A Bayesian approach to estimating the intraclass correlation coefficient

A Bayesian approach to estimating the intraclass correlation coefficient was used for this research project. The background of the intraclass correlation coefficient, a summary of its standard estimators, and a review of basic Bayesian terminology and methodology were presented. The conditional posterior density of the intraclass correlation coefficient was then derived and estimation procedures related to this derivation were shown in detail. Three examples of applications of the conditional posterior density to specific data sets were also included. Two sets of simulation experiments were performed to compare the mean and mode of the conditional posterior density of the intraclass correlation coefficient to more traditional estimators. Non-Bayesian methods of estimation used were: the methods of analysis of variance and maximum likelihood for balanced data; and the methods of MIVQUE (Minimum Variance Quadratic Unbiased Estimation) and maximum likelihood for unbalanced data. The overall conclusion of this research project was that Bayesian estimates of the intraclass correlation coefficient can be appropriate, useful and practical alternatives to traditional methods of estimation. ^

THE IMPROVEMENT REGION IN RIDGE REGRESSION

One of the difficulties in the practical application of ridge regression is that, for a given data set, it is unknown whether a selected ridge estimator has smaller squared error than the least squares estimator. The concept of the improvement region is defined, and a technique is developed which obtains approximate confidence intervals for the value of ridge k which produces the maximum reduction in mean squared error. Two simulation experiments were conducted to investigate how accurate these approximate confidence intervals might be. ^

Computer simulation of glioma growth and morphology.

Despite major advances in the study of glioma, the quantitative links between intra-tumor molecular/cellular properties, clinically observable properties such as morphology, and critical tumor behaviors such as growth and invasiveness remain unclear, hampering more effective coupling of tumor physical characteristics with implications for prognosis and therapy. Although molecular biology, histopathology, and radiological imaging are employed in this endeavor, studies are severely challenged by the multitude of different physical scales involved in tumor growth, i.e., from molecular nanoscale to cell microscale and finally to tissue centimeter scale. Consequently, it is often difficult to determine the underlying dynamics across dimensions. New techniques are needed to tackle these issues. Here, we address this multi-scalar problem by employing a novel predictive three-dimensional mathematical and computational model based on first-principle equations (conservation laws of physics) that describe mathematically the diffusion of cell substrates and other processes determining tumor mass growth and invasion. The model uses conserved variables to represent known determinants of glioma behavior, e.g., cell density and oxygen concentration, as well as biological functional relationships and parameters linking phenomena at different scales whose specific forms and values are hypothesized and calculated based on in vitro and in vivo experiments and from histopathology of tissue specimens from human gliomas. This model enables correlation of glioma morphology to tumor growth by quantifying interdependence of tumor mass on the microenvironment (e.g., hypoxia, tissue disruption) and on the cellular phenotypes (e.g., mitosis and apoptosis rates, cell adhesion strength). Once functional relationships between variables and associated parameter values have been informed, e.g., from histopathology or intra-operative analysis, this model can be used for disease diagnosis/prognosis, hypothesis testing, and to guide surgery and therapy. In particular, this tool identifies and quantifies the effects of vascularization and other cell-scale glioma morphological characteristics as predictors of tumor-scale growth and invasion.

Computer simulation of glioma growth and morphology.

Despite major advances in the study of glioma, the quantitative links between intra-tumor molecular/cellular properties, clinically observable properties such as morphology, and critical tumor behaviors such as growth and invasiveness remain unclear, hampering more effective coupling of tumor physical characteristics with implications for prognosis and therapy. Although molecular biology, histopathology, and radiological imaging are employed in this endeavor, studies are severely challenged by the multitude of different physical scales involved in tumor growth, i.e., from molecular nanoscale to cell microscale and finally to tissue centimeter scale. Consequently, it is often difficult to determine the underlying dynamics across dimensions. New techniques are needed to tackle these issues. Here, we address this multi-scalar problem by employing a novel predictive three-dimensional mathematical and computational model based on first-principle equations (conservation laws of physics) that describe mathematically the diffusion of cell substrates and other processes determining tumor mass growth and invasion. The model uses conserved variables to represent known determinants of glioma behavior, e.g., cell density and oxygen concentration, as well as biological functional relationships and parameters linking phenomena at different scales whose specific forms and values are hypothesized and calculated based on in vitro and in vivo experiments and from histopathology of tissue specimens from human gliomas. This model enables correlation of glioma morphology to tumor growth by quantifying interdependence of tumor mass on the microenvironment (e.g., hypoxia, tissue disruption) and on the cellular phenotypes (e.g., mitosis and apoptosis rates, cell adhesion strength). Once functional relationships between variables and associated parameter values have been informed, e.g., from histopathology or intra-operative analysis, this model can be used for disease diagnosis/prognosis, hypothesis testing, and to guide surgery and therapy. In particular, this tool identifies and quantifies the effects of vascularization and other cell-scale glioma morphological characteristics as predictors of tumor-scale growth and invasion.