Rare variants create synthetic genome-wide associations.

Genome-wide association studies (GWAS) have now identified at least 2,000 common variants that appear associated with common diseases or related traits (http://www.genome.gov/gwastudies), hundreds of which have been convincingly replicated. It is generally thought that the associated markers reflect the effect of a nearby common (minor allele frequency >0.05) causal site, which is associated with the marker, leading to extensive resequencing efforts to find causal sites. We propose as an alternative explanation that variants much less common than the associated one may create "synthetic associations" by occurring, stochastically, more often in association with one of the alleles at the common site versus the other allele. Although synthetic associations are an obvious theoretical possibility, they have never been systematically explored as a possible explanation for GWAS findings. Here, we use simple computer simulations to show the conditions under which such synthetic associations will arise and how they may be recognized. We show that they are not only possible, but inevitable, and that under simple but reasonable genetic models, they are likely to account for or contribute to many of the recently identified signals reported in genome-wide association studies. We also illustrate the behavior of synthetic associations in real datasets by showing that rare causal mutations responsible for both hearing loss and sickle cell anemia create genome-wide significant synthetic associations, in the latter case extending over a 2.5-Mb interval encompassing scores of "blocks" of associated variants. In conclusion, uncommon or rare genetic variants can easily create synthetic associations that are credited to common variants, and this possibility requires careful consideration in the interpretation and follow up of GWAS signals.

Rare targets are rarely missed in correctable search.

Failing to find a tumor in an x-ray scan or a gun in an airport baggage screening can have dire consequences, making it fundamentally important to elucidate the mechanisms that hinder performance in such visual searches. Recent laboratory work has indicated that low target prevalence can lead to disturbingly high miss rates in visual search. Here, however, we demonstrate that misses in low-prevalence searches can be readily abated. When targets are rarely present, observers adapt by responding more quickly, and miss rates are high. Critically, though, these misses are often due to response-execution errors, not perceptual or identification errors: Observers know a target was present, but just respond too quickly. When provided an opportunity to correct their last response, observers can catch their mistakes. Thus, low target prevalence may not be a generalizable cause of high miss rates in visual search.

Sticky central limit theorems on open books

Given a probability distribution on an open book (a metric space obtained by gluing a disjoint union of copies of a half-space along their boundary hyperplanes), we define a precise concept of when the Fréchet mean (barycenter) is sticky. This nonclassical phenomenon is quantified by a law of large numbers (LLN) stating that the empirical mean eventually almost surely lies on the (codimension 1 and hence measure 0) spine that is the glued hyperplane, and a central limit theorem (CLT) stating that the limiting distribution is Gaussian and supported on the spine.We also state versions of the LLN and CLT for the cases where the mean is nonsticky (i.e., not lying on the spine) and partly sticky (i.e., is, on the spine but not sticky). © Institute of Mathematical Statistics, 2013.

Rare hereditary COL4A3/COL4A4 variants may be mistaken for familial focal segmental glomerulosclerosis.

Focal segmental glomerulosclerosis (FSGS) is a histological lesion with many causes, including inherited genetic defects, with significant proteinuria being the predominant clinical finding at presentation. Mutations in COL4A3 and COL4A4 are known to cause Alport syndrome (AS), thin basement membrane nephropathy, and to result in pathognomonic glomerular basement membrane (GBM) findings. Secondary FSGS is known to develop in classic AS at later stages of the disease. Here, we present seven families with rare or novel variants in COL4A3 or COL4A4 (six with single and one with two heterozygous variants) from a cohort of 70 families with a diagnosis of hereditary FSGS. The predominant clinical finding at diagnosis was proteinuria associated with hematuria. In all seven families, there were individuals with nephrotic-range proteinuria with histologic features of FSGS by light microscopy. In one family, electron microscopy showed thin GBM, but four other families had variable findings inconsistent with classical Alport nephritis. There was no recurrence of disease after kidney transplantation. Families with COL4A3 and COL4A4 variants that segregated with disease represent 10% of our cohort. Thus, COL4A3 and COL4A4 variants should be considered in the interpretation of next-generation sequencing data from such patients. Furthermore, this study illustrates the power of molecular genetic diagnostics in the clarification of renal phenotypes.