Mediation hypothesis testing for a large number of mediators is challenging due to the composite structure of the null hypothesis, H αβ : = 0 0

Timely diagnostic testing for active SARS-CoV-2 viral infections is key to controlling the spread of the virus and preventing severe disease. A central public health challenge is defining test allocation strategies with limited resources. In this paper, we provide a mathematical framework for defining an optimal strategy for allocating viral diagnostic tests. The framework accounts for imperfect test results, selective testing in certain high-risk patient populations, practical constraints in terms of budget and/or total number of available tests, and the purpose of testing. Our method is not only useful for detecting infections, but can also be used for long-time surveillance to detect new outbreaks. In our proposed approach, tests can be allocated across population strata defined by symptom severity and other patient characteristics, allowing the test allocation plan to prioritize higher risk patient populations. We illustrate our framework using historical data from the initial wave of the COVID-19 outbreak in New York City.We extend our proposed method to address the challenge of allocating two different types of diagnostic tests with different costs and accuracy, for example, the RT-PCR and the rapid antigen test (RAT), under budget constraints. We show how this latter framework can be useful to reopening of college campuses where university administrators are challenged with finite resources for community surveillance. We provide a R Shiny web application allowing users to explore test allocation strategies across a variety of pandemic scenarios. This work can serve as a useful tool for guiding public health decision-making at a community level and adapting testing plans to different stages of an epidemic.The conceptual framework has broader relevance beyond the current COVID-19 pandemic.

Low socioeconomic status (SES) and living in a disadvantaged neighborhood are associated with poor cardiovascular health. Multiple lines of evidence have linked DNA methylation to both cardiovascular risk factors and social disadvantage indicators. However, limited research has investigated the role of DNA methylation in mediating the associations of individual- and neighborhood-level disadvantage with multiple cardiovascular risk factors in large, multi-ethnic, population-based cohorts. We examined whether disadvantage at the individual level (childhood and adult SES) and neighborhood level (summary neighborhood SES as assessed by Census data and social environment as assessed by perceptions of aesthetic quality, safety, and social cohesion) were associated with 11 cardiovascular risk factors including measures of obesity, diabetes, lipids, and hypertension in 1,154 participants from the Multi-Ethnic Study of Atherosclerosis (MESA). For significant associations, we conducted epigenome-wide mediation analysis to identify methylation sites mediating the relationship between individual/neighborhood disadvantage and cardiovascular risk factors using the JT-Comp method that assesses sparse mediation effects under a composite null hypothesis. In models adjusting for age, sex, race/ethnicity, smoking, medication use, and genetic principal components of ancestry, epigenetic mediation was detected for the associations of adult SES with body mass index (BMI), insulin, and high-density lipoprotein cholesterol (HDL-C), as well as for the association between neighborhood socioeconomic disadvantage and HDL-C at FDR q < 0.05. The 410 CpG mediators identified for the SES-BMI association were enriched for CpGs associated with gene expression (expression quantitative trait methylation loci, or eQTMs), and corresponding genes were enriched in antigen processing and presentation pathways. For cardiovascular risk factors other than BMI, most of the epigenetic mediators lost significance after controlling for BMI. However, 43 methylation sites showed evidence of mediating the neighborhood socioeconomic disadvantage and HDL-C association after BMI adjustment. The identified mediators were enriched for eQTMs, and corresponding genes were enriched in inflammatory and apoptotic pathways. Our findings support the hypothesis that DNA methylation acts as a mediator between individual- and neighborhood-level disadvantage and cardiovascular risk factors, and shed light on the potential underlying epigenetic pathways. Future studies are needed to fully elucidate the biological mechanisms that link social disadvantage to poor cardiovascular health.

Epigenetic researchers often evaluate DNA methylation as a mediator between social/environmental exposures and disease, but modern statistical methods for jointly evaluating many mediators have not been widely adopted. We compare seven methods for high-dimensional mediation analysis with continuous outcomes through both diverse simulations and analysis of DNAm data from a large national cohort in the United States, while providing an R package for their implementation. Among the considered choices, the best-performing methods for detecting active mediators in simulations are the Bayesian sparse linear mixed model by Song et al. (2020) and high-dimensional mediation analysis by Gao et al. (2019); while the superior methods for estimating the global mediation effect are high-dimensional linear mediation analysis by Zhou et al. (2021) and principal component mediation analysis by Huang and Pan (2016). We provide guidelines for epigenetic researchers on choosing the best method in practice and offer suggestions for future methodological development.

Penalized regression methods, such as lasso and elastic net, are used in many biomedical applications when simultaneous regression coefficient estimation and variable selection is desired. However, missing data complicates the implementation of these methods, particularly when missingness is handled using multiple imputation. Applying a variable selection algorithm on each imputed dataset will likely lead to different sets of selected predictors, making it difficult to ascertain a final active set without resorting to ad hoc combination rules.In this paper we consider a general class of penalized objective functions which, by construction, force selection of the same variables across multiplyimputed datasets. By pooling objective functions across imputations, optimization is then performed jointly over all imputed datasets rather than separately for each dataset. We consider two objective function formulations that exist in the literature, which we will refer to as "stacked" and "grouped" objective functions. Building on existing work, we (a) derive and implement efficient cyclic coordinate descent and majorization-minimization optimization algorithms for both continuous and binary outcome data, (b) incorporate adaptive shrinkage penalties, (c) compare these methods through simulation, and (d) develop an R package miselect for easy implementation. Simulations demonstrate that the "stacked" objective function approaches tend to be more computationally efficient and have better estimation and selection properties. We apply these methods to data from the University of Michigan ALS Patients Repository (UMAPR) which aims to identify the association between persistent organic pollutants and ALS risk.