Multivariate meta-analysis of mixed outcomes: a Bayesian approach

An autoregressive moving average (ARMA) is a time series model that is applied in everyday life for pattern recognition and forecasting. The ARMA model contains a noise which is assumed to have a specific distribution. The noise is often considered to have a Gaussian distribution. However in applications, the noise is sometimes found that does not have a Gaussian distribution. The first objective is to develop the ARMA model in which noise has a Laplacian distribution. The second objective is to estimate the parameters of the ARMA model. The ARMA model parameters include ARMA model orders, ARMA model coefficients, and noise variance. The parameter estimation of the ARMA model is carried out in the Bayesian framework. In the Bayesian framework, the ARMA model parameters are treated as a variable that has a prior distribution. The prior distribution for the ARMA model parameters is combined with the likelihood function for the data to get the posterior distribution for the parameter. The posterior distribution for parameters has a complex form so that the Bayes estimator cannot be determined analytically. The reversible jump Markov chain Monte Carlo (MCMC) algorithm was adopted to determine the Bayes estimator. The first result, the ARMA model can be developed by assuming Laplacian distribution noise. The second result, the performance of the algorithm was tested using simulation studies. The simulation shows that the reversible jump MCMC algorithm can estimate the parameters of the ARMA model correctly.

This paper proposed a Bayesian method-based structural equation model (SEM) of miners’ work injury for an underground coal mine in India. The environmental and behavioural variables for work injury were identified and causal relationships were developed. For Bayesian modelling, prior distributions of SEM parameters are necessary to develop the model. In this paper, two approaches were adopted to obtain prior distribution for factor loading parameters and structural parameters of SEM. In the first approach, the prior distributions were considered as a fixed distribution function with specific parameter values, whereas, in the second approach, prior distributions of the parameters were generated from experts’ opinions. The posterior distributions of these parameters were obtained by applying Bayesian rule. The Markov Chain Monte Carlo sampling in the form Gibbs sampling was applied for sampling from the posterior distribution. The results revealed that all coefficients of structural and measurement model parameters are statistically significant in experts’ opinion-based priors, whereas, two coefficients are not statistically significant when fixed prior-based distributions are applied. The error statistics reveals that Bayesian structural model provides reasonably good fit of work injury with high coefficient of determination (0.91) and less mean squared error as compared to traditional SEM.

Objective To compare the risk for all cause and overdose mortality in people with opioid dependence during and after substitution treatment with methadone or buprenorphine and to characterise trends in...

Bayesian meta-analysis is an increasingly important component of clinical research, with multivariate meta-analysis a promising tool for studies with multiple endpoints. Model assumptions, including the choice of priors, are crucial aspects of multivariate Bayesian meta-analysis (MBMA) models. In a given model, two different prior distributions can lead to different inferences about a particular parameter. A simulation study was performed in which the impact of families of prior distributions for the covariance matrix of a multivariate normal random effects MBMA model was analyzed. Inferences about effect sizes were not particularly sensitive to prior choice, but the related covariance estimates were. A few families of prior distributions with small relative biases, tight mean squared errors, and close to nominal coverage for the effect size estimates were identified. Our results demonstrate the need for sensitivity analysis and suggest some guidelines for choosing prior distributions in this class of problems. The MBMA models proposed here are illustrated in a small meta-analysis example from the periodontal field and a medium meta-analysis from the study of stroke. Copyright © 2015 John Wiley & Sons, Ltd.

This article discusses the Bayesian approach for count data using non-homogeneous Poisson processes, considering different prior distributions for the model parameters. A Bayesian approach using Markov Chain Monte Carlo (MCMC) simulation methods for this model was first introduced by [1], taking into account software reliability data and considering non-informative prior distributions for the parameters of the model. With the non-informative prior distributions presented by these authors, computational difficulties may occur when using MCMC methods. This article considers different prior distributions for the parameters of the proposed model, and studies the effect of such prior distributions on the convergence and accuracy of the results. In order to illustrate the proposed methodology, two examples are considered: the first one has simulated data, and the second has a set of data for pollution issues at a region in Mexico City.

This study evaluated idionomic methods for identifying within-person links between therapeutically relevant processes and outcomes, using an ecological momentary assessment dataset of valued action and hedonic well-being (participants (n) = 425; 71.76% female; age = M(SD) = 22.20 (6.85); sampling design: 3–4 prompts per day; total measurements (n) = 6456). We compared the idionomic approach, integrating idiographic and nomothetic insights, with traditional multilevel modeling (MLM). Our methods included idiographic autoregressive integrative moving average models with an exogenous variable (i-ARIMAX), multivariate random-effects meta-analysis (RE-MA), deep Gaussian mixture modeling (DGMM), and multilevel vector autoregression modeling (Multilevel-VAR). The results showed that i-ARIMAX outperformed MLM in capturing within-person heterogeneity in the links between valued action and affect variables. Increases in values-based living were positively related to hedonic well-being but this effect showed a high degree of heterogeneity. A sub-group was identified, which we labeled the ‘Stoics,’ whose daily engagement in valued actions did not produce higher hedonic well-being (e.g., lower sadness or higher joy). Multilevel-VAR further revealed that for Stoics, stressful situations were linked to valued action, but not hedonic well-being. For Non-Stoics, valued action was less likely in stressful situations, but when valued action did occur it was associated with more joy and less sadness. The study offers initial evidence suggesting the superiority of an idionomic approach over a purely nomothetic one in capturing diverse pathways to clinically relevant outcomes. Idionomic methods may be useful or even necessary in personalizing psychological interventions, and thus may need to be considered by researchers and practitioners alike.

The objective of this study is to examine the properties of Bayes estimators of the shape parameter of the Power Function Distribution (PFD-I), by using two different prior distributions for the parameter θ and different loss functions that were compared with the maximum likelihood estimators. In many practical applications, we may have two different prior information about the prior distribution for the shape parameter of the Power Function Distribution, which influences the parameter estimation. So, we used two different kinds of conjugate priors of shape parameter θ of the Power Function Distribution (PFD-I) to estimate it. The conjugate prior function of the shape parameter θ was considered as a combination of two different prior distributions such as gamma distribution with Erlang distribution and Erlang distribution with exponential distribution and Erlang distribution with non-informative distribution and exponential distribution with the non-informative distribution. We derived Bayes estimators for shape parameter θ of the Power Function Distribution (PFD-I) according to different loss functions such as the squared error loss function (SELF), the weighted error loss function (WSELF) and modified linear exponential (MLINEX) loss function (MLF), with two different double priors. In addition to the classical estimation (maximum likelihood estimation). We used simulation to get the results of this study, for different cases of the shape parameter of the Power Function Distribution used to generate data for different samples sizes.

Due to the lack of data, a reservoir engineer needs to calibrate unknown petrophysical parameters based on production history. However, because the observations cannot constrain all the subsurface properties over a field, production forecasts for reservoirs are essentially uncertain. In general, many parameters of the model must be adjusted in the history-matching process, and the amount of computation required to solve the inverse problem may be prohibitive. To address this issue, we proposed a new methodology which restricts the parameter ranges of the calibration by using physically based prior information, extracted from geological and petrophysical input. The aim of the work is to have a sound basis for forecasting uncertainty in reservoir production. We demonstrate the applicability of the methodology using quarter five-spot pattern waterflooding models. The petrophysical properties to be adjusted in this paper are coarse-scale relative permeabilities. Coarse-scale models have the disadvantage of omitting the effects of fine-scale heterogeneity and suffering from solution errors, although in practice they are often employed in field-scale simulation because of the computational cost. Here, we history-match relative permeabilities at the coarse scale in order to encapsulate physical dispersion and compensate for numerical dispersion. The prior information was estimated from a range of possible geostatistical parameters. It allowed us not only to determine the parameterisation of the grouped relative permeabilities but also to set up the bounds of each type of curve. We used a synthetic data set for which the true solution is known. The resulting posterior expectations and P10 / P90 cut-offs of the production data and the relative permeabilities were examined in comparison with the reference results. We conclude that this new approach enabled us to quantify the uncertainty of sub-grid heterogeneity through the use of coarse-scale relative permeabilities without refining the model.

Thorough health economic research of budget-relevant diseases should be one of the major tasks in the German health care system. Up to now cost studies were only performed for special research questions and/or with very limited focuses, e.g. the patients' view. Hence, federal programmes, like competence networks for certain diseases, which were introduced by the German Ministry for Research and Education in the late 1990s, should give a broader focus on health services research. With such an approach health politicians may obtain a deeper insight into areas of the health care sector which are likely to be more efficient after reorganisation. The process of a structured analysis of certain diseases will be demonstrated using the example of rheumatoid arthritis (RA). To this end, the results of a research programme sponsored within the Competence Network for Musculoskeletal Diseases will be presented. Direct costs, indirect costs as well as values for health-related quality of life of German RA patients in routine care by generalists and specialists will be discussed.

Thermodynamic modeling and uncertainty quantification of CO2-loaded aqueous MEA solutions

We introduce and test a workflow that integrates petrophysical constraints and geological data in joint geophysical inversion in order to decrease the uncertainty of the results. This workflow uses statistical petrophysical properties to constrain the values retrieved by the geophysical inversion and geological prior information to decrease the effect of non-uniqueness. We integrate the different sources of information in a Bayesian framework, which takes into account the state of information. This permits us to quantify the posterior state of knowledge, the reduction of the uncertainty and to calculate the influence of prior information using quality indicators based on fixed-point statistics. This workflow was first tested using simple synthetic datasets to validate the method and assess the robustness of the workflow. As a result, the use of petrophysical constraints permits us to retrieve sharper boundaries, while prior structural information from geology permits to retrieve the geometry more accurately. Overall, the integration of the different constraints provides a model, with reduced uncertainties and better resolved parameters.

Bayesian statistical methods have recently been combined with conventional methods for fisheries stock assessment (e.g. catch-age analysis) to provide a conceptually elegant approach for providing fishery management advice under uncertainty. Uncertainties in the advice provided can be conveyed using posterior probability distributions (or “posteriors”) for the potential outcomes of each policy option. Posteriors can be estimated using data (e.g. catch-age data and relative abundance indices) for the fish population of interest and prior probability distributions for population model parameters (e.g. stock-recruit function parameters) based on data from similar fish populations. Despite growing interest, Bayesian methods remain accessible to relatively few. To increase the accessibility of these methods, the conceptual basis for Bayesian statistical estimation is reviewed and set in the context of fisheries stock assessment. The use of Bayesian methods is illustrated by fitting a logistic model to relative abundance indices for Namibian hake (Merlucius capensis and M. paradoxus) and presenting a decision analysis of alternative harvest policy options. Some alternative approaches are outlined for constructing prior and posterior probability distributions and some recent applications in fisheries. Some of the problems that can be encountered while implementing Bayesian methods are also discussed.

The directional flame thermometer (DFT) is a robust device used to measure heat fluxes in harsh environments such as fire scenarios but is large when compared to other standard heat flux measurement devices. To better understand the uncertainties associated with heat flux measurements in these environments, a Bayesian framework is utilized to propagate uncertainties of both known and unknown parameters describing the thermal model of a modified, smaller DFT. Construction of the modified DFT is described along with a derivation of the thermal model used to predict the incident heat flux to its sensing surface. Parameters of the model are calibrated to data collected using a Schmidt–Boelter (SB) gauge with an accuracy of ±3% at incident heat fluxes of 5 kW/m2, 10 kW/m2, and 15 kW/m2. Markov Chain Monte Carlo simulations were used to obtain posterior distributions for the free parameters of the thermal model as well as the modeling uncertainty. The parameter calibration process produced values for the free parameters that were similar to those presented in the literature with relative uncertainties at 5 kW/m2, 10 kW/m2, and 15 kW/m2 of 17%, 9%, and 7%, respectively. The derived model produced root-mean-squared errors between the prediction and SB gauge output of 0.37, 0.77, and 1.13 kW/m2 for the 5, 10, and 15 kW/m2 cases, respectively, compared to 0.53, 1.12, and 1.66 kW/m2 for the energy storage method (ESM) described in ASTM E3057.

Arthroscopy is an important diagnostic procedure which can be used in rheumatology practice to provide direct visualization of the joint cavity, permitting macroscopic evaluation of the synovium, sampling for histopathologic and microbiologic examination and the potential therapeutic benefit of lavage. The term 'medical arthroscopy' is used here to refer to arthroscopy performed by rheumatologists for these purposes. This term differentiates arthroscopy performed by orthopedic surgeons for structural interventions such as meniscal debridement and ligament repair. Medical arthroscopy finds a place in rheumatology as an aid to diagnosis, to confirm the presence of synovitis when not expected, to provide histologic or microbiologic diagnosis, and potential stratification for therapy, for example in rheumatoid arthritis, as well as a range of other research purposes. It is performed with local anesthetic using a small bore arthroscope, most usually inserted into the knee, although the wrist and metacarpophalangeal joints may also be inspected in this way. In experienced hands it is well tolerated, safe and complications are comparable to those reported by orthopedic surgeons.

Probabilistic ship corrosion wastage model with Bayesian inference