As as example of a cluster randomized trial, we describe the Child and Adolescent Trial for Cardiovascular Health (CATCH). Details concerning the design of this trial are reported in Zucker et al. (1995), and the main trial results are reported in Luepker et al. (1996). The CATCH study investigated a school-based educational and environmental intervention aimed at promoting heart-healthy habits in elementary school children.
Because the intervention was implemented the school level, a cluster randomization design was mandatory.
The trial involved randomization of 96 schools, of which 40 were assigned to the control group C, 28 were assigned to receive the school-based intervention S, and 28 were assigned to receive the school-based intervention plus a supplementary family-based intervention (S + F). The main trial comparison was that between the combination of S and S + F groups and the control group.
The intervention was aimed at changing a number of behaviors, principally fat and salt consumption and physical exercise. The primary trial endpoint was taken to be serum total cholesterol, because it was felt that dietary and exercise habit measures would be susceptible to reporting bias, whereas cholesterol would be free of such bias but responsive enough to reflect true diet and exercise changes. Various diet, exercise, and other endpoints were included as secondary endpoints.
The primary study cohort was defined to be those students who underwent a baseline cholesterol measurement. Provisions were made to track outmigrating students and to attempt to measure cholesterol in these students at the end of the study.
The sample size was determined by the following slightly extended version of the formula (7):
J = [CSy(1 - y)]-1[1 + (S - 1)p, + (C - 1)3^] ^ +/b)V (9)
where C denotes the number of classrooms in a school, S denotes the number of students per classroom with available data, p1 denotes the within-classroom correlation, p2 denotes the within-school correlation for students in different classrooms in the same school, and g denotes the proportion of clusters assigned to the intervention arm.
The CATCH calculations assumed 3-4 classrooms per school (3.5 on average) and 17 students with available data per class. On the basis of past studies the standard deviation r was estimated to be 28 mg/dl. The correlations p1 and p2 were estimated on the basis of a variance components analysis of a small data set on cholesterol levels among schoolchildren in a prior observational study conducted by one of the study centers in CATCH. The estimates were p1 = 0.023 and p2 = 0.003. The projected treatment difference on cholesterol (S and S + Fversus C) was determined to be 5.1 mg/dl. A conservative adjustment factor was incorporated to account for possible missing data bias; see Zucker et al. (1995) for details. The effect of the adjustment was to reduce the difference d to be detected from 5.1 mg/dl to an effective difference, after the adjustment, of 2.9 mg/dl. The intervention (S + F and S) to control C allocation ratio was 7:5 (to enhance the power of the S + F versus S comparison), so that y = 0.583. Substituting these parameters into the formula (9) yields a sample size requirement of 102 schools total for 90% power at the two-sided 0.05 level. Based on administrative considerations, the final sample size was taken to be 96 schools total.
The sample size calculation incorporated both school and classroom effects because at the design stage it was felt important to do so. As regards the analysis, with school-level assignment the randomization theory of statistical testing requires school to be the primary unit of analysis. However, the theory does not require incorporation of classroom as a factor for the analysis to be valid in terms of type I error. In fact, the final CATCH analysis did not include classroom as a factor.
The serum cholesterol results were analyzed using a mixed linear model of the form (3), with experimental arm, CATCH center, baseline cholesterol level, and a number of relevant covariates as fixed effect terms and school as a random effect. The post-study mean cholesterol levels were 168.3 mg/dl for treatment (S and S + F) and 169.5 mg/dl for control; the treatment-control difference was not statistically significant. On the other hand, nominally statistically significant though modest differences were found on dietary and physical activity measures. As possible explanations for the negative finding on cholesterol, the investigators point up the smaller than projected dietary changes and the effects of puberty.
In regard to cooperation with study procedures, the percentage of students in the study schools who had a baseline cholesterol measurement and were entered into the primary CATCH cohort was 60% as opposed to the projected 80%. Among the students in the primary cohort, 72% continued in CATCH schools up to the end of the study. Of these, 90% underwent the final cholesterol measurement. Of the students who migrated out of CATCH schools, 50% underwent the final cholesterol measurement. Thus, overall, 79% of the students in the primary CATCH cohort had a final cholesterol measurement, representing a data completeness level not too far from the projected 85%.
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