Novel Statistical Methods for Constructing Decision-making Test Procedures with Applications to Health Related Studie

We present novel developments related to the following statistical topics: 1) A Statistical Software Procedure for Exact Parametric and Nonparametric Likelihood-ratio Tests for Two-sample Comparisons; 2) Expected p-values in Light of an ROC Curve Analysis Applied to Optimal Multiple Testing Procedures; 3) Expected p-value Based Comparisons of Statistical Tests.;In Topic 1, we consider two-sample test schemes that belong to basic class of statistical inference extensively applied in practice. Many powerful statistical techniques are assumed to be based on normally distributed data. In practice, the alternative distributions of compared samples are commonly unknown. In this case, one can propose a combined test based on the following decision rules: (a) the likelihood-ratio test (LRT) for equality of two normal populations and (b) the Shapiro-Wilk (S-W) test for normality. The rules (a) and (b) can be merged by, e.g., using the Bonferroni correction technique to offer the correct comparison of the samples distribution. Alternatively, we propose the exact density-based empirical likelihood (DBEL) ratio test. We develop the tsc package as the first R package available to perform the two-sample comparisons using the exact test procedures: the LRT; the LRT combined with the S-W test; as well as the newly developed DBEL ratio test.;In Topic 2, we focus on the modern statistical publications to explore the potential usefulness of understanding the stochastic essential nature of p-values. We consider the expected p-value (EPV) as an alternative to the more familiar concepts of significance level and power. Our novel concept shows that the EPV can be considered in a context of the receiver operating characteristic (ROC) curve analysis, a well-known biostatistical methodology. This approach provides new and efficient perspectives, for example: (1) to evaluate and visualize properties of different statistical decision-making mechanisms; (2) to obtain optimal test procedures, minimizing corresponding EPVs; (3) to develop novel methods for optimal combining multiple test-statistics. We show that the proposed EPV based approach implies maximization of the integrated test-powers with respect to various significant levels. In this context, we demonstrate how the ROC curve technique can be used to provide best combinations and best linear combinations of test-statistics in the common problems related to multiple testing tasks.;In Topic 3, we demonstrate a new approach based on the EPV/ROC methodology for visualizing of comparisons between different decision-making procedures. In various scenarios, we compare the following procedures: the t-test, the Wilcoxon signed rank test and the empirical likelihood ratio test.;The proposed methods are shown to be very efficient in applications to practical problems related to the myocardial infarction disease and the asthma disease.