The spike-and-slab quantile LASSO for robust variable selection in cancer genomics studies.

Data irregularity in cancer genomics studies has been widely observed in the form of outliers and heavy-tailed distributions in the complex traits. In the past decade, robust variable selection methods have emerged as powerful alternatives to the nonrobust ones to identify important genes associated with heterogeneous disease traits and build superior predictive models. In this study, to keep the remarkable features of the quantile LASSO and fully Bayesian regularized quantile regression while overcoming their disadvantage in the analysis of high-dimensional genomics data, we propose the spike-and-slab quantile LASSO through a fully Bayesian spike-and-slab formulation under the robust likelihood by adopting the asymmetric Laplace distribution (ALD). The proposed robust method has inherited the prominent properties of selective shrinkage and self-adaptivity to the sparsity pattern from the spike-and-slab LASSO (Roc̆ková and George, J Am Stat Associat, 2018, 113(521): 431-444). Furthermore, the spike-and-slab quantile LASSO has a computational advantage to locate the posterior modes via soft-thresholding rule guided Expectation-Maximization (EM) steps in the coordinate descent framework, a phenomenon rarely observed for robust regularization with nondifferentiable loss functions. We have conducted comprehensive simulation studies with a variety of heavy-tailed errors in both homogeneous and heterogeneous model settings to demonstrate the superiority of the spike-and-slab quantile LASSO over its competing methods. The advantage of the proposed method has been further demonstrated in case studies of the lung adenocarcinomas (LUAD) and skin cutaneous melanoma (SKCM) data from The Cancer Genome Atlas (TCGA).

Bayesian modeling of quantiles of body mass index among under-five children in Ethiopia.

BACKGROUND: Body Mass Index (BMI) is a measurement of nutritional status, which is a vital pre-condition for good health. The prevalence of childhood malnutrition and the potential long-term health risks associated with obesity in Ethiopia have recently increased globally. The main objective of this study was to investigate the factors associated with the quantiles of under-five children's BMI in Ethiopia. METHODS: Data on 5,323 children, aged between 0-59 months from March 21, 2019, to June 28, 2019, were obtained from the Ethiopian Mini Demographic Health Survey (EMDHS, 2019), based on the standards set by the World Health Organization. The study used a Bayesian quantile regression model to investigate the association of factors with the quantiles of under-five children's body mass index. Markov Chain Monte Carlo (MCMC) with Gibbs sampling was used to estimate the country-specific marginal posterior distribution estimates of model parameters, using the Brq R package. RESULTS: Out of a total of 5323 children included in this study, 5.09% were underweight (less than 12.92 BMI), 10.05% were overweight (BMI: 17.06 - 18.27), and 5.02% were obese (greater than or equal to 18.27 BMI) children's. The result of the Bayesian quantile regression model, including marginal posterior credible intervals (CIs), showed that for the prediction of the 0.05 quantile of BMI, the current age of children [ ß = -0.007, 95% CI :(-0.01, -0.004)], the region Afar [ ß = - 0.32, 95% CI: (-0.57, -0.08)] and Somalia[ ß = -0.72, 95% CI: (-0.96, -0.49)] were negatively associated with body mass index while maternal age [ ß = 0.01, 95% CI: (0.005, 0.02)], mothers primary education [ ß = 0.19, 95% CI: (0.08, 0.29)], secondary and above [ ß = 0.44, 95% CI: (0.29, 0.58)], and family follows protestant [ ß = 0.22, 95% CI: (0.07, 0.37)] were positively associated with body mass index. In the prediction of the 0.95 (or 0.85?) quantile of BMI, in the upper quantile, still breastfeeding [ ß = -0.25, 95% CI: (-0.41, -0.10)], being female [ ß = -0.13, 95% CI: (-0.23, -0.03)] were negatively related while wealth index [ ß = 0.436, 95% CI: (0.25, 0.62)] was positively associated with under-five children's BMI. CONCLUSIONS: In conclusion, the research findings indicate that the percentage of lower and higher BMI for under-five children in Ethiopia is high. Factors such as the current age of children, sex of children, maternal age, religion of the family, region and wealth index were found to have a significant impact on the BMI of under-five children both at lower and upper quantile levels. Thus, these findings highlight the need for administrators and policymakers to devise and implement strategies aimed at enhancing the normal or healthy weight status among under-five children in Ethiopia.

Bayesian hierarchical quantile regression with application to characterizing the immune architecture of lung cancer.

The successful development and implementation of precision immuno-oncology therapies requires a deeper understanding of the immune architecture at a patient level. T-cell receptor (TCR) repertoire sequencing is a relatively new technology that enables monitoring of T-cells, a subset of immune cells that play a central role in modulating immune response. These immunologic relationships are complex and are governed by various distributional aspects of an individual patient's tumor profile. We propose Bayesian QUANTIle regression for hierarchical COvariates (QUANTICO) that allows simultaneous modeling of hierarchical relationships between multilevel covariates, conducts explicit variable selection, estimates quantile and patient-specific coefficient effects, to induce individualized inference. We show QUANTICO outperforms existing approaches in multiple simulation scenarios. We demonstrate the utility of QUANTICO to investigate the effect of TCR variables on immune response in a cohort of lung cancer patients. At population level, our analyses reveal the mechanistic role of T-cell proportion on the immune cell abundance, with tumor mutation burden as an important factor modulating this relationship. At a patient level, we find several outlier patients based on their quantile-specific coefficient functions, who have higher mutational rates and different smoking history.

A latent class based imputation method under Bayesian quantile regression framework using asymmetric Laplace distribution for longitudinal medication usage data with intermittent missing values.

Evaluating the association between diseases and the longitudinal pattern of pharmacological therapy has become increasingly important. However, in many longitudinal studies, self-reported medication usage data collected at patients' follow-up visits could be missing for various reasons. These pieces of missing or inaccurate/untenable information complicate determining the trajectory of medication use and its complete effects for patients. Although longitudinal models can deal with specific types of missing data, inappropriate handling of this issue can lead to a biased estimation of regression parameters especially when missing data mechanisms are complex and depend upon multiple sources of variation. We propose a latent class-based multiple imputation (MI) approach using a Bayesian quantile regression (BQR) that incorporates cluster of unobserved heterogeneity for medication usage data with intermittent missing values. Findings from our simulation study indicate that the proposed method performs better than traditional MI methods under certain scenarios of data distribution. We also demonstrate applications of the proposed method to data from the Prospective Study of Outcomes in Ankylosing Spondylitis (AS) cohort when assessing an association between longitudinal nonsteroidal anti-inflammatory drugs (NSAIDs) usage and radiographic damage in AS, while the longitudinal NSAID index data are intermittently missing.

Statistical regression modeling for energy consumption in wastewater treatment.

Wastewater treatment is one of critical issues faced by water utilities, and receives more and more attentions recently. The energy consumption modeling in biochemical wastewater treatment was investigated in the study via a general and robust approach based on Bayesian semi-parametric quantile regression. The dataset was derived from a municipal wastewater treatment plant, where the energy consumption of unit chemical oxygen demand (COD) reduction was the response variable of interest. Via the proposed approach, the comprehensive regression pictures of the energy consumption and truly influencing factors, i.e., the regression relationships at lower, median and higher energy consumption levels were characterized respectively. Meanwhile, the proposals for energy saving in different cases were also facilitated specifically. First, the lower level of energy consumption was closely associated with the temperature of influent wastewater, and the chroma-rich wastewater also showed helpful in the execution of energy saving. Second, at median energy consumption level, the COD-rich wastewater played a determinative role in the reduction of energy consumption, while the higher quality of treated water led to slightly energy intensive. Third, the higher level of energy consumption was most likely to be attributed to the relatively high temperature of wastewater and total nitrogen (TN)-rich wastewater, and both of the factors were preferably to be avoided to alleviate the burden of energy consumption. The study provided an efficient approach to controlling the energy consumption of wastewater treatment in the perspective of statistical regression modeling, and offered valuable suggestions for the future energy saving.

Heterogeneity effects of environmental regulation policy synergy on ecological resilience: considering the moderating role of industrial structure.

Given the great importance attached to ecological civilization and green development, exploring the heterogeneous effects of environmental regulation policy synergy on ecological resilience holds significance for improving environmental protection and the design of environmental policies. Based on the policy synergy perspective, this paper uses 30 provinces (municipalities and autonomous) in China as the research sample. Bayesian quantile regression is employed to explore the heterogeneous effects of environmental regulation policy synergy on ecological resilience from 2007 to 2021, and the moderating effect of the industrial structure is examined. The results indicate the following: (1) there is significant heterogeneity and variability in the effect of environmental regulation policy synergy on ecological resilience. Specifically, the effects of policy mixes 12, 13, and 23 on ecological resilience shows a U-shaped trend, while the impact of policy mix 123 on ecological resilience shows a positive effect. (2) There are significant differences in the effects of environmental regulation policy synergy under different quantiles of ecological resilience. Taking policy mix 12 as an example, we find that the effect of policy synergy on ecological resilience tends to decrease and then increase at a lower quantile. Additionally, the effect of policy synergy on ecological resilience tends to be positive at a higher quantile. (3) There are significant differences in the moderating effects of the industrial structure. Policy mix 12 can effectively enhance ecological resilience through industrial structure upgrading, while the moderating effects of alternative policy combinations are deemed insufficient. Finally, relevant policy recommendations are proposed to effectively improve ecological resilience.

Effect of agricultural carbon emissions on farmers' health expenditure of China: evidence from the educational threshold effect.

Environmental pollution, especially agricultural carbon emissions (ACE), has led to public health problems to rural areas in China and accompanied by a heavy medical economic burden. However, most studies on carbon dioxide emissions and healthcare expenditures focused on the industrial sector, and the effect of ACE was overlooked. Therefore, studying the effect of ACE on rural residents' healthcare expenditures (NHCE) is not only conducive to accelerating the low-carbon transformation of agriculture but also has important implications for reducing healthcare expenditures. In addition, the effect of ACE on NHCE in different areas might be complex and nonlinear due to differences in years of schooling (EDU) leading to different awareness of environmental protection and health among farmers. Therefore, this paper used the Bayesian quantile regression (BQR) model and the panel threshold model to explore the effect of ACE on NHCE in different areas, based on the panel data of 31 provinces in China from 2007 to 2019. The results showed that ACE and NHCE experienced similar spatial distribution from 2007 to 2019. The BQR estimation results found that ACE had a significant positive effect on NHCE at different quantile levels during the sample period, public health concern, and thereby increasing the medical and economic burden of rural households. Meanwhile, ACE had a positive effect on NHCE with a significant single threshold effect from EDU. Specifically, farmers gradually realize the harm of environmental pollution to health with the continuous improvement of education level, and then ACE aggravated the improvement of NHCE after exceeding the threshold. EDU was more essential for farmers in contiguous poverty (CP) areas than in relatively developed (RD) areas and played an important role between ACE and NHCE. Furthermore, demographic structure, economic development, and public services were also positive driving factors for NHCE. The results of analysis provide a valuable reference for understanding the factors influencing NHCE and enable formulation of ACE emission reduction policies according to local conditions.

Leading pedestrian intervals - Yay or Nay? A Before-After evaluation of multiple conflict types using an enhanced Non-Stationary framework integrating quantile regression into Bayesian hierarchical extreme value analysis.

A pedestrian was estimated to be killed every 85 min and injured every 7 min on US roads in 2019. Targeted safety treatments are particularly required at urban intersections where pedestrians regularly conflict with turning vehicles. Leading Pedestrian Intervals (LPIs) are an innovative, low-cost treatment where the pedestrian and vehicle usage of the potential conflict area (a crosswalk) is staggered in time to give the pedestrians a head start of a few seconds and reduce the "element of surprise" for right-turning vehicles. The effectiveness of LPI treatment on pedestrian safety is mixed, and most importantly, its effect on vehicle-vehicle conflicts is unknown. This study investigates the before-after effects of LPI treatments on vehicle-pedestrian and vehicle-vehicle crash risk by applying traffic conflict techniques. In particular, this study has developed a quantile regression technique within the extreme value model to estimate and compare crash risks before and after the installation of the LPI treatment. The before-after traffic movement video data (504 h in total) were collected from three signalized intersections in the City of Bellevue, Washington. The recorded movements were analyzed using Microsoft's proprietary computer vision platform, Edge Video Service, and Advanced Mobility Analytics Group's cloud-based SMART SafetyTM platform to automatedly extract traffic conflicts by analyzing road user trajectories. The treatment effect was measured using a Bayesian hierarchical extreme value model with the peak-over threshold approach. For the extreme value model, a Bayesian quantile regression analysis was conducted to estimate the conflict thresholds corresponding to a high (95th) quantile. Odds ratios were estimated for both conflict types using untreated crossing as a control group. Results indicate that the LPI treatment reduces the crash risk of pedestrians as measured by the reduction in extreme vehicle-pedestrian conflicts by about 42%. The LPI treatment has also been found not to negatively affect rear-end conflicts along the approaches leading to the LPI-treated pedestrian crossing at the signalized intersections. The findings of this study further emphasize the effectiveness of video analytics in proactive safety evaluations of engineering treatments.

Modelling of South African Hypertension: Comparative Analysis of the Classical and Bayesian Quantile Regression Approaches.

Hypertension has become a major public health challenge and a crucial area of research due to its high prevalence across the world including the sub-Saharan Africa. No previous study in South Africa has investigated the impact of blood pressure risk factors on different specific conditional quantile functions of systolic and diastolic blood pressure using Bayesian quantile regression. Therefore, this study presents a comparative analysis of the classical and Bayesian inference techniques to quantile regression. Both classical and Bayesian inference techniques were demonstrated on a sample of secondary data obtained from South African National Income Dynamics Study (2017-2018). Age, BMI, gender male, cigarette consumption and exercises presented statistically significant associations with both SBP and DBP across all the upper quantiles (τ∈{0.75,0.95}). The white noise phenomenon was observed on the diagnostic tests of convergence used in the study. Results suggested that the Bayesian approach to quantile regression reveals more precise estimates than the frequentist approach due to narrower width of the 95% credible intervals than the width of the 95% confidence intervals. It is therefore suggested that Bayesian approach to quantile regression modelling to be used to estimate hypertension.

Influencing factors of disability among the elderly in China, 2003-2016: application of Bayesian quantile regression.

Background: More and more disabled elderly need long-term care as China becomes an aging society. In 2016, there were 220 million people over the age of 60, and nearly 10 million completely disabled elderly people who cannot complete Activities of Daily Living (ADLs). Therefore, the topic of influencing factors for disability among the elderly in China has attracted close attention from researchers, most of which use the traditional empirical methods, such as Ordinary Least Squares (OLS) and logistic. Objective: The purpose of this paper was to introduce the Bayesian Quantile Regression (BQR) method to the topic of the disabled elderly, which was achieved by using BQR to study the influencing factors of disability among the elderly in China during 2003-2016. Methods: This paper was the first attempt to use the BQR for the influencing factors of disability among the elderly in China. Furthermore, a comparison was made between the regression results of BQR, OLS, Quantile Regression (QR), and Bayesian Linear Regression (BLR). Results: It was found that there was a relatively stable relationship between chronic diseases and disability, although there was a little difference in different quantiles. In addition, the BQR can obtain results similar to the traditional method. For instance, the coefficient of chronic diseases (to total disability) obtained by OLS, QR, and BLR were basically consistent (around 0.778), which was similar to BQR. The BQR not only provided estimates for all the quantiles, but also provided upper and lower values of a certain confidence interval. Conclusions: By applying the BQR to the influencing factors of disability among the elderly in China, we reached the conclusion that BQR methods are adaptable for this research topic because of their characteristics and advantages over the traditional methods, such as less strict constraints, the estimates for all quantiles, and the combination of historical information with prior information. Moreover, the BQR method appropriately obtained the lower and upper values in a confidence interval, which can provide prediction space for the future.

How Does Industrial Waste Gas Emission Affect Health Care Expenditure in Different Regions of China: An Application of Bayesian Quantile Regression.

Industrial development has brought about not only rapid economic growth, but also serious environmental pollution in China, which has led to serious health problems and heavy economic burdens on healthcare. Therefore, the relationship between the industrial air pollution and health care expenditure (HCE) has attracted the attention of researchers, most of which used the traditional empirical methods, such as ordinary least squares (OLS), logistic and so on. By collecting the panel data of 30 provinces of China during 2005-2016, this paper attempts to use the Bayesian quantile regression (BQR) to reveal the impact of industrial air pollution represented by industrial waste gas emission (IWGE) on HCE in high-, middle-, low-income regions. It was found that double heterogeneity in the influence of IWGE on HCE was obvious, which revealed that people in high-, middle-, low-income regions have significantly different understandings of environmental pollution and health problems. In addition, the BQR method provided more information than the traditional empirical methods, which verified that the BQR method, as a new empirical method for previous studies, was applicable in this topic and expanded the discussion space of this research field.

Is Carbon Dioxide (CO2) Emission an Important Factor Affecting Healthcare Expenditure? Evidence from China, 2005-2016.

As a result of China's economic growth, air pollution, including carbon dioxide (CO2) emission, has caused serious health problems and accompanying heavy economic burdens on healthcare. Therefore, the effect of carbon dioxide emission on healthcare expenditure (HCE) has attracted the interest of many researchers, most of which have adopted traditional empirical methods, such as ordinary least squares (OLS) or quantile regression (QR), to analyze the issue. This paper, however, attempts to introduce Bayesian quantile regression (BQR) to discuss the relationship between carbon dioxide emission and HCE, based on the longitudinal data of 30 provinces in China (2005-2016). It was found that carbon dioxide emission is, indeed, an important factor affecting healthcare expenditure in China, although its influence is not as great as the income variable. It was also revealed that the effect of carbon dioxide emission on HCE at a higher quantile was much smaller, which indicates that most people are not paying sufficient attention to the correlation between air pollution and healthcare. This study also proves the applicability of Bayesian quantile regression and its ability to offer more valuable information, as compared to traditional empirical tools, thus expanding and deepening research capabilities on the topic.