Related papers: On the Formalism of The Screening Paradox
Bayes' Theorem confers inherent limitations on the accuracy of screening tests as a function of disease prevalence. We have shown in previous work that a testing system can tolerate significant drops in prevalence, up until a certain…
In previous work by this author, the screening paradox - the loss of predictive power of screening tests over time $t$ - was mathematically formalized using Bayesian theory. Where $J$ is Youden's statistic, $b$ is the specificity of the…
The relationship between a screening tests' positive predictive value, $\rho$, and its target prevalence, $\phi$, is proportional - though not linear in all but a special case. In consequence, there is a point of local extrema of curvature…
Using Bayes' Theorem, we derive generalized equations to determine the positive and negative predictive value of screening tests undertaken sequentially. Where a is the sensitivity, b is the specificity, $\phi$ is the pre-test probability,…
From the fundamental theorem of screening (FTS) we obtain the following mathematical relationship relaying the pre-test probability of disease $\phi$ to the positive predictive value $\rho(\phi)$ of a screening test:…
Jeffreys-Lindley paradox is a case where frequentist and Bayesian hypothesis testing methodologies contradict with each other. This has caused confusion among data analysts for selecting a methodology for their statistical inference tasks.…
The accuracy of binary classification systems is defined as the proportion of correct predictions - both positive and negative - made by a classification model or computational algorithm. A value between 0 (no accuracy) and 1 (perfect…
The principle of peer review is central to the evaluation of research, by ensuring that only high-quality items are funded or published. But peer review has also received criticism, as the selection of reviewers may introduce biases in the…
Testing the equality of two proportions is a common procedure in science, especially in medicine and public health. In these domains it is crucial to be able to quantify evidence for the absence of a treatment effect. Bayesian hypothesis…
For decades, forensic statisticians have debated whether searching large DNA databases undermines the evidential value of a match. Modern surveillance faces an exponentially harder problem: screening populations across thousands of…
In the last year more than 70,000 people have been brought to the UK hospitals with serious injuries. Each time a clinician has to urgently take a patient through a screening procedure to make a reliable decision on the trauma treatment.…
The Jeffreys-Lindley paradox exposes a rift between Bayesian and frequentist hypothesis testing that strikes at the heart of statistical inference. Contrary to what most current literature suggests, the paradox was central to the Bayesian…
Datasets are rarely a realistic approximation of the target population. Say, prevalence is misrepresented, image quality is above clinical standards, etc. This mismatch is known as sampling bias. Sampling biases are a major hindrance for…
False positive results in screening tests have potentially severe psychological, medical, and financial consequences for the recipient. However, there have been few efforts to quantify how the risk of a false positive accumulates over time.…
Feature or variable selection is a problem inherent to large data sets. While many methods have been proposed to deal with this problem, some can scale poorly with the number of predictors in a data set. Screening methods scale linearly…
In this manuscript, we present various proposed methods estimate the prevalence of disease, a critical prerequisite for the adequate interpretation of screening tests. To address the limitations of these approaches, which revolve primarily…
We investigate the discrimination of two candidates of an unknown parameter in quantum systems with continuous weak measurement, inspired by the application of hypothesis testing in distinguish-ing two Hamiltonians [Kiilerich and M{\o}lmer,…
Bayesian hypothesis testing is re-examined from the perspective of an a priori assessment of the test statistic distribution under the alternative. By assessing the distribution of an observable test statistic, rather than prior parameter…
Scientific theories can often be formulated using equality and order constraints on the relative effects in a linear regression model. For example, it may be expected that the effect of the first predictor is larger than the effect of the…
Many sequential decision settings in healthcare feature funnel structures characterized by a series of stages, such as screenings or evaluations, where the number of patients who advance to each stage progressively decreases and decisions…