Use Of Bayesian Statistical Methods Research Articles

BEAT CF pulmonary exacerbations core protocol for evaluating the management of pulmonary exacerbations in people with cystic fibrosis

BackgroundCystic fibrosis (CF) is a rare, inherited, life-limiting condition predominantly affecting the lungs, for which there is no cure. The disease is characterized by recurrent pulmonary exacerbations (PEx), which are thought to drive progressive lung damage. Management of these episodes is complex and generally involves multiple interventions targeting different aspects of disease. The emergence of innovative trials and use of Bayesian statistical methods has created renewed opportunities for studying heterogeneous populations in rare diseases. Here, we present the protocol for the BEAT CF PEx cohort, a prospective, multi-site, perpetual, platform enrolling adults and children with CF. The BEAT CF PEx cohort will be used to evaluate the comparative effectiveness of interventions for the treatment of PEx requiring intensive therapy (PERITs), with a primary focus on short-term improvements in lung function. This will be achieved through the conduct of cohort-nested studies, including adaptive clinical trials, within the BEAT CF PEx cohort. This protocol will outline key features of the BEAT CF PEx cohort, including the design, implementation, data collection and management, governance and analysis, and dissemination of results.MethodsThis platform will be conducted across multiple sites, commencing with CF treatment centers in Australia. People of all ages with a clinical diagnosis of CF will be eligible to participate, except those who have previously received a lung transplant. Data including demographic and clinical information, treatment details, and outcomes (including safety, microbiology, and patient-reported outcome measures including quality of life scores) will be systematically collected and securely stored via a digital centralized trial management system (CTMS). The primary endpoint is the absolute change in the percentage predicted forced expiratory volume in 1 s (ppFEV1) from the commencement of intensive therapy to 7 to 10 days afterwards.DiscussionThe BEAT CF PEx cohort will report clinical, treatment, and outcome data for PEx among people with CF and is intended to serve as a core (master) protocol for future nested, interventional trials evaluating treatment(s) for these episodes. The protocols for nested sub-studies are beyond the scope of this document and will be reported separately.Trial registrationANZCTR BEAT CF Platform – ACTRN12621000638831. Registration date: Sept. 26, 2022.

An Empirical Investigation of Bayesian Clinical Trial Design in Metastatic Breast Cancer.

Over the past 20years, there has been increasing interest in the use of Bayesian statistical methods for the analysis of clinical trials used to support regulatory decisions. Bayesian methods for the analysis of clinical trials are an attractive option when good prior information is available. Yet, in many cases, prior information is scarce and only tentative or proprietary prior information exists. In these situations, it is necessary to use noninformative type or skeptical-type priors. We undertook a systematic study of Bayesian methods and applied them to 13 randomized clinical trials in metastatic breast cancer submitted to the U.S. Food and Drug Administration for registrational purposes. Across all 13 studies, there were a total of 10,521 patients using 10 experimental agents. Our results demonstrated that Bayesian analyses with noninformative priors provided similar results to more traditional analyses. We also found that early interim looks at the study results can vary widely based upon the type of prior used. Finally, we found that pre-defined threshold stopping rules need to be relatively strong to prevent trials from stopping very early. Our results suggest that, when prior information is limited and a noninformative prior is used, there is little numerical difference between Bayesian methods and more traditional analysis methods. Bayesian methods, however, may provide additional summaries of the data that are more easily interpretable than means and confidence intervals.

Bayesian Sensitivity Analysis for Non-ignorable Missing Data in Longitudinal Studies

The use of Bayesian statistical methods to handle missing data in biomedical studies has become popular in recent years. In this paper, we propose a novel Bayesian sensitivity analysis (BSA) technique that accounts for the influences of missing outcome data on the estimation of treatment effects in longitudinal studies with non-ignorable missing data. The approach uses a pattern-mixture model for the complete data, which is indexed by non-identifiable sensitivity parameters that accounts for the effect of missingness on the observations. We implement the method using the probabilistic programming language Stan, and apply it to data from the Vancouver At Home Study, which is a randomized control trial that provided housing to homeless people with mental illness. We compare the results of BSA to those from an existing Bayesian longitudinal model that ignores the missing data mechanism in the outcome. Furthermore, we demonstrate in a simulation study that when we use a diffuse conservative prior that describes a range of assumptions about the non-ignorable missingness, then BSA credible intervals have greater length and higher coverage rate of the target parameters than existing methods.

A simple Bayesian approach to tree‐ring dating

Tree‐ring dating involves matching sequences of ring widths from undated timbers to dated sequences known as ‘master’ chronologies. Conventionally, the undated timbers (from a building or woodland) are sequentially matched against one another, using t‐tests to identify the relative offsets with the ‘best’ match, thus producing a ’site’ chronology. A date estimate is obtained when this is matched to a local master chronology of known calendar age. Many tree‐ring sequences in the UK produce rather low t‐values and are thus declared not to have a ‘best’ match to a master chronology. Motivated by this and the routine use of Bayesian statistical methods to provide a probabilistic approach to radiocarbon dating, this paper investigates the practicality of Bayesian dendrochronology. We explore a previously published model for the relationship between ring widths and the underlying climatic signal, implementing it within the Bayesian framework via a simulation‐based approach. Probabilities for a match at each offset are produced, removing the need to identify a single ‘best’ match. The Bayesian model proves successful at matching in both simulated and real examples.

Characterizing Driver Trust in Vehicle Control Algorithm Parameters

Human factors research in vehicle automation has focused on user interfaces such as performance feedback through visual and auditory displays (Blanco et al., 2015). Another approach is to use vehicle dynamics and vibrations as communicative tools for guiding attention (e.g., Morando, Victor, & Dozza, 2016; Walker, Stanton, & Young, 2006; Wiese & Lee, 2007). In our previous study (Price, Venkatraman, Gibson, Lee, & Mutlu, 2016), we showed that the steering wheel deadband, or lateral movement of the vehicle while maintaining lane position, was negatively associated with trust—more lateral movement led to less trust in the algorithm. The present study extends these findings by using Bayesian statistical methods with new control algorithm data. Although the inclusion of additional algorithm characteristics did not improve the trust model, the use of Bayesian statistical methods provides a useful tool to incorporate prior knowledge into an analysis.

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About the Authors

Bayesian Approaches in Medical Device Clinical Trials: A Discussion with Examples in the Regulatory Setting

Challenging statistical issues often arise in the design and analysis of clinical trials to assess safety and effectiveness of medical devices in the regulatory setting. The use of Bayesian methods in the design and analysis of medical device clinical trials has been increasing significantly in the past decade, not only due to the availability of prior information, but mainly due to the appealing nature of Bayesian clinical trial designs. The Center for Devices and Radiological Health at the Food and Drug Administration (FDA) has gained extensive experience with the use of Bayesian statistical methods and has identified some important issues that need further exploration. In this article, we discuss several topics relating to the use of Bayesian statistical methods in medical device trials, based on our experience and real applications. We illustrate the benefits and challenges of Bayesian approaches when incorporating prior information to evaluate the effectiveness and safety of a medical device. We further present an example of a Bayesian adaptive clinical trial and compare it to a traditional frequentist design. Finally, we discuss the use of Bayesian hierarchical models for multiregional trials and highlight the advantages of the Bayesian approach when specifying clinically relevant study hypotheses.

An update on FIV and FeLV test performance using a Bayesian statistical approach

Screening tests for feline retroviruses are thought to have high sensitivity and specificity, although previous studies that evaluated these tests have limitations. Novel statistical approaches have been developed that allow the estimation of sensitivity and specificity in situations where the true state of the disease in individual animals cannot be assured. The purpose of this study was to evaluate the sensitivity and specificity of a variety of retrovirus tests, including some screening tests, in a population of cats potentially infected with either feline leukemia virus (FeLV) and/or feline immunodeficiency virus (FIV) by using a Bayesian statistical approach. Four hundred and ninety blood samples from cats being evaluated for FIV infection were tested by 2 rapid immunomigration tests (Witness single [WS], Witness combi [WC]) and a plate-based ELISA (Petcheck) for FIV antibody, and by a newly designed real-time polymerase chain reaction (PCR) assay for FIV provirus. Four hundred and ninety-five blood samples from cats being evaluated for FeLV infection were tested by 2 rapid immunomigration tests (WS, WC) and a plate-based ELISA (Petcheck) for FeLV antigen, and by a FeLV virus isolation technique. Results were then analyzed by using a Bayesian statistical method. For FIV tests, median sensitivity estimates were 0.98 for WS, 0.97 for WC, 0.98 for ELISA, and 0.92 for PCR. Median specificity estimates were 0.96 for WS, 0.96 for WC, 0.93 for ELISA, and 0.99 for PCR. For FeLV tests, median sensitivity estimates were 0.97 for WS, 0.97 for WC, 0.98 for ELISA, and 0.91 for virus isolation. Median specificity estimates were 0.96 for WS, 0.96 for WC, 0.98 for ELISA, and 0.99 for virus isolation. The use of Bayesian statistical methods overcomes a variety of methodologic problems associated with diagnostic test evaluations, including the lack of a definitive reference test. The sensitivity and the specificity of all 6 evaluated screening tests was high: however, specificity estimates were slightly lower than those reported by most recent studies.

An application of Bayesian statistical methods to adaptive radiotherapy

In adaptive radiotherapy, measured patient-specific setup variations are used to modify the patient setup and treatment plan, potentially many times during the treatment course. To estimate the setup adjustments and re-plan the treatment, the measured data are usually processed using Kalman filtering or by computing running averages. We propose, as an alternative, the use of Bayesian statistical methods, which combine a population (prior) distribution of systematic and random setup errors with the measurements to determine a patient-specific (posterior) probability distribution. The posterior distribution can either be used directly in the re-planning of the treatment or in the generation of statistics needed for adjustments. Based on the assumption that day-to-day setup variations are independent and identically distributed Normal distributions, we can efficiently compute parameters of the posterior distribution from parameters of the prior distribution and statistics of the measurements. We illustrate a simple procedure to apply the method in practice to adaptive radiotherapy, allowing for multiple adjustments of treatment parameters during the course of treatment.

Inheritance of hereditary equine regional dermal asthenia in Quarter Horses

To assess heritability and mode of inheritance for hereditary equine regional dermal asthenia (HERDA) in Quarter Horses. 1,295 horses with Quarter Horse bloodlines, including 58 horses affected with HERDA. Horses were classified as affected or unaffected or as undetermined when data were insufficient to assess phenotype. Pedigree data were analyzed to determine the probable mode of inheritance. Heritability was estimated by use of Bayesian statistical methods. Heritability (mean+/-SD) of HERDA was estimated to be 0.38+/-0.13, with both sexes having an equal probability of being affected. Results for evaluation of the pedigrees were consistent with a single Mendelian autosomal recessive mode of inheritance. HERDA in Quarter Horses is an inherited disease, and affected horses are more likely to produce affected offspring. An autosomal recessive mode of inheritance should be considered by people making breeding decisions involving Quarter Horses when a first-degree relative has been confirmed with HERDA or has produced affected offspring. In addition, breeders whose horses have produced affected offspring can reduce the likelihood of producing affected horses in the future by avoiding inbreeding.

A survey of current Bayesian gene mapping method

Recently, there has been much interest in the use of Bayesian statistical methods for performing genetic analyses. Many of the computational difficulties previously associated with Bayesian analysis, such as multidimensional integration, can now be easily overcome using modern high-speed computers and Markov chain Monte Carlo (MCMC) methods. Much of this new technology has been used to perform gene mapping, especially through the use of multi-locus linkage disequilibrium techniques. This review attempts to summarise some of the currently available methods and the software available to implement these methods.

The X‐Ray–derived Cosmological Star Formation History and the Galaxy X‐Ray Luminosity Functions in the Chandra Deep Fields North and South

The cosmological star formation rate in the combined Chandra Deep Fields North and South is derived from our X-ray luminosity function for galaxies in these deep fields. Mild evolution is seen up to redshift order unity with star formation rate ~ (1 + z)2.7. This is the first directly observed normal star-forming galaxy X-ray luminosity function (XLF) at cosmologically interesting redshifts (z > 0). This provides the most direct measure yet of the X-ray-derived cosmic star formation history of the universe. We make use of Bayesian statistical methods to classify the galaxies and the two types of active galactic nuclei (AGNs), finding the most useful discriminators to be the X-ray luminosity, X-ray hardness ratio, and X-ray to optical flux ratio. There is some residual AGN contamination in the sample at the bright end of the luminosity function. Incompleteness slightly flattens the XLF at the faint end of the luminosity function. The XLF has a lognormal distribution and agrees well with the radio and infrared luminosity functions. However, the XLF does not agree with the Schechter luminosity function for the Hα LF, indicating that, as discussed in the text, additional and different physical processes may be involved in the establishment of the lognormal form of the XLF. The agreement of our star formation history points with the other star formation determinations in different wavebands (IR, radio, Hα) gives an interesting constraint on the initial mass function (IMF). The X-ray emission in the Chandra band is most likely due to binary stars, although X-ray emission from nonstellar sources (e.g., intermediate-mass black holes and/or low-luminosity AGNs) remains a possibility. Under the assumption that it is due to binary stars, the overall consistency and correlations between single-star effects and binary-star effects indicate that not only is the one-parameter IMF (M) constant but also the bivariate IMF(M1, M2) must be constant, at least at the high-mass end. Another way to put this, quite simply, is that X-ray observations may be measuring directly the binary-star formation history of the universe. X-ray studies will continue to be useful for probing the star formation history of the universe by avoiding problems of obscuration. Star formation may therefore be measured in more detail by deep surveys with future X-ray missions.

The Bayesian population approach to physiological toxicokinetic–toxicodynamic models—an example using the MCSim software

The calibration of physiologically based toxicokinetic models against experimental data encompasses the merging of prior knowledge with information present in the data. This prior knowledge is manifested in the scientific literature and associated with various degrees of uncertainty. The most convenient way to combine these sources of information is via the use of Bayesian statistical methods. Furthermore, toxicokinetic models are subject to both inter- and intra-individual variability. This variability may be handled statistically by the use of a population model. The MCSim software, which is available for free download on the Internet, permits the use of a population model in combination with a Bayesian statistical approach. An example of the use of MCSim in a recent model-based risk assessment of dichloromethane (DCM) is given and discussed.

Inheritance of hypoadrenocorticism in bearded collies.

To assess heritability and mode of inheritance for hypoadrenocorticism in Bearded Collies. 635 Bearded Collies. Dogs were classified as affected by hypoadrenocorticism or unaffected. Phenotypic and pedigree data were analyzed. Heritability was estimated by use of Bayesian statistical methods. Regressive logistic models for complex segregation analyses were used to characterize mode of inheritance. Hypoadrenocorticism was diagnosed in 60 (9.4%) dogs. Heritability of hypoadrenocorticism was estimated to be 0.76 with both sexes affected with equal probability. Evaluation of the pedigrees did not support a Mendelian autosomal dominant mode of inheritance. Evidence from the complex segregation analysis for a single locus of large effect on hypoadrenocorticism was not convincing. Hypoadrenocorticism in Bearded Collies is highly heritable. Although a precise genetic mechanism responsible for inheritance of the disorder remains undetermined, breeding decisions must include consideration of the genetic likelihood of passing on this deleterious disorder to offspring of affected dams and sires.

Formulating quantitative methods to evaluate fishery-management systems: what fishery processes should be modelled and what trade-offs should be made?

A wide variety of modelling approaches have been developed over the past few decades to provide quantitative advice to fishery managers about the potential consequences of proposed alternative management actions and to improve the design of fishery- management systems. This article surveys these approaches to identify the main differences among them in their application of decision theory, particularly in the methods used to account for uncertainty, and to identify model structures that need to be considered. Six interlinked model structures are identified: population dynamics, data collection, data analysis and stock assessment, setting harvest controls, the harvest decision process, and imperfect implementation. Their inclusion and design will depend on the institutional arrangements for fishery management. For example, some evaluations have included the last two structures to account for the flexibility of fishery managers in their making of annual harvest decisions and limitations on their ability to implement management policy precisely. Other evaluations have excluded them because they have evaluated “management procedures” whereby all participants would be bound to strictly follow a preset protocol for data collection, data analysis, and a harvest decision rule. In addition, this article identifies some trade-offs that are often made when modelling methods are formulated that can strongly affect model results and the advice given. Partly as a result of these trade-offs, analysts have recently been combining some of the originally divergent aspects of different modelling approaches. Examples of this include combining the use of Bayesian statistical methods with the use of alternative operating models (rather than only one) to account for both parameter and model uncertainty.

Determination of order parameters and correlation times in proteins: a comparison between Bayesian, Monte Carlo and simple graphical methods.

We describe a novel approach to deducing order parameters and correlation times in proteins using a Bayesian statistical method, and show how likelihood contours, P(tau,S), and confidence levels can be obtained. These results are then compared with those obtained from a simple graphical method, as well as those from Monte Carlo simulations. The Bayes approach has the advantage that it is simple and accurate. Unlike Monte Carlo methods, it gives useful contour plots of probability (also not provided by the simple graphical method), and provides likelihood/confidence information. In addition, the Bayesian approach gives results in very good agreement with those obtained from Monte Carlo simulations, and as such use of Bayesian statistical methods appears to have a promising future for studies of order and dynamics in macromolecules.