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1 St. Luke’s Hospital and Health Network, Bethlehem, Pa
CORRESPONDING AUTHOR: James F. Reed III, PhD, Research Institute, St. Luke’s Hospital and Health Network, 801 Ostrum Street, Bethlehem, PA 18015, ReedJ{at}slhn.org
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONCLUSTER RANDOMIZED TRIALS: 3...DISCUSSIONREFERENCES |
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Key Words: Clinical trials • cluster analysis • epidemiologic studies
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONCLUSTER RANDOMIZED TRIALS: 3...DISCUSSIONREFERENCES |
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Analytic methods specific to randomized cluster trials include estimating the ICC and computing adjustments to the Pearson chi-square as proposed by Brier7 (
2b), Rosner and Milton8 (2rm), and Donner and Donald9 (2dd). In addition, Rao and Scott10 proposed 2 statistics that adjust for the clustering design effect (2rs and 2prs). Details of each of these methods are included in the Appendix 1 (which is available online as supplemental data at http://www.annfammed.org/cgi/content/full/2/3/201/DC1).
The purpose of this article is to provide an introduction to the problem of analyzing binary data from clustered data in clinical research. A FORTRAN program in a executable format that produces the statistics outlined in this article is available from the author on request.*
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CLUSTER RANDOMIZED TRIALS: 3 EXAMPLES |
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TOPABSTRACTINTRODUCTIONCLUSTER RANDOMIZED TRIALS: 3...DISCUSSIONREFERENCES |
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Example 1
The first example uses hypothetical data to compare the effectiveness of an intervention targeting physician care of their diabetic patients. Suppose that 17 primary care providers were provided baseline information and agreed to participate in an intervention designed to improve the care delivered to patients with diabetes. Twelve primary care providers were also provided baseline information and chose not to participate in the intervention program. The question to be assessed is the effectiveness of the intervention program. In this example, the physician is the unit of analysis, and the patient is considered nested within physicians. For each physician the number of patients that had a documented foot examination (numerator), and the total number of patient records abstracted (denominator) were recorded as follows:
For the intervention group: {30/30, 22/22, 19/19, 24/30, 28/30, 26/30, 29/30, 28/30, 27/30, 29/30, 24/30, 21/30, 14/22, 16/22, 22/32, 27/31, 16/20}.
For the nonintervention group: {14/16, 8/11, 29/35, 9/10, 6/9, 8/11, 4/6, 7/12, 7/25, 4/25, 4/23, 3/24}.
Using the Pearson chi-square, the test statistic and P value (2 = 99.58, P = .0001) indicate a significant difference between intervention group and nonintervention group compliance rates. The conclusion would be that the intervention was effective. The estimated ICC (r) is 0.2051, however. Statistics that adjust the Pearson’s chi-square (2b = 16.17, P = .0001; 2dd = 17.92, P = .0001; and 2rm = 16.17, P = .0001) all indicate a significant intervention effect. The 2 methods that adjust for the design or clustering effect (2rs = 17.13, P = .0001; and 2prs = 26.66, P = .0001) also indicate a significant intervention effect. The effect of the large ICC (0.2051) affects the Pearson chi-square. Had the intervention effect not been as large, one would have incorrectly concluded that there was an intervention effect.
Example 2
In the second example, the same set of physicians is used to assess the proportion of patients that had an annual HbA1c indicator. The number of patients that met this quality indicator (numerator) and the total number of patient records abstracted (denominator) were recorded as follows:
For the intervention group: {29/30, 22/22, 11/19, 29/30, 29/30, 27/30, 28/30, 29/30, 23/30, 26/30, 30/30, 29/30, 20/22, 20/22, 18/32, 27/31, 15/20}.
For the nonintervention group: {14/16, 10/11, 27/35, 8/10, 9/9, 7/11, 4/6, 5/12, 17/25, 23/25, 19/23, 18/24}.
Again, if one were to use the Pearson chi-square, the test statistic and P value (2 = 11.7694, P = .0007) would indicate a significant difference between the intervention group and nonintervention group compliance rates. The conclusion would be that the intervention was effective. The estimated ICC is 0.0938. Statistics that adjust the Pearson’s chi-square (2b = 3.51, P = .0579; 2dd = 3.81, P = .0513; and 2rm = 3.51, P = .0579) all indicate a non-significant intervention effect. The 2 methods that adjust for the design or clustering effect (2rs = 4.22, P = .0377; and 2prs = 1.16, P = .2812) contradict one another. Cluster-specific analytic methods use the cluster as the unit of analysis and have the same consequences as many studies (eg, smaller sample sizes—number of physician practices as well as the number of patients within each physician practice—have a tendency to reduce the power of the study). In this example, a relatively small ICC can affect the analysis of randomized cluster trials.
Example 3
The third hypothetical example again uses the same set of physicians in assessing the annual lipid profile indicator. The number of patients that met this quality indicator (numerator) and the total number of patient records abstracted (denominator) were recorded as follows:
For the intervention group: {21/30, 13/22, 10/19, 24/30, 13/30, 14/30, 18/30, 24/30, 17/30, 22/30, 20/30, 21/30, 14/22, 19/22, 14/32, 25/31, 14/20}
For the nonintervention group: {11/16, 7/11, 23/35, 7/10, 6/9, 7/11, 4/6, 6/12, 17/25, 20/25, 17/23, 14/24}
First look at the ICC (r = 0.0141). I would not expect that the magnitude of this ICC to influence the analysis. The Pearson chi-square (2 = 0.3637, P = .5519) indicates that there is no difference between the intervention and nonintervention physician groups in the proportion of patients that have completed an annual lipid profile. When one has a randomized cluster design, however, the appropriate analysis should be reflected in the analysis. Adjustments to the Pearson chi-square (2b = 0.27, P = .6088; 2dd = 0.28, P = .6038 ; and 2rm = 0.27, P = .6088) all agree as expected. The statistics that use the design effect also concur (2rs = 0.35, P = .5624; and 2prs = 0.09, P = .7528). There is no apparent intervention effect between the 2 physician groups regarding the proportion of patients that have completed an annual lipid profile.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONCLUSTER RANDOMIZED TRIALS: 3...DISCUSSIONREFERENCES |
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For some interventions, it may be necessary to randomize clusters rather than individuals. For instance, in a typical randomized cluster design, randomizing the physician rather than the patient prevents contamination of the intervention, because patient management by a physician tends to be the same from patient to patient. Standard statistical methods are not appropriate when analyzing cluster randomized trials. There is no consensus, however, as to which analytical approach should be used to analyze all cluster randomized trials.3
Which analytic method is preferred when analyzing binary responses from a randomized cluster trial? Adjustments to the Pearson chi-square are based on the clustering and homogeneity of design effects for the treatment groups, are computationally friendly, and provide excellent design-specific alternatives. Their behavior in relatively small numbers of clusters within a treatment group, however, may be problematic. Analysis-of-variance methods are simple and may be used in multifactorial designs. A disadvantage is that they do not stabilize the variances—a necessary requirement for analysis of variance. I prefer the adjustments to the Pearson chi-square statistic and recommend adapting the analytical plan to the study design by analyzing binomial responses from cluster trials using cluster-specific methods.
Cluster-randomized trials represent an important experimental design. They are particularly relevant when evaluating interventions at the clinic level, with physicians, or in physician group practices. Serious design and analysis implications abound, and the use of clusters as the unit of randomization must be justified. Sample sizes, the number of individuals within the cluster variable, and the number of clusters usually need to be larger, and the analysis must certainly allow for the cluster design.1
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ACKNOWLEDGMENTS |
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FOOTNOTES |
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* An executable program that produces cluster-specific statistics 2b, 2dd, 2rm, 2rs, and 2prs and sample data are available from the author (e-mail only). The input file is in free-format form (treatment, group, outcome), where the treatment variable is either a 1 or 2, the group variable identifies the cluster number (1, 2, . . ., k), and the outcome variable is binomial (1 = success, 0 = failure). Data must be in an integer format. 
Received for publication February 12, 2003. Revision received March 4, 2003. Accepted for publication March 24, 2003.
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TOPABSTRACTINTRODUCTIONCLUSTER RANDOMIZED TRIALS: 3...DISCUSSIONREFERENCES |
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