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In grouprar: Group Response Adaptive Randomization for Clinical Trials
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grouprar-package: Group Response-Adaptive Randomization for Clinical Trials
Description
Implements group response-adaptive randomization procedures, which include standard (non-group) response-adaptive randomization methods as special cases. The package also handles delayed and missing responses, which broadens its use in real-world trials. It offers functions for simulating a variety of response-adaptive randomization procedures, to help guide the choice of design for a clinical trial.
Urn designs: RPWRule, WeiUrn, PolyaUrn, DLRule, GDLRule, Bai.Hu.Shen.Urn and BirthDeathUrn, with CRDesign (complete randomization) as a non-adaptive benchmark.
Doubly adaptive biased coin designs (DBCD) for binary and continuous responses, with immediate or delayed responses, for individual patients or groups of patients: DBCD_Bin, DBCD_Cont, dyldDBCD_Bin, dyldDBCD_Cont, Group.DBCD_Bin, Group.DBCD_Cont, Group.dyldDBCD_Bin and Group.dyldDBCD_Cont. These designs support any number of arms, the allocation function of Hu and Zhang (2004) or the multi-arm efficient randomized adaptive design (ERADE), several target allocations including the k-arm optimal allocations of Tymofyeyev, Rosenberger and Hu (2007) with a lower bound, and missing responses.
Further tools: nextAlloc computes the allocation probabilities of the next patient or group in an ongoing trial, and sqMonitor and sqBoundary add group sequential monitoring with alpha spending to two-arm designs (Zhu and Hu, 2010). Every design accepts a user-supplied test (test.fun), can estimate the type I error (typeI) and takes a seed. The results are objects of class "grouprar" with print and summary methods (print.grouprar), and contain the allocation sequences of all simulated trials and, for delayed designs, the trial duration.
For details of the methods and algorithms, see the following references:
Wei, L. J. (1979) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1214/aos/1176344614")};
Wei, L. J. and Durham, S. (1978) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/01621459.1978.10480109")};
Durham, S. D., Flournoy, N. and Li, W. (1998) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.2307/3315771")};
Ivanova, A., Rosenberger, W. F., Durham, S. D. and Flournoy, N. (2000) https://www.jstor.org/stable/25053121;
Bai, Z. D., Hu, F. and Shen, L. (2002) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1006/jmva.2001.1987")};
Ivanova, A. (2003) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s001840200220")};
Hu, F. and Zhang, L. X. (2004) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1214/aos/1079120137")};
Hu, F. and Rosenberger, W. F. (2006, ISBN:978-0-471-65396-7);
Zhang, L. X., Chan, W. S., Cheung, S. H. and Hu, F. (2007) https://www.jstor.org/stable/26432528;
Zhang, L. and Rosenberger, W. F. (2006) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/j.1541-0420.2005.00496.x")};
Tymofyeyev, Y., Rosenberger, W. F. and Hu, F. (2007) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1198/016214506000000906")};
Hu, F., Zhang, L. X., Cheung, S. H. and Chan, W. S. (2008) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/cjs.5550360404")};
Hu, F., Zhang, L. X. and He, X. (2009) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1214/08-AOS655")};
Zhu, H. and Hu, F. (2010) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1214/10-AOS796")};
Zhai, G., Li, Y., Zhang, L. and Hu, F. (2024) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/sim.10220")};
Alkhnefr, N., Hu, F. and Zhai, G. (2025) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1177/09622802251362644")}.
Author(s)
Guannan Zhai guannanzhai1996@gmail.com; Feifang Hu feifang@gwu.edu.
References
Alkhnefr, N., Hu, F. and Zhai, G. (2025). Efficient randomized adaptive designs for multi-arm clinical trials. Statistical Methods in Medical Research, 34(9), 1886-1898.
Bai, Z. D., Hu, F. and Shen, L. (2002). An adaptive design for multi-arm clinical trials. Journal of Multivariate Analysis, 81(1), 1-18.
Durham, S. D., Flournoy, N. and Li, W. (1998). A sequential design for maximizing the probability of a favourable response. Canadian Journal of Statistics, 26(3), 479-495.
Hu, F. and Rosenberger, W. F. (2003). Optimality, variability, power: evaluating response-adaptive randomization procedures for treatment comparisons. Journal of the American Statistical Association, 98(463), 671-678.
Hu, F. and Rosenberger, W. F. (2006). The Theory of Response-Adaptive Randomization in Clinical Trials. John Wiley & Sons.
Hu, F. and Zhang, L. X. (2004). Asymptotic properties of doubly adaptive biased coin designs for multitreatment clinical trials. The Annals of Statistics, 32(1), 268-301.
Hu, F., Zhang, L. X. and He, X. (2009). Efficient randomized-adaptive designs. The Annals of Statistics, 37(5A), 2543-2560.
Hu, F., Zhang, L. X., Cheung, S. H. and Chan, W. S. (2008). Doubly adaptive biased coin designs with delayed responses. Canadian Journal of Statistics, 36(4), 541-559.
Ivanova, A. (2003). A play-the-winner-type urn design with reduced variability. Metrika, 58, 1-13.
Ivanova, A., Rosenberger, W. F., Durham, S. D. and Flournoy, N. (2000). A birth and death urn for randomized clinical trials: asymptotic methods. Sankhya, Series B, 62(1), 104-118.
Tymofyeyev, Y., Rosenberger, W. F. and Hu, F. (2007). Implementing optimal allocation in sequential binary response experiments. Journal of the American Statistical Association, 102(477), 224-234.
Wei, L. J. (1979). The generalized Polya's urn design for sequential medical trials. The Annals of Statistics, 7(2), 291-296.
Wei, L. J. and Durham, S. (1978). The randomized play-the-winner rule in medical trials. Journal of the American Statistical Association, 73(364), 840-843.
Zelen, M. (1969). Play the winner rule and the controlled clinical trial. Journal of the American Statistical Association, 64(325), 131-146.
Zhai, G., Li, Y., Zhang, L. and Hu, F. (2024). Group response-adaptive randomization with delayed and missing responses. Statistics in Medicine, 43(27), 5047-5059.
Zhang, L. and Rosenberger, W. F. (2006). Response-adaptive randomization for clinical trials with continuous outcomes. Biometrics, 62(2), 562-569.
Zhang, L. X., Chan, W. S., Cheung, S. H. and Hu, F. (2007). A generalized drop-the-loser urn for clinical trials with delayed responses. Statistica Sinica, 17(1), 387-409.
Zhu, H. and Hu, F. (2010). Sequential monitoring of response-adaptive randomized clinical trials. The Annals of Statistics, 38(4), 2218-2241.
grouprar documentation built on Oct. 9, 2026, 9:07 a.m.
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| grouprar | R Documentation |
grouprar-package: Group Response-Adaptive Randomization for Clinical Trials
Description
Implements group response-adaptive randomization procedures, which include standard (non-group) response-adaptive randomization methods as special cases. The package also handles delayed and missing responses, which broadens its use in real-world trials. It offers functions for simulating a variety of response-adaptive randomization procedures, to help guide the choice of design for a clinical trial.
Urn designs: RPWRule, WeiUrn, PolyaUrn, DLRule, GDLRule, Bai.Hu.Shen.Urn and BirthDeathUrn, with CRDesign (complete randomization) as a non-adaptive benchmark.
Doubly adaptive biased coin designs (DBCD) for binary and continuous responses, with immediate or delayed responses, for individual patients or groups of patients: DBCD_Bin, DBCD_Cont, dyldDBCD_Bin, dyldDBCD_Cont, Group.DBCD_Bin, Group.DBCD_Cont, Group.dyldDBCD_Bin and Group.dyldDBCD_Cont. These designs support any number of arms, the allocation function of Hu and Zhang (2004) or the multi-arm efficient randomized adaptive design (ERADE), several target allocations including the k-arm optimal allocations of Tymofyeyev, Rosenberger and Hu (2007) with a lower bound, and missing responses.
Further tools: nextAlloc computes the allocation probabilities of the next patient or group in an ongoing trial, and sqMonitor and sqBoundary add group sequential monitoring with alpha spending to two-arm designs (Zhu and Hu, 2010). Every design accepts a user-supplied test (test.fun), can estimate the type I error (typeI) and takes a seed. The results are objects of class "grouprar" with print and summary methods (print.grouprar), and contain the allocation sequences of all simulated trials and, for delayed designs, the trial duration.
For details of the methods and algorithms, see the following references: Wei, L. J. (1979) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1214/aos/1176344614")}; Wei, L. J. and Durham, S. (1978) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/01621459.1978.10480109")}; Durham, S. D., Flournoy, N. and Li, W. (1998) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.2307/3315771")}; Ivanova, A., Rosenberger, W. F., Durham, S. D. and Flournoy, N. (2000) https://www.jstor.org/stable/25053121; Bai, Z. D., Hu, F. and Shen, L. (2002) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1006/jmva.2001.1987")}; Ivanova, A. (2003) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s001840200220")}; Hu, F. and Zhang, L. X. (2004) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1214/aos/1079120137")}; Hu, F. and Rosenberger, W. F. (2006, ISBN:978-0-471-65396-7); Zhang, L. X., Chan, W. S., Cheung, S. H. and Hu, F. (2007) https://www.jstor.org/stable/26432528; Zhang, L. and Rosenberger, W. F. (2006) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/j.1541-0420.2005.00496.x")}; Tymofyeyev, Y., Rosenberger, W. F. and Hu, F. (2007) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1198/016214506000000906")}; Hu, F., Zhang, L. X., Cheung, S. H. and Chan, W. S. (2008) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/cjs.5550360404")}; Hu, F., Zhang, L. X. and He, X. (2009) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1214/08-AOS655")}; Zhu, H. and Hu, F. (2010) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1214/10-AOS796")}; Zhai, G., Li, Y., Zhang, L. and Hu, F. (2024) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/sim.10220")}; Alkhnefr, N., Hu, F. and Zhai, G. (2025) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1177/09622802251362644")}.
Author(s)
Guannan Zhai guannanzhai1996@gmail.com; Feifang Hu feifang@gwu.edu.
References
Alkhnefr, N., Hu, F. and Zhai, G. (2025). Efficient randomized adaptive designs for multi-arm clinical trials. Statistical Methods in Medical Research, 34(9), 1886-1898.
Bai, Z. D., Hu, F. and Shen, L. (2002). An adaptive design for multi-arm clinical trials. Journal of Multivariate Analysis, 81(1), 1-18.
Durham, S. D., Flournoy, N. and Li, W. (1998). A sequential design for maximizing the probability of a favourable response. Canadian Journal of Statistics, 26(3), 479-495.
Hu, F. and Rosenberger, W. F. (2003). Optimality, variability, power: evaluating response-adaptive randomization procedures for treatment comparisons. Journal of the American Statistical Association, 98(463), 671-678.
Hu, F. and Rosenberger, W. F. (2006). The Theory of Response-Adaptive Randomization in Clinical Trials. John Wiley & Sons.
Hu, F. and Zhang, L. X. (2004). Asymptotic properties of doubly adaptive biased coin designs for multitreatment clinical trials. The Annals of Statistics, 32(1), 268-301.
Hu, F., Zhang, L. X. and He, X. (2009). Efficient randomized-adaptive designs. The Annals of Statistics, 37(5A), 2543-2560.
Hu, F., Zhang, L. X., Cheung, S. H. and Chan, W. S. (2008). Doubly adaptive biased coin designs with delayed responses. Canadian Journal of Statistics, 36(4), 541-559.
Ivanova, A. (2003). A play-the-winner-type urn design with reduced variability. Metrika, 58, 1-13.
Ivanova, A., Rosenberger, W. F., Durham, S. D. and Flournoy, N. (2000). A birth and death urn for randomized clinical trials: asymptotic methods. Sankhya, Series B, 62(1), 104-118.
Tymofyeyev, Y., Rosenberger, W. F. and Hu, F. (2007). Implementing optimal allocation in sequential binary response experiments. Journal of the American Statistical Association, 102(477), 224-234.
Wei, L. J. (1979). The generalized Polya's urn design for sequential medical trials. The Annals of Statistics, 7(2), 291-296.
Wei, L. J. and Durham, S. (1978). The randomized play-the-winner rule in medical trials. Journal of the American Statistical Association, 73(364), 840-843.
Zelen, M. (1969). Play the winner rule and the controlled clinical trial. Journal of the American Statistical Association, 64(325), 131-146.
Zhai, G., Li, Y., Zhang, L. and Hu, F. (2024). Group response-adaptive randomization with delayed and missing responses. Statistics in Medicine, 43(27), 5047-5059.
Zhang, L. and Rosenberger, W. F. (2006). Response-adaptive randomization for clinical trials with continuous outcomes. Biometrics, 62(2), 562-569.
Zhang, L. X., Chan, W. S., Cheung, S. H. and Hu, F. (2007). A generalized drop-the-loser urn for clinical trials with delayed responses. Statistica Sinica, 17(1), 387-409.
Zhu, H. and Hu, F. (2010). Sequential monitoring of response-adaptive randomized clinical trials. The Annals of Statistics, 38(4), 2218-2241.
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