Causal mediation modeling has become a popular approach for studying the effect of an exposure on an outcome through a mediator. However, current methods are not applicable to the setting with a large number of mediators. We propose a testing procedure for mediation effects of high-dimensional continuous mediators. We characterize the marginal mediation effect, the multivariate component-wise mediation effects, and the L2 norm of the component-wise effects, and develop a Monte-Carlo procedure for evaluating their statistical significance. To accommodate the setting with a large number of mediators and a small sample size, we further propose a transformation model using the spectral decomposition. Under the transformation model, mediation effects can be estimated using a series of regression models with a univariate transformed mediator, and examined by our proposed testing procedure. Extensive simulation studies are conducted to assess the performance of our methods for continuous and dichotomous outcomes. We apply the methods to analyze genomic data investigating the effect of microRNA miR-223 on a dichotomous survival status of patients with glioblastoma multiforme (GBM). We identify nine gene ontology sets with expression values that significantly mediate the effect of miR-223 on GBM survival.

Various studies have reported the physical and mental health benefits from exposure to “green” neighborhoods, such as proximity to neighborhoods with trees and vegetation. However, no studies have explicitly assessed the association between exposure to “green” surroundings and cognitive function in terms of student academic performance. This study investigated the association between the “greenness” of the area surrounding a Massachusetts public elementary school and the academic achievement of the school’s student body based on standardized tests with an ecological setting. Researchers used the composite school-based performance scores generated by the Massachusetts Comprehensive Assessment System (MCAS) to measure the percentage of 3rd-grade students (the first year of standardized testing for 8–9 years-old children in public school), who scored “Above Proficient” (AP) in English and Mathematics tests (Note: Individual student scores are not publically available). The MCAS results are comparable year to year thanks to an equating process. Researchers included test results from 2006 through 2012 in 905 public schools and adjusted for differences between schools in the final analysis according to race, gender, English as a second language (proxy for ethnicity and language facility), parent income, student-teacher ratio, and school attendance. Surrounding greenness of each school was measured using satellite images converted into the Normalized Difference Vegetation Index (NDVI) in March, July and October of each year according to a 250-meter, 500-meter, 1,000-meter, and 2000-meter circular buffer around each school. Spatial Generalized Linear Mixed Models (GLMMs) estimated the impacts of surrounding greenness on school-based performance. Overall the study results supported a relationship between the “greenness” of the school area and the school-wide academic performance. Interestingly, the results showed a consistently positive significant association between the greenness of the school in the Spring (when most Massachusetts students take the MCAS tests) and school-wide performance on both English and Math tests, even after adjustment for socio-economic factors and urban residency.

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