Integrating external summary information in the presence of prior probability shift: an application to assessing essential hypertension.

Recent years have witnessed a rise in the popularity of information integration without sharing of raw data. By leveraging and incorporating summary information from external sources, internal studies can achieve enhanced estimation efficiency and prediction accuracy. However, a noteworthy challenge in utilizing summary-level information is accommodating the inherent heterogeneity across diverse data sources. In this study, we delve into the issue of prior probability shift between two cohorts, wherein the difference of two data distributions depends on the outcome. We introduce a novel semi-parametric constrained optimization-based approach to integrate information within this framework, which has not been extensively explored in existing literature. Our proposed method tackles the prior probability shift by introducing the outcome-dependent selection function and effectively addresses the estimation uncertainty associated with summary information from the external source. Our approach facilitates valid inference even in the absence of a known variance-covariance estimate from the external source. Through extensive simulation studies, we observe the superiority of our method over existing ones, showcasing minimal estimation bias and reduced variance for both binary and continuous outcomes. We further demonstrate the utility of our method through its application in investigating risk factors related to essential hypertension, where the reduced estimation variability is observed after integrating summary information from an external data.

A Color- and Geometric-Feature-Based Approach for Denoising Three-Dimensional Cultural Relic Point Clouds.

In the acquisition process of 3D cultural relics, it is common to encounter noise. To facilitate the generation of high-quality 3D models, we propose an approach based on graph signal processing that combines color and geometric features to denoise the point cloud. We divide the 3D point cloud into patches based on self-similarity theory and create an appropriate underlying graph with a Markov property. The features of the vertices in the graph are represented using 3D coordinates, normal vectors, and color. We formulate the point cloud denoising problem as a maximum a posteriori (MAP) estimation problem and use a graph Laplacian regularization (GLR) prior to identifying the most probable noise-free point cloud. In the denoising process, we moderately simplify the 3D point to reduce the running time of the denoising algorithm. The experimental results demonstrate that our proposed approach outperforms five competing methods in both subjective and objective assessments. It requires fewer iterations and exhibits strong robustness, effectively removing noise from the surface of cultural relic point clouds while preserving fine-scale 3D features such as texture and ornamentation. This results in more realistic 3D representations of cultural relics.

The challenges of identifying and studying type 1 diabetes in adults.

Diagnosing type 1 diabetes in adults is difficult since type 2 diabetes is the predominant diabetes type, particularly with an older age of onset (approximately >30 years). Misclassification of type 1 diabetes in adults is therefore common and will impact both individual patient management and the reported features of clinically classified cohorts. In this article, we discuss the challenges associated with correctly identifying adult-onset type 1 diabetes and the implications of these challenges for clinical practice and research. We discuss how many of the reported differences in the characteristics of autoimmune/type 1 diabetes with increasing age of diagnosis are likely explained by the inadvertent study of mixed populations with and without autoimmune aetiology diabetes. We show that when type 1 diabetes is defined by high-specificity methods, clinical presentation, islet-autoantibody positivity, genetic predisposition and progression of C-peptide loss remain broadly similar and severe at all ages and are unaffected by onset age within adults. Recent clinical guidance recommends routine islet-autoantibody testing when type 1 diabetes is clinically suspected or in the context of rapid progression to insulin therapy after a diagnosis of type 2 diabetes. In this moderate or high prior-probability setting, a positive islet-autoantibody test will usually confirm autoimmune aetiology (type 1 diabetes). We argue that islet-autoantibody testing of those with apparent type 2 diabetes should not be routinely undertaken as, in this low prior-prevalence setting, the positive predictive value of a single-positive islet antibody for autoimmune aetiology diabetes will be modest. When studying diabetes, extremely high-specificity approaches are needed to identify autoimmune diabetes in adults, with the optimal approach depending on the research question. We believe that until these recommendations are widely adopted by researchers, the true phenotype of late-onset type 1 diabetes will remain largely misunderstood.

Wireless Body Area Network (WBAN)-Based Telemedicine for Emergency Care.

This paper is a collection of telemedicine techniques used by wireless body area networks (WBANs) for emergency conditions. Furthermore, Bayes' theorem is proposed for predicting emergency conditions. With prior knowledge, the posterior probability can be found along with the observed evidence. The probability of sending emergency messages can be determined using Bayes' theorem with the likelihood evidence. It can be viewed as medical decision-making, since diagnosis conditions such as emergency monitoring, delay-sensitive monitoring, and general monitoring are analyzed with its network characteristics, including data rate, cost, packet loss rate, latency, and jitter. This paper explains the network model with 16 variables, with one describing immediate consultation, as well as another three describing emergency monitoring, delay-sensitive monitoring, and general monitoring. The remaining 12 variables are observations related to latency, cost, packet loss rate, data rate, and jitter.

Reliability of the Buttock Applied Strain Test to Diagnose Radicular Pain in Patients With Low Back Pain.

BACKGROUND: Low-back pain (LBP) pathophysiological conditions include nociceptive back pain, somatic referred pain, radicular pain (RP), and radiculopathy. Differential diagnosis is challenging; guidance may come from patients' thorough clinical history and physical examination and, particularly for lumbar RP, from the evaluation of subjective responses of injured lumbar nerves to a strain applied at the buttock (buttock applied strain [BUAS] test). METHODS: In a sample of 395 consecutive patients with LBP, sensitivity, specificity, and prior probability (positive predictive values [PPVs] and negative predictive values [NPVs]) of the BUAS test were evaluated against 2 reference tests: the straight leg raising test (SLRT) and the painDETECT (PD) questionnaire. Multinomial logistic regression (MLR) and χ2 analyses were used to evaluate the BUAS test outcomes' dependence upon independent variables (gender, age group, pain localization, SLRT outcomes, and PD outcomes). Cohen's kappa statistic was used to assess inter-rater agreement. RESULTS: Compared with the PD questionnaire, the BUAS test showed a sensitivity of 92%, specificity of 100%, PPV of 100%, and NPV of 82%; compared with the SLRT, the BUAS test showed a sensitivity of 82%, NPV of 82%, specificity of 40%, and PPV of 40%. Inter-rater agreement of Cohen's kappa was 0.911. Significant associations were found between BUAS test outcomes and pain localization, SLRT outcomes, and PD outcomes, but not with the predictors gender or age group. MLR showed significant congruent relationships between BUAS test and PD outcomes. CONCLUSION: Among patients with LBP, the BUAS test showed satisfactory sensitivity, specificity, prior probability, and inter-rater reliability; thus, it may be considered a useful adjunctive tool to diagnose RP in patients with LBP. For more generalized results, more research, in clinical settings other than pain clinics, is needed.

Bayesian Update with Information Quality under the Framework of Evidence Theory.

Bayesian update is widely used in data fusion. However, the information quality is not taken into consideration in classical Bayesian update method. In this paper, a new Bayesian update with information quality under the framework of evidence theory is proposed. First, the discounting coefficient is determined by information quality. Second, the prior probability distribution is discounted as basic probability assignment. Third, the basic probability assignments from different sources can be combined with Dempster's combination rule to obtain the fusion result. Finally, with the aid of pignistic probability transformation, the combination result is converted to posterior probability distribution. A numerical example and a real application in target recognition show the efficiency of the proposed method. The proposed method can be seen as the generalized Bayesian update. If the information quality is not considered, the proposed method degenerates to the classical Bayesian update.

Prior probabilities modulate cortical surprise responses: A study of event-related potentials.

The human brain predicts events in its environment based on expectations, and unexpected events are surprising. When probabilistic contingencies in the environment are precisely instructed, the individual can form expectations based on quantitative probabilistic information ('inference-based learning'). In contrast, when probabilistic contingencies are imprecisely instructed, expectations are formed based on the individual's cumulative experience ('experience-based learning'). Here, we used the urn-ball paradigm to investigate how variations in prior probabilities and in the precision of information about these priors modulate choice behavior and event-related potential (ERP) correlates of surprise. In the urn-ball paradigm, participants are repeatedly forced to infer hidden states responsible for generating observable events, given small samples of factual observations. We manipulated prior probabilities of the states, and we rendered the priors calculable or incalculable, respectively. The analysis of choice behavior revealed that the tendency to consider prior probabilities when making decisions about hidden states was stronger when prior probabilities were calculable, at least in some of our participants. Surprise-related P3b amplitudes were observed in both the calculable and the incalculable prior probability condition. In contrast, calculability of prior probabilities modulated anteriorly distributed ERP amplitudes: when prior probabilities were calculable, surprising events elicited enhanced P3a amplitudes. However, when prior probabilities were incalculable, surprise was associated with enhanced N2 amplitudes. Furthermore, interindividual variability in reliance on prior probabilities was associated with attenuated P3b surprise responses under calculable in comparison to incalculable prior probabilities. Our results suggest two distinct neural systems for probabilistic learning that are recruited depending on contextual cues such as the precision of probabilistic information. Individuals with stronger tendencies to rely on calculable prior probabilities seem to have better adapted expectations at their disposal, as indicated by an attenuation of their P3b surprise responses when prior probabilities are calculable.

Modeling senescence changes of the pubic symphysis in historic Italian populations: a comparison of the Rostock and forensic approaches to aging using transition analysis.

Age-related anatomical changes to the surface of the pubic symphysis are well-documented in the literature. However, aligning these morphological changes with chronological age has proven problematic, often resulting in biased age estimates. Statistical modeling provides an avenue for forensic anthropologists and bioarchaeologists to increase the accuracy of traditional aging methods. Locating appropriate samples to use as a basis for modeling age estimations can be challenging due to differing sample age distributions and potentially varying patterns of senescence. We compared two approaches, Rostock and Forensic, coupled with a Bayesian methodology, to address these issues. Transition analysis was run specific to each method (which differ by sample selection). A Gompertz model was derived from an informative prior that yielded the mortality and senescence parameters for constructing highest posterior density ranges, i.e., coverages, which are analogous to age ranges. These age ranges were generated from both approaches and are presented as reference tables useful for historic male and female Italian samples. The age ranges produced from each approach were tested on an historic Italian sample, using cumulative binomial tests. These two approaches performed similarly, with the Forensic approach showing a slight advantage. However, the Forensic approach is unable to identify varying senescence patterns between populations, thus preference for one approach over the other will depend on research design. Finally, we demonstrate that while populations exhibit similar morphological changes with advancing age, there are no significant sex differences in these samples, and the timing of these changes varies from population to population.

A Software Tool for Estimating Uncertainty of Bayesian Posterior Probability for Disease.

The role of medical diagnosis is essential in patient care and healthcare. Established diagnostic practices typically rely on predetermined clinical criteria and numerical thresholds. In contrast, Bayesian inference provides an advanced framework that supports diagnosis via in-depth probabilistic analysis. This study's aim is to introduce a software tool dedicated to the quantification of uncertainty in Bayesian diagnosis, a field that has seen minimal exploration to date. The presented tool, a freely available specialized software program, utilizes uncertainty propagation techniques to estimate the sampling, measurement, and combined uncertainty of the posterior probability for disease. It features two primary modules and fifteen submodules, all designed to facilitate the estimation and graphical representation of the standard uncertainty of the posterior probability estimates for diseased and non-diseased population samples, incorporating parameters such as the mean and standard deviation of the test measurand, the size of the samples, and the standard measurement uncertainty inherent in screening and diagnostic tests. Our study showcases the practical application of the program by examining the fasting plasma glucose data sourced from the National Health and Nutrition Examination Survey. Parametric distribution models are explored to assess the uncertainty of Bayesian posterior probability for diabetes mellitus, using the oral glucose tolerance test as the reference diagnostic method.

Modelling decision-making biases.

Biases are a fundamental aspect of everyday life decision-making. A variety of modelling approaches have been suggested to capture decision-making biases. Statistical models are a means to describe the data, but the results are usually interpreted according to a verbal theory. This can lead to an ambiguous interpretation of the data. Mathematical cognitive models of decision-making outline the structure of the decision process with formal assumptions, providing advantages in terms of prediction, simulation, and interpretability compared to statistical models. We compare studies that used both signal detection theory and evidence accumulation models as models of decision-making biases, concluding that the latter provides a more comprehensive account of the decision-making phenomena by including response time behavior. We conclude by reviewing recent studies investigating attention and expectation biases with evidence accumulation models. Previous findings, reporting an exclusive influence of attention on the speed of evidence accumulation and prior probability on starting point, are challenged by novel results suggesting an additional effect of attention on non-decision time and prior probability on drift rate.

A Bayesian Inference Based Computational Tool for Parametric and Nonparametric Medical Diagnosis.

Medical diagnosis is the basis for treatment and management decisions in healthcare. Conventional methods for medical diagnosis commonly use established clinical criteria and fixed numerical thresholds. The limitations of such an approach may result in a failure to capture the intricate relations between diagnostic tests and the varying prevalence of diseases. To explore this further, we have developed a freely available specialized computational tool that employs Bayesian inference to calculate the posterior probability of disease diagnosis. This novel software comprises of three distinct modules, each designed to allow users to define and compare parametric and nonparametric distributions effectively. The tool is equipped to analyze datasets generated from two separate diagnostic tests, each performed on both diseased and nondiseased populations. We demonstrate the utility of this software by analyzing fasting plasma glucose, and glycated hemoglobin A1c data from the National Health and Nutrition Examination Survey. Our results are validated using the oral glucose tolerance test as a reference standard, and we explore both parametric and nonparametric distribution models for the Bayesian diagnosis of diabetes mellitus.

Probabilistic machine learning for breast cancer classification.

A probabilistic neural network has been implemented to predict the malignancy of breast cancer cells, based on a data set, the features of which are used for the formulation and training of a model for a binary classification problem. The focus is placed on considerations when building the model, in order to achieve not only accuracy but also a safe quantification of the expected uncertainty of the calculated network parameters and the medical prognosis. The source code is included to make the results reproducible, also in accordance with the latest trending in machine learning research, named Papers with Code. The various steps taken for the code development are introduced in detail but also the results are visually displayed and critically analyzed also in the sense of explainable artificial intelligence. In statistical-classification problems, the decision boundary is the region of the problem space in which the classification label of the classifier is ambiguous. Problem aspects and model parameters which influence the decision boundary are a special aspect of practical investigation considered in this work. Classification results issued by technically transparent machine learning software can inspire more confidence, as regards their trustworthiness which is very important, especially in the case of medical prognosis. Furthermore, transparency allows the user to adapt models and learning processes to the specific needs of a problem and has a boosting influence on the development of new methods in relevant machine learning fields (transfer learning).

Remote, real-time expert elicitation to determine the prior probability distribution for Bayesian sample size determination in international randomised controlled trials: Bronchiolitis in Infants Placebo Versus Epinephrine and Dexamethasone (BIPED) study.

BACKGROUND: Bayesian methods are increasing in popularity in clinical research. The design of Bayesian clinical trials requires a prior distribution, which can be elicited from experts. In diseases with international differences in management, the elicitation exercise should recruit internationally, making a face-to-face elicitation session expensive and more logistically challenging. Thus, we used a remote, real-time elicitation exercise to construct prior distributions. These elicited distributions were then used to determine the sample size of the Bronchiolitis in Infants with Placebo Versus Epinephrine and Dexamethasone (BIPED) study, an international randomised controlled trial in the Pediatric Emergency Research Network (PERN). The BIPED study aims to determine whether the combination of epinephrine and dexamethasone, compared to placebo, is effective in reducing hospital admission for infants presenting with bronchiolitis to the emergency department. METHODS: We developed a Web-based tool to support the elicitation of the probability of hospitalisation for infants with bronchiolitis. Experts participated in online workshops to specify their individual prior distributions, which were aggregated using the equal-weighted linear pooling method. Experts were then invited to provide their comments on the aggregated distribution. The average length criterion determined the BIPED sample size. RESULTS: Fifteen paediatric emergency medicine clinicians from Canada, the USA, Australia and New Zealand participated in three workshops to provide their elicited prior distributions. The mean elicited probability of admission for infants with bronchiolitis was slightly lower for those receiving epinephrine and dexamethasone compared to supportive care in the aggregate distribution. There were substantial differences in the individual beliefs but limited differences between North America and Australasia. From this aggregate distribution, a sample size of 410 patients per arm results in an average 95% credible interval length of less than 9% and a relative predictive power of 90%. CONCLUSION: Remote, real-time expert elicitation is a feasible, useful and practical tool to determine a prior distribution for international randomised controlled trials. Bayesian methods can then determine the trial sample size using these elicited prior distributions. The ease and low cost of remote expert elicitation mean that this approach is suitable for future international randomised controlled trials. TRIAL REGISTRATION: ClinicalTrials.gov NCT03567473.

Bayesian Statistics for Surgical Decision Making.

Background: Application of clinical study findings to surgical decision making requires accurate interpretation of the results, integration of the findings within the context of pre-existing knowledge and use of statistics to answer clinically relevant questions. Bayesian analyses are optimally suited for interpretation of study findings, supporting translation to the bedside. Discussion: Surgical decision making is a complex process that draws on an individual clinician's medical knowledge, experience, data, and the patient's unique characteristics and preferences. Subjective and objective knowledge may be merged to derive a probability of benefit or harm of a treatment under consideration. Bayesian reasoning complements the clinical decision-making process by incorporating known evidence and data from a new study to determine the probability of an outcome of interest. Bayesian analyses are statistically robust and intuitive when translating findings of a study into clinical care. In contrast, frequentist statistics are poorly suited to translate study findings to clinical application. This review aims to highlight the benefits of incorporating Bayesian analyses into clinical research. Conclusion: Bayesian analyses offer clinically relevant information including the probability of benefit or harm of a treatment under consideration while accounting for uncertainty. This information may be incorporated easily and accurately into surgical decision making.

Evaluation of an integrative Bayesian peptide detection approach on a combinatorial peptide library.

Detection of peptides lies at the core of bottom-up proteomics analyses. We examined a Bayesian approach to peptide detection, integrating match-based models (fragments, retention time, isotopic distribution, and precursor mass) and peptide prior probability models under a unified probabilistic framework. To assess the relevance of these models and their various combinations, we employed a complete- and a tail-complete search of a low-precursor-mass synthetic peptide library based on oncogenic KRAS peptides. The fragment match was by far the most informative match-based model, while the retention time match was the only remaining such model with an appreciable impact--increasing correct detections by around 8 %. A peptide prior probability model built from a reference proteome greatly improved the detection over a uniform prior, essentially transforming de novo sequencing into a reference-guided search. The knowledge of a correct sequence tag in advance to peptide-spectrum matching had only a moderate impact on peptide detection unless the tag was long and of high certainty. The approach also derived more precise error rates on the analyzed combinatorial peptide library than those estimated using PeptideProphet and Percolator, showing its potential applicability for the detection of homologous peptides. Although the approach requires further computational developments for routine data analysis, it illustrates the value of peptide prior probabilities and presents a Bayesian approach for their incorporation into peptide detection.

Bayes' rule in diagnosis.

Establishing an accurate diagnosis is crucial in everyday clinical practice. It forms the starting point for clinical decision-making, for instance regarding treatment options or further testing. In this context, clinicians have to deal with probabilities (instead of certainties) that are often hard to quantify. During the diagnostic process, clinicians move from the probability of disease before testing (prior or pretest probability) to the probability of disease after testing (posterior or posttest probability) based on the results of one or more diagnostic tests. This reasoning in probabilities is reflected by a statistical theorem that has an important application in diagnosis: Bayes' rule. A basic understanding of the use of Bayes' rule in diagnosis is pivotal for clinicians. This rule shows how both the prior probability (also called prevalence) and the measurement properties of diagnostic tests (sensitivity and specificity) are crucial determinants of the posterior probability of disease (predictive value), on the basis of which clinical decisions are made. This article provides a simple explanation of the interpretation and use of Bayes' rule in diagnosis.

The new accounting for expected adjusted effect test (AEAE test) has higher positive predictive value than a zero-order significance test.

OBJECTIVE: The present simulation study aimed to assess positive predictive value (PPV) and negative predictive value (NPV) for our newly introduced Accounting for Expected Adjusted Effect test (AEAE test) and compare it to PPV and NPV for a traditional zero-order significance test. RESULTS: The AEAE test exhibited greater PPV compared to a traditional zero-order significance test, especially with a strong true adjusted effect, low prior probability, high degree of confounding, large sample size, high reliability in the measurement of predictor X and outcome Y, and low reliability in the measurement of confounder Z. The zero-order significance test, on the other hand, exhibited higher NPV, except for some combinations of high degree of confounding and large sample size, or low reliability in the measurement of Z and high reliability in the measurement of X/Y, in which case the zero-order significance test can be completely uninformative. Taken together, the findings demonstrate desirable statistical properties for the AEAE test compared to a traditional zero-order significance test.

Comparing Objective and Subjective Bayes Factors for the Two-Sample Comparison: The Classification Theorem in Action.

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?"

[Coordinated distributed experiments 2.0 (CDE 2.0): A novelty methodology of ecological field investigation]. / 协同分布式实验2.0 (CDE 2.0):ç”Ÿæ€å­¦é‡Žå¤–ç ”ç©¶æ–°æ–¹æ³•.

The global field experiment network is rapidly growing in ecological research in recent years. Some specific methods have emerged, such as the Coordinated Distributed Experiments (CDE), Distributed Collaborative Experiments (DCE), and field observational network of British Biological Records Centre (BRC). However, problems including too small scale, short duration and biased data are criticized in these methods. Construction of the protocol of field experiment network should follow several principles: controlled experiment prior to observation, quantity prior to quality of data, and scale prior to operation. Here, I advocated the application of citizen science to the obtaining of the data in large field, at multi-scale, and with a long duration. Environmental factors could be considered as covariant to test the dataset provided by citizen participants. Furthermore, the same dataset, as posterior probability, could be compared with the priori data set provided by ecologists to test the validity of data. This methodology, with the corresponding statistical model, would overcome the shortcoming of qualitative bias of data in citizen science. The application of priori probability, logistical relation between priori and posteriori probability, and possibility of discovering new causality of evolutionary process in ecological experimental data were discussed. Compared with CDE, CED, and BRC, this method improved the match between statistical norm and sampling quantity in large spatial and temporal scales. This new method would help discover the general theory of ecology researches and it could be termed "Coordinated Distributed Experiments 2.0" (CDE 2.0).