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.

Bayes' theorem: scientific assessment of experience

Homeopathy is based on experience and this is a scientific procedure if we follow Bayes' theorem. Unfortunately this is not the case at the moment. Symptoms are added to our materia medica based on absolute occurrence, while Bayes theorem tells us that this should be based on relative occurrence. Bayes theorem can be applied on prospective research, but also on retrospective research and consensus based on a large number of cases. Confirmation bias is an important source of false data in experience based systems like homeopathy. Homeopathic doctors should become more aware of this and longer follow-up of cases could remedy this. The existing system of adding symptoms to our materia medica is obsolete.

Providing a Forensic Expert Opinion on the “Degree of Force”: Evidentiary Considerations

Forensic pathologists and anthropologists are often asked in court for an opinion about the degree of force required to cause a specific injury. This paper examines and discusses the concept of ‘degree of force’ and why it is considered a pertinent issue in legal proceedings. This discussion identifies the implicit assumptions that often underpin questions about the ‘degree of force’. The current knowledge base for opinions on the degree of force is then provided by means of a literature review. A critical appraisal of this literature shows that much of the results from experimental research is of limited value in routine casework. An alternative approach to addressing the issue is provided through a discussion of the application of Bayes’ theorem, also called the likelihood ratio framework. It is argued that the use of this framework makes it possible for an expert to provide relevant and specific evidence, whilst maintaining the boundaries of their field of expertise.

A Multilayer Perceptron Neural Network Model to Classify Hypertension in Adolescents Using Anthropometric Measurements: A Cross-Sectional Study in Sarawak, Malaysia

This study outlines and developed a multilayer perceptron (MLP) neural network model for adolescent hypertension classification focusing on the use of simple anthropometric and sociodemographic data collected from a cross-sectional research study in Sarawak, Malaysia. Among the 2,461 data collected, 741 were hypertensive (30.1%) and 1720 were normal (69.9%). During the data gathering process, eleven anthropometric measurements and sociodemographic data were collected. The variable selection procedure in the methodology proposed selected five parameters: weight, weight-to-height ratio (WHtR), age, sex, and ethnicity, as the input of the network model. The developed MLP model with a single hidden layer of 50 hidden neurons managed to achieve a sensitivity of 0.41, specificity of 0.91, precision of 0.65, F -score of 0.50, accuracy of 0.76, and Area Under the Receiver Operating Characteristic (ROC) Curve (AUC) of 0.75 using the imbalanced data set. Analyzing the performance metrics obtained from the training, validation and testing data sets show that the developed network model is well-generalized. Using Bayes’ Theorem, an adolescent classified as hypertensive using this created model has a 66.2% likelihood of having hypertension in the Sarawak adolescent population, which has a hypertension prevalence of 30.1%. When the prevalence of hypertension in the Sarawak population was increased to 50%, the developed model could predict an adolescent having hypertension with an 82.0% chance, whereas when the prevalence of hypertension was reduced to 10%, the developed model could only predict true positive hypertension with a 33.6% chance. With the sensitivity of the model increasing to 65% and 90% while retaining a specificity of 91%, the true positivity of an adolescent being hypertension would be 75.7% and 81.2%, respectively, according to Bayes’ Theorem. The findings show that simple anthropometric measurements paired with sociodemographic data are feasible to be used to classify hypertension in adolescents using the developed MLP model in Sarawak adolescent population with modest hypertension prevalence. However, a model with higher sensitivity and specificity is required for better positive hypertension predictive value when the prevalence is low. We conclude that the developed classification model could serve as a quick and easy preliminary warning tool for screening high-risk adolescents of developing hypertension.

PENERAPAN METODE TEOREMA BAYES UNTUK MENDETEKSI HAMA PADA TANAMAN PADI MAYAS KALIMANTAN TIMUR

The community very much needs the nutritional needs of food during a pandemic. One source of nutrition that can be obtained is rice or rice derived from rice plants. Mayas rice is a rice plant with advantages in terms of high taste quality and components of certain physiological functions that are beneficial to health. However, Mayas rice has quite a lot of pest attacks, thus reducing agricultural production. On the other hand, the knowledge possessed by the community regarding pests in Mayas rice is still very minimal. Hence, people find it difficult to determine the proper pest control method. Bayes theorem applied in an expert system can be a solution to diagnose the types of pests that attack Mayas rice. The research data is a knowledge base that contains 32 symptoms that appear and 10 types of pests that attack Mayas rice. The results showed that the percentage of certainty in the diagnosis of the types of pests that pounded Mayas rice was based on the symptoms given by the user. The level of testing using ten test cases displays the results of an expert system for identifying types of pests that attack Mayas rice which is suitable for use with a percentage of 90%.

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.

SentiProdBR: Building Domain-Specific Sentiment Lexicons for the Portuguese Language

Online reviews are readily available on the Web and widely used for decision-making. However, only a few studies on Portuguese sentiment analysis are reported due to the lack of resources including domain-specific sentiment lexical collections. In this paper, we present an effective methodology using probabilities of the Bayes’ Theorem for building a set of lexicons, called SentiProdBR, for 10 different product categories for the Portuguese language. Experimental results indicate that our methodology significantly outperforms several alternative approaches of building domain-specific sentiment lexicons.

Making Sense of Medical Statistics

Do you want to know what a parametric test is and when not to perform one? Do you get confused between odds ratios and relative risks? Want to understand the difference between sensitivity and specificity? Would like to find out what the fuss is about Bayes' theorem? Then this book is for you! Physicians need to understand the principles behind medical statistics. They don't need to learn the formula. The software knows it already! This book explains the fundamental concepts of medical statistics so that the learner will become confident in performing the most commonly used statistical tests. Each chapter is rich in anecdotes, illustrations, questions, and answers. Not enough? There is more material online with links to free statistical software, webpages, multimedia content, a practice dataset to get hands-on with data analysis, and a Single Best Answer questionnaire for the exam.

Bayesian Statistics

The chapter “Bayesian Statistics” gives a brief overview of the Bayesian approach to statistical analysis. It starts off by examining the difference between frequentist statistics and Bayesian statistics. Next, it introduces Bayes’ theorem and explains how the theorem is used in statistics and model selection, with the prosecutor’s fallacy given as a practice example. The chapter then goes on to discuss priors and Bayesian parameter estimation. It concludes with some final thoughts on Bayesian approaches. The chapter does not answer the question “Should ecologists become Bayesian?” However, to the extent that alternative models can be posed as alternative values of parameters, Bayesian parameter estimation can help assign probabilities to those hypotheses.