, Journal of the American Statistical Association 60, 967–978.
- 10 Dixon, W. J. & Mood, A. M. (1948). A method for obtaining and analyzing sensitivity data, Journal of the American Statistical Association 43, 109–126.
- 11 Eales, J. D. & Jennison, C. (1992). An improved method for deriving optimal one-sided group sequential tests, Biometrika 79, 13–24.
- 12 Emerson, S. S. & Fleming, T. R. (1990). Parameter estimation following group sequential hypothesis testing, Biometrika 77, 875–892.
- 13 Fleming, T. R., Harrington, D. P. & O'Brien, P. C. (1984). Designs for group sequential tests, Controlled Clinical Trials 5, 348–361.
- 14 Frees, E. W. & Ruppert, D. (1990). Estimation following a Robbins–Monro designed experiment, Journal of the American Statistical Association 85, 1123–1129.
- 15 Ghosh, B. K. & Sen, P. K. (1991). Handbook of Sequential Analysis. Marcel Dekker, New York.
- 16 Hall, P. (1981). Asymptotic theory of triple sampling for sequential estimation of a mean, Annals of Statistics 9, 1229–1238.
- 17 Haybittle, J. L. (1971). Repeated assessments of results in clinical trials of cancer treatment, British Journal of Radiology 44, 793–797.
- 18 Jennison, C. & Turnbull, B. W. (1989). Interim analysis: the repeated confidence interval approach (with discussion), Journal of the Royal Statistical Society, Series B 51, 306–361.
- 19 Jennison, C. & Turnbull, B. W. (2001). Group Sequential Methods with Applications to Clinical Trials. Chapman and Hall & CRC, Boca Raton & London.
- 20 Lai, T. L. (1973). Optimal stopping and sequential tests which minimize the maximum expected sample size. Annals of Statistics 1, 659–673.
- 21 Lai, T. L. (2001). Sequential analysis: Some classical problems and new challenges. Statistica Sinica 11, 303–408.
- 22 Lai, T. L. (2003). Stochastic approximation. Annals of Statistics 31, 391–406.
- 23 Lai, T. L. (2003). Interim and terminal analyses of clinical trials with failure-time endpoints and related group sequential designs. In Applications of Sequential Methodologies, N. Mukhopadhyay, S. Datta & S. Chattopadhyay, eds. Marcel Dekker, New York, in press.
- 24 Lai, T. L. & Robbins, H. (1979). Adaptive design and stochastic approximation, Annals of Statistics 7, 1196–1221.
- 25 Lan, K. K. G. & DeMets, D. L. (1983). Discrete sequential boundaries for clinical trials, Biometrika 70, 659–663.
- 26 Morton, N. E. (1955). Sequential tests for the detection of linkage, American Journal of Human Genetics 7, 277–318.
- 27 O'Brien, P. C. & Fleming, T. R. (1979). A multiple testing procedure for clinical trials, Biometrics 35, 549–556.
- 28 Peto, R., Pike, M. C., Armitage, P., Breslow, N. E., Cox, D. R., Howard, S. V., Mantel, N., McPherson, K., Peto, J. & Smith, P. G. (1976). Design and analysis of randomized clinical trials requiring prolonged observation of each patient. I. Introduction and design, British Journal of Cancer 34, 585–712.
- 29 Pocock, S. J. (1977). Group sequential methods in the design and analysis of clinical trials, Biometrika 64, 191–199.
- 30 Robbins, H. & Monro, S. (1951). A stochastic approximation method, Annals of Mathematical Statistics 22, 400–407.
- 31 Rosner, G. L. & Tsiatis, A. A. (1988). Exact confidence intervals following sequential tests, Biometrika 65, 341–349.
- 32 Schmidt, B., Cornée, J. & Delachaume-Salem, E. (1970). Application de procédures statistiques séquentielles à l'étude des concentrations enzymatiques du suc pancréatiques humain normal, Comptes Rendus des Séances de la Societé de Biologie Paris 164, 1813–1818.
- 33 Siegmund, D. (1978). Estimation following sequential tests, Biometrika 65, 341–349.
- 34
Siegmund, D.
(1985).
Sequential Analysis: Tests and Confidence Intervals.
Springer-Verlag,
New York.
10.1007/978-1-4757-1862-1 Google Scholar
- 35 Slud, E. V. & Wei, L. J. (1982). Two-sample repeated significance tests based on the modified Wilcoxon statistic, Journal of the American Statistical Association 157, 357–416.
- 36 Spiegelhalter, D. J., Freedman, L. S. & Parmar, M. K. B. (1994). Bayesian approaches to randomized trials (with discussion), Journal of the Royal Statistical Society, Series A 157, 357–416.
- 37 Stein, C. (1945). A two sample test for a linear hypothesis whose power is independent of the variance, Annals of Mathematical Statistics 16, 243–258.
- 38 Tsiatis, A. A. (1982). Repeated significance testing for a general class of statistics used in censored survival analysis, Journal of the American Statistical Association 77, 855–861.
- 39 Wald, A. (1945). Sequential tests of statistical hypotheses, Annals of Mathematical Statistics 16, 117–186.
- 40 Wald, A. (1947). Sequential Analysis. Wiley, New York.
- 41 Wald, A. & Wolfowitz, J. (1948). Optimum character of the sequential probability ratio test, Annals of Mathematical Statistics 19, 326–339.
- 42 Whitehead, J. (1992). The Design and Analysis of Sequential Clinical Trials, 2nd Ed. Ellis Horwood, Chichester.
Citing Literature
