Sparse high-dimensional linear mixed modeling with a partitioned empirical Bayes ECM algorithm

High-dimensional longitudinal data is increasingly used in a wide range of scientific studies. However, there are few statistical methods for high-dimensional linear mixed models (LMMs), as most Bayesian variable selection or penalization methods are designed for independent observations. Additionally, the few available software packages for high-dimensional LMMs suffer from scalability issues. This work presents an efficient and accurate Bayesian framework for high-dimensional LMMs. We use empirical Bayes estimators of hyperparameters for increased flexibility and an Expectation-Conditional-Minimization (ECM) algorithm for computationally efficient maximum a posteriori probability (MAP) estimation of parameters. The novelty of the approach lies in its partitioning and parameter expansion as well as its fast and scalable computation. We illustrate Linear Mixed Modeling with PaRtitiOned empirical Bayes ECM (LMM-PROBE) in simulation studies evaluating fixed and random effects estimation along with computation time. A real-world example is provided using data from a study of lupus in children, where we identify genes and clinical factors associated with a new lupus biomarker and predict the biomarker over time

The Intersection of Rural Residence and Minority Race/Ethnicity in Cancer Disparities in the United States

One in every twenty-five persons in America is a racial/ethnic minority who lives in a rural area. Our objective was to summarize how racism and, subsequently, the social determinants of health disproportionately affect rural racial/ethnic minority populations, provide a review of the cancer disparities experienced by rural racial/ethnic minority groups, and recommend policy, research, and intervention approaches to reduce these disparities. We found that rural Black and American Indian/Alaska Native populations experience greater poverty and lack of access to care, which expose them to greater risk of developing cancer and experiencing poorer cancer outcomes in treatment and ultimately survival. There is a critical need for additional research to understand the disparities experienced by all rural racial/ethnic minority populations. We propose that policies aim to increase access to care and healthcare resources for these communities. Further, that observational and interventional research should more effectively address the intersections of rurality and race/ethnicity through reduced structural and interpersonal biases in cancer care, increased data access, more research on newer cancer screening and treatment modalities, and continued intervention and implementation research to understand how evidence-based practices can most effectively reduce disparities among these populations

The Intersection of Rural Residence and Minority Race/Ethnicity in Cancer Disparities in the United States

One in every twenty-five persons in America is a racial/ethnic minority who lives in a rural area. Our objective was to summarize how racism and, subsequently, the social determinants of health disproportionately affect rural racial/ethnic minority populations, provide a review of the cancer disparities experienced by rural racial/ethnic minority groups, and recommend policy, research, and intervention approaches to reduce these disparities. We found that rural Black and American Indian/Alaska Native populations experience greater poverty and lack of access to care, which expose them to greater risk of developing cancer and experiencing poorer cancer outcomes in treatment and ultimately survival. There is a critical need for additional research to understand the disparities experienced by all rural racial/ethnic minority populations. We propose that policies aim to increase access to care and healthcare resources for these communities. Further, that observational and interventional research should more effectively address the intersections of rurality and race/ethnicity through reduced structural and interpersonal biases in cancer care, increased data access, more research on newer cancer screening and treatment modalities, and continued intervention and implementation research to understand how evidence-based practices can most effectively reduce disparities among these populations

Sparse high-dimensional linear regression with a partitioned empirical Bayes ECM algorithm

Bayesian variable selection methods are powerful techniques for fitting and inferring on sparse high-dimensional linear regression models. However, many are computationally intensive or require restrictive prior distributions on model parameters. In this paper, we proposed a computationally efficient and powerful Bayesian approach for sparse high-dimensional linear regression. Minimal prior assumptions on the parameters are used through the use of plug-in empirical Bayes estimates of hyperparameters. Efficient maximum a posteriori (MAP) estimation is completed through a Parameter-Expanded Expectation-Conditional-Maximization (PX-ECM) algorithm. The PX-ECM results in a robust computationally efficient coordinate-wise optimization, which adjusts for the impact of other predictor variables. The completion of the E-step uses an approach motivated by the popular two-groups approach to multiple testing. The result is a PaRtitiOned empirical Bayes Ecm (PROBE) algorithm applied to sparse high-dimensional linear regression, which can be completed using one-at-a-time or all-at-once type optimization. We compare the empirical properties of PROBE to comparable approaches with numerous simulation studies and an analysis of cancer cell lines drug response study. The proposed approach is implemented in the R package probe

Heteroscedastic sparse high-dimensional linear regression with a partitioned empirical Bayes ECM algorithm

Sparse linear regression methods for high-dimensional data often assume that residuals have constant variance. When this assumption is violated, it can lead to bias in estimated coefficients, prediction intervals (PI) with improper length, and increased type I errors. We propose a heteroscedastic high-dimensional linear regression model through a partitioned empirical Bayes Expectation Conditional Maximization (H-PROBE) algorithm. H-PROBE is a computationally efficient maximum a posteriori estimation approach based on a Parameter-Expanded Expectation-Conditional-Maximization algorithm. It requires minimal prior assumptions on the regression parameters through plug-in empirical Bayes estimates of hyperparameters. The variance model uses a multivariate log-Gamma prior on coefficients that can incorporate covariates hypothesized to impact heterogeneity. The motivation of our approach is a study relating Aphasia Quotient (AQ) to high-resolution T2 neuroimages of brain damage in stroke patients. AQ is a vital measure of language impairment and informs treatment decisions, but it is challenging to measure and subject to heteroscedastic errors. It is, therefore, of clinical importance -- and the goal of this paper -- to use high-dimensional neuroimages to predict and provide PIs for AQ that accurately reflect the heterogeneity in residual variance. Our analysis demonstrates that H-PROBE can use markers of heterogeneity to provide narrower PI widths than standard methods without sacrificing coverage. Through extensive simulation studies, we exhibit that H-PROBE results in superior prediction, variable selection, and predictive inference than competing methods