Sequential monitoring with conditional randomization tests. (English) Zbl 1246.62177

Summary: Sequential monitoring in clinical trials is often employed to allow for early stopping and other interim decisions, while maintaining the type I error rate. However, sequential monitoring is typically described only in the context of a population model. We describe a computational method to implement sequential monitoring in a randomization-based context. In particular, we discuss a new technique for the computation of approximate conditional tests following restricted randomization procedures and then apply this technique to approximate the joint distribution of sequentially computed conditional randomization tests. We also describe the computation of a randomization-based analog of the information fraction. We apply these techniques to a restricted randomization procedure, B. Efron’s [Biometrika 58, 403–417 (1971; Zbl 0226.62086)] biased coin design. These techniques require derivation of certain conditional probabilities and conditional covariances of the randomization procedure. We employ combinatoric techniques to derive these for the biased coin design.


62L05 Sequential statistical design
62P10 Applications of statistics to biology and medical sciences; meta analysis
62L10 Sequential statistical analysis
62L15 Optimal stopping in statistics
65C60 Computational problems in statistics (MSC2010)


Zbl 0226.62086
Full Text: DOI arXiv Euclid


[1] Antognini, A. B. (2008). A theoretical analysis of the power of biased coin designs. J. Statist. Plann. Inference 138 1792-1798. · Zbl 1255.62225 · doi:10.1016/j.jspi.2007.06.033
[2] Berger, V. W. (2000). Pros and cons of permutation tests in clinical trials. Stat. Med. 19 1319-1328.
[3] Chen, J. and Lazar, N. A. (2010). Quantile estimation for discrete data via empirical likelihood. J. Nonparametr. Stat. 22 237-255. · Zbl 1182.62064 · doi:10.1080/10485250903301525
[4] Cox, D. R. (1982). A remark on randomization in clinical trials. Util. Math. 21A 242-252. · Zbl 0507.62092
[5] Efron, B. (1971). Forcing a sequential experiment to be balanced. Biometrika 58 403-417. · Zbl 0226.62086 · doi:10.1093/biomet/58.3.403
[6] Hollander, M. and Peña, E. (1988). Nonparametric tests under restricted treatment-assignment rules. J. Amer. Statist. Assoc. 83 1144-1151. · Zbl 0689.62033 · doi:10.2307/2290147
[7] Lan, K. K. G. and DeMets, D. L. (1983). Discrete sequential boundaries for clinical trials. Biometrika 70 659-663. · Zbl 0543.62059 · doi:10.2307/2336502
[8] Lehmann, E. L. (1986). Testing Statistical Hypotheses , 2nd ed. Wiley, New York. · Zbl 0608.62020
[9] Markaryan, T. and Rosenberger, W. F. (2010). Exact properties of Efron’s biased coin randomization procedure. Ann. Statist. 38 1546-1567. · Zbl 1189.62130 · doi:10.1214/09-AOS758
[10] Mehta, C. R., Patel, N. R. and Senchaudhuri, P. (1988). Importance sampling for estimating exact probabilities in permutational inference. J. Amer. Statist. Assoc. 83 999-1005.
[11] Mehta, C. R., Patel, N. R. and Wei, L. J. (1988). Constructing exact significance tests with restricted randomization rules. Biometrika 75 295-302. · Zbl 0639.62094 · doi:10.1093/biomet/75.2.295
[12] O’Brien, P. C. and Fleming, T. R. (1979). A multiple testing procedure for clinical trials. Biometrics 35 549-556.
[13] Plamadeala, V. and Rosenberger, W. F. (2011). Supplement to “Sequential monitoring with conditional randomization tests.” . · Zbl 1246.62177
[14] Rosenberger, W. F. and Lachin, J. M. (2002). Randomization in Clinical Trials : Theory and Practice . Wiley, New York. · Zbl 1007.62091
[15] Smythe, R. T. (1988). Conditional inference for restricted randomization designs. Ann. Statist. 16 1155-1161. · Zbl 0651.62019 · doi:10.1214/aos/1176350952
[16] Smythe, R. T. and Wei, L. J. (1983). Significance tests with restricted randomization design. Biometrika 70 496-500. · Zbl 0536.62090 · doi:10.1093/biomet/70.2.496
[17] Wei, L. J. (1978). The adaptive biased coin design for sequential experiments. Ann. Statist. 6 92-100. · Zbl 0374.62075 · doi:10.1214/aos/1176344068
[18] Zhang, Y. and Rosenberger, W. F. (2008). Sequential monitoring of conditional randomization tests: Generalized biased coin designs. Sequential Anal. 27 234-253. · Zbl 1147.62068 · doi:10.1080/07474940802240969
[19] Zhang, L. and Rosenberger, W. F. (2011). Adaptive randomization in clinical trials. In Design and Analysis of Experiments , Vol. III. (K. Hinkelmann, ed.). Wiley, Hoboken.
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