Bayesian hierarchical modeling of substate area estimates from the Medicare CAHPS survey

Each year, surveys are conducted to assess the quality of care for Medicare beneficiaries, using instruments from the Consumer Assessment of Healthcare Providers and Systems (CAHPS®) program. Currently, survey measures presented for Fee-for-Service beneficiaries are either pooled at the state level or unpooled for smaller substate areas nested within the state; the choice in each state is based on statistical tests of measure heterogeneity across areas within state. We fit spatial-temporal Bayesian random-effects models using a flexible parameterization to estimate mean scores for each of the domains formed by 94 areas in 32 states measured over 5 years. A Bayesian hat matrix provides a heuristic interpretation of the way the model combines information for estimates in these domains. The model can be used to choose between reporting of state- or substate-level direct estimates in each state, or as a source of alternative small-area estimates superior to either direct estimate. We compare several candidate models using log pseudomarginal likelihood and posterior predictive checks. Results from the best-performing model for 8 measures surveyed from 2012 to 2016 show substantial reductions in mean squared error (MSE) over direct estimates.     

Bayesian oligogenic analysis of quantitative and qualitative traits in general pedigrees

A Bayesian method for multipoint oligogenic analysis of quantitative and qualitative traits is presented. This method can be applied to general pedigrees, which do not necessarily have to be “peelable” and can have large numbers of markers. The number of quantitative/qualitative trait loci (QTL), their map positions in the genome, and phenotypic effects (mode of inheritances) are all estimated simultaneously within the same framework. The summaries of the estimated parameters are based on the marginal posterior distributions that are obtained through Markov chain Monte Carlo (MCMC) methods. The method uses founder alleles together with segregation indicators in order to determine the genotypes of the trait loci of all individuals in the pedigree. To improve mixing properties of the sampler, we propose (1) joint sampling of map position and segregation indicators, (2) omitting data augmentation for untyped or uninformative markers (homozygous parent), and (3) updating several markers jointly within a single block. The performance of the method was tested with two replicate GAW10 data sets (considering two levels of available marker information). The results were concordant and similar to those presented earlier with other methods. These analyses clearly illustrate the utility and wide applicability of the method. Genet. Epidemiol. 21:224–242, 2001. © 2001 Wiley‐Liss, Inc.     

Reducing Monte Carlo error in the Bayesian estimation of risk ratios using log‐binomial regression models

In cohort studies, binary outcomes are very often analyzed by logistic regression. However, it is well known that when the goal is to estimate a risk ratio, the logistic regression is inappropriate if the outcome is common. In these cases, a log‐binomial regression model is preferable. On the other hand, the estimation of the regression coefficients of the log‐binomial model is difficult owing to the constraints that must be imposed on these coefficients. Bayesian methods allow a straightforward approach for log‐binomial regression models and produce smaller mean squared errors in the estimation of risk ratios than the frequentist methods, and the posterior inferences can be obtained using the software WinBUGS. However, Markov chain Monte Carlo methods implemented in WinBUGS can lead to large Monte Carlo errors in the approximations to the posterior inferences because they produce correlated simulations, and the accuracy of the approximations are inversely related to this correlation. To reduce correlation and to improve accuracy, we propose a reparameterization based on a Poisson model and a sampling algorithm coded in R. Copyright © 2015 John Wiley & Sons, Ltd.     

Comprehensive decision analytical modelling in economic evaluation: a Bayesian approach

Decision analytical models are widely used in economic evaluation of health care interventions with the objective of generating valuable information to assist health policy decision-makers to allocate scarce health care resources efficiently. The whole decision modelling process can be summarised in four stages: (i) a systematic review of the relevant data (including meta-analyses), (ii) estimation of all inputs into the model (including effectiveness, transition probabilities and costs), (iii) sensitivity analysis for data and model specifications, and (iv) evaluation of the model. The aim of this paper is to demonstrate how the individual components of decision modelling, outlined above, may be addressed simultaneously in one coherent Bayesian model (sometimes known as a comprehensive decision analytical model) and evaluated using Markov Chain Monte Carlo simulation implemented in the specialist software WinBUGS. To illustrate the method described, it is applied to two illustrative examples: (1) The prophylactic use of neurominidase inhibitors for the prevention of influenza. (2) The use of taxanes for the second-line treatment of advanced breast cancer.The advantages of integrating the four stages outlined into one comprehensive decision analytical model, compared to the conventional 'two-stage' approach, are discussed.     

A Bayesian approach to analysing the cost-effectiveness of two primary care interventions aimed at improving attendance for breast screening

AIMS: To assess the cost-effectiveness of two primary care interventions, a letter and a flag, aimed at improving attendance for breast screening among (i) all women invited for breast screening and (ii) non-attenders. METHODS: A probabilistic decision analytic model was developed using Markov chain Monte Carlo simulation implemented in WinBUGS. The model was populated using economic and effectiveness data collected alongside two randomised controlled trials. RESULTS: For all women invited, the incremental cost-effectiveness ratio (ICER) for the letter compared with no intervention is 27 pounds per additional attendance, and the ICER for the combined letter and flag intervention compared to the letter alone is 171 pounds. The corresponding ICERs for non-attenders are 41 pounds and 90 pounds. The flag intervention is an inefficient option in both settings. A large proportion of the costs fall on the practices (25-67%), depending on the intervention and target population. The total costs incurred do not, however, seem prohibitive.Expected value of perfect information suggests that there is greater value in carrying out further research on the intervention implemented among all women invited for breast screening rather than on non-attenders. CONCLUSIONS: The flag intervention alone does not appear to be an efficient option. The choice between the letter and both interventions combined is subjective, depending on the willingness to pay for an additional screening attendance.     

Bayesian estimation,simulation and uncertainty analysis: the cost-effectiveness of ganciclovir prophylaxis in liver transplantation

This paper demonstrates the usefulness of combining simulation with Bayesian estimation methods in analysis of cost-effectiveness data collected alongside a clinical trial. Specifically, we use Markov Chain Monte Carlo (MCMC) to estimate a system of generalized linear models relating costs and outcomes to a disease process affected by treatment under alternative therapies. The MCMC draws are used as parameters in simulations which yield inference about the relative cost-effectiveness of the novel therapy under a variety of scenarios. Total parametric uncertainty is assessed directly by examining the joint distribution of simulated average incremental cost and effectiveness. The approach allows flexibility in assessing treatment in various counterfactual premises and quantifies the global effect of parametric uncertainty on a decision-maker's confidence in adopting one therapy over the other.     

Bayesian mixture modeling of gene‐environment and gene‐gene interactions

With the advent of rapid and relatively cheap genotyping technologies there is now the opportunity to attempt to identify gene‐environment and gene‐gene interactions when the number of genes and environmental factors is potentially large. Unfortunately the dimensionality of the parameter space leads to a computational explosion in the number of possible interactions that may be investigated. The full model that includes all interactions and main effects can be unstable, with wide confidence intervals arising from the large number of estimated parameters. We describe a hierarchical mixture model that allows all interactions to be investigated simultaneously, but assumes the effects come from a mixture prior with two components, one that reflects small null effects and the second for epidemiologically significant effects. Effects from the former are effectively set to zero, hence increasing the power for the detection of real signals. The prior framework is very flexible, which allows substantive information to be incorporated into the analysis. We illustrate the methods first using simulation, and then on data from a case‐control study of lung cancer in Central and Eastern Europe. Genet. Epidemiol. 34:16–25, 2010. © 2009 Wiley‐Liss, Inc.     

A Bayesian MCMC approach to study transmission of influenza: application to household longitudinal data

We propose a transmission model to estimate the main characteristics of influenza transmission in households. The model details the risks of infection in the household and in the community at the individual scale. Heterogeneity among subjects is investigated considering both individual susceptibility and infectiousness. The model was applied to a data set consisting of the follow-up of influenza symptoms in 334 households during 15 days after an index case visited a general practitioner with virologically confirmed influenza.Estimating the parameters of the transmission model was challenging because a large part of the infectious process was not observed: only the dates when new cases were detected were observed. For each case, the data were augmented with the unobserved dates of the start and the end of the infectious period. The transmission model was included in a 3-levels hierarchical structure: (i) the observation level ensured that the augmented data were consistent with the observed data, (ii) the transmission level described the underlying epidemic process, (iii) the prior level specified the distribution of the parameters. From a Bayesian perspective, the joint posterior distribution of model parameters and augmented data was explored by Markov chain Monte Carlo (MCMC) sampling.The mean duration of influenza infectious period was estimated at 3.8 days (95 per cent credible interval, 95 per cent CI [3.1,4.6]) with a standard deviation of 2.0 days (95 per cent CI [1.1,2.8]). The instantaneous risk of influenza transmission between an infective and a susceptible within a household was found to decrease with the size of the household, and established at 0.32 person day(-1) (95 per cent CI [0.26,0.39]); the instantaneous risk of infection from the community was 0.0056 day(-1) (95 per cent CI [0.0029,0.0087]). Focusing on the differences in transmission between children (less than 15 years old) and adults, we estimated that the former were more likely to transmit than adults (posterior probability larger than 99 per cent), but that the mean duration of the infectious period was similar in children (3.6 days, 95 per cent CI [2.3,5.2]) and adults (3.9 days, 95 per cent CI [3.2,4.9]). The posterior probability that children had a larger community risk was 76 per cent and the posterior probability that they were more susceptible than adults was 79 per cent.     

Assessing noninferiority in a three-arm trial using the Bayesian approach

Non-inferiority trials, which aim to demonstrate that a test product is not worse than a competitor by more than a pre-specified small amount, are of great importance to the pharmaceutical community. As a result, methodology for designing and analyzing such trials is required, and developing new methods for such analysis is an important area of statistical research. The three-arm trial consists of a placebo, a reference and an experimental treatment, and simultaneously tests the superiority of the reference over the placebo along with comparing this reference to an experimental treatment. In this paper, we consider the analysis of non-inferiority trials using Bayesian methods which incorporate both parametric as well as semi-parametric models. The resulting testing approach is both flexible and robust. The benefit of the proposed Bayesian methods is assessed via simulation, based on a study examining home-based blood pressure interventions.     

Computational toxicology of chloroform: reverse dosimetry using Bayesian inference, Markov chain Monte Carlo simulation, and human biomonitoring data

BACKGROUND: One problem of interpreting population-based biomonitoring data is the reconstruction of corresponding external exposure in cases where no such data are available. OBJECTIVES: We demonstrate the use of a computational framework that integrates physiologically based pharmacokinetic (PBPK) modeling, Bayesian inference, and Markov chain Monte Carlo simulation to obtain a population estimate of environmental chloroform source concentrations consistent with human biomonitoring data. The biomonitoring data consist of chloroform blood concentrations measured as part of the Third National Health and Nutrition Examination Survey (NHANES III), and for which no corresponding exposure data were collected. METHODS: We used a combined PBPK and shower exposure model to consider several routes and sources of exposure: ingestion of tap water, inhalation of ambient household air, and inhalation and dermal absorption while showering. We determined posterior distributions for chloroform concentration in tap water and ambient household air using U.S. Environmental Protection Agency Total Exposure Assessment Methodology (TEAM) data as prior distributions for the Bayesian analysis. RESULTS: Posterior distributions for exposure indicate that 95% of the population represented by the NHANES III data had likely chloroform exposures < or = 67 microg/L [corrected] in tap water and < or = 0.02 microg/L in ambient household air. CONCLUSIONS: Our results demonstrate the application of computer simulation to aid in the interpretation of human biomonitoring data in the context of the exposure-health evaluation-risk assessment continuum. These results should be considered as a demonstration of the method and can be improved with the addition of more detailed data.     

A Bayesian approach to joint analysis of multivariate longitudinal data and parametric accelerated failure time

Impairment caused by Parkinson's disease (PD) is multidimensional (e.g., sensoria, functions, and cognition) and progressive. Its multidimensional nature precludes a single outcome to measure disease progression. Clinical trials of PD use multiple categorical and continuous longitudinal outcomes to assess the treatment effects on overall improvement. A terminal event such as death or dropout can stop the follow‐up process. Moreover, the time to the terminal event may be dependent on the multivariate longitudinal measurements. In this article, we consider a joint random‐effects model for the correlated outcomes. A multilevel item response theory model is used for the multivariate longitudinal outcomes and a parametric accelerated failure time model is used for the failure time because of the violation of proportional hazard assumption. These two models are linked via random effects. The Bayesian inference via MCMC is implemented in ‘BUGS ’ language. Our proposed method is evaluated by a simulation study and is applied to DATATOP study, a motivating clinical trial to determine if deprenyl slows the progression of PD. © 2013 The authors. Statistics in Medicine published by John Wiley & Sons, Ltd.     

A Bayesian integrative genomic model for pathway analysis of complex traits

With new technologies, multiple types of genomic data are commonly collected on a single set of samples. However, standard analysis methods concentrate on a single data type at a time and ignore the relationships between genes, proteins, and biochemical reactions that give rise to complex phenotypes. In this paper, we propose a novel integrative model to incorporate multiple types of genomic data into an association analysis with a complex phenotype. The method combines path analysis and stochastic search variable selection into a Bayesian hierarchical model that simultaneously identifies both direct and indirect genomic effects on the phenotype. Results from a simulation study and application of the Bayesian model to a pharmacogenomic study of the drug gemcitabine demonstrate greater sensitivity to detect genomic effects in some simulation scenarios, when compared to the standard single data type analysis. Further research is required to extend and modify this integrative modeling framework to increase computational efficiency to best capitalize on the wealth of information available across multiple genomic data types.     

A unified Bayesian hierarchical model for MRI tissue classification

Various works have used magnetic resonance imaging (MRI) tissue classification extensively to study a number of neurological and psychiatric disorders. Various noise characteristics and other artifacts make this classification a challenging task. Instead of splitting the procedure into different steps, we extend a previous work to develop a unified Bayesian hierarchical model, which addresses both the partial volume effect and intensity non‐uniformity, the two major acquisition artifacts, simultaneously. We adopted a normal mixture model with the means and variances depending on the tissue types of voxels to model the observed intensity values. We modeled the relationship among the components of the index vector of tissue types by a hidden Markov model, which captures the spatial similarity of voxels. Furthermore, we addressed the partial volume effect by construction of a higher resolution image in which each voxel is divided into subvoxels. Finally, We achieved the bias field correction by using a Gaussian Markov random field model with a band precision matrix designed in light of image filtering. Sparse matrix methods and parallel computations based on conditional independence are exploited to improve the speed of the Markov chain Monte Carlo simulation. The unified model provides more accurate tissue classification results for both simulated and real data sets. Copyright © 2013 John Wiley & Sons, Ltd.     

Application of the Bayesian dynamic survival model in medicine

The Bayesian dynamic survival model (BDSM), a time‐varying coefficient survival model from the Bayesian prospective, was proposed in early 1990s but has not been widely used or discussed. In this paper, we describe the model structure of the BDSM and introduce two estimation approaches for BDSMs: the Markov Chain Monte Carlo (MCMC) approach and the linear Bayesian (LB) method. The MCMC approach estimates model parameters through sampling and is computationally intensive. With the newly developed geoadditive survival models and software BayesX, the BDSM is available for general applications. The LB approach is easier in terms of computations but it requires the prespecification of some unknown smoothing parameters. In a simulation study, we use the LB approach to show the effects of smoothing parameters on the performance of the BDSM and propose an ad hoc method for identifying appropriate values for those parameters. We also demonstrate the performance of the MCMC approach compared with the LB approach and a penalized partial likelihood method available in software R packages. A gastric cancer trial is utilized to illustrate the application of the BDSM. Copyright © 2009 John Wiley & Sons, Ltd.     

Bayesian approaches to multiple sources of evidence and uncertainty in complex cost-effectiveness modelling

Increasingly complex models are being used to evaluate the cost-effectiveness of medical interventions. We describe the multiple sources of uncertainty that are relevant to such models, and their relation to either probabilistic or deterministic sensitivity analysis. A Bayesian approach appears natural in this context. We explore how sensitivity analysis to patient heterogeneity and parameter uncertainty can be simultaneously investigated, and illustrate the necessary computation when expected costs and benefits can be calculated in closed form, such as in discrete-time discrete-state Markov models. Information about parameters can either be expressed as a prior distribution, or derived as a posterior distribution given a generalized synthesis of available data in which multiple sources of evidence can be differentially weighted according to their assumed quality. The resulting joint posterior distributions on costs and benefits can then provide inferences on incremental cost-effectiveness, best presented as posterior distributions over net-benefit and cost-effectiveness acceptability curves. These ideas are illustrated with a detailed running example concerning the cost-effectiveness of hip prostheses in different age-sex subgroups. All computations are carried out using freely available software for conducting Markov chain Monte Carlo analysis.     

A Bayesian hierarchical model for the estimation of two incomplete surveillance data sets

A model-based approach to analyze two incomplete disease surveillance datasets is described. Such data typically consist of case counts, each originating from a specific geographical area. A Bayesian hierarchical model is proposed for estimating the total number of cases with disease while simultaneously adjusting for spatial variation. This approach explicitly accounts for model uncertainty and can make use of covariates.The method is applied to two surveillance datasets maintained by the Centers for Disease Control and Prevention on Rocky Mountain spotted fever (RMSF). An inference is drawn using Markov Chain Monte Carlo simulation techniques in a fully Bayesian framework. The central feature of the model is the ability to calculate and estimate the total number of cases and disease incidence for geographical regions where RMSF is endemic.The information generated by this model could significantly reduce the public health impact of RMSF and other vector-borne zoonoses, as well as other infectious or chronic diseases, by improving knowledge of the spatial distribution of disease risk of public health officials and medical practitioners. More accurate information on populations at high risk would focus attention and resources on specific areas, thereby reducing the morbidity and mortality caused by some of the preventable and treatable diseases.     

Combining multiple continuous tests for the diagnosis of kidney impairment in the absence of a gold standard

Receiver operating characteristic (ROC) curves are commonly used to summarize the classification accuracy of diagnostic tests. It is not uncommon in medical practice that multiple diagnostic tests are routinely performed or multiple disease markers are available for the same individuals. When the true disease status is verified by a gold standard (GS) test, a variety of methods have been proposed to combine such potential correlated tests to increase the accuracy of disease diagnosis. In this article, we propose a method of combining multiple diagnostic tests in the absence of a GS. We assume that the test values and their classification accuracies are dependent on covariates. Simulation studies are performed to examine the performance of the combination method. The proposed method is applied to data from a population-based aging study to compare the accuracy of three screening tests for kidney function and to estimate the prevalence of moderate kidney impairment.     

Bayesian model choice and infection route modelling in an outbreak of Norovirus

A data set from an outbreak of gastroenteritis in a school is analysed using a stochastic transmission model. The causative agent of the outbreak is believed to be a Norovirus, spread through person-to-person contact. Particular attention is given to the question of whether or not vomiting episodes enhance the spread of the virus via aerosol transmission. The methodology developed uses Bayesian model choice, implemented with reversible-jump Markov chain Monte Carlo methods. The methodology appears to be highly sensitive to assumptions made concerning the data, which provides some assurance that the conclusions are driven by observations rather than the underlying model and methodology.     

Functional form and risk adjustment of hospital costs: Bayesian analysis of a Box-Cox random coefficients model

While risk-adjusted outcomes are often used to compare the performance of hospitals and physicians, the most appropriate functional form for the risk adjustment process is not always obvious for continuous outcomes such as costs. Semi-log models are used most often to correct skewness in cost data, but there has been limited research to determine whether the log transformation is sufficient or whether another transformation is more appropriate. This study explores the most appropriate functional form for risk-adjusting the cost of coronary artery bypass graft (CABG) surgery. Data included patients undergoing CABG surgery at four hospitals in the midwest and were fit to a Box-Cox model with random coefficients (BCRC) using Markov chain Monte Carlo methods. Marginal likelihoods and Bayes factors were computed to perform model comparison of alternative model specifications. Rankings of hospital performance were created from the simulation output and the rankings produced by Bayesian estimates were compared to rankings produced by standard models fit using classical methods. Results suggest that, for these data, the most appropriate functional form is not logarithmic, but corresponds to a Box-Cox transformation of -1. Furthermore, Bayes factors overwhelmingly rejected the natural log transformation. However, the hospital ranking induced by the BCRC model was not different from the ranking produced by maximum likelihood estimates of either the linear or semi-log model.