USING THE R PACKAGE crlmm FOR GENOTYPING AND COPY NUMBER ESTIMATION

Genotyping platforms such as Affymetrix can be used to assess genotype-phenotype as well as copy number-phenotype associations at millions of markers. While genotyping algorithms are largely concordant when assessed on HapMap samples, tools to assess copy number changes are more variable and often discordant. One explanation for the discordance is that copy number estimates are susceptible to systematic differences between groups of samples that were processed at different times or by different labs. Analysis algorithms that do not adjust for batch effects are prone to spurious measures of association. The R package crlmm implements a multilevel model that adjusts for batch effects and provides allele-specific estimates of copy number. This paper illustrates a workflow for the estimation of allele-specific copy number, develops markerand study-level summaries of batch effects, and demonstrates how the marker-level estimates can be integrated with complimentary Bioconductor software for inferring regions of copy number gain or loss. All analyses are performed in the statistical environment R. A compendium for reproducing the analysis is available from the author’s website (http://www.biostat.jhsph.edu/~rscharpf/crlmmCompendium/index.html).

Inequity Measures for Evaluations of Environmental Justice: A Case Study of Close Proximity to Highways in NYC

Assessments of environmental and territorial justice are similar in that both assess whether empirical relations between the spatial arrangement of undesirable hazards (or desirable public goods and services) and socio-demographic groups are consistent with notions of social justice, evaluating the spatial distribution of benefits and burdens (outcome equity) and the process that produces observed differences (process equity. Using proximity to major highways in NYC as a case study, we review methodological issues pertinent to both fields and discuss choice and computation of exposure measures, but focus primarily on measures of inequity. We present inequity measures computed from the empirically estimated joint distribution of exposure and demographics and compare them to traditional measures such as linear regression, logistic regression and Theil’s entropy index. We find that measures computed from the full joint distribution provide more unified, transparent and intuitive operational definitions of inequity and show how the approach can be used to structure siting and decommissioning decisions.