An application of Bayesian estimation in daily clinical practice of anesthesia

The data obtained from the clinical practice are not unanimous, because we cannot assume the patient condition constant. It is, however, important to estimate real time patient condition individually to make more appropriate decision on treatment. In the classical statistical approach to the estimation problem, the patient condition is, so to speak, viewed as an unknown constant, which does not change with time. This is a wrong assumption in the clinical world. In Bayesian statistics, an available datum or information prior to the event (prior probability) is used in the estimation process to obtain the posterior probability. Furthermore, datum or information gained in the clinical setting is considered as a fact instead of a random variable and is utilized to join itself with prior probability. In other word, in Bayesian statistics, estimation is changed to prediction. We utilize our subjective thinking in making decision in our daily practice of anesthesia. In fact, subjectivity is based on the beliefs or opinions, depending on the experience and information possessed by the anesthesiologist who is making the assessment. In Bayesian estimation, subjectivity, a measure of belief is incorporated as a prior probability which, I believe, is more flexible in dealing with the real world problems than any other statistical estimation.     

Bayesian statistical analysis of protein side-chain rotamer preferences

We present a Bayesian statistical analysis of the conformations of side chains in proteins from the Protein Data Bank. This is an extension of the backbone-dependent rotamer library, and includes rotamer populations and average chi angles for a full range of phi, psi values. The Bayesian analysis used here provides a rigorous statistical method for taking account of varying amounts of data. Bayesian statistics requires the assumption of a prior distribution for parameters over their range of possible values. This prior distribution can be derived from previous data or from pooling some of the present data. The prior distribution is combined with the data to form the posterior distribution, which is a compromise between the prior distribution and the data. For the chi 2, chi 3, and chi 4 rotamer prior distributions, we assume that the probability of each rotamer type is dependent only on the previous chi rotamer in the chain. For the backbone-dependence of the chi 1 rotamers, we derive prior distributions from the product of the phi-dependent and psi-dependent probabilities. Molecular mechanics calculations with the CHARMM22 potential show a strong similarity with the experimental distributions, indicating that proteins attain their lowest energy rotamers with respect to local backbone-side-chain interactions. The new library is suitable for use in homology modeling, protein folding simulations, and the refinement of X-ray and NMR structures.     

Bayesian Storm-Water Quality Model and Its Application to Water Quality Monitoring

A Bayesian statistical approach for determining the parameter uncertainty of a storm-water treatment model is reported. The storm-water treatment technologies included a sand filter and a subsurface gravel wetland. The two field systems were loaded and monitored in a side-by-side fashion over a two-year period. The loading to each system was storm-water runoff generated by ambient rainfall on a commuter parking lot. Contaminant transport is simulated by using a one-dimensional advection-dispersion model. The unknown parameters of the model are the contaminant deposition rate and the hydrodynamic dispersion. The following contaminants are considered in the study: total suspended solids, total petroleum hydrocarbons–diesel range hydrocarbons, and zinc. Parameter uncertainties are addressed by estimating the posterior probability distributions through a conventional Metropolis-Hastings algorithm. Results indicate that the posterior distributions are unimodal and, in some instances, exhibit some level of skewness. The Bayesian approach allowed the estimation of the 10th, 25th, 50th, 75th, and 95th percentiles of the posterior probability distributions. The prediction capabilities of the model were explored by performing a Monte Carlo simulation using the calculated posterior distributions and two rainfall-runoff events not considered during the calibration phase. The objective is to estimate effluent concentrations from the treatment systems under different scenarios of flow and contaminant loads. In general, estimated effluent concentrations and the total estimated mass fell within the defined uncertainty limits.     

Models of jury decision making: A critical review.

Reviews several models of jury decision making. In each instance the model is described and compared with related models, its assumptions are scrutinized, its fit to normative data is evaluated, and possible revisions and extensions of the model are discussed. Models reviewed include (a) multinomial decision schemes designed to adduce implicit decision rules used in jury decision making; (b) binomial models of jury voting that use simplifying assumptions about jury decision making to assess the impact of explicit decision rules and jury size on verdict distributions; (c) Bayesian models that use normative data to estimate prior probabilities of defendants' "convictability" and juror accuracy; (d) models that assess the relationships among jury size, decision rule, and jury accuracy; (e) models that examine the relationship between juror and jury errors; and (f) a computer simulation that uses simple assumptions about group persuasion and individual differences in jurors' resistance to persuasion to model results from empirical studies of jury decision making. (41 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Reporting Bayesian analyses of clinical trials

Many clinicians wrongly interpret p-values as probabilities that treatment has an adverse effect and confidence intervals as probability intervals. Such inferences can be validly drawn from Bayesian analyses of trial results. These analyses use the data to update the prior (or pre-trial) beliefs to give posterior (or post-trial) beliefs about the magnitude of a treatment effect. However, for these methods to gain acceptance in the medical literature, understanding between statisticians and clinicians of the issues involved in choosing appropriate prior distributions for trial reporting needs to be reached. I focus on two types of prior that deserve consideration. The first is the non-informative prior giving standardized likelihood distributions as post-trial probability distributions. Their use is unlikely to be controversial among statisticians whilst being intuitively appealing to clinicians. The second type of prior has a spike of probability mass at the point of no treatment effect. Varying the magnitude of the spike illustrates the sensitivity of the conclusions drawn to the degree of prior scepticism in a treatment effect. With both, graphical displays provide clinical readers with the opportunity to explore the results more fully. An example of how a clinical trial might be reported in the medical literature using these methods is given.     

Decision processes in discrimination: Fundamental misrepresentations of signal detection theory.

A new approach to studying decision making in discrimination tasks is described that does not depend on the technical assumptions of signal detection theory (e.g., normality of the encoding distributions). In 3 different experiments, results of these new distribution-free tests converge on a single, surprising conclusion: response biases had substantial effects on the encoding distributions but no effect on the decision rule, which was uniformly unbiased in equal and unequal base rate conditions and in symmetric and asymmetric payoff conditions. This seemingly paradoxical result is fundamentally inconsistent with the entire family of signal detection theory models, raising some important questions about the significance of many published results in the human performance literature. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Robustness considerations in Bayesian analysis

All statistical analyses demand uncertain inputs or assumptions. This is especially true of Bayesian analyses. In addition to the usual concerns about the agreement of the data and model, a Bayesian must contemplate the effect of an uncertain prior specification. The degree to which inferences are robust to changes in the prior is of primary interest. This article discusses some robust techniques that have been suggested in the literature. One goal is to make apparent the relevance of some of these techniques to biostatistical work.     

Bootstrap Technique for Risk Analysis with Interval Numbers in Bridge Construction Projects

Bridges are principal and vital transportation structures. If risk management is not considered in bridge construction projects, objectives cannot be delivered on time, on budget, or with suitable quality results. Risk data set sizes and experts’ judgments are not usually sufficient for analyzing significant risks in bridge construction projects; moreover, the statistical distributions for risk parameter estimates are usually unknown. Standard parametric statistical techniques cannot provide appropriate solutions for cases with small data sets or unknown distributions. This paper proposes a new hybrid approach by using a nonparametric resampling technique and interval computations for risk analysis, in particular, for bridge construction projects. Bootstrap techniques produce more accurate inferences for comparing parametric techniques and are an alternative when the underlying parametric assumptions are not considered. Increasingly, because of the complexity and uncertainty in decision making at bridge projects, it is easier or more natural to provide interval values for parts or all of decision-making judgments. Furthermore, the goal of reducing standard deviations for both risk probability and risk impact compared with the conventional approach is another conclusion of this paper. The proposed approach is applied to a case in Iran to show the validity of the approach.     

A Bayesian characterization of Hardy-Weinberg disequilibrium

A Bayesian method for determining if there are large departures from independence between pairs of alleles at a locus, Hardy-Weinberg equilibrium (HWE), is presented. We endorse the view that a population will never be exactly in HWE and that there will be occasions when there is a need for an alternative to the usual hypothesis-testing setting. Bayesian methods provide such an alternative, and our approach differs from previous Bayesian treatments in using the disequilibrium and inbreeding coefficient parameterizations. These are easily interpretable but may be less mathematically tractable than other parameterizations. We examined the posterior distributions of our parameters for evidence that departures from HWE were large. For either parameterization, when a conjugate prior was used, the prior probability for small departures was itself small, i.e., the prior was weighted against small departures from independence. We could avoid this uneven weighting by using a step prior which gave equal weighting to both small and large departures from HWE. In most cases, the Bayesian methodology makes it clear that there are not enough data to draw a conclusion.     

Large sample Bayesian inference on the parameters of the proportional hazard models

This paper considers large sample Bayesian analysis of the proportional hazards model when interest is in inference on the parameters and estimation of the log relative risk for specified covariate vectors rather than on prediction of the survival function. We use a normal prior distribution for the parameters and make inferences based on the derived posterior distribution. The suggested approach is much simpler than alternative Bayesian analyses previously suggested for the proportional hazards models. Using simulated data we compare estimates obtained from the Bayesian analysis with those obtained from the full proportional hazards model and the reduced model after backwards elimination. We show that under a wider range of assumptions, the Bayesian analysis provides reduced estimation errors and improved rejection of noise variables. Finally, we illustrate the methodology using data from a large study of prognostic markers in breast cancer.     

Classical statistical hypotheses testing within the context of Bayesian theory.

A portion of results that are judged significant on the basis of classical statistical tests will be due to chance. The conditional probability of error in the presence of statistical significance depends upon the significance level employed, the power of the test, and the prior probability that a valid null hypothesis was chosen for testing. Bayesian theory provides a logical model for the design of experiments in which classical hypothesis testing is to be used. In this manner, Bayesian objectives can be realized while the safeguards of classical statistical hypothesis testing are retained. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Bayesian analysis of mixtures applied to post-synaptic potential fluctuations

Bayesian inference techniques have been applied to the analysis of fluctuation of post-synaptic potentials in the hippocampus. The underlying statistical model assumes that the varying synaptic signals are characterized by mixtures of (unknown) numbers of individual gaussian, or normal, component distributions. Each solution consists of a group of individual components with unique mean values and relative probabilities of occurrence and a predictive probability density. The advantages of bayesian inference techniques over the alternative method of maximum likelihood estimation (MLE) of the parameters of an unknown mixture distribution include the following: (1) prior information may be incorporated in the estimation of model parameters; (2) conditional probability estimates of the number of individual components in the mixture are calculated; (3) flexibility exists in the extent to which the estimated noise standard deviation indicates the width of each component; (4) posterior distributions for component means are calculated, including measures of uncertainty about the means; and (5) probability density functions of the component distributions and the overall mixture distribution are estimated in relation to the raw grouped data, together with measures of uncertainty about these estimates. This expository report describes this novel approach to the unconstrained identification of components within a mixture, and provides demonstration of the usefulness of the technique in the context of both simulations and the analysis of distributions of synaptic potential signals.     

Decision making during a phase III randomized controlled trial

Experiments such as clinical trials should be carried out with specific objectives. For example, in a trial designed to prevent disease, specific considerations should be made concerning the impact of the trial on the health of the target population, including the participants in the trial. These objectives should be assessed continually in light of data accumulating from the trial. Accumulating evidence should be judged in the context of changing circumstances external to the trial, and the trial's design possibly modified. An important type of modification is stopping the trial. This is a sequential decision problem that can be addressed using a Bayesian approach and the methods of dynamic programming. As an example we consider a vaccine trial for the prevention of haemophilus influenzae type b. The objective we consider is minimizing the number of cases of this disease in a Native American population over a specified horizon. We assess the prior probability distribution of vaccine efficacy. We also assess the probability of regulatory approval for widespread use of the vaccine, depending on the data presented to the regulatory officials. In deciding whether to continue the trial we weigh the impact of the possible future results by their (predictive) probabilities. We address the sensitivity of the optimal stopping policy to the prior probability distribution, to the assessed probability of regulatory approval, and to the horizon.     

Bayesian inference in two-phase prevalence studies

This paper discusses Bayesian methods for the assessment of the prevalence of a disorder based on data from a two-phase design with a short screening instrument administered at the first phase followed by an in-depth diagnostic instrument given at the second phase. In calculating the posterior distributions of the quantities of interest, for example, the prevalence, sensitivity and specificity, and predictive distributions, we used the Gibbs sampler. We illustrate our approach by assessing the prevalence of depression in adolescents with use of data attained from a two-phase design.     

Grouped random effects models for Bayesian meta-analysis

Meta-analysis refers to quantitative methods to combine results from independent studies so as to draw overall conclusions. Frequently, results from dissimilar studies are inappropriately combined, resulting in suspect inferential synthesis. We present a straightforward method to identify and address this problem through the development of grouped random effect models for meta-analysis. We examine 15 comparative studies that investigate the efficacy of a new anti-epileptic drug, progabide. The flexibility of this modelling scheme is exemplified by the result that the open studies support the efficacy of progabide while the closed studies support the reverse hypothesis. Bayesian approaches for meta-analysis are preferable because of the small number of studies prevalent in meta-analysis. We specify diffuse proper prior and hyperprior distributions to assure posterior propriety. We investigate sensitivity of the posterior to choice of prior. We use Gibbs sampling and the Metropolis algorithm to generate samples from the relevant posteriors. We analyse posterior summaries and plots of model parameters to suggest solutions to questions of interest.     

Plastic surgical problems in the neonatal intensive care unit

A Bayesian decision rule for early termination of an experimental study of binary responses is presented. This early termination occurs when the predictive probability of reversing the decision when utilizing the delayed observations is small. The proposed approach utilizes Bayesian inferential tools such as Bayes factors and predictive distributions. A simulation study is conducted to evaluate the performance of the proposed approach. Some guidelines are given to determine when the study should be terminated early and when the investigator should wait for delayed observations before making a conclusion.     

Bayesian Updating of Parameters for a Sediment Entrainment Model via Markov Chain Monte Carlo

A Bayesian framework incorporating Markov chain Monte Carlo (MCMC) for updating the parameters of a sediment entrainment model is presented. Three subjects were pursued in this study. First, sensitivity analyses were performed via univariate MCMC. The results reveal that the posteriors resulting from two- and three-chain MCMC were not significantly different; two-chain MCMC converged faster than three chains. The proposal scale factor significantly affects the rate of convergence, but not the posteriors. The sampler outputs resulting from informed priors converged faster than those resulting from uninformed priors. The correlation coefficient of the Gram–Charlier (GC) probability density function (PDF) is a physical constraint imposed on MCMC in which a higher correlation would slow the rate of convergence. The results also indicate that the parameter uncertainty is reduced with increasing number of input data. Second, multivariate MCMC were carried out to simultaneously update the velocity coefficient C and the statistical moments of the GC PDF. For fully rough flows, the distribution of C was significantly modified via multivariate MCMC. However, for transitional regimes the posterior values of C resulting from univariate and multivariate MCMC were not significantly different. For both rough and transitional regimes, the differences between the prior and posterior distributions of the statistical moments were limited. Third, the practical effect of updated parameters on the prediction of entrainment probabilities was demonstrated. With all the parameters updated, the sediment entrainment model was able to compute more accurately and realistically the entrainment probabilities. The present work offers an alternative approach to estimating the hydraulic parameters not easily observed.     

Assessing placebo response using Bayesian hierarchical survival models

The National Institute of Mental Health (NIMH) Collaborative Study of Long-Term Maintenance Drug Therapy in Recurrent Affective Illness was a multicenter randomized controlled clinical trial designed to determine the efficacy of a pharmacotherapy for the prevention of the recurrence of unipolar affective disorders. The outcome of interest in this study was the time until the recurrence of a depressive episode. The data show much heterogeneity between centers for the placebo group. The aim of this paper is to use Bayesian hierarchical survival models to investigate the heterogeneity of placebo effects among centers in the NIMH study. This heterogeneity is explored in terms of the marginal posterior distributions of parameters of interest and predictive distributions of future observations. The Gibbs sampling algorithm is used to approximate posterior and predictive distributions. Sensitivity of results to the assumption of a constant hazard survival distribution at the first stage of the hierarchy is examined by comparing results derived from a two component exponential mixture and a two component exponential changepoint model to the results derived from an exponential model. The second component of the mixture and changepoint models is assumed to be a surviving fraction. For each of these first stage parametric models sensitivity of results to second stage prior distributions is also examined.     

Contextual effects on the calibration of probabilistic judgments.

24 practicing auditors employed by public accounting firms participated in a study to determine the extent to which contextual factors affect the calibration of their subjective prior probability distributions (PPDs). Probabilistic responses to general-knowledge (almanac) questions were analyzed and compared to responses obtained in a previous study by the present 3rd author et al (see record 1983-07156-001), which used the same type of Ss and methods in a substantive audit judgment context. Results indicate that Ss' judgments in the general-knowledge task context were miscalibrated and significantly overconfident, whereas their judgments in the substantive audit task context were less miscalibrated and predominantly underconfident. Findings suggest that calibration research results may not be generalizable across applied judgment–decision contexts. Implications for practical applications of Bayesian decision models, improvement of preexperimental training methods, and the effects of incentives on miscalibration are discussed. (23 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)