zbMATH — the first resource for mathematics

Comparison of three-level cluster randomized trials using quantile dispersion graphs. (English) Zbl 07269660
Summary: The purpose of this article is to evaluate and compare several three-level cluster randomized designs on the basis of their power functions. The power function of cluster designs depends on the intracluster correlations (ICCs), which are generally unknown at the planning stage. Thus, to compare these designs a prior knowledge of the ICCs is required. Three interval estimation methods are proposed for assigning joint confidence intervals to the two ICCs (corresponding to each cluster level). A detailed simulation study comparing the confidence intervals attained by the different techniques is given. The technique of quantile dispersion graphs is used for comparing the three-level cluster designs. For a given design, quantiles of the power function, are obtained for various effect sizes. These quantiles are functions of the unknown ICC coefficients. To address the dependence of the quantiles on the correlations, a \(100(1 - \alpha)\%\) confidence region is computed, and used as a parameter space. A three-level nested data set collected by the University of Michigan to study various school reforms on the achievements of students is used to illustrate the proposed methodology.
62 Statistics
Full Text: DOI
[1] B.D. Burch and I.R. Harris, Bayesian estimators of the intraclass correlation coefficient in the one-way random effects model, Commun. Stat. - Theory Methods 28 (1999), pp. 1247-1272. doi: 10.1080/03610929908832356 · Zbl 0941.62029
[2] J. Cohen, Statistical Power Analysis for the Behavioral Sciences, 2nd ed., Lawrence Erlbaum Associates, Hillsdale, 1988. · Zbl 0747.62110
[3] M. Daniels, A prior for the variance components in hierarchical models, Can. J. Stat. 27 (1999), pp. 569-580. doi: 10.2307/3316112 · Zbl 0942.62026
[4] A. Donner, Some aspects of the design and analysis of cluster randomization trials, Appl. Stat. 48 (1998), pp. 95-113.
[5] A. Donner and N. Klar, Statistical considerations in the design and analysis of community intervention trials, J. Clin. Epidemiol. 49 (1996), pp. 435-439. doi: 10.1016/0895-4356(95)00511-0
[6] A. Donner and N. Klar, Design and Analysis of Cluster Randomised Trials in Health Research, Arnold, London, 2000.
[7] Z. Feng and J.E. Grizzle, Correlated binomial variates: Properties of estimator of intraclass correlation and its effect on sample size calculation, Stat. Med. 11 (1992), pp. 1607-1614. doi: 10.1002/sim.4780111208
[8] A. Gelman, Prior distributions for variance parameters in hierarchical models, Bayesian Anal. 1 (2006), pp. 515-534. doi: 10.1214/06-BA117A · Zbl 1331.62139
[9] F.A. Graybill, An Introduction to Linear Statistical Model, Vol. 1. McGraw-Hill, New York, 1961. · Zbl 0121.35605
[10] D.A. Harville and A.P. Fenech, Confidence intervals for a variance ratio, or for heritability, in an unbalanced mixed linear model, Biometrics 41 (1985), pp. 137-152. doi: 10.2307/2530650 · Zbl 0607.62031
[11] M. Heo, Y. Kim, X. Xue, and Y. Mimi, Sample size requirement to detect an intervention effect at the end of follow-up in a longitudinal cluster randomized trial, Stat. Med. 29 (2009), pp. 382-390.
[12] M. Heo and A.C. Leon, Statistical power and sample size requirements for three level hierarchical cluster randomized trials, Biometrics 64 (2008), pp. 1256-1262. doi: 10.1111/j.1541-0420.2008.00993.x · Zbl 1151.62084
[13] B.C. Jung, A. Khuri, and J. Lee, Comparison of designs for the three-fold nested random model, J. Appl. Stat. 35 (2008), pp. 701-715. doi: 10.1080/02664760801924079 · Zbl 1147.62352
[14] S.M. Kerry and J.M. Bland, Unequal cluster sizes for trials in English and welsh general practice: Implications for sample size calculations, Stat. Med. 20 (2001), pp. 377-390. doi: 10.1002/1097-0258(20010215)20:3<377::AID-SIM799>3.0.CO;2-N
[15] A.I. Khuri, Simultaneous confidence intervals for functions of variance components in random models, J. Am. Statist. Assoc. 76 (1981), pp. 878-885. doi: 10.1080/01621459.1981.10477736
[16] A.I. Khuri, Quantile dispersion graphs for analysis of variance estimates of variance components, J. Appl. Stat. 24 (1997), pp. 711-722. doi: 10.1080/02664769723440
[17] A. Khuri and J. Lee, A graphical approach for evaluating and comparing designs for nonlinear models, Comput. Stat. Data Anal. 27 (1998), pp. 433-443. doi: 10.1016/S0167-9473(98)00016-4 · Zbl 1042.62501
[18] A. Khuri and S. Mukhopadhyay, GLM Designs: The Dependence on Unknown Parameters Dilemma in Response Surface Methodology and Related Topics, World Scientific, Singapore, 2006, pp. 203-223.
[19] S. Lake, E. Kammann, N. Klar, and R. Betensky, Sample size re-estimation in cluster randomization trials, Stat. Med. 21 (2002), pp. 1337-1350. doi: 10.1002/sim.1121
[20] P.C. Lambert, A.J. Sutton, P.R. Burton, K.R. Abrams, and D.R. Jones, How vague is vague? A simulation study of the impact of the use of vague prior distributions in MCMC using WinBUGS, Stat. Med. 24 (2005), pp. 2401-2428. doi: 10.1002/sim.2112
[21] A.K. Manatunga, M.G. Hudgens, and S. Chen, Sample size estimation in cluster randomized studies with varying cluster size, Biom. J. 1 (2001), pp. 75-86. doi: 10.1002/1521-4036(200102)43:1<75::AID-BIMJ75>3.0.CO;2-N · Zbl 0997.62094
[22] S. Mukhopadhyay and A.I. Khuri, Comparison of designs for generalized linear models under model misspecification, Statist. Methodol. 9 (2012), pp. 285-304. doi: 10.1016/j.stamet.2011.08.004 · Zbl 1365.62297
[23] S. Mukhopadhyay and S.W. Looney, Quantile dispersion graphs to compare the efficiencies of cluster randomized designs, J. Appl. Stat. 36 (2009), pp. 1293-1305. doi: 10.1080/02664760902914508
[24] K.S. Robinson and A.I. Khuri, Quantile dispersion graphs for evaluating and comparing designs for logistic regression models, Comput. Stat. Data Anal. 43 (2003), pp. 47-62. doi: 10.1016/S0167-9473(02)00182-2 · Zbl 1375.62012
[25] S.R. Searle, Linear Models, Vol. 1. Wiley, New York, 1971. · Zbl 0218.62071
[26] D. Spiegelhalter, Bayesian methods for cluster randomized trials with continuous responses, Stat. Med. 20 (2001), pp. 435-452. doi: 10.1002/1097-0258(20010215)20:3<435::AID-SIM804>3.0.CO;2-E
[27] S. Teerenstra, B. Lu, J.S. Preisser, T. van Achterberg, and G.F. Borm, Sample size considerations for gee analyses of three-level cluster randomized trials, Biometrics 66 (2010), pp. 1230-1237. doi: 10.1111/j.1541-0420.2009.01374.x · Zbl 1233.62190
[28] R.M. Turner, S.G. Thompson, and D.J. Spiegelhalter, Prior distributions for the intracluster correlation coefficient, based on multiple previous estimates, and their application in cluster randomized trials, Clin. Trials 2 (2005), pp. 108-118. doi: 10.1191/1740774505cn072oa
[29] O. Ukoumunne, Confidence intervals for the intraclass correlation coefficient in cluster randomized trials, Ph.D. thesis, King’s College, University of London, 2004.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.