Bayesian updating and sequential testing: overcoming inferential limitations of screening tests

Background Bayes’ theorem confers inherent limitations on the accuracy of screening tests as a function of disease prevalence. Herein, we establish a mathematical model to determine whether sequential testing with a single test overcomes the aforementioned Bayesian limitations and thus improves the reliability of screening tests. Methods We use Bayes’ theorem to derive the positive predictive value equation, and apply the Bayesian updating method to obtain the equation for the positive predictive value (PPV) following repeated testing. We likewise derive the equation which determines the number of iterations of a positive test needed to obtain a desired positive predictive value, represented graphically by the tablecloth function. Results For a given PPV ($$\rho$$ ρ ) approaching k, the number of positive test iterations needed given a prevalence of disease ($$\phi$$ ϕ ) is: $$n_i =\lim _{\rho \rightarrow k}\left\lceil \frac{ln\left[ \frac{\rho (\phi -1)}{\phi (\rho -1)}\right] }{ln\left[ \frac{a}{1-b}\right] }\right\rceil \qquad \qquad (1)$$ n i = lim ρ → k l n ρ ( ϕ - 1 ) ϕ ( ρ - 1 ) l n a 1 - b ( 1 ) where $$n_i$$ n i = number of testing iterations necessary to achieve $$\rho$$ ρ , the desired positive predictive value, ln = the natural logarithm, a = sensitivity, b = specificity, $$\phi$$ ϕ = disease prevalence/pre-test probability and k = constant. Conclusions Based on the aforementioned derivation, we provide reference tables for the number of test iterations needed to obtain a $$\rho (\phi )$$ ρ ( ϕ ) of 50, 75, 95 and 99% as a function of various levels of sensitivity, specificity and disease prevalence/pre-test probability. Clinical validation of these concepts needs to be obtained prior to its widespread application.

Bayesian Updating and Sequential Testing: Overcoming Inferential Limitations of Screening Tests

Background: Bayes’ Theorem confers inherent limitations on the accuracy of screening tests as a function of disease prevalence. Herein, we establish a mathematical model to determine whether sequential testing with a single test overcomes the aforementioned Bayesian lim- itations and thus improves the reliability of screening tests. Methods: We use Bayes’ Theorem to derive the positive predictive value equation, and apply the Bayesian updating method to obtain the equation for the positive predictive value (PPV) following repeated testing. We likewise derive the equation which determines the number of iterations of a positive test needed to obtain a desired positive pre- dictive value, represented graphically by the tablecloth function. Results: For a given PPV ρ approaching k, the number of positive test iterations given a prevalence φ needed is: [see equation], where ni = number of testing iterations necessary to achieve ρ, the desired positive predictive value, ln = the natural logarithm, a = sensitivity, b = specificity, φ = disease prevalence/pre-test probability and k = constant. Conclusions: Based on the aforementioned derivation, we provide reference tables for the number of test iterations needed to obtain a ρ(φ) of 50, 75, 95 and 99% as a function of various levels of sensitivity, specificity and disease prevalence/pre-test probability. Clinical vali- dation of these concepts needs to be obtained prior to its widespread application.

Statistical sequential hypotheses testing on para meters of probability distributions of random binary data

An important mathematical problem of computer data analysis – the problem of statistical sequential testing of simple hypotheses on parameters of probability distributions of observed binary data – is considered in the paper. This problem is being solved for two models of observation: for independent observations and for homogeneous Markov chains. Explicit expressions of the sequential tests statistics are derived, transparent for interpretation and convenient for computer realisation. An approach is developed to calculate the performance characteristics – error probabilities and mathematical expectations of the random number of observations required to guarantee the requested accuracy for decision rules. Asymptotic expansions for the mentioned performance characteristics are constructed under «contamination» of the probability distributions of observed data.

Mapping pleiotropic loci using a fast-sequential testing algorithm

Pleiotropy (i.e., genes with effects on multiple traits) leads to genetic correlations between traits and contributes to the development of many syndromes. Identifying variants with pleiotropic effects on multiple health-related traits can improve the biological understanding of gene action and disease etiology, and can help to advance disease-risk prediction. Sequential testing is a powerful approach for mapping genes with pleiotropic effects. However, the existing methods and the available software do not scale to analyses involving millions of SNPs and large datasets. This has limited the adoption of sequential testing for pleiotropy mapping at large scale. In this study, we present a sequential test and software that can be used to test pleiotropy in large systems of traits with biobank-sized data. Using simulations, we show that the methods implemented in the software are powerful and have adequate type-I error rate control. To demonstrate the use of the methods and software, we present a whole-genome scan in search of loci with pleiotropic effects on seven traits related to metabolic syndrome (MetS) using UK-Biobank data (n~300 K distantly related white European participants). We found abundant pleiotropy and report 170, 44, and 18 genomic regions harboring SNPs with pleiotropic effects in at least two, three, and four of the seven traits, respectively. We validate our results using previous studies documented in the GWAS-catalog and using data from GTEx. Our results confirm previously reported loci and lead to several novel discoveries that link MetS-related traits through plausible biological pathways.

Strategies for antigen testing: An alternative approach to widespread PCR testing

ABSTRACTMultiple applications of low cost and rapid antigen tests for individuals, in parallel (at the same time) or at times sufficiently close to each other, when appropriately interpreted can considerably increase sensitivity of these tests, improving on their performance greatly. Under reasonable assumptions, this occurs when considering a positive to arise in a composite test if at least one of two underlying repeated tests are positive. Parallel Rapid Testing can potentially provide a form of testing that is accessible (combining wide availability and lack of expense) and quick. Moreover, it can provide a level of sensitivity that is comparable to seemingly more sophisticated but more expensive alternatives. In combination with sequential testing, this strategy offers an alternative method of testing that can be applied immediately and on a widespread basis.