Bayes' theorem, COVID19, and screening tests
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ABSTRACT:
SUBMITTER: Chan G
PROVIDER: S-EPMC7315940 | biostudies-literature | 2020 Jun
REPOSITORIES: biostudies-literature
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Project description:ObjectivesPositive predictive values (PPVs) and negative predictive values (NPVs) are frequently reported to put estimates of accuracy of a diagnostic test in clinical context and to obtain risk estimates for a given patient taking into account baseline prevalence in the population. In order to calculate PPV and NPV, tests with ordinally or continuously scaled results are commonly dichotomized at the expense of a loss of information.MethodsExtending the rationale for the calculation of PPV and NPV, Bayesian theorem is used to calculate the probability of disease given the outcome of a continuously or ordinally scaled test. Probabilities of test results conditional on disease status are modeled in a Bayesian framework and subsequently transformed to probabilities of disease status conditional on test result.ResultsUsing publicly available data, probability of a clinical depression diagnosis given PROMIS Depression scores was estimated. Comparison with PPV and NPV based on dichotomized scores shows that a more fine-grained interpretation of test scores is possible.ConclusionsThe proposed method bears the chance to facilitate accurate and meaningful interpretation of test results in clinical settings by avoiding unnecessary dichotomization of test scores.
| S-EPMC8170576 | biostudies-literature
Project description:Using classroom activities to motivate the teaching and learning of Bayes’ theorem is not new. However, many of the textbook exercises and published simulations gloss over how the requisite probabilities are determined. In our case study, Able Construction is a fictional company hoping to exploit historical bidding data to inform its own bidding strategy on a municipal construction project. Unlike most other classroom activities, we challenge students to calculate the necessary probabilities directly from a given dataset. In our experience with implementing this case in introductory business analytics courses at the undergraduate- and graduate-level, we find that this spreadsheet activity gives students the opportunity to exercise their own judgement regarding data manipulation and definition of states of nature. This autonomy in analysis develops in students a deeper appreciation for practical skills required for possible analytics careers after graduation, and leads to engaging discussions of the applicability of Bayes’ theorem in practice. Supplementary Information The online version contains supplementary material available at 10.1007/s43069-021-00119-3.
| S-EPMC8784234 | biostudies-literature
Project description:Medicine is diagnosis, treatment and care. To diagnose is to consider the probability of the cause of discomfort experienced by the patient. The physician may face many options and all decisions are liable to uncertainty to some extent. The rational action is to perform selected tests and thereby increase the pre-test probability to reach a superior post-test probability of a particular option. To draw the right conclusions from a test, certain background information about the performance of the test is necessary. We set up a partially artificial dataset with measured results obtained from the laboratory information system and simulated diagnosis attached. The dataset is used to explore the use of contingency tables with a unique graphic design and software to establish and compare ROC graphs. The loss of information in the ROC curve is compensated by a cumulative data analysis (CDA) plot linked to a display of the efficiency and predictive values. A standard for the contingency table is suggested and the use of dynamic reference intervals discussed.
| S-EPMC5707117 | biostudies-literature
Project description:Many Bayes factors have been proposed for comparing population means in two-sample (independent samples) studies. Recently, Wang and Liu (2015) presented an "objective" Bayes factor (BF) as an alternative to a "subjective" one presented by Gönen et al. (2005). Their report was evidently intended to show the superiority of their BF based on "undesirable behavior" of the latter. A wonderful aspect of Bayesian models is that they provide an opportunity to "lay all cards on the table." What distinguishes the various BFs in the two-sample problem is the choice of priors (cards) for the model parameters. This article discusses desiderata of BFs that have been proposed, and proposes a new criterion to compare BFs, no matter whether subjectively or objectively determined: A BF may be preferred if it correctly classifies the data as coming from the correct model most often. The criterion is based on a famous result in classification theory to minimize the total probability of misclassification. This criterion is objective, easily verified by simulation, shows clearly the effects (positive or negative) of assuming particular priors, provides new insights into the appropriateness of BFs in general, and provides a new answer to the question, "Which BF is best?"
| S-EPMC6424525 | biostudies-literature
Project description:Background: Birt-Hogg-Dubé syndrome (BHD) is a rare inherited disorder characterized by cutaneous fibrofolliculomas, multiple pulmonary cysts, recurrent spontaneous pneumothorax (SP), and renal tumors. More than 40 years after its description, the prevalence of BHD in the general population remains unknown. This study aimed at determining the prevalence of BHD by applying the Bayes theorem of conditional probability to epidemiological data on SP. Methods: We performed a meta-analysis of published data on: (1) the probability of having BHD among patients with apparent primary SP (4 studies), (2) the incidence rate of primary SP in the general population (9 studies), and (3) the probability of experiencing a SP in BHD (16 studies). Results were corrected for SP relapses, stratified by gender and year of study publication (before and after 2000), and computed with the Bayes equation. Results: The probability of having BHD among patients with apparent primary SP was 0.09 (95% confidence interval: 0.07, 0.11) or 9%. It was 0.20 (0.14, 0.27) in women and 0.05 (0.04, 0.07) in men. The incidence rate of primary SP in the general population was 8.69 (6.58, 11.46) per 100,000 person-years (p-y). It was 3.44 (2.36, 4.99) per 100,000 p-y in women and 13.96 (10.72, 18.18) per 100,000 p-y in men, and was about 2 times higher in studies published after 2000 than in those published before 2000. The probability of experiencing at least one SP among patients with BHD was 0.43 (0.31, 0.54) or 43%, without gender difference. By combining these data in the Bayes equation, we found a prevalence of BHD in the general population of 1.86 (1.16, 3.00) per million, with values of 1.86 (1.02, 3.39) per million in men, and 1.88 (0.97, 3.63) per million in women. Conclusion: The prevalence of BHD in the general population is about 2 cases per million, without difference between genders.
| S-EPMC8111214 | biostudies-literature
Project description:IntroductionSensitivity, specificity, and predictive values-the basic statistics behind using and interpreting screening and diagnostic tests-are taught in all medical schools, yet studies have shown that a majority of physicians cannot correctly define and apply these concepts. Previous work has not rigorously examined this disconnect and attempted to address it.MethodsWe used adult learning theory to design a case-based interactive workshop to review biostatistics and apply them to clinical decision-making using Bayes' theorem. Participants took an anonymous multiple-choice pretest, posttest, and delayed posttest on definitions and application of the concepts, and we compared the scores between the three tests. Several experiences with early iterations provided feedback to improve the workshop but were not included for analysis.ResultsWe conducted the finalized workshop with 54 pediatrics students, residents, and faculty. All learners completed the immediate pre- and posttests, and eight completed the delayed posttest. Average scores rose from 4.5/8 (56%) on the pretest to 6.5/8 (81%) on the posttest and 6.4/8 (80%) on the delayed posttest. Two-tailed t tests showed p < .001 for the difference between the pretest and both posttests, and post hoc power analysis showed a power of 99% to detect the observed differences. There was no significant difference (p = .8) between the posttest and delayed posttest.DiscussionOur work demonstrates that an interactive workshop reviewing basic biostatistics and teaching rational diagnostic testing using Bayes' theorem can be effective in connecting theoretical knowledge of biostatistics to evidence-based decision-making in real clinical practice.
| S-EPMC6346275 | biostudies-literature
Project description:BackgroundWhen a new disease such starts to spread, the commonly asked questions are how deadly is it? and how many people are likely to die of this outbreak? The World Health Organization (WHO) announced in a press conference on January 29, 2020 that the death rate of COVID-19 was 2% on the case fatality rate (CFR). It was underestimated assuming no lag days from symptom onset to deaths while many CFR formulas have been proposed, the estimation on Bays theorem is worthy of interpretation. Hence, it is hypothesized that the over-loaded burdens of treating patients and capacities to contain the outbreak (LSBHRS) may increase the CFR.MethodsWe downloaded COVID-19 outbreak numbers from January 21 to February 14, 2020, in countries/regions on a daily basis from Github that contains information on confirmed cases in >30 Chinese locations and other countries/regions. The pros and cons were compared among the 5 formula of CFR, including [A] deaths/confirmed; [B] deaths/(deaths + recovered); [C] deaths/(cases x days ago); [D] Bayes estimation based on [A] and the outbreak (LSBHRS) in each country/region; and [E] Bayes estimation based on [C] deaths/(cases x days ago). The coefficients of variance (CV = the ratio of the standard deviation to the mean) were applied to measure the relative variability for each CFR. A dashboard was developed for daily display of the CFR across each region.ResultsThe Bayes based on (A)[D] has the lowest CV (=0.10) followed by the deaths/confirmed (=0.11) [A], deaths/(deaths + recoveries) (=0.42) [B], Bayes based on (C) (=0.49) [E], and deaths/(cases x days ago) (=0.59) [C]. All final CFRs will be equal using the formula (from, A to E). A dashboard was developed for the daily reporting of the CFR. The CFR (3.7%) greater than the prior CFR of 2.2% was evident in LSBHRS, increasing the CFR. A dashboard was created to present the CFRs on COVID-19.ConclusionWe suggest examining both trends of the Bayes based on both deaths/(cases 7 days ago) and deaths/confirmed cases as a reference to the final CFR. An app developed for displaying the provisional CFR with the 2 CFR trends can improve the underestimated CFR reported by WHO and media.
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Project description:In the renal collecting duct, binding of AVP to the V2 receptor triggers signaling changes that regulate osmotic water transport. Short-term regulation of water transport is dependent on vasopressin-induced phosphorylation of aquaporin-2 (AQP2) at Ser256. The protein kinase that phosphorylates this site is not known. We use Bayes' theorem to rank all 521 rat protein kinases with regard to the likelihood of a role in Ser256 phosphorylation on the basis of prior data and new experimental data. First, prior probabilities were estimated from previous transcriptomic and proteomic profiling data, kinase substrate specificity data, and evidence for kinase regulation by vasopressin. This ranking was updated using new experimental data describing the effects of several small-molecule kinase inhibitors with known inhibitory spectra (H-89, KN-62, KN-93, and GSK-650394) on AQP2 phosphorylation at Ser256 in inner medullary collecting duct suspensions. The top-ranked kinase was Ca2+/calmodulin-dependent protein kinase II (CAMK2), followed by protein kinase A (PKA) and protein kinase B (AKT). Liquid chromatography-tandem mass spectrometry (LC-MS/MS)-based in vitro phosphorylation studies compared the ability of three highly ranked kinases to phosphorylate AQP2 and other inner medullary collecting duct proteins, PKA, CAMK2, and serum/glucocorticoid-regulated kinase (SGK). All three proved capable of phosphorylating AQP2 at Ser256, although CAMK2 and PKA were more potent than SGK. The in vitro phosphorylation experiments also identified candidate protein kinases for several additional phosphoproteins with likely roles in collecting duct regulation, including Nedd4-2, Map4k4, and 3-phosphoinositide-dependent protein kinase 1. We conclude that Bayes' theorem is an effective means of integrating data from multiple data sets in physiology.
| S-EPMC4101623 | biostudies-literature
Project description:Ruling out disease often requires expensive or potentially harmful confirmation testing. For such testing, a less invasive triage test is often used. Intuitively, few negative confirmatory tests suggest success of this approach. However, if negative confirmation tests become too rare, too many disease cases could have been missed. It is therefore important to know how many negative tests are needed to safely exclude a diagnosis. We quantified this relationship using Bayes' theorem, and applied this to the example of pulmonary embolism (PE), for which triage is done with a Clinical Decision Rule (CDR) and D-dimer testing, and CT-angiography (CTA) is the confirmation test. For a maximum proportion of missed PEs of 1% in triage-negative patients, we calculate a 67% 'mandatory minimum' proportion of negative CTA scans. To achieve this, the proportion of patients with PE undergoing triage testing should be appropriately low, in this case no higher than 24%. Pre-test probability, triage test characteristics, the proportion of negative confirmation tests, and the number of missed diagnoses are mathematically entangled. The proportion of negative confirmation tests--not too high, but definitely not too low either--could be a quality benchmark for diagnostic processes.
| S-EPMC4777363 | biostudies-literature
Project description:Screening tests are widely used in medicine to assess the likelihood that members of a defined population have a particular disease. This article presents an overview of such tests including the definitions of key technical (sensitivity and specificity) and population characteristics necessary to assess the benefits and limitations of such tests. Several examples are used to illustrate calculations, including the characteristics of low dose computed tomography as a lung cancer screen, choice of an optimal PSA cutoff and selection of the population to undergo mammography. The importance of careful consideration of the consequences of both false positives and negatives is highlighted. Receiver operating characteristic curves are explained as is the need to carefully select the population group to be tested.
| S-EPMC4389712 | biostudies-other