Research Article
Balance in cluster randomized trials
First published: 23 January 2001
Citations: 67
Abstract
This paper explores the role of balancing covariates between treatment groups in the design of cluster randomized trials. General expressions are obtained for two criteria to evaluate designs for parallel group studies with two treatments. The first is the variance of the estimated treatment effect and the second is the extent to which the estimated treatment effect is changed by adjusting for covariates. It is argued that the second of these is more important for cluster randomized trials. Methods of obtaining balanced designs from covariates which are available at the start of a study are proposed. An imbalance measure is used to compare the extent to which designs balance important covariates between the arms of a trial. Several approaches to selecting a well balanced design are possible. A method that randomly selects one member from the class of designs with acceptable bias will allow randomization inference as well as model‐based inference. The methods are illustrated with data from a trial of school‐based sex education. Copyright © 2001 John Wiley & Sons, Ltd.
Citing Literature
Number of times cited according to CrossRef: 67
- Siyun Yang, Monique Anderson Starks, Adrian F. Hernandez, Elizabeth L. Turner, Robert M. Califf, Christopher M. O'Connor, Robert J. Mentz, Kingshuk Roy Choudhury, Impact of baseline covariate imbalance on bias in treatment effect estimation in cluster randomized trials: Race as an example, Contemporary Clinical Trials, 10.1016/j.cct.2019.04.016, 88, (105775), (2020).
- Oye Gureje, Lola Kola, Bibilola D. Oladeji, Jibril Abdulmalik, Olatunde Ayinde, Phyllis Zelkowitz, Ian Bennett, Responding to the challenge of Adolescent Perinatal Depression (RAPiD): protocol for a cluster randomized hybrid trial of psychosocial intervention in primary maternal care, Trials, 10.1186/s13063-020-4086-9, 21, 1, (2020).
- Lawrence H. Moulton, Richard J. Hayes, Cluster Randomized Trials, Principles and Practice of Clinical Trials, 10.1007/978-3-319-52677-5, (1-19), (2020).
- Ahmed A. Al-Jaishi, Christopher W. McIntyre, Jessica M. Sontrop, Stephanie N. Dixon, Sierra Anderson, Amit Bagga, Derek Benjamin, David Berry, Peter G. Blake, Laura Chambers, Patricia C. K. Chan, Nicole Delbrouck, P. J. Devereaux, Luis F. Ferreira-Divino, Richard Goluch, Laura Gregor, Jeremy M. Grimshaw, Garth Hanson, Eduard Iliescu, Arsh K. Jain, Charmaine E. Lok, Reem A. Mustafa, Bharat Nathoo, Gihad E. Nesrallah, Matthew J. Oliver, Sanjay Pandeya, Malvinder S. Parmar, David Perkins, Justin Presseau, Eli Rabin, Joanna Sasal, Tanya Shulman, Manish M. Sood, Andrew Steele, Paul Tam, Daniel Tascona, Davinder Wadehra, Ron Wald, Michael Walsh, Paul Watson, Walter Wodchis, Phillip Zager, Merrick Zwarenstein, Amit X. Garg, Major Outcomes With Personalized Dialysate TEMPerature (MyTEMP): Rationale and Design of a Pragmatic, Registry-Based, Cluster Randomized Controlled Trial, Canadian Journal of Kidney Health and Disease, 10.1177/2054358119887988, 7, (205435811988798), (2020).
- Douglas J Opel, Jeffrey D Robinson, Heather Spielvogle, Christine Spina, Kathleen Garrett, Amanda F Dempsey, Cathryn Perreira, Miriam Dickinson, Chuan Zhou, Barbara Pahud, James A Taylor, Sean T O'Leary, ‘Presumptively Initiating Vaccines and Optimizing Talk with Motivational Interviewing’ (PIVOT with MI) trial: a protocol for a cluster randomised controlled trial of a clinician vaccine communication intervention, BMJ Open, 10.1136/bmjopen-2020-039299, 10, 8, (e039299), (2020).
- David L. Roth, Jin Huang, Laura N. Gitlin, Joseph E. Gaugler, Application of randomization techniques for balancing site covariates in the adult day service plus pragmatic cluster-randomized trial, Contemporary Clinical Trials Communications, 10.1016/j.conctc.2020.100628, (100628), (2020).
- John N. S. Matthews, Highly efficient stepped wedge designs for clusters of unequal size, Biometrics, 10.1111/biom.13218, 0, 0, (2020).
- Erik Lenguerrand, Cathy Winter, Dimitrios Siassakos, Graeme MacLennan, Karen Innes, Pauline Lynch, Alan Cameron, Joanna Crofts, Alison McDonald, Kirsty McCormack, Mark Forrest, John Norrie, Siladitya Bhattacharya, Tim Draycott, Effect of hands-on interprofessional simulation training for local emergencies in Scotland: the THISTLE stepped-wedge design randomised controlled trial, BMJ Quality & Safety, 10.1136/bmjqs-2018-008625, 29, 2, (122-134), (2019).
- Evaluation of a policy intervention to promote the health and wellbeing of workers in small and medium sized enterprises – a cluster randomised controlled trial, BMC Public Health, 10.1186/s12889-019-6582-y, 19, 1, (2019).
- Edward R Melnick, Molly Moore Jeffery, James D Dziura, Jodi A Mao, Erik P Hess, Timothy F Platts-Mills, Yauheni Solad, Hyung Paek, Shara Martel, Mehul D Patel, Laura Bankowski, Charles Lu, Cynthia Brandt, Gail D’Onofrio, User-centred clinical decision support to implement emergency department-initiated buprenorphine for opioid use disorder: protocol for the pragmatic group randomised EMBED trial, BMJ Open, 10.1136/bmjopen-2018-028488, 9, 5, (e028488), (2019).
- Jody D. Ciolino, Alicia Diebold, Jessica K. Jensen, Gerald W. Rouleau, Kimberly K. Koloms, Darius Tandon, Choosing an imbalance metric for covariate-constrained randomization in multiple-arm cluster-randomized trials, Trials, 10.1186/s13063-019-3324-5, 20, 1, (2019).
- Hubert Wong, Yongdong Ouyang, Mohammad Ehsanul Karim, The randomization-induced risk of a trial failing to attain its target power: assessment and mitigation, Trials, 10.1186/s13063-019-3471-8, 20, 1, (2019).
- Tamsin Ford, Rachel Hayes, Sarah Byford, Vanessa Edwards, Malcolm Fletcher, Stuart Logan, Brahm Norwich, Will Pritchard, Kate Allen, Matthew Allwood, Poushali Ganguli, Katie Grimes, Lorraine Hansford, Bryony Longdon, Shelley Norman, Anna Price, Abigail Emma Russell, Obioha C Ukoumunne, Training teachers in classroom management to improve mental health in primary school children: the STARS cluster RCT, Public Health Research, 10.3310/phr07060, 7, 6, (1-150), (2019).
- Andrew J Copas, Richard Hooper, Cluster randomised trials with different numbers of measurements at baseline and endline: Sample size and optimal allocation, Clinical Trials, 10.1177/1740774519873888, (174077451987388), (2019).
- Tamsin Ford, Rachel Hayes, Sarah Byford, Vanessa Edwards, Malcolm Fletcher, Stuart Logan, Brahm Norwich, Will Pritchard, Kate Allen, Matthew Allwood, Poushali Ganguli, Katie Grimes, Lorraine Hansford, Bryony Longdon, Shelley Norman, Anna Price, Obioha C. Ukoumunne, The effectiveness and cost-effectiveness of the Incredible Years ® Teacher Classroom Management programme in primary school children: results of the STARS cluster randomised controlled trial , Psychological Medicine, 10.1017/S0033291718001484, 49, 5, (828-842), (2018).
- Thomas Grischott, The Shiny Balancer - software and imbalance criteria for optimally balanced treatment allocation in small RCTs and cRCTs, BMC Medical Research Methodology, 10.1186/s12874-018-0551-5, 18, 1, (2018).
- Joseph Okebe, Joan Muela Ribera, Julie Balen, Fatou Jaiteh, Yoriko Masunaga, Davis Nwakanma, John Bradley, Shunmay Yeung, Koen Peeters Grietens, Umberto D’Alessandro, Reactive community-based self-administered treatment against residual malaria transmission: study protocol for a randomized controlled trial, Trials, 10.1186/s13063-018-2506-x, 19, 1, (2018).
- John A. Gallis, Fan Li, Hengshi Yu, Elizabeth L. Turner, Cvcrand and Cptest: Commands for Efficient Design and Analysis of Cluster Randomized Trials Using Constrained Randomization and Permutation Tests, The Stata Journal: Promoting communications on statistics and Stata, 10.1177/1536867X1801800204, 18, 2, (357-378), (2018).
- Wendy K. Tam Cho, An evolutionary algorithm for subset selection in causal inference models, Journal of the Operational Research Society, 10.1057/s41274-017-0258-8, 69, 4, (630-644), (2018).
- Qiu Wang, Richard T. Houang, Kimberly Maier, Multilevel structural equation modeling-based quasi-experimental synthetic cohort design, Behaviormetrika, 10.1007/s41237-018-0053-0, 45, 2, (261-294), (2018).
- Hillary K Rono, Andrew Bastawrous, David Macleod, Emmanuel Wanjala, Gian Luca Di Tanna, Helen A Weiss, Matthew J Burton, Smartphone-based screening for visual impairment in Kenyan school children: a cluster randomised controlled trial, The Lancet Global Health, 10.1016/S2214-109X(18)30244-4, 6, 8, (e924-e932), (2018).
- Jessica K Jensen, Jody D Ciolino, Alicia Diebold, Melissa Segovia, Aria Degillio, Jesus Solano-Martinez, S Darius Tandon, Comparing the Effectiveness of Clinicians and Paraprofessionals to Reduce Disparities in Perinatal Depression via the Mothers and Babies Course: Protocol for a Cluster-Randomized Controlled Trial, JMIR Research Protocols, 10.2196/11624, 7, 11, (e11624), (2018).
- Peymane Adab, Timothy Barrett, Raj Bhopal, Janet E Cade, Alastair Canaway, Kar Keung Cheng, Joanne Clarke, Amanda Daley, Jonathan Deeks, Joan Duda, Ulf Ekelund, Emma Frew, Paramjit Gill, Tania Griffin, Karla Hemming, Kiya Hurley, Emma R Lancashire, James Martin, Eleanor McGee, Miranda J Pallan, Jayne Parry, Sandra Passmore, The West Midlands ActiVe lifestyle and healthy Eating in School children (WAVES) study: a cluster randomised controlled trial testing the clinical effectiveness and cost-effectiveness of a multifaceted obesity prevention intervention programme targeted at children aged 6–7 years, Health Technology Assessment, 10.3310/hta22080, 22, 8, (1-608), (2018).
- William G. Henderson, Clinical trials design and conduct, Biostatistics & Epidemiology, 10.1080/24709360.2018.1477467, (1-14), (2018).
- H Kitchener, M Gittins, M Cruickshank, C Moseley, S Fletcher, R Albrow, A Gray, L Brabin, D Torgerson, EJ Crosbie, A Sargent, C Roberts, A cluster randomized trial of strategies to increase uptake amongst young women invited for their first cervical screen: The STRATEGIC trial, Journal of Medical Screening, 10.1177/0969141317696518, 25, 2, (88-98), (2017).
- Allison Kempe, Alison W. Saville, Brenda Beaty, L. Miriam Dickinson, Dennis Gurfinkel, Sheri Eisert, Heather Roth, Diana Herrero, Lynn Trefren, Rachel Herlihy, Centralized Reminder/Recall to Increase Immunization Rates in Young Children: How Much Bang for the Buck?, Academic Pediatrics, 10.1016/j.acap.2016.11.016, 17, 3, (330-338), (2017).
- Erik Lenguerrand, Catherine Winter, Karen Innes, Graeme MacLennan, Dimitrios Siassakos, Pauline Lynch, Alan Cameron, Joanna Crofts, Alison McDonald, Kirsty McCormack, Mark Forrest, John Norrie, Siladitya Bhattacharya, Tim Draycott, THISTLE: trial of hands-on Interprofessional simulation training for local emergencies: a research protocol for a stepped-wedge clustered randomised controlled trial, BMC Pregnancy and Childbirth, 10.1186/s12884-017-1455-9, 17, 1, (2017).
- Fan Li, Elizabeth L. Turner, Patrick J. Heagerty, David M. Murray, William M. Vollmer, Elizabeth R. DeLong, An evaluation of constrained randomization for the design and analysis of group‐randomized trials with binary outcomes, Statistics in Medicine, 10.1002/sim.7410, 36, 24, (3791-3806), (2017).
- Fan Li, Yuliya Lokhnygina, David M. Murray, Patrick J. Heagerty, Elizabeth R. DeLong, An evaluation of constrained randomization for the design and analysis of group‐randomized trials, Statistics in Medicine, 10.1002/sim.6813, 35, 10, (1565-1579), (2015).
- Yael Perry, Alison L. Calear, Andrew Mackinnon, Philip J. Batterham, Julio Licinio, Catherine King, Noel Thomsen, Jan Scott, Tara Donker, Sally Merry, Theresa Fleming, Karolina Stasiak, Aliza Werner-Seidler, Helen Christensen, Trial for the Prevention of Depression (TriPoD) in final-year secondary students: study protocol for a cluster randomised controlled trial, Trials, 10.1186/s13063-015-0929-1, 16, 1, (2015).
- Neil Wright, Noah Ivers, Sandra Eldridge, Monica Taljaard, Stephen Bremner, A review of the use of covariates in cluster randomized trials uncovers marked discrepancies between guidance and practice, Journal of Clinical Epidemiology, 10.1016/j.jclinepi.2014.12.006, 68, 6, (603-609), (2015).
- Jeremy Segrott, Heather Rothwell, Gillian Hewitt, Rebecca Playle, Chao Huang, Simon Murphy, Laurence Moore, Matthew Hickman, Hayley Reed, Preventing alcohol misuse in young people: an exploratory cluster randomised controlled trial of the Kids, Adults Together (KAT) programme, Public Health Research, 10.3310/phr03150, 3, 15, (1-188), (2015).
- Paul Stallard, Elena Skryabina, Gordon Taylor, Rob Anderson, Obioha C Ukoumunne, Harry Daniels, Rhiannon Phillips, Neil Simpson, A cluster randomised controlled trial comparing the effectiveness and cost-effectiveness of a school-based cognitive–behavioural therapy programme (FRIENDS) in the reduction of anxiety and improvement in mood in children aged 9/10 years, Public Health Research, 10.3310/phr03140, 3, 14, (1-88), (2015).
- Paul Stallard, Elena Skryabina, Gordon Taylor, Rhiannon Phillips, Harry Daniels, Rob Anderson, Neil Simpson, Classroom-based cognitive behaviour therapy (FRIENDS): a cluster randomised controlled trial to Prevent Anxiety in Children through Education in Schools (PACES), The Lancet Psychiatry, 10.1016/S2215-0366(14)70244-5, 1, 3, (185-192), (2014).
- Sara Ramzan, Ebba Holme Hansen, Lotte Stig Nørgaard, Lourdes Cantarero Arevalo, Ramune Jacobsen, Validation of the Danish translation of the Medicine Knowledge Questionnaire among elementary school children, Research in Social and Administrative Pharmacy, 10.1016/j.sapharm.2014.02.004, 10, 6, (918-922), (2014).
- Russell Jago, Simon J Sebire, Ben Davies, Lesley Wood, Mark J Edwards, Kathryn Banfield, Kenneth R Fox, Janice L Thompson, Jane E Powell, Alan A Montgomery, Randomised feasibility trial of a teaching assistant led extracurricular physical activity intervention for 9 to 11 year olds: Action 3:30, International Journal of Behavioral Nutrition and Physical Activity, 10.1186/s12966-014-0114-z, 11, 1, (2014).
- Betina Durovni, Valeria Saraceni, Lawrence H Moulton, Antonio G Pacheco, Solange C Cavalcante, Bonnie S King, Silvia Cohn, Anne Efron, Richard E Chaisson, Jonathan E Golub, Effect of improved tuberculosis screening and isoniazid preventive therapy on incidence of tuberculosis and death in patients with HIV in clinics in Rio de Janeiro, Brazil: a stepped wedge, cluster-randomised trial, The Lancet Infectious Diseases, 10.1016/S1473-3099(13)70187-7, 13, 10, (852-858), (2013).
- Simon de Lusignana, Hugh Gallagher, Simon Jones, Tom Chan, Jeremy van Vlymen, Aumran Tahir, Nicola Thomas, Neerja Jain, Olga Dmitrieva, Imran Rafi, Andrew McGovern, Kevin Harris, Audit-based education lowers systolic blood pressure in chronic kidney disease: the Quality Improvement in CKD (QICKD) trial results, Kidney International, 10.1038/ki.2013.96, 84, 3, (609-620), (2013).
- Lan Xiao, Veronica Yank, Jun Ma, Algorithm for balancing both continuous and categorical covariates in randomized controlled trials, Computer Methods and Programs in Biomedicine, 10.1016/j.cmpb.2012.06.001, 108, 3, (1185-1190), (2012).
- Sandra Eldridge, Sally Kerry, Design, A Practical Guide to Cluster Randomised Trials in Health Services Research, 10.1002/9781119966241, (74-98), (2012).
- Ricardo Araya, Alan A Montgomery, Rosemarie Fritsch, David Gunnell, Paul Stallard, Sian Noble, Vania Martinez, Sergio Barroilhet, Paul Vohringer, Viviana Guajardo, Felix Cova, Jorge Gaete, Alejandro Gomez, Graciela Rojas, School-based intervention to improve the mental health of low-income, secondary school students in Santiago, Chile (YPSA): study protocol for a randomized controlled trial, Trials, 10.1186/1745-6215-12-49, 12, 1, (2011).
- Nefyn H Williams, Elvis Amoakwa, John Belcher, Rhiannon T Edwards, Hossein Hassani, Maggie Hendry, Kim Burton, Ruth Lewis, Kerenza Hood, Jeremy Jones, Paul Bennett, Pat Linck, Richard D Neal, Clare Wilkinson, Activity Increase Despite Arthritis (AÏDA): phase II randomised controlled trial of an active management booklet for hip and knee osteoarthritis in primary care, British Journal of General Practice, 10.3399/bjgp11X588411, 61, 589, (e452-e458), (2011).
- Shrikant I. Bangdiwala, The ‘goddess of randomisation’ in small samples, International Journal of Injury Control and Safety Promotion, 10.1080/17457300.2011.552940, 18, 1, (89-93), (2011).
- Clio Spanou, Sharon A Simpson, Kerry Hood, Adrian Edwards, David Cohen, Stephen Rollnick, Ben Carter, Jim McCambridge, Laurence Moore, Elizabeth Randell, Timothy Pickles, Christine Smith, Claire Lane, Fiona Wood, Hazel Thornton, Chris C Butler, Preventing disease through opportunistic, rapid engagement by primary care teams using behaviour change counselling (PRE-EMPT): protocol for a general practice-based cluster randomised trial, BMC Family Practice, 10.1186/1471-2296-11-69, 11, 1, (2010).
- Paul Stallard, Alan A Montgomery, Ricardo Araya, Rob Anderson, Glynn Lewis, Kapil Sayal, Rhiannon Buck, Abigail Millings, John A Taylor, Protocol for a randomised controlled trial of a school based cognitive behaviour therapy (CBT) intervention to prevent depression in high risk adolescents (PROMISE), Trials, 10.1186/1745-6215-11-114, 11, 1, (2010).
- Ben Carter, Cluster size variability and imbalance in cluster randomized controlled trials, Statistics in Medicine, 10.1002/sim.4050, 29, 29, (2984-2993), (2010).
- Jun Ma, Peg Strub, Carlos A Camargo, Lan Xiao, Estela Ayala, Christopher D Gardner, A Sonia Buist, William L Haskell, Phillip W Lavori, Sandra R Wilson, The Breathe Easier through Weight Loss Lifestyle (BE WELL) Intervention: A randomized controlled trial, BMC Pulmonary Medicine, 10.1186/1471-2466-10-16, 10, 1, (2010).
- Nefyn H Williams, Elvis Amoakwa, Kim Burton, Maggie Hendry, John Belcher, Ruth Lewis, Kerenza Hood, Jeremy Jones, Paul Bennett, Rhiannon T Edwards, Richard D Neal, Glynne Andrew, Clare Wilkinson, Activity Increase Despite Arthritis (AÏDA): design of a Phase II randomised controlled trial evaluating an active management booklet for hip and knee osteoarthritis [ISRCTN24554946], BMC Family Practice, 10.1186/1471-2296-10-62, 10, 1, (2009).
- Sharon A Simpson, Christopher C Butler, Kerry Hood, David Cohen, Frank Dunstan, Meirion R Evans, Stephen Rollnick, Laurence Moore, Monika Hare, Marie-Jet Bekkers, John Evans, Stemming the Tide of Antibiotic Resistance (STAR): A protocol for a trial of a complex intervention addressing the 'why' and 'how' of appropriate antibiotic prescribing in general practice, BMC Family Practice, 10.1186/1471-2296-10-20, 10, 1, (2009).
- Paul J. Nietert, Ruth G. Jenkins, Lynne S. Nemeth, Steven M. Ornstein, An application of a modified constrained randomization process to a practice-based cluster randomized trial to improve colorectal cancer screening, Contemporary Clinical Trials, 10.1016/j.cct.2008.10.002, 30, 2, (129-132), (2009).
- Ben B. Hansen, Jake Bowers, Attributing Effects to a Cluster-Randomized Get-Out-the-Vote Campaign, Journal of the American Statistical Association, 10.1198/jasa.2009.ap06589, 104, 487, (873-885), (2009).
- Marion Henderson, Isabella Butcher, Daniel Wight, Lisa Williamson, Gillian Raab, What explains between-school differences in rates of sexual experience?, BMC Public Health, 10.1186/1471-2458-8-53, 8, 1, (2008).
- Ben R Carter, Kerenza Hood, Balance algorithm for cluster randomized trials, BMC Medical Research Methodology, 10.1186/1471-2288-8-65, 8, 1, (2008).
- Thomas E. Love, Randall D. Cebul, Douglas Einstadter, Anil K. Jain, Holly Miller, C. Martin Harris, Peter J. Greco, Scott S. Husak, Neal V. Dawson, Electronic Medical Record-Assisted Design of a Cluster-Randomized Trial to Improve Diabetes Care and Outcomes, Journal of General Internal Medicine, 10.1007/s11606-007-0454-3, 23, 4, (383-391), (2008).
- Marion Henderson, Russell Ecob, Daniel Wight, Charles Abraham, What explains between-school differences in rates of smoking?, BMC Public Health, 10.1186/1471-2458-8-218, 8, 1, (2008).
- Fernando Althabe, Pierre Buekens, Eduardo Bergel, José M. Belizán, Marci K. Campbell, Nancy Moss, Tyler Hartwell, Linda L. Wright, A Behavioral Intervention to Improve Obstetrical Care, New England Journal of Medicine, 10.1056/NEJMsa071456, 358, 18, (1929-1940), (2008).
- B. Giraudeau, P. Ravaud, A. Donner, Sample size calculation for cluster randomized cross‐over trials, Statistics in Medicine, 10.1002/sim.3383, 27, 27, (5578-5585), (2008).
- Peter C. Austin, A critical appraisal of propensity‐score matching in the medical literature between 1996 and 2003, Statistics in Medicine, 10.1002/sim.3150, 27, 12, (2037-2049), (2007).
- Robert J. Glynn, M Alan Brookhart, Margaret Stedman, Jerry Avorn, Daniel H. Solomon, Design of Cluster-Randomized Trials of Quality Improvement Interventions Aimed at Medical Care Providers, Medical Care, 10.1097/MLR.0b013e318070c0a0, 45, Suppl 2, (S38-S43), (2007).
- M. Ashraf Chaudhary, Lawrence H. Moulton, A SAS macro for constrained randomization of group-randomized designs, Computer Methods and Programs in Biomedicine, 10.1016/j.cmpb.2006.04.011, 83, 3, (205-210), (2006).
- Mirjam Moerbeek, Power and money in cluster randomized trials: when is it worth measuring a covariate?, Statistics in Medicine, 10.1002/sim.2297, 25, 15, (2607-2617), (2005).
- Donald Hoover, Design and Analysis of Group (or Neighborhood) Level Urban Studies, Handbook of Urban Health, 10.1007/b104167, (277-294), (2005).
- Charles Abraham, Marion Henderson, Geoff Der, Cognitive impact of a research-based school sex education programme, Psychology & Health, 10.1080/08870440410001722921, 19, 6, (689-703), (2004).
- J. D. Lewsey, Comparing completely and stratified randomized designs in cluster randomized trials when the stratifying factor is cluster size: a simulation study, Statistics in Medicine, 10.1002/sim.1665, 23, 6, (897-905), (2004).
- Jim Todd, Lucy Carpenter, Xianbin Li, Jessica Nakiyingi, Ron Gray, Richard Hayes, The effects of alternative study designs on the power of community randomized trials: evidence from three studies of human immunodeficiency virus prevention in East Africa, International Journal of Epidemiology, 10.1093/ije/dyg150, 32, 5, (755-762), (2003).
- Donald R. Hoover, Clinical trials of behavioural interventions with heterogeneous teaching subgroup effects, Statistics in Medicine, 10.1002/sim.1139, 21, 10, (1351-1364), (2002).
- Helen Moore, Carolyn D. Summerbell, Andy Vail, Darren C. Greenwood, Ashley J. Adamson, The design features and practicalities of conducting a pragmatic cluster randomized trial of obesity management in primary care, Statistics in Medicine, 10.1002/1097-0258(20010215)20:3<331::AID-SIM795>3.0.CO;2-K, 20, 3, (331-340), (2001).
