Fully Gibbs Sampling Algorithms for Bayesian Variable Selection in Latent Regression Models

This study proposed efficient Gibbs sampling algorithms for variable selection in a latent regression model under a unidimensional two-parameter logistic item response theory model. Three types of shrinkage priors were employed to obtain shrinkage estimates: double-exponential (i.e., Laplace), horseshoe, and horseshoe+ priors. These shrinkage priors were compared to a uniform prior case in both simulation and real data analysis. The simulation study revealed that two types of horseshoe priors had a smaller root mean square errors and shorter 95% credible interval lengths than double-exponential or uniform priors. In addition, the horseshoe prior+ was slightly more stable than the horseshoe prior. The real data example successfully proved the utility of horseshoe and horseshoe+ priors in selecting effective predictive covariates for math achievement. In the final section, we discuss the benefits and limitations of the three types of Bayesian variable selection methods.

Bayesian Variable Selection for Semiparametric Logistic Regression

Lasso variable selection is an attractive approach to improve the prediction accuracy. Bayesian lasso approach is suggested to estimate and select the important variables for single index logistic regression model. Laplace distribution is set as prior to the coefficients vector and prior to the unknown link function (Gaussian process). A hierarchical Bayesian lasso semiparametric logistic regression model is constructed and MCMC algorithm is adopted for posterior inference. To evaluate the performance of the proposed method BSLLR is through comparing it to three existing methods BLR, BPR and BBQR. Simulation examples and numerical data are to be considered. The results indicate that the proposed method get the smallest bias, SD, MSE and MAE in simulation and real data. The proposed method BSLLR performs better than other methods.

Identifying Gene–Environment Interactions With Robust Marginal Bayesian Variable Selection

In high-throughput genetics studies, an important aim is to identify gene–environment interactions associated with the clinical outcomes. Recently, multiple marginal penalization methods have been developed and shown to be effective in G×E studies. However, within the Bayesian framework, marginal variable selection has not received much attention. In this study, we propose a novel marginal Bayesian variable selection method for G×E studies. In particular, our marginal Bayesian method is robust to data contamination and outliers in the outcome variables. With the incorporation of spike-and-slab priors, we have implemented the Gibbs sampler based on Markov Chain Monte Carlo (MCMC). The proposed method outperforms a number of alternatives in extensive simulation studies. The utility of the marginal robust Bayesian variable selection method has been further demonstrated in the case studies using data from the Nurse Health Study (NHS). Some of the identified main and interaction effects from the real data analysis have important biological implications.

Bayesian variable selection in hierarchical difference-in-differences models

A popular method for estimating a causal treatment effect with observational data is the difference-in-differences model. In this work, we consider an extension of the classical difference-in-differences setting to the hierarchical context in which data cannot be matched at the most granular level. Our motivating example is an application to assess the impact of primary care redesign policy on diabetes outcomes in Minnesota, in which the policy is administered at the clinic level and individual outcomes are not matched from pre- to post-intervention. We propose a Bayesian hierarchical difference-in-differences model, which estimates the policy effect by regressing the treatment on a latent variable representing the mean change in group-level outcome. We present theoretical and empirical results showing a hierarchical difference-in-differences model that fails to adjust for a particular class of confounding variables, biases the policy effect estimate. Using a structured Bayesian spike-and-slab model that leverages the temporal structure of the difference-in-differences context, we propose and implement variable selection approaches that target sets of confounding variables leading to unbiased and efficient estimation of the policy effect. We evaluate the methods’ properties through simulation, and we use them to assess the impact of primary care redesign of clinics in Minnesota on the management of diabetes outcomes from 2008 to 2017.

Bayesian variable selection and survival modeling: Assessing the most important comorbidities that impact lung and colorectal cancer survival in Spain

Cancer survival represents one of the main indicators of interest in cancer epidemiology. However, the survival of cancer patients can be affected by a number of factors, such as comorbidities, that may interact with the cancer tumour. Moreover, it is of interest to understand how different cancer sites and tumour stages are affected by different comorbidities. Identifying the comorbidities that affect cancer survival is thus of interest as it can be used to identify factors driving the survival of cancer patients. This information can also be used to identify vulnerable groups of patients with comorbidities that may lead to a worst prognosis of cancer. We address these questions and propose a principled selection and evaluation of the effect of comorbidities in the overall survival in cancer patients. In the first step, we apply a Bayesian variable selection method that can be used to identify the comorbidities that predict overall survival. In the second step, we build a general Bayesian survival model that accounts for time-varying effects. In the third step, we derive several posterior predictive measures to quantify the effect of individual comorbidities on the population overall survival. We present applications to data on lung and colorectal cancers from two Spanish population-based cancer registries. The proposed methodology is implemented with a combination of the R-packages mombf and rstan. We provide the code for reproducibility at https://github.com/migariane/BayesVarImpComorbiCancer.

Blood Type Does Not Affect Morbidity or Mortality in COVID-19 Infections, As Assessed By a Clinical Severity Scoring System

Introduction: Coronavirus disease (COVID-19), caused by the novel coronavirus Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2), continues to lead to worldwide morbidity and mortality. This study aimed to determine if there was an association between blood type and clinical outcomes measured by a calculated morbidity score and mortality rates in patients infected with SARS-CoV-2 at our institution. The secondary aim was to investigate the association between patient characteristics (specifically age, gender, comorbid conditions, and race) and clinical outcomes and mortality in patients with confirmed SARS-COV-2 infection. Methods: Logistic regression was used to determine what factors were associated with death. A total morbidity score was constructed based on overall patient's COVID-19 clinical course. This score was modeled using Quasi-Poisson regression. Bayesian variable selection was used for the logistic regression to obtain a posterior probability that blood type is important in predicting worsened clinical outcomes and death. Results: Patients with blood type B were more likely to be African American, and patients with blood type AB were less likely to be male. Neither Blood type nor Rh+ status was a significant moderator of death or total morbidity score in regression analyses. Deviance based tests showed that blood type and Rh+ status could be omitted from each regression without a significant decrease in prediction accuracy. Bayesian variable selection showed that the posterior probability that any blood type related covariates were important in predicting death was .10. Increased age (aOR = 3.37, 95% CI = 2.44 - 4.67), male gender (aOR = 1.35, 95% CI = 1.08-1.69), and number of comorbid conditions (aOR = 1.28, 95% CI = 1.01-1.63) were the only covariates that were significantly associated with death. The only significant factors in predicting total morbidity score were age (aOR = 1.45; 95% CI = 1.349-1.555) and gender (aOR = 1.17; 95% CI = 1.109-1.243). Conclusion: In a large cohort of COVID-19 positive patients treated at a tertiary care hospital serving a low income population in New Orleans, there is strong evidence that blood type was not a significant predictor of clinical course or death in patients hospitalized with COVID 19. Older age and male gender led to worse clinical outcomes and higher rates of death; whereas older age, male gender, and comorbidities predicted a worse clinical course and higher morbidity score. Race was not a predictor of clinical course or death. Disclosures No relevant conflicts of interest to declare.