Statistical Inferences Of Correlation Coefficient And Mean Vector Of Bivariate Responses With Applications

Selection of appropriate statistical method or models is an important step in analysis of biomedical data.In this thesis,we focus on two basic inferential problems,(i)modeling for Pearson correlation coefficients and(ii)simultaneous confidence intervals(SCIs)of a vector of two or multiple parameters from continuous or binary responses.Both problems have many applications in biomedical or social research.We shall illustrate their applications by real examples.In the first part of the thesis,we investigate two simple regression models of Pearson correlation coefficient of two normal responses or binary responses to assess the effect of covariates of interest.Likelihood based inference is established to estimate the regression coefficients,upon which bootstrap-based method is used for testing the significance of covariate and constructing confidence intervals.Simulation studies show the effectiveness of the method in terms of type-I error control,power performance in moderate sample size and robustness with respect to model mis-specification.We illustrate the application of the proposed method to some real data concerning health measurements with sensible findings.Then,we extend these models for Pearson correlation coefficient of a pair of response with one of them presented in ordinal scale.In the second part of the thesis,we propose methods to construct simultaneous confidence intervals for a parameter vector from inverting a series of randomization tests.The randomization tests are facilitated by an efficient multivariate Robbins-Monro procedure that takes the correlation information of all components into account.The estimation method does not require any distributional assumption of the population other than the existence of the second moments.The resulting simultaneous confidence intervals are not necessarily symmetric about the point estimate of the parameter vector,but possess the property of equal tails in all dimensions.In particular,we present the constructing the mean vector of one population and the difference between two mean vectors of two populations.Extensive simulation is conducted to show numerical comparison with four methods.We illustrate the application of the proposed method to test bioequivalence with multiple endpoints on some real data.We further study methods of constructing simultaneous confidence intervals for parameters in terms of binomial proportions that are associated with bivariate or multiple binary responses.Numerical study through simulation shows the proposed methods have desired performance in coverage.