A review of expected P-values and their applications in biomarkers studies

Numerous statistical studies provide P-values for inferential purposes. However, in various cases, researchers tend to overlook the stochastic nature of P-values, leading to potential inaccuracies in conclusions drawn from real data experiments. This stochastic aspect of P-values complicates their utility in assessing the performance of testing procedures or relationships between investigated factors. To address this issue, we shift our attention to the contemporary statistical literature and explore the concept of the expected P-value (EPV) as a measure to evaluate the performance of decision-making rules. Herein, we show that the EPV can be interpreted in the context of receiver operating characteristic (ROC) curve analysis, a well-established biostatistical methodology. The ROC-based framework provides a new and efficient methodology for investigating and constructing statistical decision-making procedures, including (1) evaluation and visualization of properties of the testing mechanisms, for example, partial EPVs; (2) developing optimal tests via the minimization of EPVs; (3) creation of novel methods for optimally combining multiple test statistics; (4) proposing a Youden type criterion for defining optimal tests' critical values via EPV/ROC technique. We demonstrate that the proposed EPV-based approach allows us to maximize the integrated power of testing algorithms with respect to various significance levels. It is also desired to motivate scholars to examine a common statistical doctrine that the conventional t-test type procedures are anticipated to be better than the corresponding Wilcoxon rank-sum test if we observe normally distributed data points. We target to examine this stereotypical view in the EPV framework. In an application, we use the proposed method to construct the optimal test and analyze a myocardial infarction disease dataset. We outline the usefulness of the EPV/ROC technique for evaluating different decision-making procedures, their constructions, and properties with an eye toward practical applications.