A Shift Algorithm for Exact Computation in Sequential Tests with Binary Outcome
A simple shift algorithm is described enabling the exact determination of power functions and sample size distributions for a large variety of closed sequential two‐sample designs with a binary outcome variable. The test statistics are assumed to be based on relative frequencies of successes or fail...
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| Published in | Biometrical journal Vol. 42; no. 2; pp. 189 - 196 |
|---|---|
| Main Authors | , , , , , , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin
WILEY-VCH Verlag Berlin GmbH
01.05.2000
WILEY‐VCH Verlag Berlin GmbH |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0323-3847 1521-4036 |
| DOI | 10.1002/(SICI)1521-4036(200005)42:2<189::AID-BIMJ189>3.0.CO;2-M |
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| Abstract | A simple shift algorithm is described enabling the exact determination of power functions and sample size distributions for a large variety of closed sequential two‐sample designs with a binary outcome variable. The test statistics are assumed to be based on relative frequencies of successes or failures, but the number of interim analyses, the monitoring times, and the continuation regions may be specified as desired. To give examples, exact properties of designs proposed by the program package EaSt (Cytel, 1992) are determined, and plans with interim analyses are considered where decisions are based on the conditional power given the observations obtained so far. |
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| AbstractList | A simple shift algorithm is described enabling the exact determination of power functions and sample size distributions for a large variety of closed sequential two‐sample designs with a binary outcome variable. The test statistics are assumed to be based on relative frequencies of successes or failures, but the number of interim analyses, the monitoring times, and the continuation regions may be specified as desired. To give examples, exact properties of designs proposed by the program package EaSt (Cytel, 1992) are determined, and plans with interim analyses are considered where decisions are based on the conditional power given the observations obtained so far. |
| Author | Högel, Josef |
| Author_xml | – sequence: 1 fullname: failures, A simple shift algorithm is described enabling the exact determination of power functions – sequence: 2 fullname: analyses, but the number of interim – sequence: 3 fullname: times, the monitoring – sequence: 4 fullname: examples, the continuation regions may be specified as desired To give – sequence: 5 fullname: (CYTEL, exact properties of designs proposed by the program package East – sequence: 6 fullname: determined, ) are – sequence: 7 fullname: far, plans with interim analyses are considered where decisions are based on the conditional power |
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| Cites_doi | 10.2307/2532394 10.2307/2530245 10.2307/2336502 10.1016/0197-2456(86)90003-6 10.1080/00401706.1968.10490540 10.2307/2533442 10.1093/biomet/44.1-2.9 10.2307/2531959 |
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| References | Armitage, P., McPherson, C.K., and Rowe, B.C., 1969: Repeated Significance Tests on Accumulating Data. J. R. Statist. Soc. A 132, 235-244. Lan, K.K.G., Simon, R., and Halperin, M., 1982: Stochastically Curtailed Tests in Long Term Clinical Trials. Sequential Analysis 1, 207-219. Mehta, C.R., Patel, N., Senchaudhuri, P., and Tsiatis, A., 1994: Exact Permutational Tests for Group Sequential Clinical Trials. Biometrics 50, 1042-1053. Lin, D.Y., Wei, L.J., and Demets, D.L., 1991: Exact Statistical Inference for Group Sequential Trials. Biometrics 47, 1399-1408. Aroian, L.A., 1968: Sequential Analysis, Direct Method. Technometrics 10, 125-132. Streitberg, B. and Röhmel, J., 1986: Exact distributions for permutation and rank tests: An introduction to some recently published algorithms. Statistical Software Newsletter 12, 10-17. Wang, S.K. and Tsiatis, A.A., 1987: Approximately Optimal One-Parameter Boundaries for Group Sequential Trials. Biometrics 43, 193-199. Armitage, P., 1957: Restricted Sequential Procedures. Biometrika 44, 9-26. O'brien, P.C. and Fleming, T.R., 1979: A Multiple Test Procedure for Clinical Trials. Biometrics 35, 549-556. Lan, K.K.G. and Demets, D.L., 1983: Discrete Sequential Boundaries for Clinical Trials. Biometrika 70, 659-663. Spiegelhalter, D.J., Freedman, L.S., and Blackburn, P.R., 1986: Monitoring Clinical Trials: Conditional or Predictive Power? Controlled Clinical Trials 7, 8-17. 1957; 44 1979; 35 1987; 43 1991; 47 1983; 70 1982; 1 1986; 7 1994; 50 1968; 10 1986; 12 1969; 132 Aroian (10.1002/(SICI)1521-4036(200005)42:2<189::AID-BIMJ189>3.0.CO;2-M-BIB3) 1968; 10 Lan (10.1002/(SICI)1521-4036(200005)42:2<189::AID-BIMJ189>3.0.CO;2-M-BIB6) 1982; 1 Whitehead (10.1002/(SICI)1521-4036(200005)42:2<189::AID-BIMJ189>3.0.CO;2-M-BIB15) Streitberg (10.1002/(SICI)1521-4036(200005)42:2<189::AID-BIMJ189>3.0.CO;2-M-BIB12) 1986; 12 Lin (10.1002/(SICI)1521-4036(200005)42:2<189::AID-BIMJ189>3.0.CO;2-M-BIB7) 1991; 47 Spiegelhalter (10.1002/(SICI)1521-4036(200005)42:2<189::AID-BIMJ189>3.0.CO;2-M-BIB11) 1986; 7 Siegmund (10.1002/(SICI)1521-4036(200005)42:2<189::AID-BIMJ189>3.0.CO;2-M-BIB10) 10.1002/(SICI)1521-4036(200005)42:2<189::AID-BIMJ189>3.0.CO;2-M-BIB13 Armitage (10.1002/(SICI)1521-4036(200005)42:2<189::AID-BIMJ189>3.0.CO;2-M-BIB2) 1969; 132 Lan (10.1002/(SICI)1521-4036(200005)42:2<189::AID-BIMJ189>3.0.CO;2-M-BIB5) 1983; 70 Mehta (10.1002/(SICI)1521-4036(200005)42:2<189::AID-BIMJ189>3.0.CO;2-M-BIB8) 1994; 50 O'brien (10.1002/(SICI)1521-4036(200005)42:2<189::AID-BIMJ189>3.0.CO;2-M-BIB9) 1979; 35 Armitage (10.1002/(SICI)1521-4036(200005)42:2<189::AID-BIMJ189>3.0.CO;2-M-BIB1) 1957; 44 10.1002/(SICI)1521-4036(200005)42:2<189::AID-BIMJ189>3.0.CO;2-M-BIB4 Wang (10.1002/(SICI)1521-4036(200005)42:2<189::AID-BIMJ189>3.0.CO;2-M-BIB14) 1987; 43 |
| References_xml | – reference: Spiegelhalter, D.J., Freedman, L.S., and Blackburn, P.R., 1986: Monitoring Clinical Trials: Conditional or Predictive Power? Controlled Clinical Trials 7, 8-17. – reference: O'brien, P.C. and Fleming, T.R., 1979: A Multiple Test Procedure for Clinical Trials. Biometrics 35, 549-556. – reference: Lin, D.Y., Wei, L.J., and Demets, D.L., 1991: Exact Statistical Inference for Group Sequential Trials. Biometrics 47, 1399-1408. – reference: Armitage, P., McPherson, C.K., and Rowe, B.C., 1969: Repeated Significance Tests on Accumulating Data. J. R. Statist. Soc. A 132, 235-244. – reference: Aroian, L.A., 1968: Sequential Analysis, Direct Method. Technometrics 10, 125-132. – reference: Armitage, P., 1957: Restricted Sequential Procedures. Biometrika 44, 9-26. – reference: Lan, K.K.G., Simon, R., and Halperin, M., 1982: Stochastically Curtailed Tests in Long Term Clinical Trials. Sequential Analysis 1, 207-219. – reference: Mehta, C.R., Patel, N., Senchaudhuri, P., and Tsiatis, A., 1994: Exact Permutational Tests for Group Sequential Clinical Trials. Biometrics 50, 1042-1053. – reference: Wang, S.K. and Tsiatis, A.A., 1987: Approximately Optimal One-Parameter Boundaries for Group Sequential Trials. Biometrics 43, 193-199. – reference: Lan, K.K.G. and Demets, D.L., 1983: Discrete Sequential Boundaries for Clinical Trials. Biometrika 70, 659-663. – reference: Streitberg, B. and Röhmel, J., 1986: Exact distributions for permutation and rank tests: An introduction to some recently published algorithms. Statistical Software Newsletter 12, 10-17. – volume: 43 start-page: 193 year: 1987 end-page: 199 article-title: Approximately Optimal One‐Parameter Boundaries for Group Sequential Trials. publication-title: Biometrics – volume: 35 start-page: 549 year: 1979 end-page: 556 article-title: A Multiple Test Procedure for Clinical Trials. publication-title: Biometrics – volume: 47 start-page: 1399 year: 1991 end-page: 1408 article-title: Exact Statistical Inference for Group Sequential Trials. publication-title: Biometrics – volume: 44 start-page: 9 year: 1957 end-page: 26 article-title: Restricted Sequential Procedures. publication-title: Biometrika – volume: 70 start-page: 659 year: 1983 end-page: 663 article-title: Discrete Sequential Boundaries for Clinical Trials. publication-title: Biometrika – volume: 10 start-page: 125 year: 1968 end-page: 132 article-title: Sequential Analysis, Direct Method. publication-title: Technometrics – volume: 12 start-page: 10 year: 1986 end-page: 17 article-title: Exact distributions for permutation and rank tests: An introduction to some recently published algorithms. publication-title: Statistical Software Newsletter – volume: 132 start-page: 235 year: 1969 end-page: 244 article-title: Repeated Significance Tests on Accumulating Data. publication-title: J. R. Statist. Soc – volume: 7 start-page: 8 year: 1986 end-page: 17 article-title: Monitoring Clinical Trials: Conditional or Predictive Power? publication-title: Controlled Clinical Trials – volume: 1 start-page: 207 year: 1982 end-page: 219 article-title: Stochastically Curtailed Tests in Long Term Clinical Trials. publication-title: Sequential Analysis – volume: 50 start-page: 1042 year: 1994 end-page: 1053 article-title: Exact Permutational Tests for Group Sequential Clinical Trials. publication-title: Biometrics – volume: 47 start-page: 1399 year: 1991 ident: 10.1002/(SICI)1521-4036(200005)42:2<189::AID-BIMJ189>3.0.CO;2-M-BIB7 publication-title: Biometrics doi: 10.2307/2532394 – volume: 35 start-page: 549 year: 1979 ident: 10.1002/(SICI)1521-4036(200005)42:2<189::AID-BIMJ189>3.0.CO;2-M-BIB9 publication-title: Biometrics doi: 10.2307/2530245 – volume: 132 start-page: 235 year: 1969 ident: 10.1002/(SICI)1521-4036(200005)42:2<189::AID-BIMJ189>3.0.CO;2-M-BIB2 publication-title: J. R. Statist. Soc – volume: 70 start-page: 659 year: 1983 ident: 10.1002/(SICI)1521-4036(200005)42:2<189::AID-BIMJ189>3.0.CO;2-M-BIB5 publication-title: Biometrika doi: 10.2307/2336502 – volume: 7 start-page: 8 year: 1986 ident: 10.1002/(SICI)1521-4036(200005)42:2<189::AID-BIMJ189>3.0.CO;2-M-BIB11 publication-title: Controlled Clinical Trials doi: 10.1016/0197-2456(86)90003-6 – ident: 10.1002/(SICI)1521-4036(200005)42:2<189::AID-BIMJ189>3.0.CO;2-M-BIB15 – ident: 10.1002/(SICI)1521-4036(200005)42:2<189::AID-BIMJ189>3.0.CO;2-M-BIB4 – ident: 10.1002/(SICI)1521-4036(200005)42:2<189::AID-BIMJ189>3.0.CO;2-M-BIB13 – volume: 12 start-page: 10 year: 1986 ident: 10.1002/(SICI)1521-4036(200005)42:2<189::AID-BIMJ189>3.0.CO;2-M-BIB12 publication-title: Statistical Software Newsletter – volume: 1 start-page: 207 year: 1982 ident: 10.1002/(SICI)1521-4036(200005)42:2<189::AID-BIMJ189>3.0.CO;2-M-BIB6 publication-title: Sequential Analysis – volume: 10 start-page: 125 year: 1968 ident: 10.1002/(SICI)1521-4036(200005)42:2<189::AID-BIMJ189>3.0.CO;2-M-BIB3 publication-title: Technometrics doi: 10.1080/00401706.1968.10490540 – volume: 50 start-page: 1042 year: 1994 ident: 10.1002/(SICI)1521-4036(200005)42:2<189::AID-BIMJ189>3.0.CO;2-M-BIB8 publication-title: Biometrics doi: 10.2307/2533442 – volume: 44 start-page: 9 year: 1957 ident: 10.1002/(SICI)1521-4036(200005)42:2<189::AID-BIMJ189>3.0.CO;2-M-BIB1 publication-title: Biometrika doi: 10.1093/biomet/44.1-2.9 – ident: 10.1002/(SICI)1521-4036(200005)42:2<189::AID-BIMJ189>3.0.CO;2-M-BIB10 – volume: 43 start-page: 193 year: 1987 ident: 10.1002/(SICI)1521-4036(200005)42:2<189::AID-BIMJ189>3.0.CO;2-M-BIB14 publication-title: Biometrics doi: 10.2307/2531959 |
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| SubjectTerms | Binary outcome variable Exact computation Group sequential plans Sequential Tests Shift Algorithm Two-sample comparison |
| Title | A Shift Algorithm for Exact Computation in Sequential Tests with Binary Outcome |
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