不完全病例对照研究基因环境交互作用的估计

目的 介绍不完全病例对照研究中基因与环境交互作用的估计方法.方法 分别导出了logistic模型、对数线性模型在传统病例对照研究、单纯病例研究、不完全病例对照研究中主效应以及基因与环境交互作用效应的极大似然估计,并通过实例分析其应用价值.结果 在传统病例对照研究中,当数据未缺失时,logistic模型与对数线性模型的结果是等价的.当无对照时,单纯病例研究的logistic模型可以估计基因与环境的交互作用.当对照组基因信息缺失但环境信息齐全时,用传统病例对照研究的logistic模型无法得到交互作用的估计;用单纯病例研究的logistic模型可以估计交互作用,但由于没有充分利用环境的信息,故得不到环境主效应的估计;不完全病例对照研究的对数线性模型,可同时得到交互作用和环境主效应的估计.结论 不完全病例对照研究采用对数线性模型既可充分利用对照的环境暴露信息,估计环境的主效应,又可估计基因与环境的交互作用.当基因与环境暴露独立时,其估计值与完全数据是等价的.     

Exploiting gene-environment independence in family-based case-control studies: increased power for detecting associations, interactions and joint effects

Family-based case-control studies are popularly used to study the effect of genes and gene-environment interactions in the etiology of rare complex diseases. We consider methods for the analysis of such studies under the assumption that genetic susceptibility (G) and environmental exposures (E) are independently distributed of each other within families in the source population. Conditional logistic regression, the traditional method of analysis of the data, fails to exploit the independence assumption and hence can be inefficient. Alternatively, one can estimate the multiplicative interaction between G and E more efficiently using cases only, but the required population-based G-E independence assumption is very stringent. In this article, we propose a novel conditional likelihood framework for exploiting the within-family G-E independence assumption. This approach leads to a simple and yet highly efficient method of estimating interaction and various other risk parameters of scientific interest. Moreover, we show that the same paradigm also leads to a number of alternative and even more efficient methods for analysis of family-based case-control studies when parental genotype information is available on the case-control study participants. Based on these methods, we evaluate different family-based study designs by examining their relative efficiencies to each other and their efficiencies compared to a population-based case-control design of unrelated subjects. These comparisons reveal important design implications. Extensions of the methodologies for dealing with complex family studies are also discussed.     

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.     

A sibling-augmented case-only approach for assessing multiplicative gene-environment interactions

Family-based designs protect analyses of genetic effects from bias that is due to population stratification. Investigators have assumed that this robustness extends to assessments of gene-environment interaction. Unfortunately, this assumption fails for the common scenario in which the genotyped variant is related to risk through linkage with a causative allele. Bias also plagues other methods of assessment of gene-environment interaction. When testing against multiplicative joint effects, the case-only design offers excellent power, but it is invalid if genotype and exposure are correlated in the population. The authors describe 4 mechanisms that produce genotype-exposure dependence: exposure-related genetic population stratification, effects of family history on behavior, genotype effects on exposure, and selective attrition. They propose a sibling-augmented case-only (SACO) design that protects against the former 2 mechanisms and is therefore valid for studying young-onset disease in which genotype does not influence exposure. A SACO design allows the ascertainment of genotype and exposure for cases and exposure for 1 or more unaffected siblings selected randomly. Conditional logistic regression permits assessment of exposure effects and gene-environment interactions. Via simulations, the authors compare the likelihood-based inference on interactions using the SACO design with that based on other designs. They also show that robust analyses of interactions using tetrads or disease-discordant sibling pairs are equivalent to analyses using the SACO design.     

Robust discovery of genetic associations incorporating gene-environment interaction and independence

This article considers the detection and evaluation of genetic effects incorporating gene-environment interaction and independence. Whereas ordinary logistic regression cannot exploit the assumption of gene-environment independence, the proposed approach makes explicit use of the independence assumption to improve estimation efficiency. This method, which uses both cases and controls, fits a constrained retrospective regression in which the genetic variant plays the role of the response variable, and the disease indicator and the environmental exposure are the independent variables. The regression model constrains the association of the environmental exposure with the genetic variant among the controls to be null, thus explicitly encoding the gene-environment independence assumption, which yields substantial gain in accuracy in the evaluation of genetic effects. The proposed retrospective regression approach has several advantages. It is easy to implement with standard software, and it readily accounts for multiple environmental exposures of a polytomous or of a continuous nature, while easily incorporating extraneous covariates. Unlike the profile likelihood approach of Chatterjee and Carroll (Biometrika. 2005;92:399-418), the proposed method does not require a model for the association of a polytomous or continuous exposure with the disease outcome, and, therefore, it is agnostic to the functional form of such a model and completely robust to its possible misspecification.     

Bayesian inference of gene–environment interaction from incomplete data: What happens when information on environment is disjoint from data on gene and disease?

Inference in gene-environment studies can sometimes exploit the assumption of mendelian randomization that genotype and environmental exposure are independent in the population under study. Moreover, in some such problems it is reasonable to assume that the disease risk for subjects without environmental exposure will not vary with genotype. When both assumptions can be invoked, we consider the prospects for inferring the dependence of disease risk on genotype and environmental exposure (and particularly the extent of any gene-environment interaction), without detailed data on environmental exposure. The data structure envisioned involves data on disease and genotype jointly, but only external information about the distribution of the environmental exposure in the population. This is relevant as for many environmental exposures individual-level measurements are costly and/or highly error-prone. Working in the setting where all relevant variables are binary, we examine the extent to which such data are informative about the interaction, via determination of the large-sample limit of the posterior distribution. The ideas are illustrated using data from a case-control study for bladder cancer involving smoking behaviour and the NAT2 genotype.     

Ascertainment bias in family-based case-control studies

In a family-matched case-control study, a population-based sample of cases is selected from a well-defined geographic region over a fixed period of time. For diseases of adult onset, the control is generally a sibling or cousin who is matched on sex and age without regard to location of residence. Such a design can lead to biased estimates of environmental relative risk if the prevalence of an environmental risk factor varies by the geographic region from which the cases and controls are drawn. However, assuming the independence of genotype and environmental exposure, the estimators for the gene and gene-environment interaction effects are consistent. This suggests that we must use caution in interpreting parameters that estimate environmental main effects from a family-based case-control study if controls are selected from outside the case-ascertainment region.     

Analysis of proportionate mortality data using logistic regression models

When only proportionate mortality data are available to an investigator studying the effect of an exposure on a particular cause of death, controls must be selected from among persons dying of other causes believed to be uninfluenced by the exposure under study. When qualitative or quantitative estimates of exposure history can be obtained for the deceased individuals, it is shown that one can use logistic regression models for the mortality odds to efficiently estimate the effect of exposure while controlling for relevant confounding factors by incorporating a priori information on baseline mortality rates available from US life tables. The proposed method is used to reanalyze data from a cohort of arsenic-exposed workers in a Montana copper smelter.     

Commentary: facing the challenge of gene-environment interaction: the two-by-four table and beyond

As a result of the Human Genome Project, epidemiologists can study thousands of genes and their interaction with the environment. The challenge is how to best present and analyze such studies of multiple genetic and environmental factors. The authors suggest emphasizing the fundamental core of gene-environment interaction-the separate assessment of the effects of individual and joint risk factors. In the simple analysis of one genotype and an exposure (both dichotomous), such study can be summarized in a two-by-four table. The advantages of such a table for data presentation and analysis are many: The table displays the data efficiently and highlights sample size issues; it allows for evaluation of the independent and joint roles of genotype and exposure on disease risk; and it emphasizes effect estimation over model testing. Researchers can easily estimate relative risks and attributable fractions and test different models of interaction. The two-by-four table is a useful tool for presenting, analyzing, and synthesizing data on gene-environment interaction. To highlight the role of gene-environment interaction in disease causation, the authors propose that the two-by-four table is the fundamental unit of epidemiologic analysis.     

Imputing gene-treatment interactions when the genotype distribution is unknown using case-only and putative placebo analyses--a new method for the Genetics of Hypertension Associated Treatment (GenHAT) study

There is a sizeable literature on methods for detecting gene-environment interaction in the framework of case-control studies, particularly with reference to the assumption of independence of genotype and exposure. In the context of a clinical trial, wherein gene-drug interactions with regard to outcomes are examined, these methods may be readily applied, as gene and drug are independent by randomization. In an active-controlled trial (experimental treatment vs standard) that has collected genotype information, gene-drug interactions can be estimated. In addition, the effect of the experimental treatment vs placebo can be imputed by using data from a historical placebo-controlled trial (standard vs placebo) if either (a) genotype information is available from the historical trial or (b) assumptions are made about the prevalence of genotype and the odds ratios of genotype and disease in the historical trial using information from other studies. Motivation for these procedures is provided by the Genetics of Hypertension Associated Treatment, a large pharmacogenetics, ancillary study of a hypertension clinical trial, and examples from published hypertension trials will be used to illustrate the methods.     

Stratified case sampling and the use of family controls

We compare the asymptotic relative efficiency (ARE) of different study designs for estimating gene and gene-environment interaction effects using matched case-control data. In the sampling schemes considered, cases are selected differentially based on their family history of disease. Controls are selected either from unrelated subjects or from among the case's unaffected siblings and cousins. Parameters are estimated using weighted conditional logistic regression, where the likelihood contributions for each subject are weighted by the fraction of cases sampled sharing the same family history. Results showed that compared to random sampling, over-sampling cases with a positive family history increased the efficiency for estimating the main effect of a gene for sib-control designs (103-254% ARE) and decreased efficiency for cousin-control and population-control designs (68-94% ARE and 67-84% ARE, respectively). Population controls and random sampling of cases were most efficient for a recessive gene or a dominant gene with an relative risk less than 9. For estimating gene-environment interactions, over-sampling positive-family-history cases again led to increased efficiency using sib controls (111-180% ARE) and decreased efficiency using population controls (68-87% ARE). Using case-cousin pairs, the results differed based on the genetic model and the size of the interaction effect; biased sampling was only slightly more efficient than random sampling for large interaction effects under a dominant gene model (relative risk ratio = 8, 106% ARE). Overall, the most efficient study design for studying gene-environment interaction was the case-sib-control design with over-sampling of positive-family-history-cases.     

Efficient Generalized Least Squares Method for Mixed Population and Family‐based Samples in Genome‐wide Association Studies

Genome‐wide association studies (GWAS) that draw samples from multiple studies with a mixture of relationship structures are becoming more common. Analytical methods exist for using mixed‐sample data, but few methods have been proposed for the analysis of genotype‐by‐environment (G×E) interactions. Using GWAS data from a study of sarcoidosis susceptibility genes in related and unrelated African Americans, we explored the current analytic options for genotype association testing in studies using both unrelated and family‐based designs. We propose a novel method—generalized least squares (GLX)—to estimate both SNP and G×E interaction effects for categorical environmental covariates and compared this method to generalized estimating equations (GEE), logistic regression, the Cochran–Armitage trend test, and the W_QLS and M_QLS methods. We used simulation to demonstrate that the GLX method reduces type I error under a variety of pedigree structures. We also demonstrate its superior power to detect SNP effects while offering computational advantages and comparable power to detect G×E interactions versus GEE. Using this method, we found two novel SNPs that demonstrate a significant genome‐wide interaction with insecticide exposure—rs10499003 and rs7745248, located in the intronic and 3' UTR regions of the FUT9 gene on chromosome 6q16.1.     

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.     

An insight on the use of multiple logistic regression analysis to estimate association between risk factor and disease occurrence

Multiple logistic regression is an accepted statistical method for assessing association between an anticedant characteristic (risk factor) and a quantal outcome (probability of disease occurrence), statistically adjusting for potential confounding effects of other covariates. Yet the method has potential drawbacks which are not generally recognized. This article considers one important drawback of logistic regression. Specifically the so-called main effect logistic model assumes that the probability of developing disease is linearly and additively related to the risk factors on the logistic scale. This assumption stipulates that for each risk factor, the odds ratio is constant over all reference exposure levels, and that the odds ratio exposed to two or more factors is equal to the product of individual risk factor odds ratios. If the observed odds ratios in the data follow this pattern, the model-predicted odds ratios will be accurate, and the meaning of the odds ratio for each risk factor will be straightforward. But if the observed odds ratios deviate from the model assumption, the model will not fit the data accurately, and the model-predicted odds ratios will not reflect those in the data. Although satisfactory fit can always be achieved by adding to the model polynomial and product terms derived from the original risk factors, the odds ratios estimated by such an interaction logistic model are difficult to interpret, viz., the odds ratio for each risk factor depends not only on the reference exposure levels of that factor, but also on the exposure level in other factors.(ABSTRACT TRUNCATED AT 250 WORDS)     

Measurement error in epidemiology: the design of validation studies I: univariate situation.

It is becoming standard practice in epidemiology to adjust relative risk estimates to remove the bias caused by non-differential errors in the exposure measurement. Estimation of the correction factor is often based on a validation study incorporating repeated measures of exposure, which are assumed to be independent. This assumption is difficult to verify and often likely to be false. We examine the effect of departures from this assumption on the correction factor estimate, and explore the design of validation studies using two or even three different types of measurement of exposure, where assumption of independence between the measures may be more realistic. The value of good biomarker measures of exposure is demonstrated even if they are feasible to use only in a validation study.     

Non-hierarchical logistic models and case-only designs for assessing susceptibility in population-based case-control studies

This article describes how genetic components of disease susceptibility can be evaluated in case-control studies, where cases and controls are sampled independently from the population at large. Subjects are assumed unrelated, in contrast to studies of familial aggregation and linkage. The logistic model can be used to test collapsibility over phenotypes or genotypes, and to estimate interactions between environmental and genetic factors. Such interactions provide an example of a context where non-hierarchical models make sense biologically. Also, if the exposure and genetic categories occur independently and the disease is rare, then analyses based only on cases are valid, and offer better precision for estimating gene-environment interactions than those based on the full data.     

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.     

Further development of the case-only design for assessing gene-environment interaction: evaluation of and adjustment for bias

BACKGROUND: The case-only study for investigating gene-environment interactions provides increased statistical efficiency over case-control analyses. This design has been criticized for being susceptible to bias arising from non-independence between the genetic and environmental factors in the population. Given that independence is critical to the validity of case-only estimates of interaction, researchers frequently use controls to evaluate whether the independence assumption is tenable, as advised in the literature. Our work investigates to what extent this approach is appropriate and how non-independence can be accounted for in case-only analyses. METHODS: We provide a formula in epidemiological terms that illustrates the relationship between the gene-environment association measured among controls and the gene-environment association in the source population. Using this formula, we conducted sensitivity analyses to describe the circumstances in which controls can be used as proxy for the source population when evaluating gene-environment independence. Lastly, we generated hypothetical cohort data to examine whether multivariable modelling approaches can be used to control for non-independence. RESULTS: Our sensitivity analyses show that controls should not be used to evaluate gene-environment independence in the population, even when the baseline risk of disease is low (i.e. 1%), and the interaction and independent effects are moderate (i.e. risk ratio = 2). When the factors are associated, it is possible to remove bias arising from non-independence using standard statistical multivariable techniques in case-only analyses. CONCLUSIONS: Even when the disease risk is low, evaluation of gene-environment independence in controls does not provide a consistent test for bias in the case-only study. Given that control for non-independence is possible when the source of the non-independence can be conceptualized, the case-only design may still be a useful epidemiological tool for examining gene-environment interactions.     

Case-only design to measure gene-gene interaction

The case-only design is an efficient and valid approach to screening for gene-environment interaction under the assumption of the independence between exposure and genotype in the population. In this paper, we show that the case-only design is also a valid and efficient approach to measuring gene-gene interaction under the assumption that the frequencies of genes are independent in the population. Just as the case-only design requires fewer cases than the case-control design to measure gene-environment interaction, it also requires fewer cases to measure gene-gene interactions.     

A general approach to detect gene (G)-environment (E) additive interaction leveraging G-E independence in case-control studies

It is increasingly of interest in statistical genetics to test for the presence of an additive interaction between genetic (G) and environmental (E) risk factors. In case-control studies involving a rare disease, a statistical test of no additive G×E interaction typically entails a test of no relative excess risk due to interaction (RERI). It has been shown that a likelihood ratio test of a null RERI incorporating the G-E independence assumption (RERI-LRT) outperforms the standard approach. The RERI-LRT relies on correct specification of a logistic model for the binary outcome, as a function of G, E, and auxiliary covariates. However, when at least one exposure is not categorical or auxiliary covariates are present, nonparametric estimation may not be feasible, while parametric logistic regression will a priori rule out the null hypothesis of no additive interaction in most practical situations, inflating type I error rate. In this paper, we present a general approach to test for G × E additive interaction exploiting G-E independence. Unlike the RERI-LRT, it allows the regression model for the binary outcome to remain unrestricted, and nonetheless still allows for covariate adjustment in order to ensure the G-E independence assumption or to rule out residual confounding. The methods are illustrated through extensive simulation studies and an ovarian cancer study.