Detecting gene-environment interactions using a case-control design

We assessed the sample size required for detecting gene-environment (G × E) interactions in a case-control study of complex diseases. The results suggest that large numbers of cases and controls will be required to detect G × E interaction for some odds ratio and exposure frequency combinations. These and other results suggest that alternative study designs may be needed to detect G × E interaction particularly with rare genes or uncommon environmental exposures. © 1997 Wiley-Liss, Inc.     

Sample size and power based on the population attributable fraction.

Most methods for calculating sample size use the relative risk (RR) to indicate the strength of the association between exposure and disease. For measuring the public health importance of a possible association, the population attributable fraction (PAF)--the proportion of disease incidence in a population that is attributable to an exposure--is more appropriate. We determined sample size and power for detecting a specified PAF in both cohort and case-control studies and compared the results with those obtained using conventional estimates based on the relative risk. When an exposure is rare, a study that has little power to detect a small RR often has adequate power to detect a small PAF. On the other hand, for common exposures, even a relatively large study may have inadequate power to detect a small PAF. These comparisons emphasize the importance of selecting the most pertinent measure of association, either relative risk or population attributable fraction, when calculating power and sample size.     

Power and sample size calculations in case-control studies of gene-environment interactions: comments on different approaches

Power and sample size considerations are critical for the design of epidemiologic studies of gene-environment interactions. Hwang et al. (Am J Epidemiol 1994;140:1029-37) and Foppa and Spiegelman (Am J Epidemiol 1997;146:596-604) have presented power and sample size calculations for case-control studies of gene-environment interactions. Comparisons of calculations using these approaches and an approach for general multivariate regression models for the odds ratio previously published by Lubin and Gail (Am J Epidemiol 1990; 131:552-66) have revealed substantial differences under some scenarios. These differences are the result of a highly restrictive characterization of the null hypothesis in Hwang et al. and Foppa and Spiegelman, which results in an underestimation of sample size and overestimation of power for the test of a gene-environment interaction. A computer program to perform sample size and power calculations to detect additive or multiplicative models of gene-environment interactions using the Lubin and Gail approach will be available free of charge in the near future from the National Cancer Institute.     

Population stratification bias in the case-only study for gene-environment interactions

The case-only study is a convenient approach and provides increased statistical efficiency in detecting gene-environment interactions. The validity of a case-only study hinges on one well-recognized assumption: The susceptibility genotypes and the environmental exposures of interest are independent in the population. Otherwise, the study will be biased. The authors show that hidden stratification in the study population could also ruin a case-only study. They derive the formulas for population stratification bias. The bias involves three terms: 1) the coefficient of variation of the exposure prevalence odds, 2) the coefficient of variation of the genotype frequency odds, and 3) the correlation coefficient between the exposure prevalence odds and the genotype frequency odds. The authors perform simulation to investigate the magnitude of bias over a wide range of realistic scenarios. It is found that the estimated interaction effect is frequently biased by more than 5%. For a rarer gene and a rarer exposure, the bias becomes even larger (>30%). Because of the potentially large bias, researchers conducting case-only studies should use the boundary formula presented in this paper to make more prudent interpretations of their results, or they should use stratified analysis or a modeling approach to adjust for population stratification bias in their studies.     

Implications of small effect sizes of individual genetic variants on the design and interpretation of genetic association studies of complex diseases

Accumulated evidence from searching for candidate gene-disease associations of complex diseases can offer some insights as the field moves toward discovery-oriented approaches with massive genome-wide testing. Meta-analyses of 50 non-human lymphocyte antigen gene-disease associations with documented overall statistical significance (752 studies) show summary odds ratios with a median of 1.43 (interquartile range, 1.28-1.65). Many different biases may operate in this field, for both single studies and meta-analyses, and these biases could invalidate some of these seemingly "validated" associations. Studies with a sample size of >500 show a median odds ratio of only 1.15. The median sample size required to detect the observed summary effects in each population addressed in the 752 studies is estimated to be 3,535 (interquartile range, 1,936-9,119 for cases and controls combined). These estimates are steeply inflated in the presence of modest bias. Population heterogeneity, as well as gene-gene and gene-environment interactions, could steeply increase these estimates and may be difficult to address even by very large biobanks and observational cohorts. The one visible solution is for a large number of teams to join forces on the same research platforms. These collaborative studies ideally should be designed up front to also assess more complex gene-gene and gene-environment interactions.     

Sample size determination for studies of gene-environment interaction.

BACKGROUND: The search for interaction effects is common in epidemiological studies, but the power of such studies is a major concern. This is a practical issue as many future studies will wish to investigate potential gene-gene and gene-environment interactions and therefore need to be planned on the basis of appropriate sample size calculations. METHODS: The underlying model considered in this paper is a simple linear regression and relating a continuous outcome to a continuously distributed exposure variable. RESULTS: The slope of the regression line is taken to be dependent on genotype, and the ratio of the slopes for each genotype is considered as the interaction parameter. Sample size is affected by the allele frequency and whether the genetic model is dominant or recessive. It is also critically dependent upon the size of the association between exposure and outcome, and the strength of the interaction term. The link between these determinants is graphically displayed to allow sample size and power to be estimated. An example of the analysis of the association between physical activity and glucose intolerance demonstrates how information from previous studies can be used to determine the sample size required to examine gene-environment interactions. CONCLUSIONS: The formulae allowing the computation of the sample size required to study the interaction between a continuous environmental exposure and a genetic factor on a continuous outcome variable should have a practical utility in assisting the design of studies of appropriate power.     

Attributable risk ratio estimation from matched-pairs case-control data

Explicit formulas are provided for estimating the attributable risk ratio among the exposed and the entire target population utilizing matched-pairs data. Large-sample standard errors and corresponding confidence intervals are provided. These estimates can be obtained from the cross-classification frequencies of matched pairs by disease and exposure status in the usual 2 X 2 table. The key to the development of these formulas lies in recognizing that attributable risk among the exposed is a direct function of the odds ratio, and population attributable risk is a direct function of the odds ratio and exposure prevalence among only the cases (assuming a rare disease). The formulas presented in this paper require only a calculator for computation. The methodology is illustrated with data from a matched-pairs case-control study of oral conjugated estrogens and endometrial cancer.     

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.     

Organisational downsizing and work stress: testing synergistic health effects in employed men and women

STUDY OBJECTIVE: To systematically study the separate and combined effects of organisational downsizing and work related stress on a measure of health in "survivors of layoffs". DESIGN: Using Rothman's approach, separate and combined effects of the two exposures in estimating the risk of poor self rated health (work related symptoms) are analysed in a large sample of male and female employees. SETTING: 0.1% cross sectional sample of the German working population. PARTICIPANTS: 12 240 men and 10 319 women, aged 16 to 59 years, surveyed in 1998-1999. MAIN RESULTS: Compared with the reference group, the group of participants who were simultaneously exposed to downsizing and work related stress (effort-reward imbalance) exhibited odds ratios (OR) of three or more work related symptoms that were by far higher (OR 4.41 in men and OR 5.37 in women) than those associated with single exposures. Altogether 21% (men) and 31% (women) of the effect size of the combined exposure was attributable to synergistic interaction. CONCLUSION: Although reduced health associated with organisational downsizing is partly attributable to an increase in work related stress these findings show an additional synergy effect produced by the combined exposure to both conditions.     

Case-parents design for gene-environment interaction

The scientific and public health implications of gene-environment interaction warrant that the most powerful study designs and methods of analysis be used. Because traditional case-control designs, which use nonrelated subjects, have demonstrated the need for large samples to detect interactions, alternative study designs may be worthwhile, such as sampling diseased cases and their parents. If the transmission of particular alleles from parents to their diseased child appears to be distorted from Mendelian expectation, then this suggests an etiologic association of the alleles with disease; if the frequency of transmission differs between exposed and nonexposed cases, then gene-environment interaction is suggested. We present likelihood-based methods to assess interaction, as well as an extension of the transmission/disequilibrium test (TDT). For these statistical tests, we also derive methods to compute sample size and power. Comparisons of sample size requirements between the case-parents design and the case-control design indicate that the case-parents design can be more powerful to detect gene-environment interactions, particularly when the disease susceptible allele is rare. Also, one of the derived likelihood methods, based on additive effects of alleles, tended to be the most robust in terms of power for a broad range of genetic mechanisms, and so may be useful for broad applications to assess gene-environment interactions.     

Potential misinterpretation of the case-only study to assess gene-environment interaction.

Novel epidemiologic study designs are often required to assess gene-environment interaction. A design using only cases, without controls, is one of several approaches that have been proposed as more efficient alternatives to the typical random sampling of cases and controls. However, it has not been pointed out that a case-only analysis estimates a different interaction parameter than does a traditional case-control analysis: The latter typically estimates departure from multiplicative population odds or rate ratios, depending on the method of control selection, while the former estimates departure from multiplicative risk ratios if genotype and environmental exposure are not associated in the population. These parameters are approximately equal if the disease risk is small at all levels of the study variables. The authors quantify the impact of allowing for higher disease risk among gene carriers, a relevant situation when the gene under study is highly penetrant. Their findings show that the cross-product ratio computed from case-only data may be substantially smaller than the odds ratio computed from case-control data and may therefore underestimate either the population odds or the rate ratio. Thus, to avoid misinterpretation of interaction parameters estimated from case-only data, the definition of multiplicative interaction should be made explicit.     

列线图法预测人群归因分值

人群归因分值（人群归因危险度百分比，PAF）是广大流行病学工作者熟悉的公共卫生学指标。PAF的计算主要根据某个危险因素对某病的相对危险度（RR）和人群中该危险因素的暴露比例（R）。文中介绍由RR和R估计PAF列线图的制作方法，以便快速简捷地估算PAF。     

Sample sizes for estimation of exposure-specific disease rates in population-based case-control studies

This paper discusses sample sizes for estimation of exposure-specific disease rates for population-based case-control studies. Neutra and Drolette's confidence limits, which are based on the approximate normality of the logarithm of the ratio of independent binomial exposure rates, are used to determine the sample sizes required for precise estimation of exposure-specific disease rates. It is shown that, for large sample sizes, the disease rate in the exposed population is more precisely estimated than the disease rate in the unexposed population when more than 50% of the cases are exposed, and that the converse is true when fewer than 50% of the cases are exposed. Expressions are derived for the optimal case and control sample sizes that ensure the required level of precision and minimize the total study size. The optimum control-to-case ratio is found to be equal to the square root of the exposure odds ratio. The optimum number of cases and the total study size are found to be smaller for precise estimation of the disease rate in the exposed population than for precise estimation of the exposure odds ratio when the disease is rare.     

弹性匹配策略在分析基因与环境交互作用中的应用

以HER-2原癌基因Ile655Val多态性、吸烟与乳腺癌之间的关联研究为例,运用大样本近似原理计算检验效能,并通过逐步提高对照组中匹配因素的比例,探索弹性匹配策略在环境与基因交互作用分析中的应用价值及其效能计算方法 .HER-2基因多态和吸烟交互作用的检验效能在非匹配的病例对照研究中为30%,应用传统的频数匹配则提高为56%,进一步增加对照组的吸烟率,则能获得更高的效能值(power=74%).结论 :与非匹配或频数匹配的病例对照研究相比,应用弹性匹配的病例对照研究,能够显著增加环境与基因交互作用的检验效能和研究效率,此匹配策略尤其适用于人群中环境暴露率较低、环境暴露与基因易感性呈负向关联或匹配对照例数较少等情况.在研究设计时可充分权衡检验效能的提高与匹配成本的增加,从而选择最佳的匹配策略.     

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.     

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.     

Cancers in Australia in 2010 attributable to tobacco smoke

Objectives: To estimate the population attributable fraction (PAF) and numbers of cancers occurring in Australia in 2010 attributable to tobacco smoking, both personal and by a partner. Methods: We used a modified Peto‐Lopez approach to calculate the difference between the number of lung cancer cases observed and the number expected assuming the entire population developed lung cancer at the same rate as never smokers. For cancers other than lung, we applied the standard PAF formula using relative risks from a large cohort and derived notional smoking prevalence. To estimate the PAF for partners' smoking, we used the standard formula incorporating the proportion of non‐smoking Australians living with an ever‐smoking partner and relative risks associated with partner smoking. Results: An estimated 15,525 (13%) cancers in Australia in 2010 were attributable to tobacco smoke, including 8,324 (81%) lung, 1,973 (59%) oral cavity and pharynx, 855 (60%) oesophagus and 951 (6%) colorectal cancers. Of these, 136 lung cancers in non‐smokers were attributable to partner tobacco smoke. Conclusions: More than one in eight cancers in Australia is attributable to tobacco smoking and would be avoided if nobody smoked. Implications: Strategies to reduce the prevalence of smoking remain a high priority for cancer control.     

Cancers in Australia in 2010 attributable to modifiable factors: introduction and overview

Objective: To describe the approach underpinning a national project to estimate the numbers and proportions of cancers occurring in Australia in 2010 that are attributable to modifiable causal factors. Methods: We estimated the population attributable fraction (PAF) (or prevented fraction) of cancers associated with exposure to causal (or preventive) factors using standard formulae. Where possible, we also estimated the potential impact on cancer incidence resulting from changes in prevalence of exposure. Analyses were restricted to factors declared causal by international agencies: tobacco smoke; alcohol; solar radiation; infectious agents; obesity; insufficient physical activity; insufficient intakes of fruits, vegetables and fibre; red and processed meat; menopausal hormone therapy (MHT); oral contraceptive pill (OCP); and insufficient breast feeding. Separately, we estimated numbers of cancers prevented by: aspirin; sunscreen; MHT; and OCP use. We discuss assumptions pertaining to latent periods between exposure and cancer onset, choices of prevalence data and risk estimates, and approaches to sensitivity analyses. Results: Numbers and population attributable fractions of cancer are presented in accompanying papers. Conclusions: This is the first systematic assessment of population attributable fractions of cancer in Australia.     

Selection bias in the assessment of gene-environment interaction in case-control studies

Selection bias is a common concern in epidemiologic studies, particularly case-control studies. Selection bias in the odds ratio occurs when participation depends jointly on exposure and disease status. General results for understanding when selection bias may affect studies involving gene-environment interactions have not yet been developed. In this paper, the authors show that the assessment of gene-environment interactions will not be subject to selection bias under the assumption that genotype does not influence participation conditional on exposure and disease status. This is true even when selection, including self-selection of subjects, is jointly influenced by exposure and disease and regardless of whether the genotype is related to exposure, disease, or both. The authors present an example to illustrate this concept.     

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.