Bayesian analysis of prevalence with covariates using simulation-based techniques: applications to HIV screening.

Ignoring the limited precision of medical diagnostic tests can incur serious bias in prevalence estimation. Conversely, treating the values of sensitivity and specificity as constants, as in most studies, inevitably underestimates the variability of prevalence estimates. Bayesian inference provides a natural framework with which to integrate the variability in the estimates of sensitivity and specificity with estimation of prevalence. However, the resulting model becomes quite complicated and presents a computational challenge. Recently, Mendoza-Blanco et al. proposed a missing-data approach with simulation-based techniques to deal with the computational difficulties. Although their approach is quite effective in reducing the computational complexity into manageable tasks, their developed methodology is not general enough for modelling the effects of covariates in prevalence estimation. In this paper, we extend their work in this direction by combining their missing-data approach with a latent variable technique for modelling discrete data. The present work also generalizes the methods of Albert and Chib for Bayesian analysis of binary response data with errors in the response. We illustrate the methodology with several real data examples extracted from the literature.     

Prediction of community prevalence of human onchocerciasis in the Amazonian onchocerciasis focus: Bayesian approach

OBJECTIVE: To develop a Bayesian hierarchical model for human onchocerciasis with which to explore the factors that influence prevalence of microfilariae in the Amazonian focus of onchocerciasis and predict the probability of any community being at least mesoendemic (>20% prevalence of microfilariae), and thus in need of priority ivermectin treatment. METHODS: Models were developed with data from 732 individuals aged > or =15 years who lived in 29 Yanomami communities along four rivers of the south Venezuelan Orinoco basin. The models' abilities to predict prevalences of microfilariae in communities were compared. The deviance information criterion, Bayesian P-values, and residual values were used to select the best model with an approximate cross-validation procedure. FINDINGS: A three-level model that acknowledged clustering of infection within communities performed best, with host age and sex included at the individual level, a river-dependent altitude effect at the community level, and additional clustering of communities along rivers. This model correctly classified 25/29 (86%) villages with respect to their need for priority ivermectin treatment. CONCLUSION: Bayesian methods are a flexible and useful approach for public health research and control planning. Our model acknowledges the clustering of infection within communities, allows investigation of links between individual- or community-specific characteristics and infection, incorporates additional uncertainty due to missing covariate data, and informs policy decisions by predicting the probability that a new community is at least mesoendemic.     

Bayesian inference on the patient population size given list mismatches

In applying capture-recapture methods for closed populations to epidemiology, one needs to estimate the total number of people with a certain disease in a certain research area by using several lists with information of patients. Problems of lists error often arise due to mistyping or misinformation. Adopting the concept of tag-loss methodology in animal populations, Seber et al. (Biometrics 2000; 56:1227-1232) proposed solutions to a two-list problem. This article reports an interesting simulation study, where Bayesian point estimates based on improper constant and Jeffreys prior for unknown population size N could have smaller frequentist standard errors and MSEs compared to the estimates proposed in Seber et al. (2000). The Bayesian credible intervals based on the same priors also have super frequentist coverage probabilities while some of the frequentist confidence intervals procedures have drastically poor coverage. Seber's real data set on gestational diabetics is analysed with the proposed new methods.     

Estimating disease prevalence in a Bayesian framework using probabilistic constraints

Studies sometimes estimate the prevalence of a disease from the results of one or more diagnostic tests that are applied to individuals of unknown disease status. This approach invariably means that, in the absence of a gold standard and without external constraints, more parameters must be estimated than the data permit. Two assumptions are regularly made in the literature, namely that the test characteristics (sensitivity and specificity) are constant over populations and the tests are conditionally independent given the true disease status. These assumptions have been criticized recently as being unrealistic. Nevertheless, to estimate the prevalence, some restrictions on the parameter estimates need to be imposed. We consider 2 types of restrictions: deterministic and probabilistic restrictions, the latter arising in a Bayesian framework when expert knowledge is available. Furthermore, we consider 2 possible parameterizations allowing incorporation of these restrictions. The first is an extension of the approach of Gardner et al and Dendukuri and Joseph to more than 2 diagnostic tests and assuming conditional dependence. We argue that this system of equations is difficult to combine with expert opinions. The second approach, based on conditional probabilities, looks more promising, and we develop this approach in a Bayesian context. To evaluate the combination of data with the (deterministic and probabilistic) constraints, we apply the recently developed Deviance Information Criterion and effective number of parameters estimated (pD) together with an appropriate Bayesian P value. We illustrate our approach using data collected in a study on the prevalence of porcine cysticercosis with verification from external data.     

Practical guidelines for adaptive seamless phase II/III clinical trials that use Bayesian methods

Hommel (Biometrical Journal; 45:581-589) proposed a flexible testing procedure for seamless phase II/III clinical trials. Schmidli et al. (Statistics in Medicine; 26:4925-4938), Kimani et al. (Statistics in Medicine; 28:917-936) and Brannath et al. (Statistics in Medicine; 28:1445-1463) exploited the flexible testing of Hommel to propose adaptation in seamless phase II/III clinical trials that incorporate prior knowledge by using Bayesian methods. In this paper, we show that adaptation incorporating prior knowledge may lead to higher power. Other important issues to consider in such adaptive designs are the gain in power (or saving in patients) over traditional testing and how utility values used to make the adaptation may be used to stop a trial early. In contrast to the aforementioned authors, we discuss these issues in detail and propose a unified approach to address them so that implementing the aforementioned designs and proposing similar designs is clearer.     

Identifying implausible gestational ages in preterm babies with Bayesian mixture models

Infant birth weight and gestational age are two important variables in obstetric research. The primary measure of gestational age used in US birth data is based on a mother's recall of her last menstrual period, which has been shown to introduce random or systematic errors. To mitigate some of those errors, Oja et al., Platt et al., and Tentoni et al. estimated the probabilities of gestational ages being misreported under the assumption that the distribution of infant birth weights for a true gestational age is approximately Gaussian. From this assumption, Oja et al. fitted a three‐component mixture model, and Tentoni et al. and Platt et al. fitted two‐component mixture models. We build on their methods and develop a Bayesian mixture model. We then extend our methods using reversible jump Markov chain Monte Carlo to incorporate the uncertainty in the number of components in the model. We conduct simulation studies and apply our methods to singleton births with reported gestational ages of 23–32 weeks using 2001–2008 US birth data. Results show that a three‐component mixture model fits the birth data better for gestational ages reported as 25 weeks or less; and a two‐component mixture model fits better for the higher gestational ages. Under the assumption that our Bayesian mixture models are appropriate for US birth data, our research provides useful statistical tools to identify records with implausible gestational ages, and the techniques can be used in part of a multiple‐imputation procedure for missing and implausible gestational ages. Published 2012. This article is a US Government work and is in the public domain in the USA.     

Estimating disease prevalence in the absence of a gold standard

When estimating disease prevalence, it is not uncommon to have data from conditionally dependent diagnostic tests. In such a situation, the estimation of prevalence is difficult if none of the tests is considered to be a gold standard. In this paper we develop a Bayesian approach to estimating disease prevalence based on the results of two diagnostic tests, allowing for the possibility that the tests are conditionally dependent, but not conditioning on any particular dependence structure. This involves the construction of four models with various forms of conditional dependence and uses Bayesian model averaging, enabled by reversible jump MCMC, to obtain an overall estimate of the prevalence. This methodology is demonstrated using a study on the prevalence of Strongyloides infection.     

Bayesian estimation of the average treatment effect on the treated using inverse weighting

We develop a Bayesian approach to estimate the average treatment effect on the treated in the presence of confounding. The approach builds on developments proposed by Saarela et al in the context of marginal structural models, using importance sampling weights to adjust for confounding and estimate a causal effect. The Bayesian bootstrap is adopted to approximate posterior distributions of interest and avoid the issue of feedback that arises in Bayesian causal estimation relying on a joint likelihood. We present results from simulation studies to estimate the average treatment effect on the treated, evaluating the impact of sample size and the strength of confounding on estimation. We illustrate our approach using the classic Right Heart Catheterization data set and find a negative causal effect of the exposure on 30-day survival, in accordance with previous analyses of these data. We also apply our approach to the data set of the National Center for Health Statistics Birth Data and obtain a negative effect of maternal smoking during pregnancy on birth weight.     

Estimating the prevalence of multiple diseases from two‐stage hierarchical pooling

Testing protocols in large‐scale sexually transmitted disease screening applications often involve pooling biospecimens (e.g., blood, urine, and swabs) to lower costs and to increase the number of individuals who can be tested. With the recent development of assays that detect multiple diseases, it is now common to test biospecimen pools for multiple infections simultaneously. Recent work has developed an expectation–maximization algorithm to estimate the prevalence of two infections using a two‐stage, Dorfman‐type testing algorithm motivated by current screening practices for chlamydia and gonorrhea in the USA. In this article, we have the same goal but instead take a more flexible Bayesian approach. Doing so allows us to incorporate information about assay uncertainty during the testing process, which involves testing both pools and individuals, and also to update information as individuals are tested. Overall, our approach provides reliable inference for disease probabilities and accurately estimates assay sensitivity and specificity even when little or no information is provided in the prior distributions. We illustrate the performance of our estimation methods using simulation and by applying them to chlamydia and gonorrhea data collected in Nebraska. Copyright © 2016 John Wiley & Sons, Ltd.     

Bayesian pharmacovigilance signal detection methods revisited in a multiple comparison setting

Pharmacovigilance spontaneous reporting systems are primarily devoted to early detection of the adverse reactions of marketed drugs. They maintain large spontaneous reporting databases (SRD) for which several automatic signalling methods have been developed. A common limitation of these methods lies in the fact that they do not provide an auto‐evaluation of the generated signals so that thresholds of alerts are arbitrarily chosen. In this paper, we propose to revisit the Gamma Poisson Shrinkage (GPS) model and the Bayesian Confidence Propagation Neural Network (BCPNN) model in the Bayesian general decision framework. This results in a new signal ranking procedure based on the posterior probability of null hypothesis of interest and makes it possible to derive with a non‐mixture modelling approach Bayesian estimators of the false discovery rate (FDR), false negative rate, sensitivity and specificity. An original data generation process that can be suited to the features of the SRD under scrutiny is proposed and applied to the French SRD to perform a large simulation study. Results indicate better performances according to the FDR for the proposed ranking procedure in comparison with the current ones for the GPS model. They also reveal identical performances according to the four operating characteristics for the proposed ranking procedure with the BCPNN and GPS models but better estimates when using the GPS model. Finally, the proposed procedure is applied to the French data. Copyright © 2009 John Wiley & Sons, Ltd.     

Bayes-LQAS: classifying the prevalence of global acute malnutrition

Lot Quality Assurance Sampling (LQAS) applications in health have generally relied on frequentist interpretations for statistical validity. Yet health professionals often seek statements about the probability distribution of unknown parameters to answer questions of interest. The frequentist paradigm does not pretend to yield such information, although a Bayesian formulation might. This is the source of an error made in a recent paper published in this journal. Many applications lend themselves to a Bayesian treatment, and would benefit from such considerations in their design. We discuss Bayes-LQAS (B-LQAS), which allows for incorporation of prior information into the LQAS classification procedure, and thus shows how to correct the aforementioned error. Further, we pay special attention to the formulation of Bayes Operating Characteristic Curves and the use of prior information to improve survey designs. As a motivating example, we discuss the classification of Global Acute Malnutrition prevalence and draw parallels between the Bayes and classical classifications schemes. We also illustrate the impact of informative and non-informative priors on the survey design. Results indicate that using a Bayesian approach allows the incorporation of expert information and/or historical data and is thus potentially a valuable tool for making accurate and precise classifications.     

Estimating the number of helminthic infections in the Republic of Cameroon from data on infection prevalence in schoolchildren

INTRODUCTION: The prevalence of infection with helminths is markedly dependent on age, yet estimates of the total number of infections are typically based on data only from school-aged children. Such estimates, although useful for advocacy, provide inadequate information for planning control programmes and for quantifying the burden of disease. Using readily available data on the prevalence of infection in schoolchildren, the relation between the prevalence of infection in school-aged children and prevalence in the wider community can be adequately described using species-specific models. This paper explores the reliability of this approach to predict the prevalence infection in the community and provides a model for estimating the total number of people infected in the Republic of Cameroon. METHODS: Using data on the prevalence of helminthic infection in school-aged children in Cameroon, the prevalence of infection in pre-school children and adults was estimated from species-specific linear and logistic regression models developed previously. The model predictions were then used to estimate the number of people infected in each district in each age group in Cameroon. RESULTS: For Cameroon, if only the prevalence of infection in schoolchildren is used, the number of people infected with each helminthic species will be overestimated by up to 32% when compared with the estimates provided by the species-specific models. The calculation of confidence intervals supports the statistical reliability of the model since a narrow range of parameter estimates is evident. Furthermore, this work suggests that estimation of national prevalence of infection and the number infected will be enhanced if data are stratified by age; this model represents a useful planning tool for obtaining more accurate estimates. Estimates based on data aggregated from three geographical levels (district, regional, and national) show that summarizing prevalence data at the national level will result in biases of up to 19%. Such biases reflect differences in the geographical distribution for the prevalence of each species. DISCUSSION: Developing more accurate estimates requires a better understanding of the differences in the spatial heterogeneity of each species and also better methods of incorporating this information when making estimates.     

Bayesian mixed hidden Markov models: a multi‐level approach to modeling categorical outcomes with differential misclassification

Questionnaire‐based health status outcomes are often prone to misclassification. When studying the effect of risk factors on such outcomes, ignoring any potential misclassification may lead to biased effect estimates. Analytical challenges posed by these misclassified outcomes are further complicated when simultaneously exploring factors for both the misclassification and health processes in a multi‐level setting. To address these challenges, we propose a fully Bayesian mixed hidden Markov model (BMHMM) for handling differential misclassification in categorical outcomes in a multi‐level setting. The BMHMM generalizes the traditional hidden Markov model (HMM) by introducing random effects into three sets of HMM parameters for joint estimation of the prevalence, transition, and misclassification probabilities. This formulation not only allows joint estimation of all three sets of parameters but also accounts for cluster‐level heterogeneity based on a multi‐level model structure. Using this novel approach, both the true health status prevalence and the transition probabilities between the health states during follow‐up are modeled as functions of covariates. The observed, possibly misclassified, health states are related to the true, but unobserved, health states and covariates. Results from simulation studies are presented to validate the estimation procedure, to show the computational efficiency due to the Bayesian approach and also to illustrate the gains from the proposed method compared to existing methods that ignore outcome misclassification and cluster‐level heterogeneity. We apply the proposed method to examine the risk factors for both asthma transition and misclassification in the Southern California Children's Health Study. Copyright © 2013 John Wiley & Sons, Ltd.     

Estimation of prevalence on the basis of screening tests

Estimates of disease prevalence based on screening tests can be severely biased unless adjusted for the sensitivity and specificity of the screening test. One such adjusted estimate, the maximum likelihood estimator proposed by Levy and Kass, can yield an extreme estimate of zero or one that has undesirable characteristics such as a standard error of zero. We develop here a Bayesian estimator which always falls between zero and one. Users without specialized software can use the maximum likelihood estimate for most circumstances and, in special cases, such as a zero estimate of prevalence, turn to the Bayesian estimate. Others can use software to carry out a complete Bayesian solution. We have provided a method to obtain numerical values for the Bayesian estimate for those ranges of sample size (20-100), sensitivity (0.7-0.9) and specificity (0.7-0.9) for which the use of this estimator seems most practical.     

Statistical methods for haplotype-based matched case-control association studies

Kraft et al. [2005] proposed a method for matched haplotype-based association studies and compared the performances of six analytic strategies for estimating the odds ratio parameters using a conditional likelihood function. Zhang et al. [2006] modified the conditional likelihood and proposed a new method for matched haplotype-based association studies. The main assumptions of Zhang et al. were that the disease was rare, the population was in Hardy-Weinberg equilibrium (HWE), and the haplotypes were independent of the covariates and matching variable(s). In this article, we modify the estimation procedure proposed by Zhang et al. and introduce a fixation index so that the assumption of HWE is relaxed. Using the Wald test, we compare the current modified method with the procedure developed by Kraft et al. through simulations. The results show that the modified method is uniformly more powerful than that described in Kraft et al. Furthermore, the results indicate that the modified method is quite robust to the rare disease assumption.     

Variation in New Zealand hospital outcomes: combining hierarchical Bayesian modeling and propensity score methods for hospital performance comparisons

Two major statistical issues confronting comparative analyses of hospital outcomes are adequacy of case-mix adjustment and proper accounting for random variation. Hierarchical modeling has been proposed to improve precision and reduce the impact of random variation but becomes difficult to implement when there are numerous case-mix factors to control. In this paper we formulate the problem of hospital performance comparisons within the framework of potential outcomes and illustrate an approach to hospital comparisons which combines multiple category propensity score methods for the control of case-mix variations with hierarchical Bayesian modeling of case-mix adjusted summaries. The approach is similar to that proposed by Huang et al. (Health Serv Res 40:253–278, 2005) but extends their approach by using a Bayesian model to accommodate hospital level attributes and to facilitate joint modeling of performance for multiple outcomes. The analytical approach is illustrated by a comparison of 30 day post admission mortality risks for patients treated for acute myocardial infarction, pneumonia or stroke in 34 New Zealand public hospitals. In a small simulation study, reported in electronic supplementary material, hierarchical models outperformed non-hierarchical models, achieving both better credible interval coverage and shorter average interval lengths for measures of between hospital variation based on contrasts between the 90th and 10th percentiles of the mortality risk distribution. Simulation performance of hierarchical and non-hierarchical models in detecting unusual performance was similar.     

Sample size calculations for disease freedom and prevalence estimation surveys

We developed a Bayesian approach to sample size calculations for studies designed to estimate disease prevalence that uses a hierarchical model for estimating the proportion of infected clusters (cluster-level prevalence) within a country or region. The clusters may, for instance, be villages within a region, cities within a state, or herds within a country. Our model allows for clusters with zero prevalence and for variability in prevalences among infected clusters. Moreover, uncertainty about diagnostic test accuracy and within-cluster prevalences is accounted for in the model. A predictive approach is used to address the issue of sample size selection in human and animal health surveys. We present sample size calculations for surveys designed to substantiate freedom of a region from an infectious agent (disease freedom surveys) and for surveys designed to estimate cluster-level prevalence of an endemic disease (prevalence estimation surveys). In disease freedom surveys, for instance, assuming the cluster-level prevalence for a particular infectious agent in the region is greater than a maximum acceptable threshold, a sample size combination consisting of the number of clusters sampled and number of subjects sampled per cluster can be determined for which authorities conducting the survey detect this excessive cluster-level prevalence with high predictive probability. The method is straightforward to implement using the Splus/R library emBedBUGS together with WinBUGS.     

Meta-analysis of diagnostic tests with imperfect reference standards.

We present a method to estimate the summary receiver operating characteristic (SROC) curve for combining information on a diagnostic test from several different studies. Unlike previous methods that assume the reference standard to be error free, our approach allows for the possibility of errors in the reference standard, through use of a latent class model. The model provides estimates of the sensitivity and specificity of the diagnostic test and the case prevalence in each study; these parameters can then be used in a meta-analysis, for example, using the regression method proposed by Moses et al., of a measure of test discrimination on a measure of the diagnostic threshold, to fit the SROC. The method is illustrated with an example on Pap smears that shows how adjusting for imperfection in the reference standard typically reduces the scatter of data in the SROC plot, and tends to indicate better performance of the test than otherwise.     

Measurement and management of work climate: Cross-validation of the CRISO Psychological Climate Questionnaire

This paper presents research results that offer answers to the “why,” “what” and “how” of work climate measurement. It also submits to the scientific community a confirmatory cross-validation procedure applied to a new measurement tool, consistent with the works of Jones and James's (1979) and of Parker et al. (2003) on psychological climate. The results depict a good model fit for both the English and French versions of the questionnaire. This new instrument offers a comprehensive and manageable approach for the development of a healthy workplace.     

A Bayesian multivariate meta-analysis of prevalence data

When conducting a meta-analysis involving prevalence data for an outcome with several subtypes, each of them is typically analyzed separately using a univariate meta-analysis model. Recently, multivariate meta-analysis models have been shown to correspond to a decrease in bias and variance for multiple correlated outcomes compared with univariate meta-analysis, when some studies only report a subset of the outcomes. In this article, we propose a novel Bayesian multivariate random effects model to account for the natural constraint that the prevalence of any given subtype cannot be larger than that of the overall prevalence. Extensive simulation studies show that this new model can reduce bias and variance when estimating subtype prevalences in the presence of missing data, compared with standard univariate and multivariate random effects models. The data from a rapid review on occupation and lower urinary tract symptoms by the Prevention of Lower Urinary Tract Symptoms Research Consortium are analyzed as a case study to estimate the prevalence of urinary incontinence and several incontinence subtypes among women in suspected high risk work environments.