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

2022 ◽  
Vol 22 (1) ◽  
Author(s):  
Jacques Balayla
Keyword(s):  
Positive Predictive Value ◽  
Predictive Value ◽  
Bayesian Updating ◽  
Bayes Theorem ◽  
Disease Prevalence ◽  
Positive Test ◽  
Screening Tests ◽  
Sequential Testing ◽  
Widespread Application ◽  
Test Probability

Abstract 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.

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

2021 ◽  
Author(s):  
Jacques Balayla
Keyword(s):  
Positive Predictive Value ◽  
Predictive Value ◽  
Bayesian Updating ◽  
Bayes Theorem ◽  
Disease Prevalence ◽  
Positive Test ◽  
Screening Tests ◽  
Sequential Testing ◽  
Widespread Application ◽  
Test Probability

Abstract 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.

scholarly journals Foundational Statistical Principles in Medical Research: Sensitivity, Specificity, Positive Predictive Value, and Negative Predictive Value

Medicina ◽  
2021 ◽  
Vol 57 (5) ◽  
pp. 503
Author(s):  
Thomas F. Monaghan ◽  
Syed N. Rahman ◽  
Christina W. Agudelo ◽  
Alan J. Wein ◽  
Jason M. Lazar ◽  
...  
Keyword(s):  
Positive Predictive Value ◽  
Negative Predictive Value ◽  
Predictive Value ◽  
Medical Literature ◽  
Disease Prevalence ◽  
Positive Test Result ◽  
Predictive Values ◽  
Sensitivity Specificity ◽  
Test Result ◽  
Test Probability

Sensitivity, which denotes the proportion of subjects correctly given a positive assignment out of all subjects who are actually positive for the outcome, indicates how well a test can classify subjects who truly have the outcome of interest. Specificity, which denotes the proportion of subjects correctly given a negative assignment out of all subjects who are actually negative for the outcome, indicates how well a test can classify subjects who truly do not have the outcome of interest. Positive predictive value reflects the proportion of subjects with a positive test result who truly have the outcome of interest. Negative predictive value reflects the proportion of subjects with a negative test result who truly do not have the outcome of interest. Sensitivity and specificity are inversely related, wherein one increases as the other decreases, but are generally considered stable for a given test, whereas positive and negative predictive values do inherently vary with pre-test probability (e.g., changes in population disease prevalence). This article will further detail the concepts of sensitivity, specificity, and predictive values using a recent real-world example from the medical literature.

scholarly journals On the formalism of the screening paradox

PLoS ONE ◽  
2021 ◽  
Vol 16 (9) ◽  
pp. e0256645
Author(s):  
Jacques Balayla
Keyword(s):  
Predictive Value ◽  
Disease Process ◽  
Population Level ◽  
Bayes Theorem ◽  
Disease Prevalence ◽  
Screening Tests ◽  
Screening Process ◽  
Screening Programs ◽  
Closed Systems ◽  
The Mathematical Model

Bayes’ Theorem imposes inevitable limitations on the accuracy of screening tests by tying the test’s predictive value to the disease prevalence. The aforementioned limitation is independent of the adequacy and make-up of the test and thus implies inherent Bayesian limitations to the screening process itself. As per the WHO’s Wilson − Jungner criteria, one of the prerequisite steps before undertaking screening is to ensure that a treatment for the condition screened for exists. However, when applying screening programs in closed systems, a paradox, henceforth termed the “screening paradox”, ensues. If a disease process is screened for and subsequently treated, its prevalence would drop in the population, which as per Bayes’ theorem, would make the tests’ predictive value drop in return. Put another way, a very powerful screening test would, by performing and succeeding at the very task it was developed to do, paradoxically reduce its ability to correctly identify individuals with the disease it screens for in the future—over some time t. In this manuscript, we explore the mathematical model which formalizes said screening paradox and explore its implications for population level screening programs. In particular, we define the number of positive test iterations (PTI) needed to reverse the effects of the paradox. Given their theoretical nature, clinical application of the concepts herein reported need validation prior to implementation. Meanwhile, an understanding of how the dynamics of prevalence can affect the PPV over time can help inform clinicians as to the reliability of a screening test’s results.

scholarly journals The positive predictive value of genetic screening tests

2019 ◽  
Author(s):  
Jill Hagenkord ◽  
Birgit Funke ◽  
Emily Qian ◽  
Madhuri Hegde ◽  
Kevin B Jacobs ◽  
...  
Keyword(s):  
Positive Predictive Value ◽  
Predictive Value ◽  
Disease Prevalence ◽  
Screening Tests ◽  
Clinical Indication ◽  
Confirmatory Test ◽  
Pathogenic Variants ◽  
Test Population ◽  
Health Communities ◽  
Asymptomatic Individuals

As the cost of DNA sequencing continues to fall, more individuals are opting to undergo genomic testing in the absence of a clinical indication. Testing asymptomatic individuals for unsuspected conditions is not new to the medical and public health communities. However, the application of screening principles to inherited diseases with unknown prevalence in an unselected (low-risk) test population raises unique challenges. This paper examines the effect of disease prevalence on the positive predictive value of a test result. Many inherited conditions have very low prevalence in an unselected population, which increases the probability that some likely pathogenic variants may be false positives. In situations where the adverse impact of a false positive result is significant, laboratories should address this issue by either increasing the interpretive specificity of the test, performing a clinical confirmatory test to establish the presence of disease, or restricting the test to a population with increased disease prevalence. Here, we review the statistical concepts relevant to screening tests, apply these concepts to genetic disease screening, create a model to estimate prevalence and positive predictive value, and provide a framework for further discussion.

Streptococcal Pharyngitis Study

PEDIATRICS ◽  
1989 ◽  
Vol 83 (5) ◽  
pp. 808-808
Author(s):  
JENNIFER S. READ ◽  
ROBERT H. BEEKMAN
Keyword(s):  
Positive Predictive Value ◽  
Diagnostic Test ◽  
Rapid Diagnostic Test ◽  
Predictive Value ◽  
Bayes Theorem ◽  
Streptococcal Pharyngitis ◽  
Pediatric Setting ◽  
Group A

Redd and co-workers found the sensitivity of their rapid diagnostic test for group A streptococcal pharyngitis to be 62.8% and its specificity to be 96.9%. Furthermore, the positive predictive value of the test was determined to be 91.5%, sufficiently high to significantly influence the care provided to their patients. We strongly disagree with the authors' conclusion that their findings can be extrapolated to the general pediatric setting. Bayes theorem clearly relates a test's positive predictive value to its sensitivity as well as to the prevalence of true disease in the population.

scholarly journals Evaluation of the risk of malignancy index in preoperative diagnosis of ovarian masses

2018 ◽  
Vol 7 (10) ◽  
pp. 4202
Author(s):  
Royyuru Suchitra ◽  
Kaustubh Burde ◽  
Nilima G. ◽  
P. L. S. Sahithi
Keyword(s):  
Positive Predictive Value ◽  
Negative Predictive Value ◽  
Predictive Value ◽  
Low Cost ◽  
Age Groups ◽  
Screening Tests ◽  
Anatomical Location ◽  
Risk Of Malignancy ◽  
Risk Of Malignancy Index ◽  
Grass Root Level

Background: Ovarian cancer possesses a challenge to screening tests due to its anatomical location, poor natural history, lack of specific lesion, symptoms and signs and low prevalence. Authors shall be considering RMI 2 and RMI 4 (forms of RMI) and comparing them with histopathology report to derive the sensitivity, specificity and other parameters of these tests.Methods: A prospective   study was conducted from September 2016- September 2017 at Mazumdar Shaw Hospital, Narayana Hrudayalaya, Bangalore.73 patients met the inclusion criteria. RMI 2   and RMI4 were calculated for all the patients and these scores were compared to the final histopathology reports.Results: In present study of 73 patients RMI2 showed a sensitivity of 86.6%, specificity of 86.5 %, Positive predictive value of 81.25% and negative predictive value of 90.24 %. Whereas RMI4 showed a sensitivity of 86.6%, specificity of 86.5 %, Positive predictive value of 83.87 and negative predictive value of 90.48 %. These results are comparable to other studies conducted.  The risk of malignancy index 2 and 4 are also almost comparable with each other and so either can be used for determining the risk of malignancy in patients with adnexal masses. These results were derived in an Indian population across all age groups showing that authors can apply this low-cost method even in resource limited settings.Conclusions: Authors found that Risk of malignancy index is a simple and affordable method to determine the likelihood of a patient having adnexal mass to be malignant. This can thus help save the resources and make the services available at grass root level.

scholarly journals Impact of COVID-19 pre-test probability on positive predictive value of high cycle threshold SARS-CoV-2 real-time reverse transcription PCR test results

2021 ◽  
pp. 1-18
Author(s):  
Jonathan B. Gubbay ◽  
Heather Rilkoff ◽  
Heather L. Kristjanson ◽  
Jessica D. Forbes ◽  
Michelle Murti ◽  
...  
Keyword(s):  
Positive Predictive Value ◽  
Real Time ◽  
Reverse Transcription ◽  
Predictive Value ◽  
Large Scale ◽  
Rdrp Gene ◽  
Nucleic Acid Detection ◽  
Rt Pcr ◽  
Pcr Assay ◽  
Test Probability

Abstract Objectives Performance characteristics of SARS-CoV-2 nucleic acid detection assays are understudied within contexts of low pre-test probability, including screening asymptomatic persons without epidemiological links to confirmed cases, or asymptomatic surveillance testing. SARS-CoV-2 detection without symptoms may represent presymptomatic or asymptomatic infection, resolved infection with persistent RNA shedding, or a false positive test. This study assessed positive predictive value of SARS-CoV-2 real-time reverse transcription polymerase chain reaction (rRT-PCR) assays by retesting positive specimens from five pre-test probability groups ranging from high to low with an alternate assay. Methods A total of 122 rRT-PCR positive specimens collected from unique patients between March and July 2020 were retested using a laboratory-developed nested RT-PCR assay targeting the RNA-dependent RNA polymerase (RdRp) gene followed by Sanger sequencing. Results Significantly fewer (15.6%) positive results in the lowest pre-test probability group (facilities with institution-wide screening having ≤ 3 positive asymptomatic cases) were reproduced with the nested RdRp gene RT-PCR assay than in each of the four groups with higher pre-test probability (individual group range 50·0% to 85·0%). Conclusions Large-scale SARS-CoV-2 screening testing initiatives among low pre-test probability populations should be evaluated thoroughly prior to implementation given the risk of false positives and consequent potential for harm at the individual and population level.

scholarly journals A Bayesian decision support sequential model for severity of illness predictors and intensive care admissions in pneumonia

2019 ◽  
Vol 19 (1) ◽  
Author(s):  
Amado Alejandro Baez ◽  
Laila Cochon ◽  
Jose Maria Nicolas
Keyword(s):  
Predictive Value ◽  
Severity Of Illness ◽  
Positive Test ◽  
Bayesian Decision ◽  
Likelihood Ratios ◽  
Negative Test ◽  
Significant Difference ◽  
Post Test ◽  
Post Test Probability ◽  
Test Probability

Abstract Background Community-acquired pneumonia (CAP) is one of the leading causes of morbidity and mortality in the USA. Our objective was to assess the predictive value on critical illness and disposition of a sequential Bayesian Model that integrates Lactate and procalcitonin (PCT) for pneumonia. Methods Sensitivity and specificity of lactate and PCT attained from pooled meta-analysis data. Likelihood ratios calculated and inserted in Bayesian/ Fagan nomogram to calculate posttest probabilities. Bayesian Diagnostic Gains (BDG) were analyzed comparing pre and post-test probability. To assess the value of integrating both PCT and Lactate in Severity of Illness Prediction we built a model that combined CURB65 with PCT as the Pre-Test markers and later integrated the Lactate Likelihood Ratio Values to generate a combined CURB 65 + Procalcitonin + Lactate Sequential value. Results The BDG model integrated a CUBR65 Scores combined with Procalcitonin (LR+ and LR-) for Pre-Test Probability Intermediate and High with Lactate Positive Likelihood Ratios. This generated for the PCT LR+ Post-test Probability (POSITIVE TEST) Posterior probability: 93% (95% CI [91,96%]) and Post Test Probability (NEGATIVE TEST) of: 17% (95% CI [15–20%]) for the Intermediate subgroup and 97% for the high risk sub-group POSITIVE TEST: Post-Test probability:97% (95% CI [95,98%]) NEGATIVE TEST: Post-test probability: 33% (95% CI [31,36%]) . ANOVA analysis for CURB 65 (alone) vs CURB 65 and PCT (LR+) vs CURB 65 and PCT (LR+) and Lactate showed a statistically significant difference (P value = 0.013). Conclusions The sequential combination of CURB 65 plus PCT with Lactate yielded statistically significant results, demonstrating a greater predictive value for severity of illness thus ICU level care.

scholarly journals 1188 Test Characteristics of a Machine Learned Electronic Medical Record Extractable Tool for OSA Case Identification in a Community-Based Population

SLEEP ◽  
2020 ◽  
Vol 43 (Supplement_1) ◽  
pp. A454-A454
Author(s):  
S I Patel ◽  
D Kukafka ◽  
C Antonescu ◽  
D Combs ◽  
J Lee-Iannotti ◽  
...  
Keyword(s):  
Positive Predictive Value ◽  
Likelihood Ratio ◽  
Predictive Value ◽  
Oxygen Desaturation ◽  
Positive Test ◽  
Community Based ◽  
Sleep Study ◽  
Case Identification ◽  
Test Characteristics ◽  
Patient Reported

Abstract Introduction Obstructive sleep apnea (OSA) is a significantly underdiagnosed medical condition. A machine learning method known as SLIM (Supersparse Linear Integer Models) that can be extracted from the Electronic Health Record (EHR) has found to be superior to patient-reported sleep-related symptoms to diagnose OSA. Such an evaluation, however, was previously validated in a laboratory-based population. Our aim was to determine the test characteristics for the EHR-extractable SLIM tool in a community-based population. Methods Subjects who participated in the Sleep Heart Health Study (SHHS) were included in this analysis. Variable definitions of OSA were determined using an Apnea Hypopnea Index (AHI) threshold of 5 per hour, 15 per hour, or the presence of any comorbidity (hypertension, ischemic heart disease, stroke, mood disorders, impairment of cognition, or sleepiness) when the AHI was between 5 to 15 per hour. Variable hypopnea definitions based upon degree of oxygen desaturation and associated arousals were considered. Results In the SHHS dataset, the Receiver Operating Characteristics (ROC) for a SLIM score threshold of 9 for men and 5 for women was good when OSA was defined by AHI > 5 per hour (hypopneas with either > 3% oxygen desaturation or arousals). Specifically, the ROC was 0.72 (95% Confidence Intervals [CI] 0.70; 0.74) with a Positive Predictive Value [PPV] of 0.98 and Likelihood Ratio of a positive test (LR+) of 11.3. The LR+ (6.0) and PPV (0.92) were also good when an AHI of 5 per hour threshold was adopted with hypopneas scored using the minimum 3% oxygen desaturation alone. Similarly, the ROC was good 0.74 (95%CI 0.73; 0.76) with a Positive Predictive Value [PPV] of 0.98 and Likelihood Ratio of a positive test (LR+) of 11.3. The LR+ (8.9) and PPV (0.81) were also good in the presence of comorbidities when AHI was 5 to 15 per hour using > 4% oxygen desaturation alone. Conclusion The EHR-extractable tool can be an actionable tool for case-identification of patients needing a referral for sleep study in a community-based population. Such an approach could facilitate an automated, rather than manual, OSA screening approach aimed at managing population health. Support HL138377

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