Gene‐environment interplay in common complex diseases: forging an integrative model—recommendations from an NIH workshop

Although it is recognized that many common complex diseases are a result of multiple genetic and environmental risk factors, studies of gene‐environment interaction remain a challenge and have had limited success to date. Given the current state‐of‐the‐science, NIH sought input on ways to accelerate investigations of gene‐environment interplay in health and disease by inviting experts from a variety of disciplines to give advice about the future direction of gene‐environment interaction studies. Participants of the NIH Gene‐Environment Interplay Workshop agreed that there is a need for continued emphasis on studies of the interplay between genetic and environmental factors in disease and that studies need to be designed around a multifaceted approach to reflect differences in diseases, exposure attributes, and pertinent stages of human development. The participants indicated that both targeted and agnostic approaches have strengths and weaknesses for evaluating main effects of genetic and environmental factors and their interactions. The unique perspectives represented at the workshop allowed the exploration of diverse study designs and analytical strategies, and conveyed the need for an interdisciplinary approach including data sharing, and data harmonization to fully explore gene‐environment interactions. Further, participants also emphasized the continued need for high‐quality measures of environmental exposures and new genomic technologies in ongoing and new studies. Genet. Epidemiol. 35: 217‐225, 2011. © 2011 Wiley‐Liss, Inc.     

EINVis: A Visualization Tool for Analyzing and Exploring Genetic Interactions in Large‐Scale Association Studies

Epistasis (gene‐gene interaction) detection in large‐scale genetic association studies has recently drawn extensive research interests as many complex traits are likely caused by the joint effect of multiple genetic factors. The large number of possible interactions poses both statistical and computational challenges. A variety of approaches have been developed to address the analytical challenges in epistatic interaction detection. These methods usually output the identified genetic interactions and store them in flat file formats. It is highly desirable to develop an effective visualization tool to further investigate the detected interactions and unravel hidden interaction patterns. We have developed EINVis, a novel visualization tool that is specifically designed to analyze and explore genetic interactions. EINVis displays interactions among genetic markers as a network. It utilizes a circular layout (specially, a tree ring view) to simultaneously visualize the hierarchical interactions between single nucleotide polymorphisms (SNPs), genes, and chromosomes, and the network structure formed by these interactions. Using EINVis, the user can distinguish marginal effects from interactions, track interactions involving more than two markers, visualize interactions at different levels, and detect proxy SNPs based on linkage disequilibrium. EINVis is an effective and user‐friendly free visualization tool for analyzing and exploring genetic interactions. It is publicly available with detailed documentation and online tutorial on the web at http://filer.case.edu/yxw407/einvis/ .     

Gene–environment interactions in case–control studies with silent disease

Genome‐wide association studies (GWAS) often measure gene–environment interactions (G × E). We consider the problem of accurately estimating a G × E in a case–control GWAS when a subset of the controls have silent, or undiagnosed, disease and the frequency of the silent disease varies by the environmental variable. We show that using case–control status without accounting for misdiagnosis can lead to biased estimates of the G × E. We further propose a pseudolikelihood approach to remove the bias and accurately estimate how the relationship between the genetic variant and the true disease status varies by the environmental variable. We demonstrate our method in extensive simulations and apply our method to a GWAS of prostate cancer.     

Case‐only genome‐wide interaction study of disease risk,prognosis and treatment

Case‐control genome‐wide association (GWA) studies have facilitated the identification of susceptibility loci for many complex diseases; however, these studies are often not adequately powered to detect gene‐environment (G×E) and gene‐gene (G×G) interactions. Case‐only studies are more efficient than case‐control studies for detecting interactions and require no data on control subjects. In this article, we discuss the concept and utility of the case‐only genome‐wide interaction (COGWI) study, in which common genetic variants, measured genome‐wide, are screened for association with environmental exposures or genetic variants of interest. An observed G‐E (or G‐G) association, as measured by the case‐only odds ratio (OR), suggests interaction, but only if the interacting factors are unassociated in the population from which the cases were drawn. The case‐only OR is equivalent to the interaction risk ratio. In addition to risk‐related interactions, we discuss how the COGWI design can be used to efficiently detect G×G, G×E and pharmacogenetic interactions related to disease outcomes in the context of observational clinical studies or randomized clinical trials. Such studies can be conducted using only data on individuals experiencing an outcome of interest or individuals not experiencing the outcome of interest. Sharing data among GWA and COGWI studies of disease risk and outcome can further enhance efficiency. Sample size requirements for COGWI studies, as compared to case‐control GWA studies, are provided. In the current era of genome‐wide analyses, the COGWI design is an efficient and straightforward method for detecting G×G, G×E and pharmacogenetic interactions related to disease risk, prognosis and treatment response. Genet. Epidemiol. 34:7–15, 2010. © 2009 Wiley‐Liss, Inc.     

Mendelian Randomization Analysis With Multiple Genetic Variants Using Summarized Data

Genome‐wide association studies, which typically report regression coefficients summarizing the associations of many genetic variants with various traits, are potentially a powerful source of data for Mendelian randomization investigations. We demonstrate how such coefficients from multiple variants can be combined in a Mendelian randomization analysis to estimate the causal effect of a risk factor on an outcome. The bias and efficiency of estimates based on summarized data are compared to those based on individual‐level data in simulation studies. We investigate the impact of gene–gene interactions, linkage disequilibrium, and ‘weak instruments’ on these estimates. Both an inverse‐variance weighted average of variant‐specific associations and a likelihood‐based approach for summarized data give similar estimates and precision to the two‐stage least squares method for individual‐level data, even when there are gene–gene interactions. However, these summarized data methods overstate precision when variants are in linkage disequilibrium. If the P‐value in a linear regression of the risk factor for each variant is less than , then weak instrument bias will be small. We use these methods to estimate the causal association of low‐density lipoprotein cholesterol (LDL‐C) on coronary artery disease using published data on five genetic variants. A 30% reduction in LDL‐C is estimated to reduce coronary artery disease risk by 67% (95% CI: 54% to 76%). We conclude that Mendelian randomization investigations using summarized data from uncorrelated variants are similarly efficient to those using individual‐level data, although the necessary assumptions cannot be so fully assessed.     

Rare variants association testing for a binary outcome when pooling individual level data from heterogeneous studies

Whole genome sequencing (WGS) and whole exome sequencing studies are used to test the association of rare genetic variants with health traits. Many existing WGS efforts now aggregate data from heterogeneous groups, for example, combining sets of individuals of European and African ancestries. We here investigate the statistical implications on rare variant association testing with a binary trait when combining together heterogeneous studies, defined as studies with potentially different disease proportion and different frequency of variant carriers. We study and compare in simulations the Type 1 error control and power of the naïve score test, the saddlepoint approximation to the score test, and the BinomiRare test in a range of settings, focusing on low numbers of variant carriers. We show that Type 1 error control and power patterns depend on both the number of carriers of the rare allele and on disease prevalence in each of the studies. We develop recommendations for association analysis of rare genetic variants. (1) The Score test is preferred when the case proportion in the sample is 50%. (2) Do not down‐sample controls to balance case–control ratio, because it reduces power. Rather, use a test that controls the Type 1 error. (3) Conduct stratified analysis in parallel with combined analysis. Aggregated testing may have lower power when the variant effect size differs between strata.     

Kernel Approach for Modeling Interaction Effects in Genetic Association Studies of Complex Quantitative Traits

The etiology of complex traits likely involves the effects of genetic and environmental factors, along with complicated interaction effects between them. Consequently, there has been interest in applying genetic association tests of complex traits that account for potential modification of the genetic effect in the presence of an environmental factor. One can perform such an analysis using a joint test of gene and gene‐environment interaction. An optimal joint test would be one that remains powerful under a variety of models ranging from those of strong gene‐environment interaction effect to those of little or no gene‐environment interaction effect. To fill this demand, we have extended a kernel machine based approach for association mapping of multiple SNPs to consider joint tests of gene and gene‐environment interaction. The kernel‐based approach for joint testing is promising, because it incorporates linkage disequilibrium information from multiple SNPs simultaneously in analysis and permits flexible modeling of interaction effects. Using simulated data, we show that our kernel machine approach typically outperforms the traditional joint test under strong gene‐environment interaction models and further outperforms the traditional main‐effect association test under models of weak or no gene‐environment interaction effects. We illustrate our test using genome‐wide association data from the Grady Trauma Project, a cohort of highly traumatized, at‐risk individuals, which has previously been investigated for interaction effects.     

Functional Logistic Regression Approach to Detecting Gene by Longitudinal Environmental Exposure Interaction in a Case‐Control Study

Most complex human diseases are likely the consequence of the joint actions of genetic and environmental factors. Identification of gene‐environment (G × E) interactions not only contributes to a better understanding of the disease mechanisms, but also improves disease risk prediction and targeted intervention. In contrast to the large number of genetic susceptibility loci discovered by genome‐wide association studies, there have been very few successes in identifying G × E interactions, which may be partly due to limited statistical power and inaccurately measured exposures. Although existing statistical methods only consider interactions between genes and static environmental exposures, many environmental/lifestyle factors, such as air pollution and diet, change over time, and cannot be accurately captured at one measurement time point or by simply categorizing into static exposure categories. There is a dearth of statistical methods for detecting gene by time‐varying environmental exposure interactions. Here, we propose a powerful functional logistic regression (FLR) approach to model the time‐varying effect of longitudinal environmental exposure and its interaction with genetic factors on disease risk. Capitalizing on the powerful functional data analysis framework, our proposed FLR model is capable of accommodating longitudinal exposures measured at irregular time points and contaminated by measurement errors, commonly encountered in observational studies. We use extensive simulations to show that the proposed method can control the Type I error and is more powerful than alternative ad hoc methods. We demonstrate the utility of this new method using data from a case‐control study of pancreatic cancer to identify the windows of vulnerability of lifetime body mass index on the risk of pancreatic cancer as well as genes that may modify this association.     

Computing a Synthetic Chronic Psychosocial Stress Measurement in Multiple Datasets and its Application in the Replication of G × E Interactions of the EBF1 Gene

Chronic psychosocial stress adversely affects health and is associated with the development of disease [Williams, 2008 ]. Systematic epidemiological and genetic studies are needed to uncover genetic variants that interact with stress to modify metabolic responses across the life cycle that are the proximal contributors to the development of cardiovascular disease and precipitation of acute clinical events. Among the central challenges in the field are to perform and replicate gene‐by‐environment (G × E) studies. The challenge of measurement of individual experience of psychosocial stress is magnified in this context. Although many research datasets exist that contain genotyping and disease‐related data, measures of psychosocial stress are often either absent or vary substantially across studies. In this paper, we provide an algorithm to create a synthetic measure of chronic psychosocial stress across multiple datasets, applying a consistent criterion that uses proxy indicators of stress components. We validated the computed scores of chronic psychosocial stress by observing moderately strong and significant correlations with the self‐rated chronic psychosocial stress in the Multi‐Ethnic Study of Atherosclerosis Cohort (Rho = 0.23, P < 0.0001) and with the measures of depressive symptoms in five datasets (Rho = 0.15–0.42, Ps = 0.005 to <0.0001) and by comparing the distributions of the self‐rated and computed measures. Finally, we demonstrate the utility of this computed chronic psychosocial stress variable by providing three additional replications of our previous finding of gene‐by‐stress interaction with central obesity traits [Singh et al., 2015 ].     

A global test for gene‐gene interactions based on random matrix theory

Statistical interactions between markers of genetic variation, or gene‐gene interactions, are believed to play an important role in the etiology of many multifactorial diseases and other complex phenotypes. Unfortunately, detecting gene‐gene interactions is extremely challenging due to the large number of potential interactions and ambiguity regarding marker coding and interaction scale. For many data sets, there is insufficient statistical power to evaluate all candidate gene‐gene interactions. In these cases, a global test for gene‐gene interactions may be the best option. Global tests have much greater power relative to multiple individual interaction tests and can be used on subsets of the markers as an initial filter prior to testing for specific interactions. In this paper, we describe a novel global test for gene‐gene interactions, the global epistasis test (GET), that is based on results from random matrix theory. As we show via simulation studies based on previously proposed models for common diseases including rheumatoid arthritis, type 2 diabetes, and breast cancer, our proposed GET method has superior performance characteristics relative to existing global gene‐gene interaction tests. A glaucoma GWAS data set is used to demonstrate the practical utility of the GET method.     

Generalized estimating equations for genome‐wide association studies using longitudinal phenotype data

Many longitudinal cohort studies have both genome‐wide measures of genetic variation and repeated measures of phenotypes and environmental exposures. Genome‐wide association study analyses have typically used only cross‐sectional data to evaluate quantitative phenotypes and binary traits. Incorporation of repeated measures may increase power to detect associations, but also requires specialized analysis methods. Here, we discuss one such method—generalized estimating equations (GEE)—in the contexts of analysis of main effects of rare genetic variants and analysis of gene‐environment interactions. We illustrate the potential for increased power using GEE analyses instead of cross‐sectional analyses. We also address challenges that arise, such as the need for small‐sample corrections when the minor allele frequency of a genetic variant and/or the prevalence of an environmental exposure is low. To illustrate methods for detection of gene‐drug interactions on a genome‐wide scale, using repeated measures data, we conduct single‐study analyses and meta‐analyses across studies in three large cohort studies participating in the Cohorts for Heart and Aging Research in Genomic Epidemiology consortium—the Atherosclerosis Risk in Communities study, the Cardiovascular Health Study, and the Rotterdam Study. Copyright © 2014 John Wiley & Sons, Ltd.     

Testing departure from additivity in Tukey's model using shrinkage: application to a longitudinal setting

While there has been extensive research developing gene–environment interaction (GEI) methods in case‐control studies, little attention has been given to sparse and efficient modeling of GEI in longitudinal studies. In a two‐way table for GEI with rows and columns as categorical variables, a conventional saturated interaction model involves estimation of a specific parameter for each cell, with constraints ensuring identifiability. The estimates are unbiased but are potentially inefficient because the number of parameters to be estimated can grow quickly with increasing categories of row/column factors. On the other hand, Tukey's one‐degree‐of‐freedom model for non‐additivity treats the interaction term as a scaled product of row and column main effects. Because of the parsimonious form of interaction, the interaction estimate leads to enhanced efficiency, and the corresponding test could lead to increased power. Unfortunately, Tukey's model gives biased estimates and low power if the model is misspecified. When screening multiple GEIs where each genetic and environmental marker may exhibit a distinct interaction pattern, a robust estimator for interaction is important for GEI detection. We propose a shrinkage estimator for interaction effects that combines estimates from both Tukey's and saturated interaction models and use the corresponding Wald test for testing interaction in a longitudinal setting. The proposed estimator is robust to misspecification of interaction structure. We illustrate the proposed methods using two longitudinal studies—the Normative Aging Study and the Multi‐ethnic Study of Atherosclerosis. Copyright © 2014 John Wiley & Sons, Ltd.     

Evaluating the Calibration and Power of Three Gene‐Based Association Tests of Rare Variants for the X Chromosome

Although genome‐wide association studies (GWAS) have identified thousands of trait‐associated genetic variants, there are relatively few findings on the X chromosome. For analysis of low‐frequency variants (minor allele frequency <5%), investigators can use region‐ or gene‐based tests where multiple variants are analyzed jointly to increase power. To date, there are no gene‐based tests designed for association testing of low‐frequency variants on the X chromosome. Here we propose three gene‐based tests for the X chromosome: burden, sequence kernel association test (SKAT), and optimal unified SKAT (SKAT‐O). Using simulated case‐control and quantitative trait (QT) data, we evaluate the calibration and power of these tests as a function of (1) male:female sample size ratio; and (2) coding of haploid male genotypes for variants under X‐inactivation. For case‐control studies, all three tests are reasonably well‐calibrated for all scenarios we evaluated. As expected, power for gene‐based tests depends on the underlying genetic architecture of the genomic region analyzed. Studies with more (haploid) males are generally less powerful due to decreased number of chromosomes. Power generally is slightly greater when the coding scheme for male genotypes matches the true underlying model, but the power loss for misspecifying the (generally unknown) model is small. For QT studies, type I error and power results largely mirror those for binary traits. We demonstrate the use of these three gene‐based tests for X‐chromosome association analysis in simulated data and sequencing data from the Genetics of Type 2 Diabetes (GoT2D) study.     

Assessing effects of disease genes and gene-environment interactions: the case-spouse design and the counterfactual-control analysis

BACKGROUND: Assessing joint genetic and environmental contributions to disease risk is the central issue in many genetic epidemiological studies. To characterise the effects of a gene, the case-control study may suffer from the problem of population stratification bias. For a late onset disease, recruiting control subjects into case-parents and case-sibling studies may be difficult. METHODS: Two novel approaches to analysing case-spouse data are introduced: the 1:1 case-counterfactual-control analysis (genotype swapping between the case and their spouse) and the 1:5 case-counterfactual-controls analysis (allele swapping). RESULTS: Both can be implemented using statistical packages that allow matched analysis (the conditional logistic regression) to yield valid estimates of the genotype relative risk, the gene-environment interaction parameter, the gene-sex interaction parameter, and the gene-environment-sex three factor interaction parameter (if desired), if certain assumptions are fulfilled. CONCLUSION: Because of the ease in recruiting subjects, and in collecting and analysing data, this approach makes a convenient tool for gene characterisation.     

Exposure enriched outcome dependent designs for longitudinal studies of gene–environment interaction

Joint effects of genetic and environmental factors have been increasingly recognized in the development of many complex human diseases. Despite the popularity of case‐control and case‐only designs, longitudinal cohort studies that can capture time‐varying outcome and exposure information have long been recommended for gene–environment (G × E) interactions. To date, literature on sampling designs for longitudinal studies of G × E interaction is quite limited. We therefore consider designs that can prioritize a subsample of the existing cohort for retrospective genotyping on the basis of currently available outcome, exposure, and covariate data. In this work, we propose stratified sampling based on summaries of individual exposures and outcome trajectories and develop a full conditional likelihood approach for estimation that adjusts for the biased sample. We compare the performance of our proposed design and analysis with combinations of different sampling designs and estimation approaches via simulation. We observe that the full conditional likelihood provides improved estimates for the G × E interaction and joint exposure effects over uncorrected complete‐case analysis, and the exposure enriched outcome trajectory dependent design outperforms other designs in terms of estimation efficiency and power for detection of the G × E interaction. We also illustrate our design and analysis using data from the Normative Aging Study, an ongoing longitudinal cohort study initiated by the Veterans Administration in 1963. Copyright © 2017 John Wiley & Sons, Ltd.     

Testing gene‐environment interactions in family‐based association studies using trait‐based ascertained samples

The study of gene‐environment interactions is an increasingly important aspect of genetic epidemiological investigation. Historically, it has been difficult to study gene‐environment interactions using a family‐based design for quantitative traits or when parent‐offspring trios were incomplete. The QBAT‐I provides researchers a tool to estimate and test for a gene‐environment interaction in families of arbitrary structure that are sampled without regard to the phenotype of interest, but is vulnerable to inflated type I error if families are ascertained on the basis of the phenotype. In this study, we verified the potential for type I error of the QBAT‐I when applied to samples ascertained on a trait of interest. The magnitude of the inflation increases as the main genetic effect increases and as the ascertainment becomes more extreme. We propose an ascertainment‐corrected score test that allows the use of the QBAT‐I to test for gene‐environment interactions in ascertained samples. Our results indicate that the score test and an ad hoc method we propose can often restore the nominal type I error rate, and in cases where complete restoration is not possible, dramatically reduce the inflation of the type I error rate in ascertained samples. Copyright © 2013 John Wiley & Sons, Ltd.     

Penetrance of ATM Gene Mutations in Breast Cancer: A Meta‐Analysis of Different Measures of Risk

The gene responsible for ataxia‐telangiectasia syndrome, ATM, is also an intermediate‐risk breast cancer (BC) susceptibility gene. Numerous studies have been carried out to determine the contribution of ATM gene mutations to BC risk. Epidemiological cohorts, segregation analyses, and case‐control studies reported BC risk in different forms, including penetrance, relative risk, standardized incidence ratio, and odds ratio. Because the reported estimates vary both qualitatively and quantitatively, we developed a general model allowing the integration of the different types of cancer risk available in the literature. We performed a comprehensive meta‐analysis identifying 19 studies, and used our model to obtain a consensus estimate of BC penetrance. We estimated the cumulative risk of BC in heterozygous ATM mutation carriers to be 6.02% by 50 years of age (95% credible interval: 4.58–7.42%) and 32.83% by 80 years of age (95% credible interval: 24.55–40.43%). An accurate assessment of cancer penetrance is crucial to help mutation carriers make medical and lifestyle decisions that can reduce their chances of developing the disease.     

gsSKAT: Rapid gene set analysis and multiple testing correction for rare‐variant association studies using weighted linear kernels

Next‐generation sequencing technologies have afforded unprecedented characterization of low‐frequency and rare genetic variation. Due to low power for single‐variant testing, aggregative methods are commonly used to combine observed rare variation within a single gene. Causal variation may also aggregate across multiple genes within relevant biomolecular pathways. Kernel‐machine regression and adaptive testing methods for aggregative rare‐variant association testing have been demonstrated to be powerful approaches for pathway‐level analysis, although these methods tend to be computationally intensive at high‐variant dimensionality and require access to complete data. An additional analytical issue in scans of large pathway definition sets is multiple testing correction. Gene set definitions may exhibit substantial genic overlap, and the impact of the resultant correlation in test statistics on Type I error rate control for large agnostic gene set scans has not been fully explored. Herein, we first outline a statistical strategy for aggregative rare‐variant analysis using component gene‐level linear kernel score test summary statistics as well as derive simple estimators of the effective number of tests for family‐wise error rate control. We then conduct extensive simulation studies to characterize the behavior of our approach relative to direct application of kernel and adaptive methods under a variety of conditions. We also apply our method to two case‐control studies, respectively, evaluating rare variation in hereditary prostate cancer and schizophrenia. Finally, we provide open‐source R code for public use to facilitate easy application of our methods to existing rare‐variant analysis results.     

An Empirical Comparison of Joint and Stratified Frameworks for Studying G × E Interactions: Systolic Blood Pressure and Smoking in the CHARGE Gene‐Lifestyle Interactions Working Group

Studying gene‐environment (G × E) interactions is important, as they extend our knowledge of the genetic architecture of complex traits and may help to identify novel variants not detected via analysis of main effects alone. The main statistical framework for studying G × E interactions uses a single regression model that includes both the genetic main and G × E interaction effects (the “joint” framework). The alternative “stratified” framework combines results from genetic main‐effect analyses carried out separately within the exposed and unexposed groups. Although there have been several investigations using theory and simulation, an empirical comparison of the two frameworks is lacking. Here, we compare the two frameworks using results from genome‐wide association studies of systolic blood pressure for 3.2 million low frequency and 6.5 million common variants across 20 cohorts of European ancestry, comprising 79,731 individuals. Our cohorts have sample sizes ranging from 456 to 22,983 and include both family‐based and population‐based samples. In cohort‐specific analyses, the two frameworks provided similar inference for population‐based cohorts. The agreement was reduced for family‐based cohorts. In meta‐analyses, agreement between the two frameworks was less than that observed in cohort‐specific analyses, despite the increased sample size. In meta‐analyses, agreement depended on (1) the minor allele frequency, (2) inclusion of family‐based cohorts in meta‐analysis, and (3) filtering scheme. The stratified framework appears to approximate the joint framework well only for common variants in population‐based cohorts. We conclude that the joint framework is the preferred approach and should be used to control false positives when dealing with low‐frequency variants and/or family‐based cohorts.     

Estimation of genotype relative risks from pedigree data by retrospective likelihoods

Pedigrees collected for linkage studies are a valuable resource that could be used to estimate genetic relative risks (RRs) for genetic variants recently discovered in case‐control genome wide association studies. To estimate RRs from highly ascertained pedigrees, a pedigree “retrospective likelihood” can be used, which adjusts for ascertainment by conditioning on the phenotypes of pedigree members. We explore a variety of approaches to compute the retrospective likelihood, and illustrate a Newton‐Raphson method that is computationally efficient particularly for single nucleotide polymorphisms (SNPs) modeled as log‐additive effect of alleles on the RR. We also illustrate, by simulations, that a naïve “composite likelihood” method that can lead to biased RR estimates, mainly by not conditioning on the ascertainment process—or as we propose—the disease status of all pedigree members. Applications of the retrospective likelihood to pedigrees collected for a prostate cancer linkage study and recently reported risk‐SNPs illustrate the utility of our methods, with results showing that the RRs estimated from the highly ascertained pedigrees are consistent with odds ratios estimated in case‐control studies. We also evaluate the potential impact of residual correlations of disease risk among family members due to shared unmeasured risk factors (genetic or environmental) by allowing for a random baseline risk parameter. When modeling only the affected family members in our data, there was little evidence for heterogeneity in baseline risks across families. Genet. Epidemiol. 34: 287–298, 2010. © 2009 Wiley‐Liss, Inc.