(2009) using Bayesian estimation and data from the United States-Veteran Microbiome Project

OBJECTIVE

Kibler et al. (2009) reported that hypertension was related to PTSD independent of depression. These two conditions have significant diagnostic overlap. The present study sought to conceptually replicate this work with a veteran sample, using Bayesian estimation to directly update past results, as well as examine symptom severity scores in relation to hypertension.

METHOD

This was a secondary analysis of data obtained from the United States-Veteran Microbiome Project. Lifetime diagnoses of PTSD and major depressive disorder (MDD) were obtained from a structured clinical interview and hypertension diagnoses were extracted from electronic medical records. PTSD and depressive symptom severity were obtained from self-report measures. Logistic regressions with Bayesian estimation were used to estimate the associations between hypertension and (a) psychiatric diagnostic history and (b) symptom severity scores.

RESULTS

Compared with veterans without lifetime diagnoses of either disorder, the PTSD-only group was estimated to have a 29% increase in hypertension risk, and the PTSD + MDD group was estimated to have a 66% increase in hypertension risk. Additionally, higher levels of PTSD symptom severity were associated with a higher risk of hypertension.

CONCLUSION

PTSD diagnosis and symptom severity are uniquely associated with hypertension, independent of MDD or depressive symptom severity. These results support previous findings that PTSD might be a modifiable risk factor for the prevention and treatment of hypertension. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Inference for Inverse Power Lomax Distribution with Progressive First-Failure Censoring

This paper investigates the statistical inference of inverse power Lomax distribution parameters under progressive first-failure censored samples. The maximum likelihood estimates (MLEs) and the asymptotic confidence intervals are derived based on the iterative procedure and asymptotic normality theory of MLEs, respectively. Bayesian estimates of the parameters under squared error loss and generalized entropy loss function are obtained using independent gamma priors. For Bayesian computation, Tierney–Kadane’s approximation method is used. In addition, the highest posterior credible intervals of the parameters are constructed based on the importance sampling procedure. A Monte Carlo simulation study is carried out to compare the behavior of various estimates developed in this paper. Finally, a real data set is analyzed for illustration purposes.

The Role of Mobility and Sanitary Measures on the Delay of Community Transmission of COVID-19 in Costa Rica

The aim of this paper is to infer the effects that change on human mobility had on the transmission dynamics during the first four months of the SARS-CoV-2 pandemic in Costa Rica, which could have played a role in delaying community transmission in the country. First, by using parametric and non-parametric change-point detection techniques, we were able to identify two different periods when the trend of daily new cases significantly changed. Second, we explored the association of these changes with data on population mobility. This also allowed us to estimate the lag between changes in human mobility and rates of daily new cases. The information was then used to establish an association between changes in population mobility and the sanitary measures adopted during the study period. Results showed that during the initial two months of the pandemic in Costa Rica, the implementation of sanitary measures and their impact on reducing human mobility translated to a mean reduction of 54% in the number of daily cases from the projected number, delaying community transmission.

Bayesian Inference for the Kumaraswamy Distribution under Generalized Progressive Hybrid Censoring

Incomplete data are unavoidable for survival analysis as well as life testing, so more and more researchers are beginning to study censoring data. This paper discusses and considers the estimation of unknown parameters featured by the Kumaraswamy distribution on the condition of generalized progressive hybrid censoring scheme. Estimation of reliability is also considered in this paper. To begin with, the maximum likelihood estimators are derived. In addition, Bayesian estimators under not only symmetric but also asymmetric loss functions, like general entropy, squared error as well as linex loss function, are also offered. Since the Bayesian estimates fail to be of explicit computation, Lindley approximation, as well as the Tierney and Kadane method, is employed to obtain the Bayesian estimates. A simulation research is conducted for the comparison of the effectiveness of the proposed estimators. A real-life example is employed for illustration.

Iteration Bayesian Reweighed Algorithm for Optical Carrier-Based Microwave Interferometry Sensing

This paper proposes a novel iteration Bayesian reweighed (IBR) algorithm to obtain accurate estimates of a measurement parameter that uses only a few noisy measurement data. The method is applied to optimize the frequency fluctuation in an optical carrier-based microwave interferometry (OCMI) system. The algorithm iteratively estimates the frequency of the S-parameter valley point by collecting training samples to rebalance the weights between prior samples, which reduces the impact of noise in the system. Simulation shows that the estimated result of this algorithm is closer to the true value than that of the maximum likelihood estimation (MLE) using the same amount of measured data. Under the influence of system noise, this algorithm optimizes the frequency fluctuation of the S-parameter and reduces the impact of individual measured data. In this study, we applied the algorithm in the strain sensing experiment and compared it with the MLE. When axial strain changes 240 με, the IBR algorithm yields a deviation of 36 με, which is a significant reduction from 138 με (using the MLE method). Moreover, the average error rate decreases from 25% to 3% (with the MLE method), suggesting that the linear fitting degree of the estimated results and accuracy of the system are improved. Moreover, the algorithm has a wide range of applicability, for it can handle different application models in the OCMI system and the systems with frequency fluctuation problems.

Sparse Ordinal Logistic Regression and Its Application to Brain Decoding

Brain decoding with multivariate classification and regression has provided a powerful framework for characterizing information encoded in population neural activity. Classification and regression models are respectively used to predict discrete and continuous variables of interest. However, cognitive and behavioral parameters that we wish to decode are often ordinal variables whose values are discrete but ordered, such as subjective ratings. To date, there is no established method of predicting ordinal variables in brain decoding. In this study, we present a new algorithm, sparse ordinal logistic regression (SOLR), that combines ordinal logistic regression with Bayesian sparse weight estimation. We found that, in both simulation and analyses using real functional magnetic resonance imaging (fMRI) data, SOLR outperformed ordinal logistic regression with non-sparse regularization, indicating that sparseness leads to better decoding performance. SOLR also outperformed classification and linear regression models with the same type of sparseness, indicating the advantage of the modeling tailored to ordinal outputs. Our results suggest that SOLR provides a principled and effective method of decoding ordinal variables.

Making 'null effects' informative: statistical techniques and inferential frameworks

Being able to interpret 'null effects?is important for cumulative knowledge generation in science. To draw informative conclusions from null-effects, researchers need to move beyond the incorrect interpretation of a non-significant result in a null-hypothesis significance test as evidence of the absence of an effect. We explain how to statistically evaluate null-results using equivalence tests, Bayesian estimation, and Bayes factors. A worked example demonstrates how to apply these statistical tools and interpret the results. Finally, we explain how no statistical approach can actually prove that the null-hypothesis is true, and briefly discuss the philosophical differences between statistical approaches to examine null-effects. The increasing availability of easy-to-use software and online tools to perform equivalence tests, Bayesian estimation, and calculate Bayes factors make it timely and feasible to complement or move beyond traditional null-hypothesis tests, and allow researchers to draw more informative conclusions about null-effects.

RELEVANCE FOR PATIENTS

Conclusions based on clinical trial data often focus on demonstrating differences due to treatments, despite demonstrating the absence of differences is an equally important statistical question. Researchers commonly conclude the absence of an effect based on the incorrect use of traditional methods. By providing an accessible overview of different approaches to exploring null-results, we hope researchers improve their statistical inferences. This should lead to a more accurate interpretation of studies, and facilitate knowledge generation about proposed treatments.

Bayesian estimation and modeling: Editorial to the second special issue on Bayesian data analysis

This editorial accompanies the second special issue on Bayesian data analysis published in this journal. The emphases of this issue are on Bayesian estimation and modeling. In this editorial, we outline the basics of current Bayesian estimation techniques and some notable developments in the statistical literature, as well as adaptations and extensions by psychological researchers to better tailor to the modeling applications in psychology. We end with a discussion on future outlooks of Bayesian data analysis in psychology. (PsycINFO Database Record

Get Over It! A Multilevel Threshold Autoregressive Model for State-Dependent Affect Regulation

Intensive longitudinal data provide rich information, which is best captured when specialized models are used in the analysis. One of these models is the multilevel autoregressive model, which psychologists have applied successfully to study affect regulation as well as alcohol use. A limitation of this model is that the autoregressive parameter is treated as a fixed, trait-like property of a person. We argue that the autoregressive parameter may be state-dependent, for example, if the strength of affect regulation depends on the intensity of affect experienced. To allow such intra-individual variation, we propose a multilevel threshold autoregressive model. Using simulations, we show that this model can be used to detect state-dependent regulation with adequate power and Type I error. The potential of the new modeling approach is illustrated with two empirical applications that extend the basic model to address additional substantive research questions.

A Bayesian framework for estimating the incremental value of a diagnostic test in the absence of a gold standard

BACKGROUND

The absence of a gold standard, i.e., a diagnostic reference standard having perfect sensitivity and specificity, is a common problem in clinical practice and in diagnostic research studies. There is a need for methods to estimate the incremental value of a new, imperfect test in this context.

METHODS

We use a Bayesian approach to estimate the probability of the unknown disease status via a latent class model and extend two commonly-used measures of incremental value based on predictive values [difference in the area under the ROC curve (AUC) and integrated discrimination improvement (IDI)] to the context where no gold standard exists. The methods are illustrated using simulated data and applied to the problem of estimating the incremental value of a novel interferon-gamma release assay (IGRA) over the tuberculin skin test (TST) for latent tuberculosis (TB) screening. We also show how to estimate the incremental value of IGRAs when decisions are based on observed test results rather than predictive values.

RESULTS

We showed that the incremental value is greatest when both sensitivity and specificity of the new test are better and that conditional dependence between the tests reduces the incremental value. The incremental value of the IGRA depends on the sensitivity and specificity of the TST, as well as the prevalence of latent TB, and may thus vary in different populations.

CONCLUSIONS

Even in the absence of a gold standard, incremental value statistics may be estimated and can aid decisions about the practical value of a new diagnostic test.

Properties of cell death models calibrated and compared using Bayesian approaches

Using models to simulate and analyze biological networks requires principled approaches to parameter estimation and model discrimination. We use Bayesian and Monte Carlo methods to recover the full probability distributions of free parameters (initial protein concentrations and rate constants) for mass-action models of receptor-mediated cell death. The width of the individual parameter distributions is largely determined by non-identifiability but covariation among parameters, even those that are poorly determined, encodes essential information. Knowledge of joint parameter distributions makes it possible to compute the uncertainty of model-based predictions whereas ignoring it (e.g., by treating parameters as a simple list of values and variances) yields nonsensical predictions. Computing the Bayes factor from joint distributions yields the odds ratio (∼20-fold) for competing 'direct' and 'indirect' apoptosis models having different numbers of parameters. Our results illustrate how Bayesian approaches to model calibration and discrimination combined with single-cell data represent a generally useful and rigorous approach to discriminate between competing hypotheses in the face of parametric and topological uncertainty.

Object tracking with particle filtering in fluorescence microscopy images: application to the motion of neurofilaments in axons

Neurofilaments are long flexible cytoplasmic protein polymers that are transported rapidly but intermittently along the axonal processes of nerve cells. Current methods for studying this movement involve manual tracking of fluorescently tagged neurofilament polymers in videos acquired by time-lapse fluorescence microscopy. Here, we describe an automated tracking method that uses particle filtering to implement a recursive Bayesian estimation of the filament location in successive frames of video sequences. To increase the efficiency of this approach, we take advantage of the fact that neurofilament movement is confined within the boundaries of the axon. We use piecewise cubic spline interpolation to model the path of the axon and then we use this model to limit both the orientation and location of the neurofilament in the particle tracking algorithm. Based on these two spatial constraints, we develop a prior dynamic state model that generates significantly fewer particles than generic particle filtering, and we select an adequate observation model to produce a robust tracking method. We demonstrate the efficacy and efficiency of our method by performing tracking experiments on real time-lapse image sequences of neurofilament movement, and we show that the method performs well compared to manual tracking by an experienced user. This spatially constrained particle filtering approach should also be applicable to the movement of other axonally transported cargoes.

Quickest detection of drug-resistant seizures: an optimal control approach

Epilepsy affects 50 million people worldwide, and seizures in 30% of the cases remain drug resistant. This has increased interest in responsive neurostimulation, which is most effective when administered during seizure onset. We propose a novel framework for seizure onset detection that involves (i) constructing statistics from multichannel intracranial EEG (iEEG) to distinguish nonictal versus ictal states; (ii) modeling the dynamics of these statistics in each state and the state transitions; you can remove this word if there is no room. (iii) developing an optimal control-based "quickest detection" (QD) strategy to estimate the transition times from nonictal to ictal states from sequential iEEG measurements. The QD strategy minimizes a cost function of detection delay and false positive probability. The solution is a threshold that non-monotonically decreases over time and avoids responding to rare events that normally trigger false positives. We applied QD to four drug resistant epileptic patients (168 hour continuous recordings, 26-44 electrodes, 33 seizures) and achieved 100% sensitivity with low false positive rates (0.16 false positive/hour). This article is part of a Supplemental Special Issue entitled The Future of Automated Seizure Detection and Prediction.

Causal assessment of surrogacy in a meta-analysis of colorectal cancer trials

When the true end points (T) are difficult or costly to measure, surrogate markers (S) are often collected in clinical trials to help predict the effect of the treatment (Z). There is great interest in understanding the relationship among S, T, and Z. A principal stratification (PS) framework has been proposed by Frangakis and Rubin (2002) to study their causal associations. In this paper, we extend the framework to a multiple trial setting and propose a Bayesian hierarchical PS model to assess surrogacy. We apply the method to data from a large collection of colon cancer trials in which S and T are binary. We obtain the trial-specific causal measures among S, T, and Z, as well as their overall population-level counterparts that are invariant across trials. The method allows for information sharing across trials and reduces the nonidentifiability problem. We examine the frequentist properties of our model estimates and the impact of the monotonicity assumption using simulations. We also illustrate the challenges in evaluating surrogacy in the counterfactual framework that result from nonidentifiability.

Dynamic insulin sensitivity index: importance in diabetes

The classical minimal model (MM) index of insulin sensitivity, S(I), does not account for how fast or slow insulin action takes place. In a recent work, we proposed a new dynamic insulin sensitivity index, S(I)(D), which is able to take into account the dynamics of insulin action as well. The new index is a function of two MM parameters, namely S(I) and p(2), the latter parameter governing the speed of rise and decay of insulin action. We have previously shown that in normal glucose tolerant subjects S(I)(D) provides a more comprehensive picture of insulin action on glucose metabolism than S(I). The aim of this study is to show that resorting to S(I)(D) rather S(I) is even more appropriate when studying diabetic patients who have a low and slow insulin action. We analyzed insulin-modified intravenous glucose tolerance test studies performed in 10 diabetic subjects and mixed meal glucose tolerance test studies exploiting the triple tracer technique in 14 diabetic subjects. We derived both S(I) and S(I)(D) resorting to Bayesian and Fisherian identification strategies. The results show that S(I)(D) is estimated more precisely than S(I) when using the Bayesian approach. In addition, the less labor-intensive Fisherian approach can still be used to obtain reliable point estimates of S(I)(D) but not of S(I). These results suggest that S(I)(D) yields a comprehensive, precise, and cost-effective assessment of insulin sensitivity in subjects with impaired insulin action like impaired glucose tolerant subjects or diabetic patients.

Field map reconstruction in magnetic resonance imaging using Bayesian estimation

Field inhomogeneities in Magnetic Resonance Imaging (MRI) can cause blur or image distortion as they produce off-resonance frequency at each voxel. These effects can be corrected if an accurate field map is available. Field maps can be estimated starting from the phase of multiple complex MRI data sets. In this paper we present a technique based on statistical estimation in order to reconstruct a field map exploiting two or more scans. The proposed approach implements a Bayesian estimator in conjunction with the Graph Cuts optimization method. The effectiveness of the method has been proven on simulated and real data.

Optimal denoising in redundant representations

Image denoising methods are often designed to minimize mean-squared error (MSE) within the subbands of a multiscale decomposition. However, most high-quality denoising results have been obtained with overcomplete representations, for which minimization of MSE in the subband domain does not guarantee optimal MSE performance in the image domain. We prove that, despite this suboptimality, the expected image-domain MSE resulting from applying estimators to subbands that are made redundant through spatial replication of basis functions (e.g., cycle spinning) is always less than or equal to that resulting from applying the same estimators to the original nonredundant representation. In addition, we show that it is possible to further exploit overcompleteness by jointly optimizing the subband estimators for image-domain MSE. We develop an extended version of Stein's unbiased risk estimate (SURE) that allows us to perform this optimization adaptively, for each observed noisy image. We demonstrate this methodology using a new class of estimator formed from linear combinations of localized "bump" functions that are applied either pointwise or on local neighborhoods of subband coefficients. We show through simulations that the performance of these estimators applied to overcomplete subbands and optimized for image-domain MSE is substantially better than that obtained when they are optimized within each subband. This performance is, in turn, substantially better than that obtained when they are optimized for use on a nonredundant representation.

Dynamic denoising of tracking sequences

In this paper, we describe an approach to the problem of simultaneously enhancing image sequences and tracking the objects of interest represented by the latter. The enhancement part of the algorithm is based on Bayesian wavelet denoising, which has been chosen due to its exceptional ability to incorporate diverse a priori information into the process of image recovery. In particular, we demonstrate that, in dynamic settings, useful statistical priors can come both from some reasonable assumptions on the properties of the image to be enhanced as well as from the images that have already been observed before the current scene. Using such priors forms the main contribution of the present paper which is the proposal of the dynamic denoising as a tool for simultaneously enhancing and tracking image sequences. Within the proposed framework, the previous observations of a dynamic scene are employed to enhance its present observation. The mechanism that allows the fusion of the information within successive image frames is Bayesian estimation, while transferring the useful information between the images is governed by a Kalman filter that is used for both prediction and estimation of the dynamics of tracked objects. Therefore, in this methodology, the processes of target tracking and image enhancement "collaborate" in an interlacing manner, rather than being applied separately. The dynamic denoising is demonstrated on several examples of SAR imagery. The results demonstrated in this paper indicate a number of advantages of the proposed dynamic denoising over "static" approaches, in which the tracking images are enhanced independently of each other.

Blind deconvolution of medical ultrasound images: a parametric inverse filtering approach

The problem of reconstruction of ultrasound images by means of blind deconvolution has long been recognized as one of the central problems in medical ultrasound imaging. In this paper, this problem is addressed via proposing a blind deconvolution method which is innovative in several ways. In particular, the method is based on parametric inverse filtering, whose parameters are optimized using two-stage processing. At the first stage, some partial information on the point spread function is recovered. Subsequently, this information is used to explicitly constrain the spectral shape of the inverse filter. From this perspective, the proposed methodology can be viewed as a "hybridization" of two standard strategies in blind deconvolution, which are based on either concurrent or successive estimation of the point spread function and the image of interest. Moreover, evidence is provided that the "hybrid" approach can outperform the standard ones in a number of important practical cases. Additionally, the present study introduces a different approach to parameterizing the inverse filter. Specifically, we propose to model the inverse transfer function as a member of a principal shift-invariant subspace. It is shown that such a parameterization results in considerably more stable reconstructions as compared to standard parameterization methods. Finally, it is shown how the inverse filters designed in this way can be used to deconvolve the images in a nonblind manner so as to further improve their quality. The usefulness and practicability of all the introduced innovations are proven in a series of both in silico and in vivo experiments. Finally, it is shown that the proposed deconvolutioh algorithms are capable of improving the resolution of ultrasound images by factors of 2.24 or 6.52 (as judged by the autocorrelation criterion) depending on the type of regularization method used.

Model-based estimation of the link between the daily survival probability and a time-varying covariate, application to mosquitofish survival data

The survival probability in a group of individuals may evolve in time due to the influence of a time-varying covariate. In this paper we present a model-based approach allowing the estimation of the functional link between the survival probability and a time-varying covariate when data are grouped and time-period censored. The approach is based on an underlying model consisting in non-stationary Markov processes and describing the survival of individuals. The underlying model is aggregated in time and at the group level to handle the group structure of data and the censoring. The aggregation yields a generalized non-linear mixed model. Then, a Bayesian procedure allows the estimation of the model parameters and the description of the link between the survival probability and the time-varying covariate. This approach is applied in order to explore the relationship between the daily survival probability of mosquitofish (Gambusia holbrooki) and their time-varying lengths (small mosquitofish die with a higher rate than large ones because they are more affected by predation, cannibalism and environmental stress).

Comparison between estimation of breeding values and fixed effects using Bayesian and empirical BLUP estimation under selection on parents and missing pedigree information

Bayesian (via Gibbs sampling) and empirical BLUP (EBLUP) estimation of fixed effects and breeding values were compared by simulation. Combinations of two simulation models (with or without effect of contemporary group (CG)), three selection schemes (random, phenotypic and BLUP selection), two levels of heritability (0.20 and 0.50) and two levels of pedigree information (0% and 15% randomly missing) were considered. Populations consisted of 450 animals spread over six discrete generations. An infinitesimal additive genetic animal model was assumed while simulating data. EBLUP and Bayesian estimates of CG effects and breeding values were, in all situations, essentially the same with respect to Spearman's rank correlation between true and estimated values. Bias and mean square error (MSE) of EBLUP and Bayesian estimates of CG effects and breeding values showed the same pattern over the range of simulated scenarios. Methods were not biased by phenotypic and BLUP selection when pedigree information was complete, albeit MSE of estimated breeding values increased for situations where CG effects were present. Estimation of breeding values by Bayesian and EBLUP was similarly affected by joint effect of phenotypic or BLUP selection and randomly missing pedigree information. For both methods, bias and MSE of estimated breeding values and CG effects substantially increased across generations.