Variational Bayes inference for hidden Markov diagnostic classification models

Diagnostic classification models (DCMs) can be used to track the cognitive learning states of students across multiple time points or over repeated measurements. This study developed an effective variational Bayes (VB) inference method for hidden Markov longitudinal general DCMs. The simulations performed in this study verified the validity of the proposed algorithm for satisfactorily recovering true parameters. Simulation and applied data analyses were conducted to compare the proposed VB method to Markov chain Monte Carlo (MCMC) sampling. The results revealed that the parameter estimates provided by the VB method were consistent with the MCMC method with the additional benefit of a faster estimation time. The comparative simulation also indicated differences between the two methods in terms of posterior standard deviation and coverage of 95% credible intervals. Thus, with limited computational resources and time, the proposed VB method can output estimations comparable to that of MCMC.

Estimating the differences between inter-operator contrast enhancement in cerebral CT angiography

BACKGROUND

Computed tomography (CT) angiography (CTA) is a non-invasive imaging method used to detect arteries and examine various brain diseases. When CTA is performed for follow-up or postoperative evaluation, reproducibility of vessel delineation is required. A reproducible and stable contrast enhancement can be achieved by manipulating the factors affecting it. Previous studies have investigated several factors that alter the contrast enhancement of arteries. However, no reports establishing the effect of different operators on contrast enhancement exist.

PURPOSE

To assess the differences between inter-operator arterial contrast enhancement in cerebral CTA using Bayesian statistical modeling.

METHODS

Image data were obtained using a multistage sampling method from the cerebral CTA scans of patients who underwent the process between January 2015 and December 2018. Several Bayesian statistical models were developed, and the objective variable was the mean CT number of the bilateral internal carotid arteries after contrast enhancement. The explanatory variables were sex, age, fractional dose (FD), and the operator's information. The posterior distributions of the parameters were computed via Bayesian inference using the Markov chain Monte Carlo (MCMC) method, with the Hamiltonian Monte Carlo method employed as the algorithm. The posterior predictive distributions were computed using the posterior distributions of the parameters. Finally, the differences between inter-operator arterial contrast enhancement on the CT number in cerebral CTA were estimated.

RESULTS

The posterior distributions showed that all parameters representing the difference between operators included zero at the 95% credible intervals (CIs). The maximum mean difference between inter-operator CT number in the posterior predictive distribution was only 12.59 Hounsfield units (HUs).

CONCLUSIONS

The Bayesian statistical modeling results suggest that contrast enhancement of cerebral CTA examination between operator-to-operator differences in postcontrast CT number was small compared to those within-operator differences resulting from factors not considered in the model.

A spectral sampling algorithm in dynamic causal modelling for resting-state fMRI

Resting-state functional magnetic resonance imaging (rs-fMRI) is widely utilized to study the directed influences among neural populations which were called effective connectivity (EC), and the spectral dynamic causal modelling (spDCM) is the state-of-the-art framework to identify them. However, spDCM used variational Laplace to approximate the posterior density by maximizing the free energy, which might underestimate the variability of posterior density and get locked to the local minima. A spectral sampling algorithm (SS-DCM) was proposed to improve the estimation accuracy of the dynamic causal model for rs-fMRI. In SS-DCM, a naïve Bayesian model was constructed in the spectral domain, which described the probabilistic relationship between the sampled parameters and cross spectra of the observed blood oxygen level-dependent signals, and the parameters were sampled using randomly walked Markov Chain Monto Carlo scheme. The root mean square errors of the estimation of EC and hemodynamic parameters of SS-DCM, spDCM and generalized filter scheme were compared in the synthetic data, and SS-DCM was the most accurate and stable. A comparative evaluation using empirical rs-fMRI data was performed to study the EC pattern of the default mode network and compare the accuracy of classification between typically developed subjects and inattentive attention deficit and hyperactivity disorder patients. The results showed high consistency of positivity and negativity of EC between spDCM and SS-DCM, and SS-DCM also provided higher classification accuracy. It is highlighted that SS-DCM improves the accuracy of the estimation of EC and provides accurate information of discrepancies between diseased and healthy subjects using rs-fMRI.

Stochastic Modelling of HIV-1 Replication in a CD4 T Cell with an IFN Response

A mathematical model of the human immunodeficiency virus Type 1 (HIV-1) life cycle in CD4 T cells was constructed and calibrated. It describes the activation of the intracellular Type I interferon (IFN-I) response and the IFN-induced suppression of viral replication. The model includes viral replication inhibition by interferon-induced antiviral factors and their inactivation by the viral proteins Vpu and Vif. Both deterministic and stochastic model formulations are presented. The stochastic model was used to predict efficiency of IFN-I-induced suppression of viral replication in different initial conditions for autocrine and paracrine effects. The probability of virion excretion for various MOIs and various amounts of IFN-I was evaluated and the statistical properties of the heterogeneity of HIV-1 and IFN-I production characterised.

Direct Estimation of Diagnostic Classification Model Attribute Mastery Profiles via a Collapsed Gibbs Sampling Algorithm

This paper proposes a novel collapsed Gibbs sampling algorithm that marginalizes model parameters and directly samples latent attribute mastery patterns in diagnostic classification models. This estimation method makes it possible to avoid boundary problems in the estimation of model item parameters by eliminating the need to estimate such parameters. A simulation study showed the collapsed Gibbs sampling algorithm can accurately recover the true attribute mastery status in various conditions. A second simulation showed the collapsed Gibbs sampling algorithm was computationally more efficient than another MCMC sampling algorithm, implemented by JAGS. In an analysis of real data, the collapsed Gibbs sampling algorithm indicated good classification agreement with results from a previous study.

Estimation for Entropy and Parameters of Generalized Bilal Distribution under Adaptive Type II Progressive Hybrid Censoring Scheme

Entropy measures the uncertainty associated with a random variable. It has important applications in cybernetics, probability theory, astrophysics, life sciences and other fields. Recently, many authors focused on the estimation of entropy with different life distributions. However, the estimation of entropy for the generalized Bilal (GB) distribution has not yet been involved. In this paper, we consider the estimation of the entropy and the parameters with GB distribution based on adaptive Type-II progressive hybrid censored data. Maximum likelihood estimation of the entropy and the parameters are obtained using the Newton–Raphson iteration method. Bayesian estimations under different loss functions are provided with the help of Lindley’s approximation. The approximate confidence interval and the Bayesian credible interval of the parameters and entropy are obtained by using the delta and Markov chain Monte Carlo (MCMC) methods, respectively. Monte Carlo simulation studies are carried out to observe the performances of the different point and interval estimations. Finally, a real data set has been analyzed for illustrative purposes.

Estimation of the kidney metabolic heat generation rate

Thermogenesis results from the cellular metabolism and has a fundamental role for body thermoregulation in endothermic species. The motivation for this work is the analysis of the kidneys' contribution for thermoregulation. An inverse problem is solved for the estimation of the heat generation rate that results from the metabolic activities in the kidney, by using transient temperature measurements of the urine. The Markov chain Monte Carlo (MCMC) method is applied for the solution of the inverse problem, which presents inherent difficulties associated with low sensitivity of the parameters of main interest that represent the transient heat source term and strong correlation of the remaining model parameters. Such difficulties are dealt with in this work by using a version of the Metropolis-Hastings algorithm that samples the parameters in blocks. Simulated temperature measurements are used for the inverse problem solution, and the convergence of the Markov chains is verified with two different techniques.

Bayesian approach for cure models with a change-point based on covariate threshold: application to breast cancer data

In this study, a Bayesian approach was suggested to estimate a change-point according to a covariate threshold when some patients never experienced the event of interest. Gibbs sampler algorithm with latent binary cure indicators was used to simplify the implementation of Markov chain Monte Carlo method. Then, the accuracy of new model was demonstrated by simulation studies to compute the point and interval estimates of parameters. Finally, an effective threshold was suggested in age at surgery time to experience the metastasis when the model was applied for a data set of breast cancer patients.

Multivariate Bayesian variable selection exploiting dependence structure among outcomes: Application to air pollution effects on DNA methylation

The analysis of multiple outcomes is becoming increasingly common in modern biomedical studies. It is well-known that joint statistical models for multiple outcomes are more flexible and more powerful than fitting a separate model for each outcome; they yield more powerful tests of exposure or treatment effects by taking into account the dependence among outcomes and pooling evidence across outcomes. It is, however, unlikely that all outcomes are related to the same subset of covariates. Therefore, there is interest in identifying exposures or treatments associated with particular outcomes, which we term outcome-specific variable selection. In this work, we propose a variable selection approach for multivariate normal responses that incorporates not only information on the mean model, but also information on the variance-covariance structure of the outcomes. The approach effectively leverages evidence from all correlated outcomes to estimate the effect of a particular covariate on a given outcome. To implement this strategy, we develop a Bayesian method that builds a multivariate prior for the variable selection indicators based on the variance-covariance of the outcomes. We show via simulation that the proposed variable selection strategy can boost power to detect subtle effects without increasing the probability of false discoveries. We apply the approach to the Normative Aging Study (NAS) epigenetic data and identify a subset of five genes in the asthma pathway for which gene-specific DNA methylations are associated with exposures to either black carbon, a marker of traffic pollution, or sulfate, a marker of particles generated by power plants.