Informative Prior Distributions Research Articles

Solutions for surrogacy validation with longitudinal outcomes for a gene therapy.

Valid surrogate endpoints S can be used as a substitute for a true outcome of interest T to measure treatment efficacy in a clinical trial. We propose a causal inference approach to validate a surrogate by incorporating longitudinal measurements of the true outcomes using a mixed modeling approach, and we define models and quantities for validation that may vary across the study period using principal surrogacy criteria. We consider a surrogate-dependent treatment efficacy curve that allows us to validate the surrogate at different time points. We extend these methods to accommodate a delayed-start treatment design where all patients eventually receive the treatment. Not all parameters are identified in the general setting. We apply a Bayesian approach for estimation and inference, utilizing more informative prior distributions for selected parameters. We consider the sensitivity of these prior assumptions as well as assumptions of independence among certain counterfactual quantities conditional on pretreatment covariates to improve identifiability. We examine the frequentist properties (bias of point and variance estimates, credible interval coverage) of a Bayesian imputation method. Our work is motivated by a clinical trial of a gene therapy where the functional outcomes are measured repeatedly throughout thetrial.

Deep convolutional correlation iterative particle filter for visual tracking

This work proposes a novel framework for visual tracking based on the integration of an iterative particle filter, a deep convolutional neural network, and a correlation filter. The iterative particle filter enables the particles to correct themselves and converge to the correct target position. We employ a novel strategy to assess the likelihood of the particles after the iterations by applying K-means clustering. Our approach ensures a consistent support for the posterior distribution. Thus, we do not need to perform resampling at every video frame, improving the utilization of prior distribution information. Experimental results on three different benchmark datasets show that our tracker performs favorably against state-of-the-art methods.

Probabilistic prediction of engineering demand parameters using Bayesian inference approach

Nonlinear time history analysis is the most accurate method for obtaining engineering demand parameters, but it is also the most time-consuming. Therefore, only a limited number of ground motions are typically used, which increases uncertainty and is highly dependent on the ground motion selection. It is critical to obtain an accurate probability density function using risk-based methods. As a result, a Bayesian inference approach that employs a significant number of linear analyses to form beliefs is proposed in this paper. First, the posterior distributions obtained from a Bayesian model are used to form informative prior distributions in a new model based on non-informative prior and linear analysis results. The Bayesian model is then updated with a new set of limited number of nonlinear responses. As a result, it is possible to simulate the artificial responses using Monte-Carlo simulations to develop the probability density functions. Furthermore, by considering the desired number of intensity measures and without the need to separately examine their efficiency and sufficiency, the proposed method reduces the uncertainty associated with selecting a specific intensity measure. The proposed method, when applied to three sample buildings with three different hazard levels, shows a significant improvement in statistical prediction and produces reliable probability density functions. Furthermore, the sensitivity to ground motion selection is significantly reduced. Case studies demonstrate the proposed method's insensitivity not only at different hazard levels, but also at different building heights.

Instance weighted SMOTE by indirectly exploring the data distribution

The synthetic minority oversampling technique (SMOTE) algorithm is considered a benchmark algorithm for addressing the class imbalance learning (CIL) problem. However, SMOTE fails to observe the distribution of the training data and to explore its internal structure, resulting in an unstable and non-robust classification result. Recently, more than 100 SMOTE variants have been developed to solve this problem. Most of them attempt to directly explore the prior distribution information of the training data, which may provide extremely inaccurate guidance in some classification scenarios. In this study, we present the instance weighted SMOTE (IW-SMOTE) algorithm, a more robust and universal solution for improving SMOTE by exploit distribution data indirectly. In particular, an UnderBagging-alike undersampling ensemble algorithm that uses classification and regression tree (CART) as the base classifier is first adopted to classify each training instance and acquire the corresponding confusing information. We can accurately estimate location information for each instance, including noise, borders and safety, based on the confusing information. Then, the noisy instances can be removed, and the borderline instances can be given more chances than the safe instances to be seed instances in the SMOTE procedure. Finally, the balanced instance set was used to train the CART, K nearest neighbors (KNN) and support vector machine (SVM) classifiers to verify whether the proposed algorithm is irrelevant to the specific classification model. We compare IW-SMOTE with several state-of-the-art SMOTE-based algorithms on many class imbalance data sets, and IW-SMOTE shows promising results.

Bayesian approach for prediction of primary water stress corrosion cracking in Alloy 690 steam generator tubing

Alloy 690 tubing has been shown to be highly resistant to primary water stress corrosion cracking (PWSCC). Nevertheless, predicting the failure by PWSCC in Alloy 690 SG tubes is indispensable. In this work, a Bayesian-based statistical approach is proposed to predict the occurrence of failure by PWSCC in Alloy 690 SG tubing. The prior distributions of the model parameters are developed based on the prior knowledge or information regarding the parameters. Since Alloy 690 is a replacement for Alloy 600, the parameter distributions of Alloy 600 tubing are used to gain prior information about the parameters of Alloy 690 tubing. In addition to estimating the model parameters, analysis of tubing reliability is also performed. Since no PWSCC has been observed in Alloy 690 tubing, only right-censored free-failure life of the tubing are available. Apparently the inference is sensitive to the choice of prior distribution when only right-censored data exist. Thus, one must be careful in choosing the prior distributions for the model parameters. It is found that the use of non-informative prior distribution yields unsatisfactory results, and strongly informative prior distribution will greatly influence the inference, especially when it is considerably optimistic relative to the observed data.

Evaluating the performance of Bayesian and restricted maximum likelihood estimation for stepped wedge cluster randomized trials with a small number of clusters

BackgroundStepped wedge trials are an appealing and potentially powerful cluster randomized trial design. However, they are frequently implemented with a small number of clusters. Standard analysis methods for these trials such as a linear mixed model with estimation via maximum likelihood or restricted maximum likelihood (REML) rely on asymptotic properties and have been shown to yield inflated type I error when applied to studies with a small number of clusters. Small-sample methods such as the Kenward-Roger approximation in combination with REML can potentially improve estimation of the fixed effects such as the treatment effect. A Bayesian approach may also be promising for such multilevel models but has not yet seen much application in cluster randomized trials.MethodsWe conducted a simulation study comparing the performance of REML with and without a Kenward-Roger approximation to a Bayesian approach using weakly informative prior distributions on the intracluster correlation parameters. We considered a continuous outcome and a range of stepped wedge trial configurations with between 4 and 40 clusters. To assess method performance we calculated bias and mean squared error for the treatment effect and correlation parameters and the coverage of 95% confidence/credible intervals and relative percent error in model-based standard error for the treatment effect.ResultsBoth REML with a Kenward-Roger standard error and degrees of freedom correction and the Bayesian method performed similarly well for the estimation of the treatment effect, while intracluster correlation parameter estimates obtained via the Bayesian method were less variable than REML estimates with different relative levels of bias.ConclusionsThe use of REML with a Kenward-Roger approximation may be sufficient for the analysis of stepped wedge cluster randomized trials with a small number of clusters. However, a Bayesian approach with weakly informative prior distributions on the intracluster correlation parameters offers a viable alternative, particularly when there is interest in the probability-based inferences permitted within this paradigm.

A dynamic criterion for failure probability prediction of GFRP laminates using Lamb wave velocity with improved accuracy and consistency

This paper presents a dynamic criterion for improving the performance on fatigue life and failure probability prediction of GFRP laminates using Lamb wave velocity. A statistic damage model is built upon a Lamb wave velocity degradation model by introducing a normal distributed random variable to represent the uncertainties. The posterior distributions of the model parameters are obtained by Bayesian inference and Metropolis-Hastings algorithm with noninformative and informative prior distributions. Most importantly, a dynamic criterion is proposed to obtain a specimen-specific failure threshold value based on an assumption that the critical damage stage (CDS) of each specimen differs due to the randomicity of initial flaws. Experimental validation is conducted to compare the predicted fatigue life with both the dynamic criterion and traditional static criterion. The results show that applications of the dynamic criterion can improve the predicting accuracy and consistency, especially during early stages when available data is limited.

Bayesian Hierarchical Modelling of Historical Data of the South African Coal Mining Industry for Compliance Testing

Bayesian hierarchical framework for exposure data compliance testing is highly recommended in occupational hygiene. However, it has not been used for coal dust exposure compliance testing in South Africa (SA). The Bayesian analysis incorporates prior information, which increases solid decision making regarding risk management. This study compared the posterior 95th percentile (P95) of the Bayesian non-informative and informative prior from historical data relative to the occupational exposure limit (OEL) and exposure categories, and the South African Mining Industry Code of Practice (SAMI CoP) approach. A total of nine homogenous exposure groups (HEGs) with a combined 243 coal mine workers’ coal dust exposure data were included in this study. Bayesian framework with Markov chain Monte Carlo (MCMC) simulation to draw a full P95 posterior distribution relative to the OEL was used to investigate compliance. We obtained prior information from historical data and employed non-informative prior distribution to generate the posterior findings. The findings were compared to the SAMI CoP. The SAMI CoP 90th percentile (P90) indicated that one HEG was compliant (below the OEL), while none of the HEGs in the Bayesian methods were compliant. The analysis using non-informative prior indicated a higher variability of exposure than the informative prior according to the posterior GSD. The median P95 from the non-informative prior were slightly lower with wider 95% credible intervals (CrI) than the informative prior. All the HEGs in both Bayesian approaches were in exposure category four (poorly controlled), with the posterior probabilities slightly lower in the non-informative uniform prior distribution. All the methods mainly indicated non-compliance from the HEGs. The non-informative prior, however, showed a possible potential of allocating HEGs to a lower exposure category, but with high uncertainty compared to the informative prior distribution from historical data. Bayesian statistics with informative prior derived from historical data should be highly encouraged in coal dust overexposure assessments in South Africa for correct decision making.

An Interpretable Double-Scale Attention Model for Enzyme Protein Class Prediction Based on Transformer Encoders and Multi-Scale Convolutions.

Background Classification and annotation of enzyme proteins are fundamental for enzyme research on biological metabolism. Enzyme Commission (EC) numbers provide a standard for hierarchical enzyme class prediction, on which several computational methods have been proposed. However, most of these methods are dependent on prior distribution information and none explicitly quantifies amino-acid-level relations and possible contribution of sub-sequences. Methods In this study, we propose a double-scale attention enzyme class prediction model named DAttProt with high reusability and interpretability. DAttProt encodes sequence by self-supervised Transformer encoders in pre-training and gathers local features by multi-scale convolutions in fine-tuning. Specially, a probabilistic double-scale attention weight matrix is designed to aggregate multi-scale features and positional prediction scores. Finally, a full connection linear classifier conducts a final inference through the aggregated features and prediction scores. Results On DEEPre and ECPred datasets, DAttProt performs as competitive with the compared methods on level 0 and outperforms them on deeper task levels, reaching 0.788 accuracy on level 2 of DEEPre and 0.967 macro-F 1 on level 1 of ECPred. Moreover, through case study, we demonstrate that the double-scale attention matrix learns to discover and focus on the positions and scales of bio-functional sub-sequences in the protein. Conclusion Our DAttProt provides an effective and interpretable method for enzyme class prediction. It can predict enzyme protein classes accurately and furthermore discover enzymatic functional sub-sequences such as protein motifs from both positional and spatial scales.

Methods for Eliciting Informative Prior Distributions: A Critical Review

Eliciting informative prior distributions for Bayesian inference can often be complex and challenging. Although popular methods rely on asking experts probability-based questions to quantify uncertainty, these methods are not without their drawbacks, and many alternative elicitation methods exist. This paper explores methods for eliciting informative priors categorized by type and briefly discusses their strengths and limitations. Most of the review literature in this field focuses on a particular type of elicitation approach. The primary aim of this work, however, is to provide a more complete yet macro view of the state of the art by highlighting new (and old) approaches in one clear easy-to-read article. Two representative applications are used throughout to explore the suitability, or lack thereof, of the existing methods, one of which highlights a challenge that has not been addressed in the literature yet. We identify some of the gaps in the present work and discuss directions for future research.

Bayesian prior distribution based on generic data and experts’ opinion: A case study in the O&G industry

Reliability estimation is an essential task to ensure predictability on the life of equipment installed in oil wells, allowing forecasting costs, planning maintenance, and estimating system availability. However, data may be rather scarce and/or expensive to obtain, especially for technologies under development in the Oil and Gas (O&G) industry. The information is frequently available in generic databases and expert opinions. In the Bayesian framework, the prior knowledge about a system's reliability is updated as a new field and/or test data are gathered. This paper proposes an approach that does not require direct elicitation of parameters to define informative prior distributions for the reliability function using fault tree analysis, expert's opinions, and/or generic data at the system level of equipment under development. Specifically, the method-of-moments and maximum-entropy are adopted to propagate downward the uncertainty from the system level through the failure modes until the basic events of the fault tree, weighted by the expert knowledge of the failure behavior. Then, in possession of all prior distributions of the basic events, the information may be propagated upward based on Monte Carlo simulation to update the system reliability distribution. Finally, we present a case study of the proposed methodology applied to a novel open-hole expandable packer, a completion equipment recently installed in a Brazilian oil field. The failure modes and failure causes are discussed, and, after expert elicitation, the definition of the informative prior distribution is achieved. Therefore, we estimate the reliability for a given time and assess if the novel equipment attains the company's risk target, taking O&G standards as reference.

Bayesian Inference for Solar Flare Extremes

AbstractWhile solar flares are a frequent occurrence, extreme flares are much rarer events and have the potential to cause disruption to life on Earth. In this paper we use Extreme Value Theory to model extreme solar flares, with inference performed in the Bayesian paradigm. The data used have been provided by the National Oceanic and Atmospheric Organisation and consist of recordings of peak flux measurements. After proposing several methods for analysis and selecting our preferred technique—which substantially increases the precision of estimates of key quantities of interest—we improve upon this technique still further by considering the use of informative prior distributions. Doing so, we estimate that a Halloween‐type solar event, and a Carrington‐type event, might occur once (on average) every 49 (29, 85) and 92 (50, 176) years respectively (95% credible intervals shown in parentheses). These findings are similar to those obtained by Tsiftsi and De la Luz (2018), https://doi.org/10.1029/2018SW001958 and Elvidge and Angling (2018), https://doi.org/10.1002/2017SW001727 however, the confidence intervals obtained in both are substantially wider than those found in our study, lending increased certainty to the estimated time between events of such magnitude in our work. We argue that taking the extremal index into account, even when this measure indicates weak temporal dependence, is beneficial to the analysis.

On the feasibility of pediatric dose-finding trials in small samples with information from a preceding trial in adults

ABSTRACT We consider the case of pediatric dose-finding trials with extremely limited sample size. The operating characteristics of the standard design, the Continual Reassessment Method (CRM), are only well described for sample sizes of about 20 patients or more. In this simulation study, we assume the situation of a pediatric trial with only 10 patients and a preceding dose-finding trial in adults. Based on the adult data, we reduce the set of pediatric doses and formulate (partially) informative prior distributions for the pediatric trial. Our simulations show that such small pediatric dose-finding trials with robustified priors may provide sufficient operating characteristics.

Borrowing information across patient subgroups in clinical trials, with application to a paediatric trial

BackgroundClinical trial investigators may need to evaluate treatment effects in a specific subgroup (or subgroups) of participants in addition to reporting results of the entire study population. Such subgroups lack power to detect a treatment effect, but there may be strong justification for borrowing information from a larger patient group within the same trial, while allowing for differences between populations. Our aim was to develop methods for eliciting expert opinions about differences in treatment effect between patient populations, and to incorporate these opinions into a Bayesian analysis.MethodsWe used an interaction parameter to model the relationship between underlying treatment effects in two subgroups. Elicitation was used to obtain clinical opinions on the likely values of the interaction parameter, since this parameter is poorly informed by the data. Feedback was provided to experts to communicate how uncertainty about the interaction parameter corresponds with relative weights allocated to subgroups in the Bayesian analysis. The impact on the planned analysis was then determined.ResultsThe methods were applied to an ongoing non-inferiority trial designed to compare antiretroviral therapy regimens in 707 children living with HIV and weighing ≥ 14 kg, with an additional group of 85 younger children weighing < 14 kg in whom the treatment effect will be estimated separately. Expert clinical opinion was elicited and demonstrated that substantial borrowing is supported. Clinical experts chose on average to allocate a relative weight of 78% (reduced from 90% based on sample size) to data from children weighing ≥ 14 kg in a Bayesian analysis of the children weighing < 14 kg. The total effective sample size in the Bayesian analysis was 386 children, providing 84% predictive power to exclude a difference of more than 10% between arms, whereas the 85 younger children weighing < 14 kg provided only 20% power in a standalone frequentist analysis.ConclusionsBorrowing information from a larger subgroup or subgroups can facilitate estimation of treatment effects in small subgroups within a clinical trial, leading to improved power and precision. Informative prior distributions for interaction parameters are required to inform the degree of borrowing and can be informed by expert opinion. We demonstrated accessible methods for obtaining opinions.

On Estimating the Parameters of the Beta Inverted Exponential Distribution under Type-II Censored Samples

This article aims to consider estimating the unknown parameters, survival, and hazard functions of the beta inverted exponential distribution. Two methods of estimation were used based on type-II censored samples: maximum likelihood and Bayes estimators. The Bayes estimators were derived using an informative gamma prior distribution under three loss functions: squared error, linear exponential, and general entropy. Furthermore, a Monte Carlo simulation study was carried out to compare the performance of different methods. The potentiality of this distribution is illustrated using two real-life datasets from difference fields. Further, a comparison between this model and some other models was conducted via information criteria. Our model performs the best fit for the real data.

A Bayesian approach to combining multiple information sources: Estimating and forecasting childhood obesity in Thailand.

We estimate and forecast childhood obesity by age, sex, region, and urban-rural residence in Thailand, using a Bayesian approach to combining multiple source of information. Our main sources of information are survey data and administrative data, but we also make use of informative prior distributions based on international estimates of obesity trends and on expectations about smoothness. Although the final model is complex, the difficulty of building and understanding the model is reduced by the fact that it is composed of many smaller submodels. For instance, the submodel describing trends in prevalences is specified separately from the submodels describing errors in the data sources. None of our Thai data sources has more than 7 time points. However, by combining multiple data sources, we are able to fit relatively complicated time series models. Our results suggest that obesity prevalence has recently starting rising quickly among Thai teenagers throughout the country, but has been stable among children under 5 years old.

Posterior Estimates for the Parameter of the Poisson Distribution by Using Two Different Loss Functions

In this paper, Bayes estimators of Poisson distribution have been derived by using two loss functions: the squared error loss function and the proposed exponential loss function in this study, based on different priors classified as the two different informative prior distributions represented by erlang and inverse levy prior distributions and non-informative prior for the shape parameter of Poisson distribution. The maximum likelihood estimator (MLE) of the Poisson distribution has also been derived. A simulation study has been fulfilled to compare the accuracy of the Bayes estimates with the corresponding maximum likelihood estimate (MLE) of the Poisson distribution based on the root mean squared error (RMSE) for different cases of the parameter of the Poisson distribution and different sample sizes.

Evaluation of the Mean Control Chart Under a Bayesian Approach

A previous study on the evaluation of control charts for the mean with a Bayesian approach, based on predictive limits, was performed in such a way that neither prior nor sample information was taken into account. This work was developed to make a more complete study to evaluate the influence of the combination of the prior distribution with the sample information. It is assumed that the quality characteristic to be controlled can be modeled by a Normal distribution and two cases are considered: known and unknown variance. A Bayesian conjugate model is established, therefore the prior distribution for the mean is Normal and, in the case where the variance is unknown, the prior distribution for the variance is defined as the Inverse-Gamma(ν, ν). The posterior predictive distribution, which is also Normal, is used to establish the control limits of the chart. Signal propability is used to measure the performance of the control chart in phase II, with the predictive limits calculated under different specifications of the prior distributions, and two different sizes of the calibration sample and the future sample. The simulation study evaluates three aspects: the effects of sample sizes, the distance of the prior mean to the mean of the calibration sample, and an indicator of how informative is the prior distribution of the population mean. In addition, in the case of unknown variance, we study what is the effect of changing values in the parameter ν. We found that the false alarm rate could be quite large if the prior distribution is very informative which in turn leads to an ARL (average run length) biased chart, that is, the maximum of the ARL is not given when the process is under control. Besides, we foundgreat influence of the prior distribution on the control chart power when the size of the calibration and future samples are small, particulary when the prior is very informative. Finally, regarding the effect of the parameter ν, we found that the smaller the value, which means having a less informative prior distribution, the lower the power of the control chart.

Distribuição a priori informativa aplicada à linhaça para estimação de parâmetros genéticos com uso de tamanho amostral reduzido

Abstract The objective of this work was to evaluate a procedure for the elicitation of informative prior distribution, compared with non-informative prior distribution, in a small sample size, using 14 traits of three linseed (Linum usitatissimum) genotypes in seven sowing seasons. The values of the hyperparameters regulate the informativeness of the prior distribution; therefore, for each season, the hyperparameters to be used in the next season were calculated. The two prior distributions, non-informative and informative, were compared by the length of the credible interval and variance of the posterior distribution. In general, when the informative prior distribution is adopted, the genetic parameters present a shorter length of the credible interval and more precise estimates. The mechanism for informative prior elicitation using previous information from breeding programs is efficient for the estimation of genetic parameters, including heritability and genetic variance, even when the sample size is small. In genetic evaluation, the use of informative prior distribution is better than that of non-informative distribution for a small sample size. In general, the results of the informative prior distributions are indicative that the genetic values of the first sowing season are greater for the following traits: cycle length, plant height, and number of non-grained capsules and of productive branches.

The Dermal Advanced REACH Tool (dART): A Bayesian Model for Dermal Exposure Assessment.

The dermal Advanced REACH Tool (dART) is a tier 2 exposure model for estimating dermal exposure to the hands (mg min-1) for non-volatile liquid and solid-in-liquid products. The dART builds upon the existing ART framework and describes three mass transport processes (deposition (Dhands), direct emission and direct contact (Ehands), and contact transfer (Thands)) that may each contribute to dermal exposure. The mechanistic model that underpins the dART and calibration of the mechanistic model, such that the dimensionless score that results from encoding contextual information about a task into the determinants of the dART can be converted into a prediction of exposure (mg min-1), have been described in previous work. This paper completes the methodological framework of the dART model through placing the mechanistic model within a wider statistical modelling framework. A mixed-effects model, within a Bayesian framework, is presented for modelling the rate of dermal exposure per minute of activity. The central estimate of exposure for a particular task is provided by a calibrated mechanistic model (and thus based upon contextual information about a task). The model also describes between- and within-worker sources of variability in dermal exposure, with prior distributions for variance components based upon the literature. Estimates of exposure based upon informative prior distributions may be updated using measurement data associated with the task. The dART model is demonstrated using three worked examples, where estimates are initially obtained based upon the prior distributions alone, and then refined through accommodating measurement data on the tasks.