Improving Microstructural Estimation in Time-Dependent Diffusion MRI With a Bayesian Method.

BACKGROUND: Accurately fitting diffusion-time-dependent diffusion MRI (td-dMRI) models poses challenges due to complex and nonlinear formulas, signal noise, and limited clinical data acquisition. PURPOSE: Introduce a Bayesian methodology to refine microstructural fitting within the IMPULSED (Imaging Microstructural Parameters Using Limited Spectrally Edited Diffusion) model and optimize the prior distribution within the Bayesian framework. STUDY TYPE: Retrospective. POPULATION: Involving 69 pediatric patients (median age 6 years, interquartile range [IQR] 3-9 years, 61% male) with 41 low-grade and 28 high-grade gliomas, of which 76.8% were identified within the brainstem or cerebellum. FIELD STRENGTH/SEQUENCE: 3 T, oscillating gradient spin-echo (OGSE) and pulsed gradient spin-echo (PGSE). ASSESSMENT: The Bayesian method's performance in fitting cell diameter ( d $$ d $$ ), intracellular volume fraction ( f in $$ {f}_{in} $$ ), and extracellular diffusion coefficient ( D ex $$ {D}_{ex} $$ ) was compared against the NLLS method, considering simulated and experimental data. The tumor region-of-interest (ROI) were manually delineated on the b0 images. The diagnostic performance in distinguishing high- and low-grade gliomas was assessed, and fitting accuracy was validated against H&E-stained pathology. STATISTICAL TESTS: T-test, receiver operating curve (ROC), area under the curve (AUC) and DeLong's test were conducted. Significance considered at P < 0.05. RESULTS: Bayesian methodology manifested increased accuracy with robust estimates in simulation (RMSE decreased by 29.6%, 40.9%, 13.6%, and STD decreased by 29.2%, 43.5%, and 24.0%, respectively for d $$ d $$ , f in $$ {f}_{in} $$ , and D ex $$ {D}_{ex} $$ compared to NLLS), indicating fewer outliers and reduced error. Diagnostic performance for tumor grade was similar in both methods, however, Bayesian method generated smoother microstructural maps (outliers ratio decreased by 45.3% ± 19.4%) and a marginal enhancement in correlation with H&E staining result (r = 0.721 for f in $$ {f}_{in} $$ compared to r = 0.698 using NLLS, P = 0.5764). DATA CONCLUSION: The proposed Bayesian method substantially enhances the accuracy and robustness of IMPULSED model estimation, suggesting its potential clinical utility in characterizing cellular microstructure. EVIDENCE LEVEL: 3 TECHNICAL EFFICACY: Stage 1.

Estimating SARS-CoV-2 infections from deaths, confirmed cases, tests, and random surveys.

There are multiple sources of data giving information about the number of SARS-CoV-2 infections in the population, but all have major drawbacks, including biases and delayed reporting. For example, the number of confirmed cases largely underestimates the number of infections, and deaths lag infections substantially, while test positivity rates tend to greatly overestimate prevalence. Representative random prevalence surveys, the only putatively unbiased source, are sparse in time and space, and the results can come with big delays. Reliable estimates of population prevalence are necessary for understanding the spread of the virus and the effectiveness of mitigation strategies. We develop a simple Bayesian framework to estimate viral prevalence by combining several of the main available data sources. It is based on a discrete-time Susceptible-Infected-Removed (SIR) model with time-varying reproductive parameter. Our model includes likelihood components that incorporate data on deaths due to the virus, confirmed cases, and the number of tests administered on each day. We anchor our inference with data from random-sample testing surveys in Indiana and Ohio. We use the results from these two states to calibrate the model on positive test counts and proceed to estimate the infection fatality rate and the number of new infections on each day in each state in the United States. We estimate the extent to which reported COVID cases have underestimated true infection counts, which was large, especially in the first months of the pandemic. We explore the implications of our results for progress toward herd immunity.

Bayesian Analysis of Multi-Factorial Experimental Designs Using SEM.

Latent repeated measures ANOVA (L-RM-ANOVA) has recently been proposed as an alternative to traditional repeated measures ANOVA. L-RM-ANOVA builds upon structural equation modeling and enables researchers to investigate interindividual differences in main/interaction effects, examine custom contrasts, incorporate a measurement model, and account for missing data. However, L-RM-ANOVA uses maximum likelihood and thus cannot incorporate prior information and can have poor statistical properties in small samples. We show how L-RM-ANOVA can be used with Bayesian estimation to resolve the aforementioned issues. We demonstrate how to place informative priors on model parameters that constitute main and interaction effects. We further show how to place weakly informative priors on standardized parameters which can be used when no prior information is available. We conclude that Bayesian estimation can lower Type 1 error and bias, and increase power and efficiency when priors are chosen adequately. We demonstrate the approach using a real empirical example and guide the readers through specification of the model. We argue that ANOVA tables and incomplete descriptive statistics are not sufficient information to specify informative priors, and we identify which parameter estimates should be reported in future research; thereby promoting cumulative research.

Point Cloud Denoising and Feature Preservation: An Adaptive Kernel Approach Based on Local Density and Global Statistics.

Noise removal is a critical stage in the preprocessing of point clouds, exerting a significant impact on subsequent processes such as point cloud classification, segmentation, feature extraction, and 3D reconstruction. The exploration of methods capable of adapting to and effectively handling the noise in point clouds from real-world outdoor scenes remains an open and practically significant issue. Addressing this issue, this study proposes an adaptive kernel approach based on local density and global statistics (AKA-LDGS). This method constructs the overall framework for point cloud denoising using Bayesian estimation theory. It dynamically sets the prior probabilities of real and noise points according to the spatial function relationship, which varies with the distance from the points to the center of the LiDAR. The probability density function (PDF) for real points is constructed using a multivariate Gaussian distribution, while the PDF for noise points is established using a data-driven, non-parametric adaptive kernel density estimation (KDE) approach. Experimental results demonstrate that this method can effectively remove noise from point clouds in real-world outdoor scenes while maintaining the overall structural features of the point cloud.

Multiscale Bayes Adaptive Threshold Wavelet Transform Geomagnetic Basemap Denoising Taking Residual Constraints into Account.

To achieve high-precision geomagnetic matching navigation, a reliable geomagnetic anomaly basemap is essential. However, the accuracy of the geomagnetic anomaly basemap is often compromised by noise data that are inherent in the process of data acquisition and integration of multiple data sources. In order to address this challenge, a denoising approach utilizing an improved multiscale wavelet transform is proposed. The denoising process involves the iterative multiscale wavelet transform, which leverages the structural characteristics of the geomagnetic anomaly basemap to extract statistical information on model residuals. This information serves as the a priori knowledge for determining the Bayes estimation threshold necessary for obtaining an optimal wavelet threshold. Additionally, the entropy method is employed to integrate three commonly used evaluation indexes-the signal-to-noise ratio, root mean square (RMS), and smoothing degree. A fusion model of soft and hard threshold functions is devised to mitigate the inherent drawbacks of a single threshold function. During denoising, the Elastic Net regular term is introduced to enhance the accuracy and stability of the denoising results. To validate the proposed method, denoising experiments are conducted using simulation data from a sphere magnetic anomaly model and measured data from a Pacific Ocean sea area. The denoising performance of the proposed method is compared with Gaussian filter, mean filter, and soft and hard threshold wavelet transform algorithms. The experimental results, both for the simulated and measured data, demonstrate that the proposed method excels in denoising effectiveness; maintaining high accuracy; preserving image details while effectively removing noise; and optimizing the signal-to-noise ratio, structural similarity, root mean square error, and smoothing degree of the denoised image.

Sub-Nyquist SAR Imaging and Error Correction Via an Optimization-Based Algorithm.

Sub-Nyquist synthetic aperture radar (SAR) based on pseudo-random time-space modulation has been proposed to increase the swath width while preserving the azimuthal resolution. Due to the sub-Nyquist sampling, the scene can be recovered by an optimization-based algorithm. However, these methods suffer from some issues, e.g., manually tuning difficulty and the pre-definition of optimization parameters, and a low signal-noise ratio (SNR) resistance. To address these issues, a reweighted optimization algorithm, named pseudo-ℒ0-norm optimization algorithm, is proposed for the sub-Nyquist SAR system in this paper. A modified regularization model is first built by applying the scene prior information to nearly acquire the number of nonzero elements based on Bayesian estimation, and then this model is solved by the Cauchy-Newton method. Additionally, an error correction method combined with our proposed pseudo-ℒ0-norm optimization algorithm is also present to eliminate defocusing in the motion-induced model. Finally, experiments with simulated signals and strip-map TerraSAR-X images are carried out to demonstrate the effectiveness and superiority of our proposed algorithm.

Multilevel mediation analysis in R: A comparison of bootstrap and Bayesian approaches.

Mediation analysis in repeated measures studies can shed light on the mechanisms through which experimental manipulations change the outcome variable. However, the literature on interval estimation for the indirect effect in the 1-1-1 single mediator model is sparse. Most simulation studies to date evaluating mediation analysis in multilevel data considered scenarios that do not match the expected numbers of level 1 and level 2 units typically encountered in experimental studies, and no study to date has compared resampling and Bayesian methods for constructing intervals for the indirect effect in this context. We conducted a simulation study to compare statistical properties of interval estimates of the indirect effect obtained using four bootstrap and two Bayesian methods in the 1-1-1 mediation model with and without random effects. Bayesian credibility intervals had coverage closest to the nominal value and no instances of excessive Type I error rates, but lower power than resampling methods. Findings indicated that the pattern of performance for resampling methods often depended on the presence of random effects. We provide suggestions for selecting an interval estimator for the indirect effect depending on the most important statistical property for a given study, as well as code in R for implementing all methods evaluated in the simulation study. Findings and code from this project will hopefully support the use of mediation analysis in experimental research with repeated measures.

A Stan tutorial on Bayesian IRTree models: Conventional models and explanatory extension.

IRTree models have been receiving increasing attention. However, to date, there are limited sources that provide a systematic introduction to Bayesian modeling techniques using modern probabilistic programming frameworks for the implementation of IRTree models. To facilitate the research and application of IRTree models, this paper introduces how to perform two families of Bayesian IRTree models (i.e., response tree models and latent tree models) in Stan and how to extend them in an explanatory way. Some suggestions on executing Stan codes and checking convergence are also provided. An empirical study based on the Oxford Achieving Resilience during COVID-19 data was conducted as an example to further illustrate how to apply Bayesian IRTree models to address research questions. Finally, strengths and future directions are discussed.

Linear Bayesian Estimation of Misrecorded Poisson Distribution.

Parameter estimation is an important component of statistical inference, and how to improve the accuracy of parameter estimation is a key issue in research. This paper proposes a linear Bayesian estimation for estimating parameters in a misrecorded Poisson distribution. The linear Bayesian estimation method not only adopts prior information but also avoids the cumbersome calculation of posterior expectations. On the premise of ensuring the accuracy and stability of computational results, we derived the explicit solution of the linear Bayesian estimation. Its superiority was verified through numerical simulations and illustrative examples.

A Bayesian Approach for Estimating the Survivor Average Causal Effect When Outcomes Are Truncated by Death in Cluster-Randomized Trials.

Many studies encounter clustering due to multicenter enrollment and nonmortality outcomes, such as quality of life, that are truncated due to death-that is, missing not at random and nonignorable. Traditional missing-data methods and target causal estimands are suboptimal for statistical inference in the presence of these combined issues, which are especially common in multicenter studies and cluster-randomized trials (CRTs) carried out among the elderly or seriously ill. Using principal stratification, we developed a Bayesian estimator that jointly identifies the always-survivor principal stratum in a clustered/hierarchical data setting and estimates the average treatment effect among them (i.e., the survivor average causal effect (SACE)). In simulations, we observed low bias and good coverage with our method. In a motivating CRT, the SACE and the estimate from complete-case analysis differed in magnitude, but both were small, and neither was incompatible with a null effect. However, the SACE estimate has a clear causal interpretation. The option to assess the rigorously defined SACE estimand in studies with informative truncation and clustering can provide additional insight into an important subset of study participants. Based on the simulation study and CRT reanalysis, we provide practical recommendations for using the SACE in CRTs and software code to support future research.

Exogenous female sex steroid hormones and new-onset asthma in women: a matched case-control study.

BACKGROUND: Evidence on the role of exogenous female sex steroid hormones in asthma development in women remains conflicting. We sought to quantify the potential causal role of hormonal contraceptives and menopausal hormone therapy (MHT) in the development of asthma in women. METHODS: We conducted a matched case-control study based on the West Sweden Asthma Study, nested in a representative cohort of 15,003 women aged 16-75 years, with 8-year follow-up (2008-2016). Data were analyzed using Frequentist and Bayesian conditional logistic regression models. RESULTS: We included 114 cases and 717 controls. In Frequentist analysis, the odds ratio (OR) for new-onset asthma with ever use of hormonal contraceptives was 2.13 (95% confidence interval [CI] 1.03-4.38). Subgroup analyses showed that the OR increased consistently with older baseline age. The OR for new-onset asthma with ever MHT use among menopausal women was 1.17 (95% CI 0.49-2.82). In Bayesian analysis, the ORs for ever use of hormonal contraceptives and MHT were, respectively, 1.11 (95% posterior interval [PI] 0.79-1.55) and 1.18 (95% PI 0.92-1.52). The respective probability of each OR being larger than 1 was 72.3% and 90.6%. CONCLUSIONS: Although use of hormonal contraceptives was associated with an increased risk of asthma, this may be explained by selection of women by baseline asthma status, given the upward trend in the effect estimate with older age. This indicates that use of hormonal contraceptives may in fact decrease asthma risk in women. Use of MHT may increase asthma risk in menopausal women.

Adaptive model-based Magnetic Resonance.

PURPOSE: Conventional sequences are static in nature, fixing measurement parameters in advance in anticipation of a wide range of expected tissue parameter values. We set out to design and benchmark a new, personalized approach-termed adaptive MR-in which incoming subject data is used to update and fine-tune the pulse sequence parameters in real time. METHODS: We implemented an adaptive, real-time multi-echo (MTE) experiment for estimating T2 s. Our approach combined a Bayesian framework with model-based reconstruction. It maintained and continuously updated a prior distribution of the desired tissue parameters, including T2 , which was used to guide the selection of sequence parameters in real time. RESULTS: Computer simulations predicted accelerations between 1.7- and 3.3-fold for adaptive multi-echo sequences relative to static ones. These predictions were corroborated in phantom experiments. In healthy volunteers, our adaptive framework accelerated the measurement of T2 for n-acetyl-aspartate by a factor of 2.5. CONCLUSION: Adaptive pulse sequences that alter their excitations in real time could provide substantial reductions in acquisition times. Given the generality of our proposed framework, our results motivate further research into other adaptive model-based approaches to MRI and MRS.

A Bayesian estimation method for cerebral blood flow measurement by area-detector CT perfusion imaging.

PURPOSE: Bayesian estimation with advanced noise reduction (BEANR) in CT perfusion (CTP) could deliver more reliable cerebral blood flow (CBF) measurements than the commonly used reformulated singular value decomposition (rSVD). We compared the efficacy of CBF measurement by CTP using BEANR and rSVD, evaluating both relative to N-isopropyl-p-[(123) I]- iodoamphetamine (123I-IMP) single-photon emission computed tomography (SPECT) as a reference standard, in patients with cerebrovascular disease. METHODS: Thirty-one patients with suspected cerebrovascular disease underwent both CTP on a 320 detector-row CT system and SPECT. We applied rSVD and BEANR in the ischemic and contralateral regions to create CBF maps and calculate CBF ratios from the ischemic side to the healthy contralateral side (CBF index). The analysis involved comparing the CBF index between CTP methods and SPECT using Pearson's correlation and limits of agreement determined with Bland-Altman analyses, before comparing the mean difference in the CBF index between each CTP method and SPECT using the Wilcoxon matched pairs signed-rank test. RESULTS: The CBF indices of BEANR and 123I-IMP SPECT were significantly and positively correlated (r = 0.55, p < 0.0001), but there was no significant correlation between the rSVD method and SPECT (r = 0.15, p > 0.05). BEANR produced smaller limits of agreement for CBF than rSVD. The mean difference in the CBF index between BEANR and SPECT differed significantly from that between rSVD and SPECT (p < 0.001). CONCLUSIONS: BEANR has a better potential utility for CBF measurement in CTP than rSVD compared to SPECT in patients with cerebrovascular disease.

Pharmacokinetic comparability between two populations using nonlinear mixed effect models: a Monte Carlo study.

'Are two populations the same or are they different' is a question that is often faced in clinical pharmacology trials e.g., a pharmacokinetic trial studying a particular drug in racially different groups. To address this question, concentration-time data were simulated from a reference and test population, where in the latter the clearance, sample size, and sampling design were systematically varied. It was of interest to determine whether the estimates of clearance from the two groups were the same or different. Two approaches were used to estimate the empirical Bayes estimates (EBEs) for clearance. One approach developed a population pharmacokinetic model for the reference population and the EBEs for the reference population were estimated from this model. The parameters of the reference population were fixed to their maximum likelihood estimates. The model was then applied to the test population dataset to estimate the EBEs of the test population using the MAXEVAL = 0 option in NONMEM. A second approach, the theta approach, combined the reference and test datasets into a single dataset and used population as a covariate in the model; the EBEs were estimated from this combined model. The power and type I error rate of each approach were calculated for each treatment combination using a variety of statistical tests to determine whether there was a difference in the distribution of the EBEs in the reference population compared to the test population. Our results suggest that either MAXEVAL or theta approaches can be used with informative sampling designs. In addition to reasonable power and type I error, both approaches gave almost identical results under a dense sampling design. To statistically compare the distribution of EBEs of pharmacokinetic parameters from a reference group to that of a test group, a T-test and DTS eCDF test are equally useful.

Social Contagion and General Diffusion Models of Adolescent Religious Transitions: A Tutorial, and EMOSA Applications.

Epidemic Models of the Onset of Social Activities (EMOSA) describe behaviors that spread through social networks. Two social influence methods are represented, social contagion (one-to-one spread) and general diffusion (spread through cultural channels). Past models explain problem behaviors-smoking, drinking, sexuality, and delinquency. We provide review, and a tutorial (including examples). Following, we present new EMOSA models explaining changes in adolescent and young adult religious participation. We fit the model to 10 years of data from the 1997 U.S. National Longitudinal Survey of Youth. Innovations include a three-stage bi-directional model, Bayesian Markov Chain Monte Carlo (MCMC) estimation, graphical innovations, and empirical validation. General diffusion dominated rapid reduction in church attendance during adolescence; both diffusion and social contagion explained church attendance stability in early adulthood.

How to go viral: A COVID-19 model with endogenously time-varying parameters.

We estimate a panel model with endogenously time-varying parameters for COVID-19 cases and deaths in U.S. states. The functional form for infections incorporates important features of epidemiological models but is flexibly parameterized to capture different trajectories of the pandemic. Daily deaths are modeled as a spike-and-slab regression on lagged cases. Our Bayesian estimation reveals that social distancing and testing have significant effects on the parameters. For example, a 10 percentage point increase in the positive test rate is associated with a 2 percentage point increase in the death rate among reported cases. The model forecasts perform well, even relative to models from epidemiology and statistics.

Dividend suspensions and cash flows during the Covid-19 pandemic: A dynamic econometric model.

Firms suspended dividend payments in unprecedented numbers in response to the outbreak of the Covid-19 pandemic. We develop a multivariate dynamic econometric model that allows dividend suspensions to affect the conditional mean, volatility, and jump probability of growth in daily industry-level dividends and demonstrate how the parameters of this model can be estimated using Bayesian Gibbs sampling methods. We find considerable heterogeneity across industries in the dynamics of daily dividend growth and the impact of dividend suspensions.

Lensless Three-Dimensional Imaging under Photon-Starved Conditions.

In this paper, we propose a lensless three-dimensional (3D) imaging under photon-starved conditions using diffraction grating and computational photon counting method. In conventional 3D imaging with and without the lens, 3D visualization of objects under photon-starved conditions may be difficult due to lack of photons. To solve this problem, our proposed method uses diffraction grating imaging as lensless 3D imaging and computational photon counting method for 3D visualization of objects under these conditions. In addition, to improve the visual quality of 3D images under severely photon-starved conditions, in this paper, multiple observation photon counting method with advanced statistical estimation such as Bayesian estimation is proposed. Multiple observation photon counting method can estimate the more accurate 3D images by remedying the random errors of photon occurrence because it can increase the samples of photons. To prove the ability of our proposed method, we implement the optical experiments and calculate the peak sidelobe ratio as the performance metric.

Bayesian estimation of two-part joint models for a longitudinal semicontinuous biomarker and a terminal event with INLA: Interests for cancer clinical trial evaluation.

Two-part joint models for a longitudinal semicontinuous biomarker and a terminal event have been recently introduced based on frequentist estimation. The biomarker distribution is decomposed into a probability of positive value and the expected value among positive values. Shared random effects can represent the association structure between the biomarker and the terminal event. The computational burden increases compared to standard joint models with a single regression model for the biomarker. In this context, the frequentist estimation implemented in the R package frailtypack can be challenging for complex models (i.e., a large number of parameters and dimension of the random effects). As an alternative, we propose a Bayesian estimation of two-part joint models based on the Integrated Nested Laplace Approximation (INLA) algorithm to alleviate the computational burden and fit more complex models. Our simulation studies confirm that INLA provides accurate approximation of posterior estimates and to reduced computation time and variability of estimates compared to frailtypack in the situations considered. We contrast the Bayesian and frequentist approaches in the analysis of two randomized cancer clinical trials (GERCOR and PRIME studies), where INLA has a reduced variability for the association between the biomarker and the risk of event. Moreover, the Bayesian approach was able to characterize subgroups of patients associated with different responses to treatment in the PRIME study. Our study suggests that the Bayesian approach using the INLA algorithm enables to fit complex joint models that might be of interest in a wide range of clinical applications.

Flexible cloglog links for binomial regression models as an alternative for imbalanced medical data.

The complementary log-log link was originally introduced in 1922 to R. A. Fisher, long before the logit and probit links. While the last two links are symmetric, the complementary log-log link is an asymmetrical link without a parameter associated with it. Several asymmetrical links with an extra parameter were proposed in the literature over last few years to deal with imbalanced data in binomial regression (when one of the classes is much smaller than the other); however, these do not necessarily have the cloglog link as a special case, with the exception of the link based on the generalized extreme value distribution. In this paper, we introduce flexible cloglog links for modeling binomial regression models that include an extra parameter associated with the link that explains some unbalancing for binomial outcomes. For all cases, the cloglog is a special case or the reciprocal version loglog link is obtained. A Bayesian Markov chain Monte Carlo inference approach is developed. Simulations study to evaluate the performance of the proposed algorithm is conducted and prior sensitivity analysis for the extra parameter shows that a uniform prior is the most convenient for all models. Additionally, two applications in medical data (age at menarche and pulmonary infection) illustrate the advantages of the proposed models.