A normalized version of the ubiquitous two-by-two contingency matrix is associated with a variety of marginal, conjunctive, and conditional probabilities that serve as appropriate indicators in diagnostic testing. If this matrix is enhanced by being interpreted as a probabilistic Universe of Discourse, it still suffers from two inter-related shortcomings, arising from lack of length/area proportionality and a potential misconception concerning a false assumption of independence between the two underlying events. This paper remedies these two shortcomings by modifying this matrix into a new Karnaugh-map-like diagram that resembles an eikosogram. Furthermore, the paper suggests the use of a pair of functionally complementary versions of this diagram to handle any ternary problem of conditional probability. The two diagrams split the unknowns and equations between themselves in a fashion that allows the use of a divide-and-conquer strategy to handle such a problem. The method of solution is demonstrated via four examples, in which the solution might be arithmetic or algebraic, and independently might be numerical or symbolic. In particular, we provide a symbolic arithmetic derivation of the well-known formulas that express the predictive values in terms of prevalence, sensitivity and specificity. Moreover, we prove a virtually unknown interdependence among the two predictive values, sensitivity, and specificity. In fact, we employ a method of symbolic algebraic derivation to express any one of these four indicators in terms of the other three. The contribution of this paper to the diagnostic testing aspects of mathematical epidemiology culminates in a timely application to the estimation of the true prevalence of the contemporary world-wide COVID-19 pandemic. It turns out that this estimation is hindered more by the lack of global testing world-wide rather than by the unavoidable imperfection of the available testing methods.

This paper is a preliminary step towards the assessment of an alarming widespread belief that victims of the novel coronavirus SARS-CoV-2 include the quality and accuracy of scientific publications about it. Our initial results suggest that this belief cannot be readily ignored, denied, dismissed or refuted, since some genuine supporting evidence can be forwarded for it. This evidence includes an obvious increase in retractions of papers published about the COVID-19 pandemic plus an extra-ordinary phenomenon of inconsistency that we report herein. In fact, we provide a novel method for validating any purported set of the four most prominent indicators of diagnostic testing (Sensitivity, Specificity, Positive Predictive Value, and Negative Predictive Value), by observing that these indicators constitute three rather than four independent quantities. This observation has virtually been unheard of in the open medical literature, and hence researchers have not taken it into consideration. We define two functions, which serve as consistency criteria, since each of them checks consistency for any set of four numerical values (naturally belonging to the interval [0.0,1.0]) claimed to be the four basic diagnostic indicators. Most of the data we came across in various international journals met our criteria for consistency, but in a few cases, there were obvious unexplained blunders. We explored the same consistency problem for some diagnostic data published in 2020 concerning the ongoing COVID-19 pandemic and observed that the afore-mentioned unexplained blunders tended to be on the rise. A systematic extensive statistical assessment of this presumed tendency is warranted.

We provide a novel method for validating any purported set of the four most prominent indicators of diagnostic testing (Sensitivity, Specificity, Positive Predictive Value, and Negative Predictive Value), by observing that these indicators constitute three rather than four independent quantities. This observation has virtually been unheard of in the open medical literature. We defined two functions, which serve as consistency criteria, since each of them checks consistency for any set of four numerical values claimed to be the four basic diagnostic indicators. Most of the data we came across in various Saudi medical journals met our criteria for consistency, but in a few cases, there were obvious unexplained blunders. We relate our present findings to the more general issue of detection and ramifications of flawed, fabricated or wrong data. We observe that the research field handling the detection of flawed data is still in its infancy, and hope that this field will reach maturity very soon.

We provide a novel method for validating any purported set of the four most prominent indicators of diagnostic testing (Sensitivity, Specificity, Positive Predictive Value, and Negative Predictive Value), by observing that these indicators constitute three rather than four independent quantities. This observation has virtually been unheard of in the open medical literature. We defined two functions, which serve as consistency criteria, since each of them checks consistency for any set of four numerical values claimed to be the four basic diagnostic indicators. Most of the data we came across in various Saudi medical journals met our criteria for consistency, but in a few cases, there were obvious unexplained blunders. We relate our present findings to the more general issue of detection and ramifications of flawed, fabricated or wrong data. We observe that the research field handling the detection of flawed data is still in its infancy, and hope that this field will reach maturity very soon.