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Analyzing dependent proportions in cluster randomized trials: Modeling inter-cluster correlation via copula function
Authors:Mohamed M. Shoukri  Pranesh Kumar  Dilek Colak
Affiliation:
  • a Department of Biostatistics and Epidemiology, King Faisal Specialist Hospital and Research Center, MBC #03, P. O. Box 3354, Riyadh 11211, Saudi Arabia
  • b Department of Epidemiology and Biostatistics, Schulich School of Medicine and Dentistry, University of Western Ontario, London, Ontario, Canada
  • c Department of Mathematics, University of Northern British Columbia, Prince George, BC, Canada
  • Abstract:When two interventions are randomized to multiple sub-clusters within a whole cluster, accounting for the within sub-cluster (intra-cluster) and between sub-clusters (inter-cluster) correlations is needed to produce valid analyses of the effect of interventions. With the growing interest in copulas and their applications in statistical research, we demonstrate, through applications, how copula functions may be used to account for the correlation among responses across sub-clusters. Copulas having asymmetric dependence property may prove useful for modeling the relationship between random functions especially in clinical, health and environmental sciences where response data are in general skewed. These functions can in general be used to study scale-free measures of dependence, and they can be used as a starting point for constructing families of bivariate distributions, with a view to simulations. The core contribution of this paper is to provide an alternative approach for estimating the inter-cluster correlation using copula to accurately estimate the treatment effect when the outcome variable is measured on the dichotomous scale. Two data sets are used to illustrate the proposed methodology.
    Keywords:Cluster randomization   Correlated proportion   Beta binomial distribution   Copula function
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