Bayesian Additive Regression Trees Research Articles

Postoperative Outcomes in Infants Undergoing ABO-incompatible Heart Transplantation in the United States

BackgroundABO-incompatible heart transplant is a method to increase the infant donor pool. However data on long-term survival and rejection after ABO-incompatible heart transplant in recent era are limited. MethodsThe United Network for Organ Sharing database was queried for infant heart transplants performed from January 2008 to March 2020. Patient demographics and known risk factors for posttransplant mortality were collected. Statistical analysis using Bayesian additive regression trees was performed to evaluate the association of ABO incompatibility and overall survival, graft survival, acute rejection episodes, and length of stay. ResultsOf 1368 included infants (age < 1 year), 280 (20.47%) were ABO incompatible. ABO incompatibility was not associated with increased all-cause mortality, acute rejection episodes, or length of stay, whereas extracorporeal membrane oxygenation and intubation status of the recipient at the time of transplantation were associated with increased all-cause mortality and graft failure. Idiopathic cardiomyopathy was associated with a decreased likelihood of posttransplant all-cause mortality. One-, 5-, and 10-year survival rates among compatible vs incompatible transplants were estimated to be 90% vs 88%, 82% vs 79%, and 77% vs 73%, respectively. ConclusionsABO-incompatible infant heart transplant does not affect posttransplant survival, incidence of rejection, or postoperative length of stay. Therefore it remains a viable and important strategy to increase the infant donor pool.

Incorporating external data into the analysis of clinical trials via Bayesian additive regression trees

Most clinical trials involve the comparison of a new treatment to a control arm (eg, the standard of care) and the estimation of a treatment effect. External data, including historical clinical trial data and real-world observational data, are commonly available for the control arm. With proper statistical adjustments, borrowing information from external data can potentially reduce the mean squared errors of treatment effect estimates and increase the power of detecting a meaningful treatment effect. In this article, we propose to use Bayesian additive regression trees (BART) for incorporating external data into the analysis of clinical trials, with a specific goal of estimating the conditional or population average treatment effect. BART naturally adjusts for patient-level covariates and captures potentially heterogeneous treatment effects across different data sources, achieving flexible borrowing. Simulation studies demonstrate that BART maintains desirable and robust performance across a variety of scenarios and compares favorably to alternatives. We illustrate the proposed method with an acupuncture trial and a colorectal cancer trial.

Probabilistic Modeling of Asteroid Diameters from Gaia DR2 Errors

Abstract The Gaia Data Release 2 provides precise astrometry for nearly 1.5 billion sources across the entire sky, including several thousand asteroids. In this work, we provide evidence that reasonably large asteroids (diameter &gt;20 km) have high correlations with Gaia relative flux uncertainties and systematic R.A. errors. We further capture these correlations using a logistic Bayesian additive regression tree model. We compile a small list of probable large asteroids that can be targeted for direct diameter measurements and shape reconstruction.

Identifying predictors of cancer prevalence at the neighborhood level in the United States: A Bayesian machine learning approach

BACKGROUND AND AIM: Cancer is the second leading cause of death in the United States (US). Individual- level factors including utilization of prevention, health behaviors, environmental exposure, and sociodemographic measures have been linked to individual-level cancer risks. However, risk factors of cancer at the neighborhood level remain understudied. To fill this research gap, we identify and rank important predictors of cancer prevalence at the neighborhood level in the US. METHODS: We developed a new neighborhood dataset by combining data from the Population Level Analysis and Community Estimates (PLACES), a dataset with population health data across all the US census tracts (n=72,337), with environmental exposure data from the Environmental Justice Screening database and sociodemographic factors from the American Community Survey. Our outcome of interest was tract-level adult cancer prevalence. We included 23 tract-level explanatory variables, including unhealthy behaviors (e.g., smoking, no leisure-time physical activity, drinking), prevention measures (e.g., cholesterol screening), environmental exposures (e.g., air toxics, lead paint), and sociodemographic factors (e.g., racial and ethnic composition, poverty, age 65 years and over). We used Bayesian additive regression trees (BART) to identify the most important predictors of cancer prevalence. RESULTS:The median prevalence of adults diagnosed with cancer was 6.7% (interquartile range: 5.4%-7.7%) across US census tracts. Based on local threshold criteria, we identified the five most important predictors of cancer prevalence: percentage of adults 65 years old or over, prevalence of routine checkup, percentage of non-Hispanic white, percentage of housing built before 1960, and percentage of individuals below the lower poverty level. CONCLUSIONS:Using an integrated neighborhood dataset with fine geographic resolution and a machine learning approach, we identified several important predictors of cancer prevalence at the neighborhood level in the US. The results may inform public health practitioners and policymakers to prioritize the improvement of environmental and neighborhood factors in reducing cancer burden. KEYWORDS: Cancer, Neighborhood-level analysis, Environmental exposures, Big data, Bayesian additive regression trees

Machine Learning Approaches for Environmental Mixtures Studies with Time-to-Event Outcomes and their Application to the Strong Heart Study

BACKGROUND AND AIM: Machine learning approaches are increasingly used in environmental mixtures epidemiology. We evaluated the operating characteristics of currently available machine learning approaches in estimating individual exposure and joint mixture effects along with interaction effects on a time-to-event outcome. METHODS: We conducted an extensive search for methods which allow for: time-to-event outcomes, multiple continuous exposures, non-linear and interaction effects on the outcome, and inferences (i.e. provide estimates and standard errors). We selected: Bayesian Additive Regression Trees (BART), Cox Proportional-Hazards model with penalized splines, Gaussian Process Regression (GPR), and Multivariate Adaptive Regression Splines (MARS). Additionally, we included the Cox Proportional-Hazards model and Cox Elastic-Net due to their popularity. We compared estimates across approaches on the association of six metals with incident cardiovascular disease in the Strong Heart Study. RESULTS:The estimates of the hazard ratio for the main metal of interest, selenium, at its 75th versus 25th percentile, holding all other metals constant, ranged from 1.29 (1.17, 1.39) to 2.00 (1.09, 3.19), estimated using Cox Elastic-Net and BART, respectively. Similar trends were found for estimates of the overall mixture effect on the hazard ratio scale when all metals are at their 75th versus 25th percentile. The estimates ranged from 2.09 (1.82, 3.29) to 4.21 (2.83, 6.93), estimated using Cox Elastic-Net and GPR, respectively. The more flexible approaches estimated higher effects with larger uncertainty. CONCLUSIONS:In this study, results across approaches tended to be the same qualitatively but different quantitatively. Increased hazards were found at higher levels of metals, but the magnitude varied. Although the overall conclusion is consistent, estimates may have different clinical impacts. The fact that the more flexible methods detected interaction and non-linear effects of metals but had higher uncertainty reveals a substantial bias-variance tradeoff. To enhance reproducibility in environmental epidemiology, it is important to show whether results are robust across different modeling approaches. KEYWORDS: Survival, Mixtures analysis, Modeling, Cardiovascular diseases

Estimating Perinatal Critical Windows to Environmental Mixtures via Structured Bayesian Regression Tree Pairs

BACKGROUND AND AIM: Maternal exposure to environmental chemicals during pregnancy can alter birth and children’s health outcomes. Research seeks to identify critical windows, time periods when exposures can change future health outcomes, and estimate the exposure-response relationship. Existing statistical approaches that allow for high temporal resolution (e.g. weekly throughout pregnancy) exposure measurements primarily account for a single environmental chemical. Extending to multiple chemicals observed at high temporal resolution poses a dimensionality problem and statistical methods are lacking. METHODS: We propose a regression tree-based model for mixtures of exposures observed at high temporal resolution. The proposed approach uses an additive ensemble of tree pairs that define structured main effects and interactions between time-resolved predictors and performs variable selection. In simulation, we show the tree-based approach performs better than existing methods for a single exposure and can accurately estimate critical windows in the exposure-response relation for mixtures. Software is made available in the R package dlmtree. RESULTS:We apply our method to estimate the relationship between five exposures measured weekly throughout pregnancy and resulting birth weight in a Denver, Colorado birth cohort. We identified critical windows during which fine particulate matter (PM₂₅), sulfur dioxide, and temperature are negatively associated with birth weight and an interaction between PM₂₅ and temperature. CONCLUSIONS:In this work we proposed a method to estimate the association between mixtures of environmental exposures observed at high-temporal resolution on birth and children’s health outcomes. Our analysis is the first analysis to identify critical windows to a mixture observed at high-temporal resolution within a distributed lag mixture model framework. As the size and resolution of the exposure data available continues to grow, our method fills a critical research gap in statistical methods for epidemiology and environmental health in being able to estimate the effects of time-resolved measures of a mixture on a continuous or binary health outcome. KEYWORDS: air pollution, Bayesian additive regression trees, birth outcomes, critical windows, distributed lag models

Spatial clustering of adult cancer prevalence in the United States

BACKGROUND AND AIM: Understanding the geographic distribution of cancer prevalence at neighborhood level may help guide cancer control and prevention measures from the perspective of neighborhoods, as opposed to individuals. We examined the spatial heterogeneity of cancer prevalence across census tracts in the contiguous United States. METHODS: We previously identified predictors of census tract-level cancer prevalence by applying Bayesian additive regression trees to a combined database of tract-level population health, environmental exposure, and socioeconomic data from multiple sources. In this study, we examined the association between the selected predictors (percentage of adults 65 years old or over, prevalence of routine checkup, percentage of non-Hispanic white, percentage of housing built before 1960, and percentage of individuals below poverty) and cancer prevalence using a linear regression model. Spatial clustering were identified based on weighted normal scan statistics (SatScan V9.7) using the tract-level cancer prevalence and the regression residuals, respectively, with the population for aged≥65 years as the weight. RESULTS:The mean cancer prevalence was 6.7% (standard deviation 1.8%). Using cancer prevalence, we identified 4 circular-shaped high-risk clusters in Florida (Latitude Longitude and radius: 27.817765 N 81.396327 W, 216km), Arizona (33.631195 N 112.350663 W, 9km), New Jersey (39.958259 N 74.345696 W, 11km), and a region encompassing parts of Michigan, Ohio, Pennsylvania, and New York (43.268491 N 78.823785 W, 468km). Their estimated cancer prevalence was 8.1%, 10.1%, 13.8%, and 7.3%, respectively. Using residuals, we identified one dominant high-risk region covering parts of Montana, Wyoming, North Dakota, South Dakota, Nebraska, Minnesota, and Iowa (47.723678 N 104.100726 W, 1834km), and four smaller clusters (radius 20km) in Florida and Maryland. CONCLUSIONS:Variations in high-risk clustering patterns based on prevalence and residual values suggest that the identified five predictors can explain much of the initial variation in tract-level cancer prevalence. However, the high-risk regions based on residuals require further investigation. KEYWORDS: Cancer prevalence, United States, Geospatial analysis, Cancer high-risk clusters

Potential distributions of invasive vertebrates in the Iberian Peninsula under projected changes in climate extreme events

AbstractAimInvasive alien species (IAS) can cause profound impacts on ecosystem function and diversity, human health, well‐being and livelihoods. Climate change is an important driver of biological invasions, so it is critical to develop models and climate‐driven scenarios of IAS range shifts to establish preventive measures. In this study, we analyse how projected changes in the frequency and magnitude of climate extreme events could affect the spread of the six most widely distributed invasive vertebrate species in the Iberian Peninsula.LocationIberian Peninsula.TaxaRed avadavat (Amandava amandava), common waxbill (Estrilda astrild), monk parakeet (Myiopsitta monachus), rose‐ringed parakeet (Psittacula krameri), American mink (Neovison vison) and pond slider (Trachemys scripta).MethodsWe followed best‐practice standards for species distribution models (SDMs) regarding handling of the response and predictor variables, model building and evaluation using metrics that assess different facets of model performance. We used an ensemble approach with four modelling methods of varying complexity, including both regression‐based and tree‐based machine‐learning algorithms. We analysed five regional models for current (1971–2000) and future climate (2021–2050). We used principal components analysis to assess consensus among model outputs and positively weighed predictions from well‐performing models.ResultsSelected models showed high consensus and good predictive capacity on block cross‐validation areas. Generalized Linear Models and Generalized Additive Models scored highest in reliability (calibration), but Bayesian Additive Regression Trees provided the best balance between calibration and discrimination capacity. Forecasts include visible changes in environmental favourability, with losses generally outweighing the gains, but with some areas becoming more favourable for several species.Main conclusionsIncreased frequency and/or intensity of climate extreme events associated with ongoing climate change are projected to reduce overall invasion risk for the species examined although increases in favourability should be expected locally.

Adaptive network reliability analysis: Methodology and applications to power grid

Flow network models can capture the underlying physics and operational constraints of many networked systems including the power grid and transportation and water networks. However, analyzing systems’ reliability using computationally expensive flow-based models faces substantial challenges, especially for rare events. Existing actively trained meta-models, which present a new promising direction in reliability analysis, are not applicable to networks due to the inability of these methods to handle high-dimensional problems as well as discrete or mixed variable inputs. This study presents the first Adaptive surrogate-based Network Reliability (ANR) analysis through integration of Bayesian Additive Regression Trees (BART) and Monte Carlo simulation (MCS). An active learning method is developed that identifies the most valuable training samples based on the credible intervals derived by BART over the space of predictor variables as well as the proximity of the points to the estimated limit state. Benchmark power grids including IEEE 30, 57, 118, and 300-bus systems and their power flow models for cascading failure analysis are considered to investigate ANR-BART, MCS, subset simulation, and passively-trained optimal BART and deep neural networks. Results indicate that ANR-BART is robust and yields accurate estimates of network failure probability, while significantly reducing the computational cost of reliability analysis.

Modelling multi-hazard threats to cultural heritage sites and environmental sustainability: The present and future scenarios

Cultural heritage sites, particularly those in mountainous regions face serious threats as mountains are hazardous places and many of them are located on shifting tectonic plates and live under the threat of earthquakes and related activities. Alongside, mountains are also exposed to atmospheric interactions and rainfall plays an important role in land movement activities through seepage of rainwater in fragile structures. Moreover, gravity pushing along with land use and climate change induced changing rainfall patterns and modification of slope lead to several hazards in mountainous regions. Environmental degradation in terms of soil erosion, loss of forests, and agricultural products are common phenomena in mountainous regions due to various multi-hazard threats. Therefore, it is necessary to conserve and management of our mountain environments as it is essential to the survival of the global ecosystem. Thus, the current research article focused on multi-hazard susceptibility mapping and evaluation of its risk assessment in some of the famous cultural heritage sites in the eastern Himalayan region of Sikkim state, India. Multi-hazard susceptibility mapping was carried out using boosted regression tree (BRT), Bayesian additive regression tree (BART) and Bayesian generalized linear model (BGLM) considering twenty-two conditioning factors and seismic activity, as this region is highly susceptible to earthquakes. The future climate and land use change were estimated using four representative concentration pathway (RCP) scenarios and Dynamic Conversion of Land-Use and its Effects (Dyna-CLUE) model respectively to identify future multi-hazard susceptibility areas and vulnerable cultural heritage sites. The novelty of this study is to a combination of machine learning, RCPs derived future climate and Dyna-CLUE induced future land use change estimation for multi-hazard modelling and identification of vulnerable cultural heritage sites. The result of this study will help land use planners and archaeologists to adopt proper management strategies for protecting the cultural heritage sites and maintaining environmental sustainability for the proper management of mountain resources.

Stochastic Tree Ensembles for Regularized Nonlinear Regression

This article develops a novel stochastic tree ensemble method for nonlinear regression, referred to as accelerated Bayesian additive regression trees, or XBART. By combining regularization and stochastic search strategies from Bayesian modeling with computationally efficient techniques from recursive partitioning algorithms, XBART attains state-of-the-art performance at prediction and function estimation. Simulation studies demonstrate that XBART provides accurate point-wise estimates of the mean function and does so faster than popular alternatives, such as BART, XGBoost, and neural networks (using Keras) on a variety of test functions. Additionally, it is demonstrated that using XBART to initialize the standard BART MCMC algorithm considerably improves credible interval coverage and reduces total run-time. Finally, two basic theoretical results are established: the single tree version of the model is asymptotically consistent and the Markov chain produced by the ensemble version of the algorithm has a unique stationary distribution.

The important role of cisplatin in the treatment of HPV-positive oropharyngeal cancer assessed by real-world data analysis

ObjectivesThe prognostic advantage of human papillomavirus (HPV)-positive oropharyngeal squamous cell carcinoma (OPSCC) resulted in the initiation of treatment de-intensification studies. Two randomized controlled trials (RCTs) reported inferior survival of HPV-positive OPSCC treated with radiotherapy plus cetuximab compared to standard of care radiotherapy plus cisplatin. In this study we investigated whether the important role of cisplatin in the treatment of HPV-positive OPSCCs would also emerge from causal inference analyses of real-world data. Material and methodsA retrospective cohort of 263 advanced-stage OPSCC-patients from 5 European clinics was studied, treated with radiotherapy (RT) alone or cisplatin-based chemoradiotherapy (CRT) based on standard clinical indications. Causal inference was applied to adjust for treatment assignment, thereby simulating a randomized setting. Average treatment effect of concurrent cisplatin on overall survival (OS) probability was estimated using Bayesian Additive Regression Trees (BART) and Bayesian logistic regression. ResultsSignificantly better survival probabilities were found for HPV-positive OPSCC treated with CRT compared to RT alone (3-year OS probability 0.961 versus 0.798, p = 0.008). ConclusionThis study using causal inference of retrospective patient data confirms the important role of cisplatin in the treatment of HPV-positive OPSCC. Causal inference analyses of real-world data complements the evidence from the published RCTs.

Leveraging machine learning methods to estimate heterogeneous effects: father absence in China as an example

Individuals differ in their personal and environmental characteristics, and the same treatment or condition may affect individuals in different ways or magnitudes. Heterogeneity in effects thus has important implications for academic research and policymaking. However, it is difficult to uncover and estimate heterogenous effects using conventional parametric models without making assumptions based on limited information, and results can be difficult to interpret when involving a large number of moderators. To address these limitations, this paper introduces three supervised machine learning methods for estimating heterogeneous treatment effects with experimental and observational data: causal forest, Bayesian Additive Regression Trees (BART), and an ensemble approach called X-learner. These methods are first applied to simulated datasets and then implemented using empirical education survey data from China to estimate heterogeneous effects of father absence on student cognitive ability across a series of individual and family characteristics.

Estimating heterogeneous survival treatment effects of lung cancer screening approaches: A causal machine learning analysis

The National Lung Screening Trial (NLST) found that low-dose computed tomography (LDCT) screening provided lung cancer (LC) mortality benefit compared to chest radiography (CXR). Considerable research concerns identifying the differential treatment effects that may exist in certain subpopulations. We shed light on several important issues in existing research and highlight the need for further investigation of the heterogeneous comparative effect of LDCT versus CXR, using more flexible and rigorous statistical approaches. We used a high-performance Bayesian machine learning approach designed for censored survival data, accelerated failure time Bayesian additive regression trees model (AFT-BART), to flexibly capture the relationships between the failure time and predictors. We then used the counterfactual framework to draw Markov chain Monte Carlo samples of the individual treatment effect for each participant. Using these posterior samples, we explored the possible treatment effect heterogeneity via a stepwise binary tree approach. When re-analyzed with AFT-BART, LDCT did not have a statistically significant LC or overall mortality benefit compared to CXR. The Asian and Black (particularly those with pack-year ≥ 37 years and without emphysema) NLST population were shown to have enhanced overall mortality benefit from LDCT than the population average. Although inconclusive for LC mortality benefit, Asians, Blacks and Whites with history of chronic obstructive pulmonary disease showed a small trend towards benefit from LDCT. Causal inference with flexible machine learning modeling can provide valuable knowledge for informing treatment decision and planning targeted clinical trials emphasizing personalized medicine approaches.

Borrowing from supplemental sources to estimate causal effects from a primary data source.

The increasing multiplicity of data sources offers exciting possibilities in estimating the effects of a treatment, intervention, or exposure, particularly if observational and experimental sources could be used simultaneously. Borrowing between sources can potentially result in more efficient estimators, but it must be done in a principled manner to mitigate increased bias and Type I error. Furthermore, when the effect of treatment is confounded, as in observational sources or in clinical trials with noncompliance, causal effect estimators are needed to simultaneously adjust for confounding and to estimate effects across data sources. We consider the problem of estimating causal effects from a primary source and borrowing from any number of supplemental sources. We propose using regression-based estimators that borrow based on assuming exchangeability of the regression coefficients and parameters between data sources. Borrowing is accomplished with multisource exchangeability models and Bayesian model averaging. We show via simulation that a Bayesian linear model and Bayesian additive regression trees both have desirable properties and borrow under appropriate circumstances. We apply the estimators to recently completed trials of very low nicotine content cigarettes investigating their impact on smoking behavior.

Estimating heterogeneous survival treatment effect in observational data using machine learning.

Methods for estimating heterogeneous treatment effect in observational data have largely focused on continuous or binary outcomes, and have been relatively less vetted with survival outcomes. Using flexible machine learning methods in the counterfactual framework is a promising approach to address challenges due to complex individual characteristics, to which treatments need to be tailored. To evaluate the operating characteristics of recent survival machine learning methods for the estimation of treatment effect heterogeneity and inform better practice, we carry out a comprehensive simulation study presenting a wide range of settings describing confounded heterogeneous survival treatment effects and varying degrees of covariate overlap. Our results suggest that the nonparametric Bayesian Additive Regression Trees within the framework of accelerated failure time model (AFT-BART-NP) consistently yields the best performance, in terms of bias, precision, and expected regret. Moreover, the credible interval estimators from AFT-BART-NP provide close to nominal frequentist coverage for the individual survival treatment effect when the covariate overlap is at least moderate. Including a nonparametrically estimated propensity score as an additional fixed covariate in the AFT-BART-NP model formulation can further improve its efficiency and frequentist coverage. Finally, we demonstrate the application of flexible causal machine learning estimators through a comprehensive case study examining the heterogeneous survival effects of two radiotherapy approaches for localized high-risk prostate cancer.

Climate Variability May Delay Post-Fire Recovery of Boreal Forest in Southern Siberia, Russia

Prolonged dry periods and increased temperatures that result from anthropogenic climate change have been shown to increase the frequency and severity of wildfires in the boreal region. There is growing evidence that such changes in fire regime can reduce forest resilience and drive shifts in post-fire plant successional trajectories. The response of post-fire vegetation communities to climate variability is under-studied, despite being a critical phase determining the ultimate successional conclusion. This study investigated the responses of post-fire recruited species to climate change and inter-annual variability at 16 study sites that experienced high-severity fire events, mostly in early 2000, within the Scots pine forest-steppe zone of southeastern Siberia, Russia. These sites were originally dominated by Scots pine, and by 2018, they were recruited by different successional species. Additionally, three mature Scots pine stands were included for comparison. A Bayesian Additive Regression Trees (BART) approach was used to model the relationship between Landsat-derived Normalized Difference Vegetation Index (NDVI) time series, temperature and precipitation in the 15 years after a stand-replacing fire. Using the resulting BART models, together with six projected climate scenarios with increased temperature and enhanced inner-annual precipitation variability, we simulated NDVI at 5-year intervals for 15 years post-fire. Our results show that the BART models performed well, with in-sample Pseudo-R2 varying from 0.49 to 0.95 for fire-disturbed sites. Increased temperature enhanced greenness across all sites and across all three time periods since fires, exhibiting a positive feedback in a warming environment. Repeatedly dry spring periods reduced NDVI at all the sites and wetter summer periods following such dry springs could not compensate for this, indicating that a prolonged dry spring has a strong impact consistently over the entire early developmental stages from the initial 5 years to 15 years post-fire. Further, young forests showed higher climate sensitivity compared to the mature forest, irrespective of species and projected climatic conditions. Our findings suggest that a dry spring not only increases fire risk, but also delays recovery of boreal forests in southern Siberia. It also highlights the importance of changing rainfall seasonality as well as total rainfall in a changing climate for post-fire recovery of forest.

Simulation-based estimators of analytically intractable causal effects.

In causal inference problems, one is often tasked with estimating causal effects which are analytically intractable functionals of the data-generating mechanism. Relevant settings include estimating intention-to-treat effects in longitudinal problems with missing data or computing direct and indirect effects in mediation analysis. One approach to computing these effects is to use the g-formula implemented via Monte Carlo integration; when simulation-based methods such as the nonparametric bootstrap or Markov chain Monte Carlo are used for inference, Monte Carlo integration must be nested within an already computationally intensive algorithm. We develop a widely-applicable approach to accelerating this Monte Carlo integration step which greatly reduces the computational burden of existing g-computation algorithms. We refer to our method as accelerated g-computation (AGC). The algorithms we present are similar in spirit to multiple imputation, but require removing within-imputation variance from the standard error rather than adding it. We illustrate the use of AGC on a mediation analysis problem using a beta regression model and in a longitudinal clinical trial subject to nonignorable missingness using a Bayesian additive regression treesmodel.

Bayesian phase II clinical trial design with noncompliance.

Noncompliance issue is common in early phase clinical trials; and may lead to biased estimation of the intent-to-treat effect and incorrect conclusions for the clinical trial. In this work, we propose a Bayesian approach for sequentially monitoring the phase II randomized clinical trials that takes account for the noncompliance information. We adopt the principal stratification framework and propose to use Bayesian additive regression trees for selecting useful baseline covariates and estimating the complier average causal effect (CACE) for both efficacy and toxicity outcomes. The decision of early termination or not is then made adaptively based on the estimated CACE from the accumulated data. Simulation studies have confirmed the excellent performance of the proposed design in the presence of noncompliance.

Potential of Bayesian additive regression trees for predicting daily global and diffuse solar radiation in arid and humid areas

This study aims to evaluate the potential of Bayesian additive regression trees (BART) for predicting global and diffuse solar radiation. Long-term daily weather data were collected at four stations in arid and humid areas. Models with different input combinations were created. The default parameters within R language package of BART were used. Model accuracy was assessed with Pearson correlation coefficient (R), root mean square error (RMSE), mean absolute error (MAE), relative root mean square error (RRMSE), and Nash-Sutcliffe efficiency coefficient (NSE). Taylor diagram was applied to illustrate model performance. On average, the model with sunshine duration, theoretical sunshine duration, mean temperature, maximum temperature, minimum temperature, relative humidity, and rainfall performed best for predicting global solar radiation, with mean R of 0.973, RMSE of 1.685 MJ/m2d, NSE of 0.944, RRMSE of 0.124, and MAE of 1.265 MJ/m2d. The model with sunshine duration, theoretical sunshine duration, global solar radiation, extraterrestrial solar radiation, and day of year outperformed others for predicting diffuse solar radiation, with mean R of 0.912, RMSE of 1.291 MJ/m2d, NSE of 0.827, RRMSE of 0.214, and MAE of 0.933 MJ/m2d. The results showed that BART was a suitable method for predicting global and diffuse solar radiation using climatic variables.