Abstract
It is becoming increasingly common for health researchers to consider randomizing intact social units (e.g. families, schools, communities) rather than independent individuals in experimental trials. Reasons are diverse, but include administrative convenience, a desire to reduce the effect of treatment contamination and the need to avoid ethical issues, which might otherwise arise. Dependencies among cluster members typical of such designs must be considered when determining sample size and analyzing the resulting data. Failure to adjust standard statistical methods for within-cluster dependencies may result in severely underpowered studies and in spuriously elevated Type I error rates. The purpose of this article is to review the key issues in the design and analysis of cluster randomization trials. These ideas will be illustrated using data from several recently completed studies.
References
- 1 Abdeljaber, M. H., Monto, A. S., Tilden, R. L., Schork, M. A. & Tarwotjo, I. (1991). The impact of vitamin A supplementation on morbidity: a randomized community intervention trial, American Journal of Public Health 81, 1654–1656.
- 2 Armitage, P. & Berry, G. (1994). Statistical Methods in Medical Research, 3rd Ed. Blackwell Scientific Publications, Oxford.
- 3 Ashby, M., Neuhaus, J. M., Hauck, W. W., Bacchetti, P., Heilbron, D. C., Jewell, N. P., Segal, M. R. & Fusaro, R. E. (1992). An annotated bibliography of methods for analyzing correlated categorical data, Statistics in Medicine 11, 67–99.
- 4 Bass, M. J., McWhinney, I. R. & Donner, A. (1986). Do family physicians need medical assistants to detect and manage hypertension?, Canadian Medical Association Journal 134, 1247–1255.
- 5 Begg, C., Cho, M., Eastwood, S., Horton, R., Moher, D., Olkin, I., Pitkin, R., Rennie, D., Schulz, K. F., Simel, D. & Stroup, D. F. (1996). Improving the quality of reporting of randomized controlled trials, The CONSORT statement, Journal of the American Medical Association 276, 637–639.
- 6 Blum, D. & Feachem, R. G. (1983). Measuring the impact of water supply and sanitation investments on diarrhoeal diseases: problems of methodology, International Journal of Epidemiology 12, 357–365.
- 7 Breslow, N. E. & Day, N. E. (1987). Statistical Methods in Cancer Research, Volume II: The Design and Analysis of Cohort Studies. International Agency for Research on Cancer, Lyon.
- 8 Brook, R. H., Ware, J. E., Jr, Rogers, W. H., Keeler, E. B., Davies, A. R., Donald, C. A., Goldberg, G. A., Lohr, K. N., Masthay, P. C. & Newhouse, J. P. (1983). Does free care improve adults' health? Results from a randomized controlled trial, New England Journal of Medicine 309, 1426–1434.
- 9
Brookmeyer, R. &
Chen, Y. -Q.
(1998).
Person-time analysis of paired community intervention trials when the number of communities is small,
Statistics in Medicine
17,
2121–2132.
10.1002/(SICI)1097-0258(19980930)17:18<2121::AID-SIM907>3.0.CO;2-S CAS PubMed Web of Science® Google Scholar
- 10 Bryk, A. S. & Raudenbush, S. W. (1992). Hierarchical Linear Models: Application and Data Analysis Methods. Sage Publications, Newbury Park.
- 11 Chalmers, T. C. & Schroeder, B. (1979). Controls in journal articles, New England Journal of Medicine 301, 1293.
- 12 Cochran, W. G. (1953). Sampling Techniques, 2nd Ed. Wiley, New York.
- 13 COMMIT Research Group. (1995). Community Intervention Trial for Smoking Cessation (COMMIT): I. Cohort results from a four-year community intervention, American Journal of Public Health 85, 183–192.
- 14 Comstock, G. W. (1978). Uncontrolled ruminations on modern controlled trials, American Journal of Epidemiology 108, 81–84.
- 15 Cornfield, J. (1978). Randomization by group: a formal analysis, American Journal of Epidemiology 108, 100–102.
- 16 Diggle, P. J., Liang, K. Y. & Zeger, S. L. (1994). Analysis of Longitudinal Data. Oxford University Press, Oxford.
- 17 Donner, A. (1987). Statistical methodology for paired cluster designs, American Journal of Epidemiology 126, 972–979.
- 18 Donner, A. (1998). Some aspects of the design and analysis of cluster randomization trials, Applied Statistics 47, 95–114.
- 19 Donner, A. & Donald, A. (1988). The statistical analysis of multiple binary measurements, Journal of Chronic Diseases 41, 899–905.
- 20 Donner, A. & Klar, N. (2000). Design and Analysis of Cluster Randomization Trials in Health Research. Arnold, London.
- 21 Donner, A., Birkett, N. & Buck, C. (1981). Randomization by cluster: sample size requirements and analysis, American Journal of Epidemiology 114, 906–914.
- 22 Donner, A., Brown, K. S. & Brasher, P. (1990). A methodological review of non-therapeutic intervention trials employing cluster randomization, 1979–1989, International Journal of Epidemiology 19, 795–800.
- 23 Dunn, O. J. & Clark, V. A. (1987). Applied Statistics: Analysis of Variance and Regression, 2nd Ed. Wiley, New York.
- 24 Edwards, S. J. L., Braunholtz, D. A., Lilford, R. J. & Stevens, A. J. (1999). Ethical issues in the design and conduct of cluster randomized controlled trials, British Medical Journal 318, 1407–1409.
- 25 Family Heart Study Group (1994). The British Family Heart Study: its design and methods, and prevalence of cardiovascular risk factors, British Journal of General Practice 44, 62–67.
- 26 Ferebee, S. H., Mount, F. W., Murray, F. J. & Livesay, V. T. (1963). A controlled trial of isoniazid prophylaxis in mental institutions, American Review of Respiratory Disease 88, 161–175.
- 27 Ferron, J. (1997). Moving between hierarchical modeling notations, Journal of Education and Behavioral Statistics 22, 119–123.
- 28 Fontanet, A. L., Saba, J., Chandelying, V., Sakondhavat, C., Bhiraleus, P., Rugpao, S., Chongsomchai, C., Kiriwat, O., Tovanabutra, S., Dally, L., Lange, J. M. & Rojanapithayakorn, W. (1998). Protection against sexually transmitted diseases by granting sex workers in Thialand the choice of using the male or female condom: results from a randomized controlled trial, AIDS 12, 1851–1859.
- 29 Freedman, L. S., Gail, M. H., Green, S. B. & Corle, M. S. for the COMMIT Study Group (1997). The efficiency of the matched pairs design of the Community Intervention Trial for Smoking Cessation (COMMIT), Controlled Clinical Trials 18, 131–139.
- 30
Gail, M. H.,
Mark, S. D.,
Carroll, R. J.,
Green, S. B. &
Pee, D.
(1996).
On design considerations and randomization-based inference for community intervention trials,
Statistics in Medicine
15,
1069–1092.
10.1002/(SICI)1097-0258(19960615)15:11<1069::AID-SIM220>3.0.CO;2-Q CAS PubMed Web of Science® Google Scholar
- 31 Ghana VAST Study Team (1993). Vitamin A supplementation in northern Ghana: effects on clinic attendances, hospital admissions, and child mortality, Lancet 342, 7–12.
- 32 Gillum, R. F., Williams, P. T. & Sondik, E. (1980). Some consideration for the planning of total-community prevention trials. When is sample size adequate?, Journal of Community Health 5, 270–278.
- 33 Glanz, K., Rimer, B. K. & Lerman, C. (1996). Ethical issues in the design and conduct of community-based intervention studies, in Ethics and Epidemiology, S. S. Coughlin & T. L. Beauchamp, eds. Oxford University Press, Oxford, Chapter 8.
- 34 Glasgow, R. E., Lichtenstein, E., Wilder, D., Hall, R., McRae, S. G. & Liberty, B. (1995). The tribal tobacco policy project: working with Northwest Indian tribes on smoking policies, Preventive Medicine 24, 434–440.
- 35 Goldstein, H. (1995). Multi-level Statistical Models, 2nd Ed. Arnold, London.
- 36 Grosskurth, H., Mosha, F., Todd, J., Mwijarubi, E., Klokke, A., Senkoro, K., Mayaud, P., Changalucha, J., Nicoll, A., ka-Gina, G., Newell, J., Mugeke, K., Mobey, D. & Hayes, R. (1995). Impact of improved treatment of sexually transmitted diseases on HIV infection in rural Tanzania: randomized controlled trial, Lancet 346, 530–536.
- 37 Hansen, M. H. & Hurwitz, W. N. (1942). Relative efficiencies of various sampling units in population inquiries, Journal of the American Statistical Association 37, 89–94.
- 38 Hayes, R. J. & Bennett, S. (1999). Simple sample size calculation for cluster-randomization trials, International Journal of Epidemiology 28, 319–326.
- 39 Herrera, M. G., Nestel, P., El Amin, A., Fawzi, W. W., Muhammad, K. A. & Weld, L. (1992). Vitamin A supplementation and child survival, Lancet 340, 267–271.
- 40 Hopkins, K. D. (1982). The unit of analysis: group means versus individual observations, American Educational Research Journal 19, 5–18.
- 41 Hsieh, F. Y. (1988). Sample size formulae for intervention studies with the cluster as unit of randomization, Statistics in Medicine 8, 1195–1201.
- 42 Huber, P. J. (1965). The behavior of maximum likelihood estimates under nonstandard conditions, in Proceedings of the Fifth Berkeley Symposium in Mathematical Statistics and Probability, L. M. Lecam & J. Neyman, eds. University of California Press, Berkeley, pp. 221–233.
- 43 Kish, L. (1965). Survey Sampling. Wiley, New York.
- 44
Klar, N. &
Donner, A.
(1997).
The merits of matching in community intervention trials,
Statistics in Medicine
16,
1753–1764.
10.1002/(SICI)1097-0258(19970815)16:15<1753::AID-SIM597>3.0.CO;2-E CAS PubMed Web of Science® Google Scholar
- 45 Koepsell, T. D. (1998). Epidemiologic issues in the design of community intervention trials, in Applied Epidemiology, Theory to Practice, R. C. Brownson & D. B. Petitti, eds. Oxford University Press, New York, Chapter 6, pp. 177–211.
- 46 Koepsell, T. D., Martin, D. C., Diehr, P. H., Psaty, B. M., Wagner, E. H., Perrin, E. B. & Cheadle, A. (1991). Data analysis and sample size issues in evaluations of community-based health promotion and disease prevention programs: a mixed-model analysis of variance approach, Journal of Clinical Epidemiology 44, 701–713.
- 47 Kreft, I. G. G. (1998). An illustration of item homogeneity scaling and multilevel analysis techniques in the evaluation of drug prevention programs, Evaluation Review 22, 46–77.
- 48
Lasater, T. M.,
Becker, D. M.,
Hill, M. N. &
Gans, K. M.
(1997).
Synthesis of findings and issues from religious-based cardiovascular disease prevention trials,
Annals of Epidemiology
S7,
S46–S53.
10.1016/S1047-2797(97)80007-5 Google Scholar
- 49 Liang, K. -Y. (1985). Odds ratio inference with dependent data, Biometrika 72, 678–682.
- 50 Liang, K. -Y. & Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models, Biometrika 73, 13–22.
- 51 Littell, R. C., Milliken, R. C., Stroup, G. A., Walter, W. & Wolfinger, R. D. (1996). SAS System for Mixed Models. SAS Institute Inc., Cary.
- 52 Luepker, R. V., Perry, C. L., McKinlay, S. M., Nader, P. R., Parcel, G. S., Stone, E. J., Feldman, H. A., Johnson, C. C., Kelder, S. H. & Wu, M. for the CATCH Collaborative Group (1996). Outcomes of a field trial to improve children's dietary patterns and physical activity, Journal of the American Medical Association 275, 768–776.
- 53 Martin, D. C., Diehr, P., Perrin, E. B. & Koepsell, T. D. (1993). The effect of matching on the power of randomized community intervention studies, Statistics in Medicine 12, 329–338.
- 54 Medical Research Council (1948). Streptomycin treatment of pulmonary tuberculosis, British Medical Journal ii, 769–782.
- 55 Murray, D. M., Perry, C. L., Griffin, G., Harty, K. C., Jacobs, D. R. Jr, Schmid, L., Daly, K. & Pallonen, U. (1992). Results from a statewide approach to adolescent tobacco use prevention, Preventive Medicine 21, 449–472.
- 56 Murray, J. P., Stam, A. & Lastovicka, J. L. (1993). Evaluating an anti-drinking and driving advertising campaign with a sample-survey and time series intervention analysis, Journal of the American Statistical Association 88, 50–56.
- 57 Neuhaus, J. M. (1992). Statistical methods for longitudinal and clustered designs with binary responses, Statistical Methods in Medical Research 1, 249–273.
- 58 Newhouse, J. P. & the Insurance Experiment Group (1993). Free for All? Lessons from the Rand Health Insurance Experiment: A Rand Study. Harvard University Press, Cambridge.
- 59 Payment, P., Richardson, L., Siemiatycki, J., Dewar, R., Edwardes, M. & Franco, E. (1991). A randomized trial to evaluate the risk of gastrointestinal disease due to consumption of drinking water meeting microbiological standards, American Journal of Public Health 81, 703–708.
- 60 Pocock, S. J. (1983). Clinical Trials. A Practical Approach. Wiley, New York, pp. 17–18.
- 61 Rao, J. N. K. & Scott, A. J. (1992). A simple method for the analysis of clustered binary data, Biometrics 48, 577–585.
- 62
Rao, J. N. K. &
Scott, A. J.
(1999).
A simple method for analysing overdispersion in clustered Poisson data,
Statistics in Medicine
18,
1373–1385.
10.1002/(SICI)1097-0258(19990615)18:11<1373::AID-SIM133>3.0.CO;2-F CAS PubMed Web of Science® Google Scholar
- 63 Ray, W. A., Taylor, J. A., Meador, K. G., Thapa, P. B., Brown, A. K., Kajihara, H. K., Davis, C., Gideon, P. & Griffin, M. R. (1997). A randomized trial of a consultation service to reduce falls in nursing homes, Journal of the American Medical Association 278, 557–562.
- 64
Searle, S. R.,
Casella, G. &
McCulloch, C. E.
(1992).
Variance Components.
Wiley,
New York.
10.1002/9780470316856 Google Scholar
- 65 Segal, M. R. & Neuhaus, J. M. (1993). Robust inference for multivariate survival data, Statistics in Medicine 12, 1019–1031.
- 66 Segal, M. R., Neuhaus, J. M. & James, I. R. (1997). Dependence estimation for marginal models of multivariate survival data, Lifetime Data Analysis 3, 251–268.
- 67 Shao, J. (1990). Ordinary and weighted least-squares estimators, Canadian Journal of Statistics 18, 327–336.
- 68 Siddiqui, O., Hedeker, D., Flay, B. & Hu, F. B. (1996). Intraclass correlation in a school-based smoking prevention study. Outcome and mediating variables, by sex and ethnicity, American Journal of Epidemiology 144, 425–433.
- 69 Siddiqui, O., Mott, J., Anderson, T. & Flay, B. (1999). The application of Poisson random-effects regression models to the analyses of adolescents' current level of smoking, Preventive Medicine 29, 91–101.
- 70 Simpson, J. M., Klar, N. & Donner, A. (1995). Accounting for cluster randomization: a review of primary prevention trials, 1990 through 1993, American Journal of Public Health 85, 1378–1382.
- 71 Smith, P. J., Moffatt, M. E. K., Gelskey, S. C., Hudson, S. & Kaita, K. (1997). Are community health interventions evaluated appropriately? A review of six journals, Journal of Clinical Epidemiology 50, 137–146.
- 72 Sommer, A., Tarwotjo, I., Djunaedi, E., West, K. P. Jr, Loeden, A. A., Tilden, M. L. & the ACEH Study Group. (1986). Impact of vitamin A supplementation on childhood mortality, Lancet, 24 May, 1169–1173.
- 73 Strasser, T., Jeanneret, O. & Raymond, L. (1987). Ethical aspects of prevention trials, in Ethical Dilemmas in Health Promotion, S. Doxiadis, ed. Wiley, New York, Chapter 15.
- 74
Verbeke, G.
(1997).
Linear mixed models for longitudinal data, in
Linear Mixed Models in Practice, A SAS-Oriented Approach,
G. Verbeke &
G. Molenberghs, eds.
Springer-Verlag,
New York, Chapter 3.
10.1007/978-1-4612-2294-1 Google Scholar
- 75 Walsh, J. E. (1947). Concerning the effect of intraclass correlation on certain significance tests, Annals of Mathematical Statistics 18, 88–96.
- 76 Walsh, M. W., Hilton, J. F., Masouredis, C. M., Gee, L., Chesney, M. A. & Ernster, V. L. (1999). Spit tobacco cessation intervention for college athletes: results after one year, American Journal of Public Health 89, 228–234.
- 77 Ware, J. H. & Liang, K. Y. (1996). The design and analysis of longitudinal studies: a historical perspective, in Advances in Biometry, P. Armitage & H. A. David, eds. Wiley, New York, Chapter 17, pp. 339–362.
- 78 Williams, R. L. (1995). Product-limit survival functions with correlated survival times, Data Analysis 1, 171–186.
- 79 World Medical Association (1997). World Medical Association Declaration of Helsinki, 1996. Republished in the Journal of the American Medical Association 277, 925–926.