Sample size calculation for stepped wedge and other longitudinal cluster randomised trials
The sample size required for a cluster randomised trial is inflated compared with an individually randomised trial because outcomes of participants from the same cluster are correlated. Sample size calculations for longitudinal cluster randomised trials (including stepped wedge trials) need to take...
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Veröffentlicht in: | Statistics in medicine 2016-11, Vol.35 (26), p.4718-4728 |
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creator | Hooper, Richard Teerenstra, Steven de Hoop, Esther Eldridge, Sandra |
description | The sample size required for a cluster randomised trial is inflated compared with an individually randomised trial because outcomes of participants from the same cluster are correlated. Sample size calculations for longitudinal cluster randomised trials (including stepped wedge trials) need to take account of at least two levels of clustering: the clusters themselves and times within clusters. We derive formulae for sample size for repeated cross‐section and closed cohort cluster randomised trials with normally distributed outcome measures, under a multilevel model allowing for variation between clusters and between times within clusters. Our formulae agree with those previously described for special cases such as crossover and analysis of covariance designs, although simulation suggests that the formulae could underestimate required sample size when the number of clusters is small. Whether using a formula or simulation, a sample size calculation requires estimates of nuisance parameters, which in our model include the intracluster correlation, cluster autocorrelation, and individual autocorrelation. A cluster autocorrelation less than 1 reflects a situation where individuals sampled from the same cluster at different times have less correlated outcomes than individuals sampled from the same cluster at the same time. Nuisance parameters could be estimated from time series obtained in similarly clustered settings with the same outcome measure, using analysis of variance to estimate variance components. Copyright © 2016 John Wiley & Sons, Ltd. |
doi_str_mv | 10.1002/sim.7028 |
format | Article |
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Sample size calculations for longitudinal cluster randomised trials (including stepped wedge trials) need to take account of at least two levels of clustering: the clusters themselves and times within clusters. We derive formulae for sample size for repeated cross‐section and closed cohort cluster randomised trials with normally distributed outcome measures, under a multilevel model allowing for variation between clusters and between times within clusters. Our formulae agree with those previously described for special cases such as crossover and analysis of covariance designs, although simulation suggests that the formulae could underestimate required sample size when the number of clusters is small. Whether using a formula or simulation, a sample size calculation requires estimates of nuisance parameters, which in our model include the intracluster correlation, cluster autocorrelation, and individual autocorrelation. A cluster autocorrelation less than 1 reflects a situation where individuals sampled from the same cluster at different times have less correlated outcomes than individuals sampled from the same cluster at the same time. Nuisance parameters could be estimated from time series obtained in similarly clustered settings with the same outcome measure, using analysis of variance to estimate variance components. Copyright © 2016 John Wiley & Sons, Ltd.</description><identifier>ISSN: 0277-6715</identifier><identifier>EISSN: 1097-0258</identifier><identifier>DOI: 10.1002/sim.7028</identifier><identifier>PMID: 27350420</identifier><identifier>CODEN: SMEDDA</identifier><language>eng</language><publisher>England: Blackwell Publishing Ltd</publisher><subject>clinical trial design ; Clinical trials ; Cluster Analysis ; cluster randomised trial ; Correlation analysis ; Cross-Over Studies ; Humans ; intracluster correlation ; Randomized Controlled Trials as Topic ; Research Design ; Sample Size ; Simulation ; stepped wedge ; Time series</subject><ispartof>Statistics in medicine, 2016-11, Vol.35 (26), p.4718-4728</ispartof><rights>Copyright © 2016 John Wiley & Sons, Ltd.</rights><rights>Copyright Wiley Subscription Services, Inc. Nov 20, 2016</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c3888-679ff7c6031f33ba5d09148a3907e9571abc12383422a5082b6e349f31ca02bc3</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fsim.7028$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fsim.7028$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,780,784,1417,27924,27925,45574,45575</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/27350420$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Hooper, Richard</creatorcontrib><creatorcontrib>Teerenstra, Steven</creatorcontrib><creatorcontrib>de Hoop, Esther</creatorcontrib><creatorcontrib>Eldridge, Sandra</creatorcontrib><title>Sample size calculation for stepped wedge and other longitudinal cluster randomised trials</title><title>Statistics in medicine</title><addtitle>Statist. Med</addtitle><description>The sample size required for a cluster randomised trial is inflated compared with an individually randomised trial because outcomes of participants from the same cluster are correlated. Sample size calculations for longitudinal cluster randomised trials (including stepped wedge trials) need to take account of at least two levels of clustering: the clusters themselves and times within clusters. We derive formulae for sample size for repeated cross‐section and closed cohort cluster randomised trials with normally distributed outcome measures, under a multilevel model allowing for variation between clusters and between times within clusters. Our formulae agree with those previously described for special cases such as crossover and analysis of covariance designs, although simulation suggests that the formulae could underestimate required sample size when the number of clusters is small. Whether using a formula or simulation, a sample size calculation requires estimates of nuisance parameters, which in our model include the intracluster correlation, cluster autocorrelation, and individual autocorrelation. A cluster autocorrelation less than 1 reflects a situation where individuals sampled from the same cluster at different times have less correlated outcomes than individuals sampled from the same cluster at the same time. Nuisance parameters could be estimated from time series obtained in similarly clustered settings with the same outcome measure, using analysis of variance to estimate variance components. Copyright © 2016 John Wiley & Sons, Ltd.</description><subject>clinical trial design</subject><subject>Clinical trials</subject><subject>Cluster Analysis</subject><subject>cluster randomised trial</subject><subject>Correlation analysis</subject><subject>Cross-Over Studies</subject><subject>Humans</subject><subject>intracluster correlation</subject><subject>Randomized Controlled Trials as Topic</subject><subject>Research Design</subject><subject>Sample Size</subject><subject>Simulation</subject><subject>stepped wedge</subject><subject>Time series</subject><issn>0277-6715</issn><issn>1097-0258</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><sourceid>EIF</sourceid><recordid>eNpd0UtLHjEUBuAgLfVTC_6CEujGzdiTnMkksxTrDWxdaBG6CZlMxkYzlyYzePn15sNLoauzOA_h5H0J2WWwzwD4t-T7fQlcbZAVg1oWwIX6QFbApSwqycQm2UrpFoAxweUnssklCig5rMjvS9NPwdHknxy1JtglmNmPA-3GSNPspsm19N61N46aoaXj_MdFGsbhxs9L6wcTqA1LdpHGvB97n7Kfozch7ZCPXR7u8-vcJr-Oj64OT4vzi5Ozw4PzwqJSKt9Xd520FSDrEBsjWqhZqQzWIF0tJDONZRwVlpwbAYo3lcOy7pBZA7yxuE32Xt6d4vh3cWnW-QrrQjCDG5ekmeI5A6g4ZPr1P3o7LjH_Yq2QK8QaRVZfXtXS9K7VU_S9iY_6LbUMihdw74N7fN8z0Os2dG5Dr9vQl2c_1vOf9zmph3dv4p2uJEqhr3-e6GuB31V9VepTfAaNu4nn</recordid><startdate>20161120</startdate><enddate>20161120</enddate><creator>Hooper, Richard</creator><creator>Teerenstra, Steven</creator><creator>de Hoop, Esther</creator><creator>Eldridge, Sandra</creator><general>Blackwell Publishing Ltd</general><general>Wiley Subscription Services, Inc</general><scope>BSCLL</scope><scope>CGR</scope><scope>CUY</scope><scope>CVF</scope><scope>ECM</scope><scope>EIF</scope><scope>NPM</scope><scope>K9.</scope><scope>7X8</scope></search><sort><creationdate>20161120</creationdate><title>Sample size calculation for stepped wedge and other longitudinal cluster randomised trials</title><author>Hooper, Richard ; Teerenstra, Steven ; de Hoop, Esther ; Eldridge, Sandra</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c3888-679ff7c6031f33ba5d09148a3907e9571abc12383422a5082b6e349f31ca02bc3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>clinical trial design</topic><topic>Clinical trials</topic><topic>Cluster Analysis</topic><topic>cluster randomised trial</topic><topic>Correlation analysis</topic><topic>Cross-Over Studies</topic><topic>Humans</topic><topic>intracluster correlation</topic><topic>Randomized Controlled Trials as Topic</topic><topic>Research Design</topic><topic>Sample Size</topic><topic>Simulation</topic><topic>stepped wedge</topic><topic>Time series</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hooper, Richard</creatorcontrib><creatorcontrib>Teerenstra, Steven</creatorcontrib><creatorcontrib>de Hoop, Esther</creatorcontrib><creatorcontrib>Eldridge, Sandra</creatorcontrib><collection>Istex</collection><collection>Medline</collection><collection>MEDLINE</collection><collection>MEDLINE (Ovid)</collection><collection>MEDLINE</collection><collection>MEDLINE</collection><collection>PubMed</collection><collection>ProQuest Health & Medical Complete (Alumni)</collection><collection>MEDLINE - Academic</collection><jtitle>Statistics in medicine</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hooper, Richard</au><au>Teerenstra, Steven</au><au>de Hoop, Esther</au><au>Eldridge, Sandra</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Sample size calculation for stepped wedge and other longitudinal cluster randomised trials</atitle><jtitle>Statistics in medicine</jtitle><addtitle>Statist. Med</addtitle><date>2016-11-20</date><risdate>2016</risdate><volume>35</volume><issue>26</issue><spage>4718</spage><epage>4728</epage><pages>4718-4728</pages><issn>0277-6715</issn><eissn>1097-0258</eissn><coden>SMEDDA</coden><abstract>The sample size required for a cluster randomised trial is inflated compared with an individually randomised trial because outcomes of participants from the same cluster are correlated. Sample size calculations for longitudinal cluster randomised trials (including stepped wedge trials) need to take account of at least two levels of clustering: the clusters themselves and times within clusters. We derive formulae for sample size for repeated cross‐section and closed cohort cluster randomised trials with normally distributed outcome measures, under a multilevel model allowing for variation between clusters and between times within clusters. Our formulae agree with those previously described for special cases such as crossover and analysis of covariance designs, although simulation suggests that the formulae could underestimate required sample size when the number of clusters is small. Whether using a formula or simulation, a sample size calculation requires estimates of nuisance parameters, which in our model include the intracluster correlation, cluster autocorrelation, and individual autocorrelation. A cluster autocorrelation less than 1 reflects a situation where individuals sampled from the same cluster at different times have less correlated outcomes than individuals sampled from the same cluster at the same time. Nuisance parameters could be estimated from time series obtained in similarly clustered settings with the same outcome measure, using analysis of variance to estimate variance components. Copyright © 2016 John Wiley & Sons, Ltd.</abstract><cop>England</cop><pub>Blackwell Publishing Ltd</pub><pmid>27350420</pmid><doi>10.1002/sim.7028</doi><tpages>11</tpages><oa>free_for_read</oa></addata></record> |
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subjects | clinical trial design Clinical trials Cluster Analysis cluster randomised trial Correlation analysis Cross-Over Studies Humans intracluster correlation Randomized Controlled Trials as Topic Research Design Sample Size Simulation stepped wedge Time series |
title | Sample size calculation for stepped wedge and other longitudinal cluster randomised trials |
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