Exact Group Sequential Methods for Estimating a Binomial Proportion
We first review existing sequential methods for estimating a binomial proportion. Afterward, we propose a new family of group sequential sampling schemes for estimating a binomial proportion with prescribed margin of error and confidence level. In particular, we establish the uniform controllability...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2013/603297 |
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| _version_ | 1832545289158787072 |
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| author | Zhengjia Chen Xinjia Chen |
| author_facet | Zhengjia Chen Xinjia Chen |
| author_sort | Zhengjia Chen |
| collection | DOAJ |
| description | We first review existing sequential methods for estimating a binomial proportion. Afterward, we propose a new family of group sequential sampling schemes for estimating a binomial proportion with prescribed margin of error and confidence level. In particular, we establish the uniform controllability of coverage probability and the asymptotic optimality for such a family of sampling schemes. Our theoretical results establish the possibility that the parameters of this family of sampling schemes can be determined so that the prescribed level of confidence is guaranteed with little waste of samples. Analytic bounds for the cumulative distribution functions and expectations of sample numbers are derived. Moreover, we discuss the inherent connection of various sampling schemes. Numerical issues are addressed for improving the accuracy and efficiency of computation. Computational experiments are conducted for comparing sampling schemes. Illustrative examples are given for applications in clinical trials. |
| format | Article |
| id | doaj-art-25fd8f9a0aa84e559a55a0b8316f41e7 |
| institution | Kabale University |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-25fd8f9a0aa84e559a55a0b8316f41e72025-02-03T07:26:13ZengWileyJournal of Probability and Statistics1687-952X1687-95382013-01-01201310.1155/2013/603297603297Exact Group Sequential Methods for Estimating a Binomial ProportionZhengjia Chen0Xinjia Chen1Department of Biostatistics and Bioinformatics, Emory University, Atlanta, GA 30322, USADepartment of Electrical Engineering, Southern University and A&M College, Baton Rouge, LA 70813, USAWe first review existing sequential methods for estimating a binomial proportion. Afterward, we propose a new family of group sequential sampling schemes for estimating a binomial proportion with prescribed margin of error and confidence level. In particular, we establish the uniform controllability of coverage probability and the asymptotic optimality for such a family of sampling schemes. Our theoretical results establish the possibility that the parameters of this family of sampling schemes can be determined so that the prescribed level of confidence is guaranteed with little waste of samples. Analytic bounds for the cumulative distribution functions and expectations of sample numbers are derived. Moreover, we discuss the inherent connection of various sampling schemes. Numerical issues are addressed for improving the accuracy and efficiency of computation. Computational experiments are conducted for comparing sampling schemes. Illustrative examples are given for applications in clinical trials.http://dx.doi.org/10.1155/2013/603297 |
| spellingShingle | Zhengjia Chen Xinjia Chen Exact Group Sequential Methods for Estimating a Binomial Proportion Journal of Probability and Statistics |
| title | Exact Group Sequential Methods for Estimating a Binomial Proportion |
| title_full | Exact Group Sequential Methods for Estimating a Binomial Proportion |
| title_fullStr | Exact Group Sequential Methods for Estimating a Binomial Proportion |
| title_full_unstemmed | Exact Group Sequential Methods for Estimating a Binomial Proportion |
| title_short | Exact Group Sequential Methods for Estimating a Binomial Proportion |
| title_sort | exact group sequential methods for estimating a binomial proportion |
| url | http://dx.doi.org/10.1155/2013/603297 |
| work_keys_str_mv | AT zhengjiachen exactgroupsequentialmethodsforestimatingabinomialproportion AT xinjiachen exactgroupsequentialmethodsforestimatingabinomialproportion |