CrossOver: an algorithm for the construction of efficient cross-over designs
A cross‐over experiment involves the application of sequences of treatments to several subjects over a number of time periods. It is thought that the observation made on each subject at the end of a time period may depend on the direct effect of the treatment applied in the current period, and the c...
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| Published in | Statistics in medicine Vol. 23; no. 17; pp. 2645 - 2658 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Chichester, UK
John Wiley & Sons, Ltd
15.09.2004
Wiley Subscription Services, Inc |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0277-6715 1097-0258 |
| DOI | 10.1002/sim.1860 |
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| Abstract | A cross‐over experiment involves the application of sequences of treatments to several subjects over a number of time periods. It is thought that the observation made on each subject at the end of a time period may depend on the direct effect of the treatment applied in the current period, and the carry‐over effects of the treatments applied in one or more previous periods. Various models have been proposed to explain the nature of the carry‐over effects. An experimental design that is optimal under one model may not be optimal if a different model is the appropriate one. In this paper an algorithm is described to construct efficient cross‐over designs for a range of models that involve the direct effects of the treatments and various functions of their carry‐over effects. The effectiveness and flexibility of the algorithm are demonstrated by assessing its performance against numerous designs and models given in the literature. Copyright © 2004 John Wiley & Sons, Ltd. |
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| AbstractList | A cross-over experiment involves the application of sequences of treatments to several subjects over a number of time periods. It is thought that the observation made on each subject at the end of a time period may depend on the direct effect of the treatment applied in the current period, and the carry-over effects of the treatments applied in one or more previous periods. Various models have been proposed to explain the nature of the carry-over effects. An experimental design that is optimal under one model may not be optimal if a different model is the appropriate one. In this paper an algorithm is described to construct efficient cross-over designs for a range of models that involve the direct effects of the treatments and various functions of their carry-over effects. The effectiveness and flexibility of the algorithm are demonstrated by assessing its performance against numerous designs and models given in the literature. A cross-over experiment involves the application of sequences of treatments to several subjects over a number of time periods. It is thought that the observation made on each subject at the end of a time period may depend on the direct effect of the treatment applied in the current period, and the carry-over effects of the treatments applied in one or more previous periods. Various models have been proposed to explain the nature of the carry-over effects. An experimental design that is optimal under one model may not be optimal if a different model is the appropriate one. In this paper an algorithm is described to construct efficient cross-over designs for a range of models that involve the direct effects of the treatments and various functions of their carry-over effects. The effectiveness and flexibility of the algorithm are demonstrated by assessing its performance against numerous designs and models given in the literature.A cross-over experiment involves the application of sequences of treatments to several subjects over a number of time periods. It is thought that the observation made on each subject at the end of a time period may depend on the direct effect of the treatment applied in the current period, and the carry-over effects of the treatments applied in one or more previous periods. Various models have been proposed to explain the nature of the carry-over effects. An experimental design that is optimal under one model may not be optimal if a different model is the appropriate one. In this paper an algorithm is described to construct efficient cross-over designs for a range of models that involve the direct effects of the treatments and various functions of their carry-over effects. The effectiveness and flexibility of the algorithm are demonstrated by assessing its performance against numerous designs and models given in the literature. A cross-over experiment involves the application of sequences of treatments to several subjects over a number of time periods. It is thought that the observation made on each subject at the end of a time period may depend on the direct effect of the treatment applied in the current period, and the carry-over effects of the treatments applied in one or more previous periods. Various models have been proposed to explain the nature of the carry-over effects. An experimental design that is optimal under one model may not be optimal if a different model is the appropriate one. In this paper an algorithm is described to construct efficient cross-over designs for a range of models that involve the direct effects of the treatments and various functions of their carry-over effects. The effectiveness and flexibility of the algorithm are demonstrated by assessing its performance against numerous designs and models given in the literature. [PUBLICATION ABSTRACT] A cross‐over experiment involves the application of sequences of treatments to several subjects over a number of time periods. It is thought that the observation made on each subject at the end of a time period may depend on the direct effect of the treatment applied in the current period, and the carry‐over effects of the treatments applied in one or more previous periods. Various models have been proposed to explain the nature of the carry‐over effects. An experimental design that is optimal under one model may not be optimal if a different model is the appropriate one. In this paper an algorithm is described to construct efficient cross‐over designs for a range of models that involve the direct effects of the treatments and various functions of their carry‐over effects. The effectiveness and flexibility of the algorithm are demonstrated by assessing its performance against numerous designs and models given in the literature. Copyright © 2004 John Wiley & Sons, Ltd. |
| Author | John, J. A. Whitaker, D. Russell, K. G. |
| Author_xml | – sequence: 1 givenname: J. A. surname: John fullname: John, J. A. email: nye@stats.waikato.ac.nz organization: Department of Statistics, University of Waikato, Hamilton, New Zealand – sequence: 2 givenname: K. G. surname: Russell fullname: Russell, K. G. organization: School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia – sequence: 3 givenname: D. surname: Whitaker fullname: Whitaker, D. organization: Department of Statistics, University of Waikato, Hamilton, New Zealand |
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| References | Jones B, Donev AN. Modelling and design of cross-over trials. Statistics in Medicine 1996; 15:1435-1446. Williams EJ. Experimental designs balanced for pairs of residual effects. Australian Journal of Science Research 1950; 3:351-363. Eccleston JA, Street DJ. An algorithm for the construction of optimal or near-optimal change-over designs. Australian Journal of Statistics 1994; 36:371-378. Kunert J. Optimality of balanced uniform repeated measurements designs. Annals of Statistics 1984; 12:1006-1017. Whitaker D. A nested simulated annealing algorithm. Journal of Statistical Computation and Simulation 1995; 53:233-241. Donev AN. An algorithm for the construction of crossover trials. Applied Statistics 1997; 46:288-289. Kempton RA, Ferris SJ, David O. Optimal change-over designs when carry-over effects are proportional to direct effects of treatments. Biometrika 2001; 88:391-399. John JA, Williams ER. Cyclic and Computer Generated Designs. Chapman & Hall: London, 1995. Williams EJ. Experimental designs balanced for the estimation of residual effects of treatments. Australian Journal of Science Research 1949; 2:149-168. Street DJ. Combinatorial problems in repeated measurement designs. Discrete Mathematics 1989; 77:323-343. Fleiss JL. A critique of recent research on the two-treatment crossover design. Controlled Clinical Trials 1989; 10:237-243. John JA. Updating formula in an analysis of variance model. Biometrika 2001; 88:1175-1178. Cheng CS, Wu CF. Balanced repeated measurement designs. Annals of Statistics 1980; 8:1272-1283. Matthews JNS. Recent development in crossover designs. International Statistics Review 1988; 56:117-127. John JA, Russell KG. Optimising changeover designs using the average efficiency factors. Journal of Statistical Planning and Inference 2003; 113:259-268. Afsarinejad K, Hedayat AS. Repeated measurements designs for a model with self and simple mixed carryover effects. Journal of Statistical Planning and Inference 2002; 106:449-459. Eccleston JA, Whitaker D. On the design of optimal change-over experiments through multi-objective simulated annealing. Statistics and Computing 1999; 9:37-42. Sen M, Mukerjee R. Optimal repeated measurement designs under interaction. Journal of Statistical Planning and Inference 1987; 17:81-91. Jones B, Kenward MG. Design and Analysis of Cross-Over Trials (2nd edn). Chapman & Hall: London, 2003. Berenblut II. Change-over designs with complete balance for first residual effects. Biometrics 1964; 20:707-712. Kunert J. Optimal design and refinement of the linear model with applications to repeated measurements designs. Annals of Statistics 1983; 11:247-257. Matthews JNS. Modelling and optimality in the design of crossover studies for medical applications. Journal of Statistical Planning and Inference 1994; 42:89-108. Kok KL, Patterson HD. Algebraic results in the theory of serial factorial design. Biometrika 1976; 63:559-565. 1995; 53 1976; 63 1989; 77 1989; 10 1949; 2 1984; 12 1997; 46 2002; 106 1980; 8 1988; 56 1994; 36 1996 1995 1964; 20 2003 2001; 88 1996; 13 2003; 113 1996; 15 1950; 3 1987; 17 1983; 11 1999; 9 1994; 42 Stufken J (e_1_2_1_17_2) 1996 Williams EJ (e_1_2_1_3_2) 1949; 2 e_1_2_1_22_2 e_1_2_1_23_2 e_1_2_1_20_2 e_1_2_1_21_2 e_1_2_1_26_2 e_1_2_1_24_2 e_1_2_1_25_2 Williams EJ (e_1_2_1_4_2) 1950; 3 e_1_2_1_6_2 e_1_2_1_7_2 e_1_2_1_5_2 e_1_2_1_2_2 e_1_2_1_12_2 e_1_2_1_10_2 e_1_2_1_15_2 e_1_2_1_16_2 e_1_2_1_13_2 e_1_2_1_14_2 Donev AN (e_1_2_1_11_2) 1996 e_1_2_1_19_2 e_1_2_1_8_2 e_1_2_1_9_2 e_1_2_1_18_2 16261645 - Stat Med. 2005 Dec 15;24(23):3675-8 |
| References_xml | – reference: Kok KL, Patterson HD. Algebraic results in the theory of serial factorial design. Biometrika 1976; 63:559-565. – reference: Jones B, Donev AN. Modelling and design of cross-over trials. Statistics in Medicine 1996; 15:1435-1446. – reference: Street DJ. Combinatorial problems in repeated measurement designs. Discrete Mathematics 1989; 77:323-343. – reference: Kempton RA, Ferris SJ, David O. Optimal change-over designs when carry-over effects are proportional to direct effects of treatments. Biometrika 2001; 88:391-399. – reference: Sen M, Mukerjee R. Optimal repeated measurement designs under interaction. Journal of Statistical Planning and Inference 1987; 17:81-91. – reference: John JA, Russell KG. Optimising changeover designs using the average efficiency factors. Journal of Statistical Planning and Inference 2003; 113:259-268. – reference: John JA, Williams ER. Cyclic and Computer Generated Designs. Chapman & Hall: London, 1995. – reference: Eccleston JA, Street DJ. An algorithm for the construction of optimal or near-optimal change-over designs. Australian Journal of Statistics 1994; 36:371-378. – reference: Fleiss JL. A critique of recent research on the two-treatment crossover design. Controlled Clinical Trials 1989; 10:237-243. – reference: Matthews JNS. Modelling and optimality in the design of crossover studies for medical applications. Journal of Statistical Planning and Inference 1994; 42:89-108. – reference: Kunert J. Optimal design and refinement of the linear model with applications to repeated measurements designs. Annals of Statistics 1983; 11:247-257. – reference: Berenblut II. Change-over designs with complete balance for first residual effects. Biometrics 1964; 20:707-712. – reference: Jones B, Kenward MG. Design and Analysis of Cross-Over Trials (2nd edn). Chapman & Hall: London, 2003. – reference: Cheng CS, Wu CF. Balanced repeated measurement designs. Annals of Statistics 1980; 8:1272-1283. – reference: Whitaker D. A nested simulated annealing algorithm. Journal of Statistical Computation and Simulation 1995; 53:233-241. – reference: Afsarinejad K, Hedayat AS. Repeated measurements designs for a model with self and simple mixed carryover effects. Journal of Statistical Planning and Inference 2002; 106:449-459. – reference: John JA. Updating formula in an analysis of variance model. Biometrika 2001; 88:1175-1178. – reference: Williams EJ. Experimental designs balanced for pairs of residual effects. Australian Journal of Science Research 1950; 3:351-363. – reference: Eccleston JA, Whitaker D. On the design of optimal change-over experiments through multi-objective simulated annealing. Statistics and Computing 1999; 9:37-42. – reference: Matthews JNS. Recent development in crossover designs. International Statistics Review 1988; 56:117-127. – reference: Williams EJ. Experimental designs balanced for the estimation of residual effects of treatments. Australian Journal of Science Research 1949; 2:149-168. – reference: Kunert J. Optimality of balanced uniform repeated measurements designs. Annals of Statistics 1984; 12:1006-1017. – reference: Donev AN. An algorithm for the construction of crossover trials. Applied Statistics 1997; 46:288-289. – volume: 10 start-page: 237 year: 1989 end-page: 243 article-title: A critique of recent research on the two‐treatment crossover design publication-title: Controlled Clinical Trials – volume: 77 start-page: 323 year: 1989 end-page: 343 article-title: Combinatorial problems in repeated measurement designs publication-title: Discrete Mathematics – volume: 53 start-page: 233 year: 1995 end-page: 241 article-title: A nested simulated annealing algorithm publication-title: Journal of Statistical Computation and Simulation – volume: 106 start-page: 449 year: 2002 end-page: 459 article-title: Repeated measurements designs for a model with self and simple mixed carryover effects publication-title: Journal of Statistical Planning and Inference – volume: 12 start-page: 1006 year: 1984 end-page: 1017 article-title: Optimality of balanced uniform repeated measurements designs publication-title: Annals of Statistics – year: 2003 – volume: 42 start-page: 89 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year: 1996 end-page: 1446 article-title: Modelling and design of cross‐over trials publication-title: Statistics in Medicine – volume: 113 start-page: 259 year: 2003 end-page: 268 article-title: Optimising changeover designs using the average efficiency factors publication-title: Journal of Statistical Planning and Inference – volume: 11 start-page: 247 year: 1983 end-page: 257 article-title: Optimal design and refinement of the linear model with applications to repeated measurements designs publication-title: Annals of Statistics – volume: 36 start-page: 371 year: 1994 end-page: 378 article-title: An algorithm for the construction of optimal or near‐optimal change‐over designs publication-title: Australian Journal of Statistics – volume: 17 start-page: 81 year: 1987 end-page: 91 article-title: Optimal repeated measurement designs under interaction publication-title: Journal of Statistical Planning and Inference – volume: 8 start-page: 1272 year: 1980 end-page: 1283 article-title: Balanced repeated measurement designs publication-title: Annals of Statistics – year: 1995 – volume: 63 start-page: 559 year: 1976 end-page: 565 article-title: Algebraic results in the theory of serial factorial design publication-title: Biometrika – volume: 9 start-page: 37 year: 1999 end-page: 42 article-title: On the design of optimal change‐over experiments through multi‐objective simulated annealing publication-title: Statistics and Computing – volume: 46 start-page: 288 year: 1997 end-page: 289 article-title: An algorithm for the construction of crossover trials publication-title: Applied Statistics – volume: 56 start-page: 117 year: 1988 end-page: 127 article-title: Recent development in crossover designs publication-title: International Statistics Review – volume: 88 start-page: 391 year: 2001 end-page: 399 article-title: Optimal change‐over designs when carry‐over effects are proportional to direct effects of treatments publication-title: Biometrika – ident: e_1_2_1_16_2 doi: 10.1016/0378-3758(94)90191-0 – ident: e_1_2_1_5_2 doi: 10.1214/aos/1176345200 – start-page: 165 volume-title: MODA‐4—Advances in Model Oriented Data Analysis year: 1996 ident: e_1_2_1_11_2 – ident: e_1_2_1_12_2 doi: 10.1111/1467-9876.00068 – ident: e_1_2_1_20_2 doi: 10.1007/978-1-4899-7220-0 – ident: e_1_2_1_25_2 doi: 10.2307/2528124 – volume-title: Handbook of Statistics year: 1996 ident: e_1_2_1_17_2 – volume: 3 start-page: 351 year: 1950 ident: e_1_2_1_4_2 article-title: Experimental designs balanced for pairs of residual effects publication-title: Australian Journal of Science Research – ident: e_1_2_1_21_2 doi: 10.1093/biomet/63.3.559 – ident: e_1_2_1_14_2 doi: 10.1016/S0378-3758(01)00304-4 – ident: e_1_2_1_19_2 doi: 10.1093/biomet/88.2.391 – ident: e_1_2_1_22_2 doi: 10.1016/0378-3758(87)90102-9 – ident: e_1_2_1_23_2 doi: 10.1093/biomet/88.4.1175 – volume: 2 start-page: 149 year: 1949 ident: e_1_2_1_3_2 article-title: Experimental designs balanced for the estimation of residual effects of treatments publication-title: Australian Journal of Science Research – ident: e_1_2_1_26_2 doi: 10.1016/S0378-3758(02)00227-6 – ident: e_1_2_1_2_2 doi: 10.1201/9781420036091 – ident: e_1_2_1_15_2 doi: 10.1016/0197-2456(89)90065-2 – ident: e_1_2_1_18_2 doi: 10.1002/(SICI)1097-0258(19960715)15:13<1435::AID-SIM278>3.0.CO;2-Y – ident: e_1_2_1_10_2 doi: 10.1111/j.1467-842X.1994.tb00890.x – ident: e_1_2_1_24_2 doi: 10.1080/00949659508811708 – ident: e_1_2_1_9_2 doi: 10.1016/0012-365X(89)90371-3 – ident: e_1_2_1_13_2 doi: 10.1023/A:1008810109585 – ident: e_1_2_1_6_2 doi: 10.1214/aos/1176346075 – ident: e_1_2_1_8_2 doi: 10.2307/1403636 – ident: e_1_2_1_7_2 doi: 10.1214/aos/1176346717 – reference: 16261645 - Stat Med. 2005 Dec 15;24(23):3675-8 |
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| SubjectTerms | Algorithms Clinical Trials as Topic - methods cross-over models Cross-Over Studies Efficiency efficiency factors Humans interchange algorithms Medical treatment Models, Statistical Research Design row-column designs updating procedures |
| Title | CrossOver: an algorithm for the construction of efficient cross-over designs |
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