Exploiting Gene-Environment Independence for Analysis of Case-Control Studies: An Empirical Bayes Approach to Trade Off between Bias and Efficiency

Standard prospective logistic regression analysis of case-control data often leads to very imprecise estimates of gene-environment interactions due to small numbers of cases or controls in cells of crossing genotype and exposure. In contrast, under the assumption of gene-environment independence, modern “retrospective” methods, including the “case-only” approach, can estimate the interaction parameters much more precisely, but they can be seriously biased when the underlying assumption of gene-environment independence is violated. In this article, we propose a novel approach to analyze case-control data that can relax the gene-environment independence assumption using an empirical Bayes framework. In the special case, involving a binary gene and a binary exposure, the framework leads to an estimator of the odds-ratio interaction parameter in a simple closed form that corresponds to an weighted average of the standard case-only and case-control estimators. We also describe a general approach for deriving the empirical Bayes estimator and its variance within the retrospective maximum-likelihood framework developed by Chatterjee and Carroll (2005). We conduct simulation studies to investigate the mean-squared-error of the proposed estimator in both fixed and random parameter settings. We also illustrate the application of this methodology using two real data examples. Both simulated and real data examples suggest that the proposed estimator strikes an excellent balance between bias and efficiency depending on the true nature of the gene-environment association and the sample size for a given study

Exploiting Gene-Environment Independence for Analysis of Case–Control Studies: An Empirical Bayes-Type Shrinkage Estimator to Trade-Off between Bias and Efficiency

Standard prospective logistic regression analysis of case–control data often leads to very imprecise estimates of gene-environment interactions due to small numbers of cases or controls in cells of crossing genotype and exposure. In contrast, under the assumption of gene-environment independence, modern “retrospective” methods, including the “case-only” approach, can estimate the interaction parameters much more precisely, but they can be seriously biased when the underlying assumption of gene-environment independence is violated. In this article, we propose a novel empirical Bayes-type shrinkage estimator to analyze case–control data that can relax the gene-environment independence assumption in a data-adaptive fashion. In the special case, involving a binary gene and a binary exposure, the method leads to an estimator of the interaction log odds ratio parameter in a simple closed form that corresponds to an weighted average of the standard case-only and case–control estimators. We also describe a general approach for deriving the new shrinkage estimator and its variance within the retrospective maximum-likelihood framework developed by Chatterjee and Carroll (2005, Biometrika 92, 399–418). Both simulated and real data examples suggest that the proposed estimator strikes a balance between bias and efficiency depending on the true nature of the gene-environment association and the sample size for a given study.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65511/1/j.1541-0420.2007.00953.x.pd

Estimation of temperature of cosmological apparent horizons: a new approach

We consider radiation from cosmological apparent horizon in Friedmann-Lemaitre-Robertson-Walker(FLRW) model in a double-null coordinate setting. As the spacetime is dynamic, there is no timelike Killing vector, instead we have Kodama vector which acts as dynamical time. We construct the positive frequency modes of the Kodama vector across the horizon. The conditional probability that a signal reaches the central observer when it is crossing from the outside gives the temperature associated with the horizon.Comment: 11 pages, A few references adde

Hawking radiation from dynamical horizons

In completely local settings, we establish that a dynamically evolving black hole horizon can be assigned a Hawking temperature. Moreover, we calculate the Hawking flux and show that the radius of the horizon shrinks.Comment: 5 Page

Hawking temperature and higher order calculations

Hawking radiation has recently been explained by using solutions of wave equations across black hole horizons in a WKB approximation. Higher order calculations using both usual and non-singular coordinates are found to change the solution for zero spin, but this change is not an alteration of the Hawking temperature. For spin 1/2, there is no correction to the simplest form of the solution.Comment: 4 pages; minor changes; comments added about fermions; comment about an 'maginary contribution included at the instance of PL

Case–Control Studies of Gene–Environment Interaction: Bayesian Design and Analysis

With increasing frequency, epidemiologic studies are addressing hypotheses regarding gene-environment interaction. In many well-studied candidate genes and for standard dietary and behavioral epidemiologic exposures, there is often substantial  prior  information available that may be used to analyze current data as well as for designing a new study. In this article, first, we propose a proper full Bayesian approach for analyzing studies of gene–environment interaction. The Bayesian approach provides a natural way to incorporate uncertainties around the assumption of gene–environment independence, often used in such an analysis. We then consider Bayesian sample size determination criteria for both estimation and hypothesis testing regarding the multiplicative gene–environment interaction parameter. We illustrate our proposed methods using data from a large ongoing case–control study of colorectal cancer investigating the interaction of N-acetyl transferase type 2 (NAT2) with smoking and red meat consumption. We use the existing data to elicit a design prior and show how to use this information in allocating cases and controls in planning a future study that investigates the same interaction parameters. The Bayesian design and analysis strategies are compared with their corresponding frequentist counterparts.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/78584/1/j.1541-0420.2009.01357.x.pd

Tests for Gene-Environment Interactions and Joint Effects with Exposure Misclassification

The number of methods for genome-wide testing of gene-environment interactions (GEI) continues to increase with the hope of discovering new genetic risk factors and obtaining insight into the disease-gene-environment relationship. The relative performance of these methods based on family-wise type 1 error rate and power depends on underlying disease-gene-environment associations, estimates of which may be biased in the presence of exposure misclassification. This simulation study expands on a previously published simulation study of methods for detecting GEI by evaluating the impact of exposure misclassification. We consider seven single step and modular screening methods for identifying GEI at a genome-wide level and seven joint tests for genetic association and GEI, for which the goal is to discover new genetic susceptibility loci by leveraging GEI when present. In terms of statistical power, modular methods that screen based on the marginal disease-gene relationship are more robust to exposure misclassification. Joints tests that include main/marginal effects of a gene display a similar robustness, confirming results from earlier studies. Our results offer an increased understanding of the strengths and limitations of methods for genome-wide search for GEI and joint tests in presence of exposure misclassification. KEY WORDS: case-control; genome-wide association; gene discovery, gene-environment independence; modular methods; multiple testing; screening test; weighted hypothesis test. Abbreviations: CC, case-control; CC(EXP), CC in the exposed subgroup; CO, case-only; CT, cocktail; DF, degree of freedom; D-G, disease-gene; EB, empirical Bayes; EB(EXP), EB in the exposed subgroup; EDGxE, joint marginal/association screening; FWER, family-wise error rate; G-E, gene-environment; GEI, gene-environment interaction; GEWIS, Gene Environment Wide Interaction Study; H2, hybrid two-step; LR, likelihood ratio; MA, marginal; OR, odds ratio; SE, sensitivity; SP, specificity; TS, two-step gene-environment screening