This article describes how genetic components of disease susceptibility can be evaluated in case-control studies, where cases and controls are sampled independently from the population at large. Subjects are assumed unrelated, in contrast to studies of familial aggregation and linkage. The logistic model can be used to test collapsibility over phenotypes or genotypes, and to estimate interactions between environmental and genetic factors. Such interactions provide an example of a context where non-hierarchical models make sense biologically. Also, if the exposure and genetic categories occur independently and the disease is rare, then analyses based only on cases are valid, and offer better precision for estimating gene-environment interactions than those based on the full data.

The Social Vulnerability Index (SoVI), created by Cutter et al. (2003), examined the spatial patterns of social vulnerability to natural hazards at the county level in the United States in order to describe and understand the social burdens of risk. The purpose of this article is to examine the sensitivity of quantitative features underlying the SoVI approach to changes in its construction, the scale at which it is applied, the set of variables used, and to various geographic contexts. First, the SoVI was calculated for multiple aggregation levels in the State of South Carolina and with a subset of the original variables to determine the impact of scalar and variable changes on index construction. Second, to test the sensitivity of the algorithm to changes in construction, and to determine if that sensitivity was constant in various geographic contexts, census data were collected at a submetropolitan level for three study sites: Charleston, SC; Los Angeles, CA; and New Orleans, LA. Fifty-four unique variations of the SoVI were calculated for each study area and evaluated using factorial analysis. These results were then compared across study areas to evaluate the impact of changing geographic context. While decreases in the scale of aggregation were found to result in decreases in the variance explained by principal components analysis (PCA), and in increases in the variance of the resulting index values, the subjective interpretations yielded from the SoVI remained fairly stable. The algorithm's sensitivity to certain changes in index construction differed somewhat among the study areas. Understanding the impacts of changes in index construction and scale are crucial in increasing user confidence in metrics designed to represent the extremely complex phenomenon of social vulnerability.

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Mutations in the p53 oncogene are extremely common in human cancers, and environmental exposure to mutagenic agents may play a role in the frequency and nature of the mutations. Differences in the patterns of p53 mutations have been observed for different tumor types. It is not trivial to determine if the differences observed in two mutational spectra are statistically significant. To this end, we present a computer program for comparison of two mutational spectra. The program runs on IBM-compatible personal computers and is freely available. The input for the program is a text file containing the number and nature of mutations observed in the two spectra. The output of the program is a P value, which indicates the probability that the two spectra are drawn from the same population. To demonstrate the program, the mutational spectra of single base substitutions in the p53 gene are compared in (i) bladder cancers from smokers and non-smokers, (ii) small-cell lung cancers, non-small-cell lung cancers and colon cancers and (iii) hepatocellular carcinomas from high- and low-aflatoxin exposure groups. p53 mutations differ in several important aspects from a typical mutational spectra experiment, where a homogeneous population of cells is treated with a specific mutagen and mutations at a specific locus are recovered by phenotypic selection. The means by which p53 mutations are recognized is by the appearance of a cancer, and this phenotype is very complex and varied.

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We study the use of simultaneous confidence bands for low-dose risk estimation with quantal response data, and derive methods for estimating simultaneous upper confidence limits on predicted extra risk under a multistage model. By inverting the upper bands on extra risk, we obtain simultaneous lower bounds on the benchmark dose (BMD). Monte Carlo evaluations explore characteristics of the simultaneous limits under this setting, and a suite of actual data sets are used to compare existing methods for placing lower limits on the BMD.

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