Robust Hierarchical Finite Mixture Modeling of Collagen Fibril Diameters

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DESCRIPTION (provided by applicant): Extracellular matrix assembly is a multi-step process, with each step requiring specific regulatory interactions. Definition of the steps in matrix assembly and the mechanisms regulating them will enhance our understanding of tendon development, growth, repair and pathological changes associated with aging or injury and repair/regeneration after wounding or surgical intervention. The mechanisms involved in tendon extracellular matrix assembly are investigated, in part, by studying decomposition of the fibril diameter distributions into subpopulations with different characteristics and functional roles. Therefore, statistical modeling of fibril diameters as finite mixtures of normal subpopulations provides insight into the mechanisms regulating collagen fibrillogenesis. The overall goal of this application is to develop robust one-objective-function estimation methods and corresponding software for fitting a hierarchical random effects model with multiple levels of random effects and conditional distributions modeled as finite mixtures of normal components. This methodology will provide a framework for novel and efficient statistical analysis of the collagen fibril diameters data generated by the ongoing study Regulated Assembly of Tendon Extracellular Matrix (NIH/NIAMSD R01AR44745) and similar studies of collagen fibrillogenesis. While statistical methodology that will be developed is geared toward the needs of robust and efficient analyses of collagen fibril diameter distributions, the proposed models and estimation methods are very general, and will be useful for analyses of most general clustered biological data. The proposed studies will (1) extend statistical methodology and software to generate novel models and develop corresponding maximum likelihood and robust estimation methods for multilevel clustered data with conditional distributions represented by finite mixtures of normal components; (2) investigate the statistical properties of the proposed models using simulations; (3) compare the performance of the maximum likelihood and robust with respect to outliers estimation methods for modeling conditional collagen fibril diameter distributions as finite mixtures of normal components; (4) analyze extensive data from the study of tendon collagen fibrillogenesis using the proposed hierarchical random effects model and robust estimating approaches that are found optimal for fibril diameters data. The studies of collagen fibril development are important for our understanding of growth, repair and pathological changes associated with aging or injury and repair/regeneration after wounding or surgical intervention. The mechanisms of fibril development may be studied by decomposing the fibril diameter distributions into subpopulations with different characteristics and functional roles. This project focuses on developing novel statistical methods for analyses of such decompositions.