Accurate modeling of replication rates in genome-wide association studies by accounting for Winner's Curse and study-specific heterogeneity.

Genome-wide association studies (GWAS) have identified thousands of genetic variants associated with complex human traits, but only a fraction of variants identified in discovery studies achieve significance in replication studies. Replication in genome-wide association studies has been well-studied in the context of Winner's Curse, which is the inflation of effect size estimates for significant variants due to statistical chance. However, Winner's Curse is often not sufficient to explain lack of replication. Another reason why studies fail to replicate is that there are fundamental differences between the discovery and replication studies. A confounding factor can create the appearance of a significant finding while actually being an artifact that will not replicate in future studies. We propose a statistical framework that utilizes genome-wide association studies and replication studies to jointly model Winner's Curse and study-specific heterogeneity due to confounding factors. We apply this framework to 100 genome-wide association studies from the Human Genome-Wide Association Studies Catalog and observe that there is a large range in the level of estimated confounding. We demonstrate how this framework can be used to distinguish when studies fail to replicate due to statistical noise and when they fail due to confounding.

Using Molecular Similarity to Develop Reliable Models of Chemical Reactions in Complex Environments.

The use of molecular similarity to develop reliable low-cost quantum mechanical models for use in quantum mechanical/molecular mechanical simulations of chemical reactions is explored, using the H + HF → H2 + F collinear reaction as a test case. The approach first generates detailed quantum chemical data for the reaction center in geometries and electrostatic environments that span those expected to arise during the molecular dynamics simulations. For each geometry and environment, both high- and low-level ab initio calculations are performed. A model is then developed to predict the high-level results using only inputs generated from the low-level theory. The inputs used here are based on principal component analysis of the low-level distributed multipoles, and the model is a simple linear regression. The distributed multipoles are monopoles, dipoles, and quadrupoles at each atomic center, and they summarize the electronic distribution in a manner that is comparable across basis set. The error in the model is dominated by extrapolation from small to large basis sets, with extrapolation from uncorrelated to correlated methods contributing much less error. A single regression can be used to make predictions for a range of reaction-center geometries and environments. For the trial collinear reaction, separate regressions were developed for the transition region and the entrance and exit channels. These models can predict the results of CCSD(T)/cc-pVTZ computations from HF/3-21G distributed multipoles, with an average error for the reaction energy profile of 0.69 kcal/mol.

Evaluation of Purkait's triangle method for determining sexual dimorphism.

The identification of sex from the skeleton is an important demographic assessment in medicolegal investigations. Rama Purkait developed a method for estimating sex using measurements from a triangle defined by three points on the proximal end of the femur using skeletal material from Bhopal, India. This method was tested with measurements on 200 Indo-European and African American adult femora from the Terry collection using discriminant function analysis to determine if Purkait's method was valuable for determining sex in Americans. A side-by-side analysis was conducted of Purkait's "triangle method" and the maximum diameter of the femoral head to determine their relative value in assessing sexual dimorphism. In the study sample a single variable from Purkait's method provided 85.5% prediction accuracy, similar to 87% for the head diameter. Combining threshold values for a single variable from Purkait's method and the femoral head diameter raised the predictability to greater than 90% for both sexes.