Statistical Inference For The Evaluation Of Two Continuous Diagnostic Tests In Matched-pair Design Experiments

With the progress of scientific development,more and more fields,including medical diagnosis,image recognition,machine learning,and data mining,need to verify the specificity and sensitivity of the test results.When evaluating the discriminatory of the diagnostic tests,due to the correlation between samples of a matched-pair design,the extent of difficulty and complexity of the corresponding statistical analysis will increase;when the test outcomes appear as continuous variables,it will bring about new challenges to their estimation and hypothesis testing;in the presence of missing data,traditional statistical methods will bias the estimation results and lose statistical efficiency,thereby invalidating the statistical inference.Therefore,it’s necessary to construct more effective confidence intervals,determine more accurate sample sizes,and perform parameter estimation in the presence of missing data,so as to establish more reliable statistical theory and methods.These are the core of solving the above-mentioned challenges and constitute the research focus of this dissertation.Specifically,the main content of this dissertation could be deciphered as follows:(1)The dissertation starts with a detailed discussion on the equivalence evaluation of two continuous diagnostic tests in a matched-pair experiment.Based on the hybrid method,thirteen confidence intervals are constructed for evaluating the difference between two correlated AUCs.These confidence intervals have closed expressions,which largely reduce the computational cost,and do not depend on special distribution assumptions.They could deliver satisfactory behavior superior to that of traditional methods.This is especially true for small-or medium-sized samples.Three Bootstrap-based confidence intervals that have not been considered in the literature associated with matched-pair continuous outcomes are also presented.Simulation studies in tandem with two real example analyses unambiguously suggest that confidence intervals constructed on the basis of hybrid method feature superior performance to those constructed by classical methods.(2)The dissertation studies the estimation of population distributions,ROC curves,and AUCs of two paired continuous diagnostic tests under the Bayesian framework and proposes a method for equivalence evaluation.Taking into account the correlation within the group,the distribution F of the diseased group and the distribution G of the non-diseased group is estimated by constructing a joint Dirichlet process prior to the location and scale parameters,respectively.Then the correlation between two tests can be evaluated by the estimator of the correlation coefficient in the scale parameter.Numerical analysis results show that the performance of the proposed model is better than the Bayesian hierarchical model based on the Normal-Inverse Wishart prior regardless of the data source,i.e.,from a normal distribution or a non-normal distribution.(3)The dissertation also addresses the Bayesian sample size determination issue of two continuous diagnostic tests in a matched-pair design experiment.Nine criteria for determining sample sizes under the Bayesian framework are defined based on the accuracy requirements of the posterior estimation for the difference between tow correlated AUCs.Meanwhile,a simulation-based procedure for determining the sample size is exemplified based on the Dirichlet process prior.Numerical analysis results show that,as the correlation coefficient between samples increases,the sample size required for the semiparametric Bayesian hierarchical model with the Dirichlet process prior or the Normal-Inverse Wishart prior both decreases,regardless of the data source,i.e.,from a normal distribution or a non-normal distribution.Moreover,it is also suggested that the sample size required by the model with the Dirichlet process prior is less than the model with the Normal-Inverse Wishart prior.(4)The last chapter of this dissertation investigates the equivalence evaluation of two continuous diagnostic tests with nonignorable missing outcomes in a matched-pair design experiment.By assuming the data missing mechanism follows a semiparametric exponential tilting model,the inverse probability weighted approach,the nonparametric approach,and the augmented inverse probability weighted approach are developed to estimate the difference between the two correlated AUCs in the presence of known and unknown tilting parameters,respectively.Meanwhile,the consistency and asymptotic normality of these estimators are proved under certain regular conditions.Numerical analysis results show that the performance of the proposed methods is better than that delivered by the method using only completely observed data.Moreover,the nonparametric estimator and the augmented inverse probability weighted estimator perform robustly even if the proposed missing mechanism model is inappropriately specified.Also,the matched-pair design can reduce the estimation error.As the sample correlation coefficient increases,the estimation effects of these estimators all become better.