Parametric Empirical Bayes Approach Research Articles

Distinctive alterations in the mesocorticolimbic circuits in various psychiatric disorders.

Increasing evidence suggests that psychiatric disorders are linked to alterations in the mesocorticolimbic dopamine-related circuits. However, the common and disease-specific alterations remain to be examined in schizophrenia (SCZ), major depressive disorder (MDD), and autism spectrum disorder (ASD). Thus, this study aimed to examine common and disease-specific features related to mesocorticolimbic circuits. This study included 555 participants from four institutes with five scanners: 140 individuals with SCZ (45.0% female), 127 individuals with MDD (44.9%), 119 individuals with ASD (15.1%), and 169 healthy controls (HC) (34.9%). All participants underwent resting-state functional magnetic resonance imaging. A parametric empirical Bayes approach was adopted to compare estimated effective connectivity among groups. Intrinsic effective connectivity focusing on the mesocorticolimbic dopamine-related circuits including the ventral tegmental area (VTA), shell and core parts of the nucleus accumbens (NAc), and medial prefrontal cortex (mPFC) were examined using a dynamic causal modeling analysis across these psychiatric disorders. The excitatory shell-to-core connectivity was greater in all patients than in the HC group. The inhibitory shell-to-VTA and shell-to-mPFC connectivities were greater in the ASD group than in the HC, MDD, and SCZ groups. Furthermore, the VTA-to-core and VTA-to-shell connectivities were excitatory in the ASD group, while those connections were inhibitory in the HC, MDD, and SCZ groups. Impaired signaling in the mesocorticolimbic dopamine-related circuits could be an underlying neuropathogenesis of various psychiatric disorders. These findings will improve the understanding of unique neural alternations of each disorder and will facilitate identification of effective therapeutic targets.

Batch effect reduction of microarray data with dependent samples using an empirical Bayes approach (BRIDGE).

Batch-effects present challenges in the analysis of high-throughput molecular data and are particularly problematic in longitudinal studies when interest lies in identifying genes/features whose expression changes over time, but time is confounded with batch. While many methods to correct for batch-effects exist, most assume independence across samples; an assumption that is unlikely to hold in longitudinal microarray studies. We propose Batch effect Reduction of mIcroarray data with Dependent samples usinGEmpirical Bayes (BRIDGE), a three-step parametric empirical Bayes approach that leverages technical replicate samples profiled at multiple timepoints/batches, so-called "bridge samples", to inform batch-effect reduction/attenuation in longitudinal microarray studies. Extensive simulation studies and an analysis of a real biological data set were conducted to benchmark the performance of BRIDGE against both ComBat and longitudinalComBat. Our results demonstrate that while all methods perform well in facilitating accurate estimates of time effects, BRIDGE outperforms both ComBat and longitudinal ComBat in the removal of batch-effects in data sets with bridging samples, and perhaps as a result, was observed to have improved statistical power for detecting genes with a time effect. BRIDGE demonstrated competitive performance in batch effect reduction of confounded longitudinal microarray studies, both in simulated and a real data sets, and may serve as a useful preprocessing method for researchers conducting longitudinal microarray studies that include bridging samples.

A Study of the Midbrain Network for Covert Attentional Orienting in Cervical Dystonia Patients using Dynamic Causal Modelling.

Understanding the neuronal network dynamics underlying the third most common movement disorder, cervical dystonia, can be achieved using dynamic causal modelling. Current literature establishes structures of the midbrain network for covert attentional orienting as dysfunctional in patients with cervical dystonia. One of these structures is the superior colliculus, for which it is hypothesised that deficient GABAergic activity therein causes cervical dystonia. To understand the role that this node plays in cervical dystonia, various connectivity models of the midbrain network were compared under the influence of a loom-recede visual stimulus fMRI paradigm. These models included the thalamus and striatum, crucial nodes in the direct/indirect pathways for motor movement and inhibition. The parametric empirical Bayes approach was used to quantify the difference in connection strengths across the winning models between patients and controls. Our findings demonstrated greater modulation by a looming stimulus event on the strength of connection from the striatum to the superior colliculus in patients. These results offer new means to understanding the pathophysiology of cervical dystonia.

Evaluating screening approaches for hepatocellular carcinoma in a cohort of HCV related cirrhosis patients from the Veteran\u2019s Affairs Health Care System

BackgroundHepatocellular carcinoma (HCC) has limited treatment options in patients with advanced stage disease and early detection of HCC through surveillance programs is a key component towards reducing mortality. The current practice guidelines recommend that high-risk cirrhosis patients are screened every six months with ultrasonography but these are done in local hospitals with variable quality leading to disagreement about the benefit of HCC surveillance. The well-established diagnostic biomarker α-Fetoprotein (AFP) is used widely in screening but the reported performance varies widely across studies. We evaluate two biomarker screening approaches, a six-month risk prediction model and a parametric empirical Bayes (PEB) algorithm, in terms of their ability to improve the likelihood of early detection of HCC compared to current AFP alone when applied prospectively in a future study.MethodsWe used electronic medical records from the Department of Veterans Affairs Hepatitis C Clinical Case Registry to construct our analysis cohort, which consists of serial AFP tests in 11,222 cirrhosis control patients and 902 HCC cases prior to their HCC diagnosis. The six-month risk prediction model incorporates routinely measured laboratory tests, age, the rate of change in AFP over the past year with the current AFP. The PEB algorithm incorporates prior AFP screening values to identify patients with a significant elevated level of AFP at their current screen. We split the analysis cohort into independent training and validation datasets. All model fitting and parameter estimation was performed using the training data and the algorithm performance was assessed by applying each approach to patients in the validation dataset.ResultsWhen the screening-level false positive rate was set at 10%, the patient-level true positive rate using current AFP alone was 53.88% while the patient-level true positive rate for the six-month risk prediction model was 58.09% (4.21% increase) and PEB approach was 63.64% (9.76% increase). Both screening approaches identify a greater proportion of HCC cases earlier than using AFP alone.ConclusionsThe two approaches show greater potential to improve early detection of HCC compared to using the current AFP only and are worthy of further study.

A Gaussian compound decision bakeoff

AbstractA non‐parametric mixture model approach to empirical Bayes compound decisions for the Gaussian location model is compared with a parametric empirical Bayes approach recently suggested by Martin and Walker and several recent more formal Bayes procedures.Copyright © 2014 John Wiley & Sons, Ltd

Bayesian Inference for the Piecewise Exponential Model for the Reliability of Multiple Repairable Systems

The piecewise exponential (PEXP) model for the reliability of multiple repairable systems is considered, and classic (maximum likelihood) and Bayesian inference are discussed under different model assumptions. In particular, inference using empirical and hierarchical Bayesian approaches are discussed. The PEXP model assumes that the times between failure are independent and exponentially distributed, but the mean is allowed to either increase or decrease with each failure. It can be an appropriate model for repairable systems in the context of reliability growth, specifically, test, analyze, and fix (TAAF), where the failure intensity remains constant as long as the system is working and can take discrete jumps at the time of a failure. It can also be applied when failures cause damage to the system, while system reliability remains constant during operation. By contrast, the nonhomogeneous Poisson process assumes that the reliability changes continuously and is unaffected by a failure. The application of this model to a real data set is presented under the hierarchical Bayesian approach and the classic and parametric empirical Bayes approach.

Selecting the Population Most Close to a Control via Empirical Bayes Approach

This article deals with the problem of selecting the population most equivalent to a control from among k independent normal populations using the parametric empirical Bayes approach. By combining useful information from the past data, an empirical Bayes selection procedure is studied. It is proved that the regret of converges to zero at a rate , where n is the number of past observations at hand. A simulation study is carried out to investigate the performance of for small to moderate values of n.

Revisiting Beal's Confidence Intervals for the Difference of Two Binomial Proportions

Confidence interval construction for the difference of two independent binomial proportions is a well-known problem with a full panoply of proposed solutions. In this paper, we focus largely on the family of intervals proposed by Beal (1987). This family, which includes the Haldane and Jeffreys–Perks intervals as special cases, assumes a symmetric prior distribution for the population proportions p 1 and p 2. We propose new methods that allow the currently observed data to set the prior distribution by taking a parametric empirical-Bayes approach; in addition, we also provide an investigation of the new interval' behaviors in small-sample situations. Unlike other solutions, our intervals can be used adaptively for experiments conducted in multiple stages over time. We illustrate this notion using data from an Argentinean study involving the Mal Rio Cuarto virus and its transmission to susceptible maize crops.

Theory & Methods: A parametric empirical Bayes approach to the analysis of capture‐recapture experiments

Empirical Bayes methods and a bootstrap bias adjustment procedure are used to estimate the size of a closed population when the individual capture probabilities are independently and identically distributed with a Beta distribution. The method is examined in simulations and applied to several well‐known datasets. The simulations show the estimator performs as well as several other proposed parametric and non‐parametric estimators.

Parametric empirical Bayes estimation for a class of extended log-linear regression models

This paper presents a fully parametric empirical Bayes approach for the analysis of count data, with emphasis on its application to environmental toxicity data. A hierarchical structure for the mean response is developed from a generalized linear model, based on a Poisson distribution. The linear predictor is embedded at the prior level of the hierarchy. This allows for enhanced flexibility when accounting for extra-Poisson variation, which is often displayed with count data from environmental bioassays. The model expands upon the traditional log-linear model in two different ways: (1) it extends the Poisson distributional assumption; and (2) it incorporates an extended family of link functions that includes the log link as a special case. The main advantage of this approach is that it combines relative computational simplicity with hierarchical modeling flexibility. In this paper, we emphasize the model's development and the practical issues related to the analysis. We describe an application of the proposed model to data from an environmental mutagenesis experiment. Copyright © 2000 John Wiley & Sons, Ltd.

Simultaneously selecting normal populations close to a control

We study the problem of selecting populations close to a control from among k normal populations using the parametric empirical Bayes approach. A Bayes selection rule is derived, which depends on certain parameters. When those parameters are unknown, using the empirical Bayes idea, we first present estimators, based on information collected from the k populations for the unknown parameters. Then, mimicking the behavior of the Bayes selection rule, an empirical Bayes selection rule is constructed. The relative regret Bayes risk is used as a measure of performance of the empirical Bayes selection rule. It is shown that the relative regret Bayes risk of the proposed empirical Bayes selection rule converges to zero at a rate of order O( k −1). A simulation study is also carried out to investigate the performance of the proposed empirical Bayes selection rule for small to moderate values of k.

Using hidden Markov chains and empirical Bayes change-point estimation for transect data

Consider a lattice of locations in one dimension at which data are observed. We model the data as a random hierarchical process. The hidden process is assumed to have a (prior) distribution that is derived from a two-state Markov chain. The states correspond to the mean values (high and low) of the observed data. Conditional on the states, the observations are modelled, for example, as independent Gaussian random variables with identical variances. In this model, there are four free parameters: the Gaussian variance, the high and low mean values, and the transition probability in the Markov chain. A parametric empirical Bayes approach requires estimation of these four parameters from the marginal (unconditional) distribution of the data and we use the EM-algorithm to do this. From the posterior of the hidden process, we use simulated annealing to find the maximum a posteriori (MAP) estimate. Using a Gibbs sampler, we also obtain the maximum marginal posterior probability (MMPP) estimate of the hidden process. We use these methods to determine where change-points occur in spatial transects through grassland vegetation, a problem of considerable interest to plant ecologists.

Parametric empirical Bayes approach to reliability analysis for the geometric life model

This paper discusses the parametric empirical Bayes approach to the estimation of the mean life of a geometric life-time model and presents the numerical results for the Bayes risk obtained on the basis of a Monte Carlo Simulation study. For purposes of comparison, the Bayes risks of the classical minimum variance unbiased estimator and the Bayes estimator corresponding to a natural conjugate prior density are also presented.

Selecting the best binomial population: parametric empirical Bayes approach

Abstract Consider k populations π 1 ,…,π k , where an observation from population π i has a binomial distribution with parameters N and p i (unknown). Let p [ k ] = max 1≤ j ≤ k P j . A population π i with p i = p [ k ] is called a best population. We are interested in selecting the best population. Let p =(p 1 ,…,p k ) and let a denote the index of the selected population. Under the loss function L( p ,a)=p [k] −p a , this statistical selection problem is studied via a parametric empirical Bayes approach. It is assumed that the binomial parameters p i , i =1,…, k , follow some conjugate beta prior distributions with unknown hyperparameters. Under the binomial-beta statistical framework, an empirical Bayes selection rule is proposed. It is shown that the Bayes risk of the proposed empirical Bayes selection rule converges to the corresponding minimum Bayes risk with rates of convergence at least of order O(exp(− cn )) for some positive constant c , where n is the number of accumulated past experience (observations) at hand.

On Analytic Empirical Bayes Estimation of Failure Rates

The estimation of plant accident rates and component failure rates is addressed within the framework of a parametric empirical Bayes approach. The observables, the numbers of failures recorded in various similar systems, obey the Poisson probability law. The parameters of a common gamma prior distribution are determined by a special moment matching method such that the results are consistent with classical (fiducial) confidence limits. Relations between Bayesian, classical, and Stein's estimation are discussed. The theory of the method is fully developed, although the suggested procedure itself is relatively simple. Solutions exist and they are in allowed ranges for all practical cases, including small samples and clustered data. They are also unbiased for large samples. Numerical examples are analyzed to illustrate the method and to allow comparisons with other methods.