A maximum likelihood method for studying gene-environment interactions under conditional independence of genotype and exposure

Given the biomedical interest in gene-environment interactions along with the difficulties inherent in gathering genetic data from controls, epidemiologists need methodologies that can increase precision of estimating interactions while minimizing the genotyping of controls. To achieve this purpose, many epidemiologists suggested that one can use case-only design. In this paper, we present a maximum likelihood method for making inference about gene-environment interactions using case-only data. The probability of disease development is described by a logistic risk model. Thus the interactions are model parameters measuring the departure of joint effects of exposure and genotype from multiplicative odds ratios. We extend the typical inference method derived under the assumption of independence between genotype and exposure to that under a more general assumption of conditional independence. Our maximum likelihood method can be applied to analyse both categorical and continuous environmental factors, and generalized to make inference about gene-gene-environment interactions. Moreover, the application of this method can be reduced to simply fitting a multinomial logistic model when we have case-only data. As a consequence, the maximum likelihood estimates of interactions and likelihood ratio tests for hypotheses concerning interactions can be easily computed. The methodology is illustrated through an example based on a study about the joint effects of XRCC1 polymorphisms and smoking on bladder cancer. We also give two simulation studies to show that the proposed method is reliable in finite sample situation.     

Semiparametric Bayesian modeling of random genetic effects in family-based association studies

We consider the inference problem of estimating covariate and genetic effects in a family-based case-control study where families are ascertained on the basis of the number of cases within the family. However, our interest lies not only in estimating the fixed covariate effects but also in estimating the random effects parameters that account for varying correlations among family members. These random effects parameters, though weakly identifiable in a strict theoretical sense, are often hard to estimate due to the small number of observations per family. A hierarchical Bayesian paradigm is a very natural route in this context with multiple advantages compared with a classical mixed effects estimation strategy based on the integrated likelihood. We propose a fully flexible Bayesian approach allowing nonparametric modeling of the random effects distribution using a Dirichlet process prior and provide estimation of both fixed effect and random effects parameters using a Markov chain Monte Carlo numerical integration scheme. The nonparametric Bayesian approach not only provides inference that is less sensitive to parametric specification of the random effects distribution but also allows possible uncertainty around a specific genetic correlation structure. The Bayesian approach has certain computational advantages over its mixed-model counterparts. Data from the Prostate Cancer Genetics Project, a family-based study at the University of Michigan Comprehensive Cancer Center including families having one or more members with prostate cancer, are used to illustrate the proposed methods. A small-scale simulation study is carried out to compare the proposed nonparametric Bayes methodology with a parametric Bayesian alternative.     

Tests for gene-environment interaction from case-control data: a novel study of type I error, power and designs

To evaluate the risk of a disease associated with the joint effects of genetic susceptibility and environmental exposures, epidemiologic researchers often test for non-multiplicative gene-environment effects from case-control studies. In this article, we present a comparative study of four alternative tests for interactions: (i) the standard case-control method; (ii) the case-only method, which requires an assumption of gene-environment independence for the underlying population; (iii) a two-step method that decides between the case-only and case-control estimators depending on a statistical test for the gene-environment independence assumption and (iv) a novel empirical-Bayes (EB) method that combines the case-control and case-only estimators depending on the sample size and strength of the gene-environment association in the data. We evaluate the methods in terms of integrated Type I error and power, averaged with respect to varying scenarios for gene-environment association that are likely to appear in practice. These unique studies suggest that the novel EB procedure overall is a promising approach for detection of gene-environment interactions from case-control studies. In particular, the EB procedure, unlike the case-only or two-step methods, can closely maintain a desired Type I error under realistic scenarios of gene-environment dependence and yet can be substantially more powerful than the traditional case-control analysis when the gene-environment independence assumption is satisfied, exactly or approximately. Our studies also reveal potential utility of some non-traditional case-control designs that samples controls at a smaller rate than the cases. Apart from the simulation studies, we also illustrate the different methods by analyzing interactions of two commonly studied genes, N-acetyl transferase type 2 and glutathione s-transferase M1, with smoking and dietary exposures, in a large case-control study of colorectal cancer.     

Using ancestry matching to combine family‐based and unrelated samples for genome‐wide association studies

We propose a method to analyze family‐based samples together with unrelated cases and controls. The method builds on the idea of matched case–control analysis using conditional logistic regression (CLR). For each trio within the family, a case (the proband) and matched pseudo‐controls are constructed, based upon the transmitted and untransmitted alleles. Unrelated controls, matched by genetic ancestry, supplement the sample of pseudo‐controls; likewise unrelated cases are also paired with genetically matched controls. Within each matched stratum, the case genotype is contrasted with control/pseudo‐control genotypes via CLR, using a method we call matched‐CLR (mCLR). Eigenanalysis of numerous SNP genotypes provides a tool for mapping genetic ancestry. The result of such an analysis can be thought of as a multidimensional map, or eigenmap, in which the relative genetic similarities and differences amongst individuals is encoded in the map. Once constructed, new individuals can be projected onto the ancestry map based on their genotypes. Successful differentiation of individuals of distinct ancestry depends on having a diverse, yet representative sample from which to construct the ancestry map. Once samples are well‐matched, mCLR yields comparable power to competing methods while ensuring excellent control over Type I error. Copyright © 2010 John Wiley & Sons, Ltd.     

Accounting for haplotype uncertainty in matched association studies: a comparison of simple and flexible techniques

Population-based case-control studies measuring associations between haplotypes of single nucleotide polymorphisms (SNPs) are increasingly popular, in part because haplotypes of a few "tagging" SNPs may serve as surrogates for variation in relatively large sections of the genome. Due to current technological limitations, haplotypes in cases and controls must be inferred from unphased genotypic data. Using individual-specific inferred haplotypes as covariates in standard epidemiologic analyses (e.g., conditional logistic regression) is an attractive analysis strategy, as it allows adjustment for nongenetic covariates, provides omnibus and haplotype-specific tests of association, and can estimate haplotype and haplotype x environment interaction effects. In principle, some adjustment for the uncertainty in inferred haplotypes should be made. Via simulation, we compare the performance (bias and mean squared error of haplotype and haplotype x environment interaction effect estimates) of several analytic strategies using inferred haplotypes in the context of matched case-control data. These strategies include using only the most likely haplotype assignment, the expectation substitution approach described by Stram et al. ([2003b] Hum. Hered. 55:179-190) and others, and an improper version of multiple imputation. For relatively uncomplicated haplotype structures and moderate haplotype relative risks (/=5). An application to progesterone-receptor haplotypes and endometrial cancer further illustrates that the performance of all these methods depends on how well the observed haplotypes "tag" the unobserved causal variant.     

Case/pseudocontrol analysis in genetic association studies: A unified framework for detection of genotype and haplotype associations, gene-gene and gene-environment interactions, and parent-of-origin effects

Estimation and testing of genetic effects (genotype relative risks) are often performed conditionally on parental genotypes, using data from case-parent trios. This strategy avoids having to estimate nuisance parameters such as parental mating type frequencies, and also avoids generating spurious results due to confounding causes of association such as population stratification. For effects at a single locus, the resulting analysis is equivalent to matched case/control analysis via conditional logistic regression, using the case and three "pseudocontrols" derived from the untransmitted parental alleles. We previously showed that a similar approach can be used for analyzing genotype and haplotype effects at a set of closely linked loci, but with a required adjustment to the conditioning argument that results in varying numbers of pseudocontrols, depending on the disease model that is to be fitted. Here we extend this method to include the analysis of epistatic effects (gene-gene interactions) at unlinked loci, to include parent-of-origin effects at one or more loci, and to allow additional incorporation of gene-environment interactions. The conditional logistic approach provides a natural and flexible framework for incorporating these additional effects. By relaxing the conditioning on parental genotypes to allow exchangeability of parental genotypes, we show how the power of this approach can be increased when studying parent-of-origin effects. Simulations suggest that there is limited power to distinguish between parent-of-origin effects and effects due to interaction between genotypes of mother and child.     

Validity and power of association testing in family-based sampling designs: evidence for and against the common wisdom

Current common wisdom posits that association analyses using family‐based designs have inflated type 1 error rates (if relationships are ignored) and independent controls are more powerful than familial controls. We explore these suppositions. We show theoretically that family‐based designs can have deflated type‐error rates. Through simulation, we examine the validity and power of family designs for several scenarios: cases from randomly or selectively ascertained pedigrees; and familial or independent controls. Family structures considered are as follows: sibships, nuclear families, moderate‐sized and extended pedigrees. Three methods were considered with the χ² test for trend: variance correction (VC), weighted (weights assigned to account for genetic similarity), and naïve (ignoring relatedness) as well as the Modified Quasi‐likelihood Score (MQLS) test. Selectively ascertained pedigrees had similar levels of disease enrichment; random ascertainment had no such restriction. Data for 1,000 cases and 1,000 controls were created under the null and alternate models. The VC and MQLS methods were always valid. The naïve method was anti‐conservative if independent controls were used and valid or conservative in designs with familial controls. The weighted association method was generally valid for independent controls, and was conservative for familial controls. With regard to power, independent controls were more powerful for small‐to‐moderate selectively ascertained pedigrees, but familial and independent controls were equivalent in the extended pedigrees and familial controls were consistently more powerful for all randomly ascertained pedigrees. These results suggest a more complex situation than previously assumed, which has important implications for study design and analysis. Genet. Epidemiol. 35:174‐181, 2011. © 2011 Wiley‐Liss, Inc.     

A simulation-based comparison of techniques to correct for measurement error in matched case-control studies

The presence of measurement errors affecting the covariates in regression models is a relevant topic in many scientific areas, as, for example, in epidemiology. An example is given by an epidemiological population-based matched case-control study on the aetiology of childhood malignancies, which is currently under completion in Italy. This study was aimed at evaluating the effects of childhood exposure to extremely low electromagnetic fields on the risk of disease occurrence by taking into account the possibility of erroneous measures of the exposure. Within this framework, we focus on the application of likelihood methods to correct for measurement error. This approach, which has received less attention in literature with respect to alternatives, is compared with commonly used methods such as regression calibration and SIMEX. The comparison is performed by simulation, under a broad range of measurement error structures.     

Maximum likelihood estimation of haplotype effects and haplotype-environment interactions in association studies

The associations between haplotypes and disease phenotypes offer valuable clues about the genetic determinants of complex diseases. It is highly challenging to make statistical inferences about these associations because of the unknown gametic phase in genotype data. We describe a general likelihood-based approach to inferring haplotype-disease associations in studies of unrelated individuals. We consider all possible phenotypes (including disease indicator, quantitative trait, and potentially censored age at onset of disease) and all commonly used study designs (including cross-sectional, case-control, cohort, nested case-control, and case-cohort). The effects of haplotypes on phenotype are characterized by appropriate regression models, which allow various genetic mechanisms and gene-environment interactions. We present the likelihood functions for all study designs and disease phenotypes under Hardy-Weinberg disequilibrium. The corresponding maximum likelihood estimators are approximately unbiased, normally distributed, and statistically efficient. We provide simple and efficient numerical algorithms to calculate the maximum likelihood estimators and their variances, and implement these algorithms in a freely available computer program. Extensive simulation studies demonstrate that the proposed methods perform well in realistic situations. An application to the Carolina Breast Cancer Study reveals significant haplotype effects and haplotype-smoking interactions in the development of breast cancer.     

Cleft palate, transforming growth factor alpha gene variants, and maternal exposures: assessing gene-environment interactions in case-parent triads

We have previously reported a threefold risk of cleft palate only (CPO) among children homozygous for the less common allele A2 at the TaqI marker site of the transforming growth factor alpha gene (TGFA) (Jugessur et al. [2003a] Genet. Epidemiol. 24:230-239). Here we assess possible interaction between the child's TGFA TaqI A2A2 genotype and maternal cigarette smoking, alcohol consumption, use of multivitamins and folic acid. This was done by comparing the strength of genetic associations between strata of exposed and unexposed case-parent triads. We also looked for possible gene-gene interaction with the polymorphic variant C677T of the folic acid-metabolizing gene MTHFR. We analyzed a total of 88 complete CPO triads selected from a population-based study of orofacial clefts in Norway (May 1996-1998). No evidence of interaction was observed with either smoking or alcohol use. The risk associated with two copies of the A2 allele at TGFA TaqI was strong among children whose mothers did not use folic acid (relative risk=4.5, 95% confidence interval=1.3-15.7), and was only marginal among children whose mothers reported using folic acid (RR=1.4, 95% CI=0.2-12.7). Although the interaction between the child's genotypes at TGFA TaqI and MTHFR-C677T was not statistically significant, the effect of the TGFA TaqI A2A2 genotype appeared to be stronger among children with either one or two copies of the T-allele at C677T (RR=4.0, 95% CI=1.1-13.9) compared to children homozygous for the C-allele (RR=1.7, 95% CI=0.2-15.7). In conclusion, we find little evidence of interaction between the child's genotypes at TGFA TaqI and various exposures for cleft palate, with the possible exception of folic acid intake.     

Tests of trait-haplotype association when linkage phase is ambiguous, appropriate for matched case-control and cohort studies with competing risks

The impact of competing risks on tests of association between disease and haplotypes has been largely ignored. We consider situations in which linkage phase is ambiguous and show that tests for disease-haplotype association can lead to rejection of the null hypothesis, even when true, with more than the nominal 5 per cent frequency. This problem tends to occur if a haplotype is associated with overall mortality, even if the haplotype is not associated with disease risk. A small simulation study illustrates the magnitude of bias (high type I error rate) in the context of a cohort study in which a modest number of disease cases (about 350) occur over time. The bias remains even if the score test is based on a logistic model that includes age as a covariate. For cohort studies, we propose a new test based on a modification of the proportional hazards model and for case-control studies, a test based on a conditional likelihood that have the correct size under the null even in the presence of competing risks, and that can be used when haplotype is ambiguous.