The use of common genetic polymorphisms to enhance the epidemiologic study of environmental carcinogens

Overwhelming evidence indicates that environmental exposures, broadly defined, are responsible for most cancer. There is reason to believe, however, that relatively common polymorphisms in a wide spectrum of genes may modify the effect of these exposures. We discuss the rationale for using common polymorphisms to enhance our understanding of how environmental exposures cause cancer and comment on epidemiologic strategies to assess these effects, including study design, genetic and statistical analysis, and sample size requirements. Special attention is given to sources of potential bias in population studies of gene--environment interactions, including exposure and genotype misclassification and population stratification (i.e., confounding by ethnicity). Nevertheless, by merging epidemiologic and molecular approaches in the twenty-first century, there will be enormous opportunities for unraveling the environmental determinants of cancer. In particular, studies of genetically susceptible subgroups may enable the detection of low levels of risk due to certain common exposures that have eluded traditional epidemiologic methods. Further, by identifying susceptibility genes and their pathways of action, it may be possible to identify previously unsuspected carcinogens. Finally, by gaining a more comprehensive understanding of environmental and genetic risk factors, there should emerge new clinical and public health strategies aimed at preventing and controlling cancer.     

Analytical Relationship between Family History and Genetic and Environmental risks,with Application to Female Breast Cancer

It is well established in genetic epidemiology that family history is an important indicator of familial aggregation of disease in a family. A strong genetic risk factor or an environmental risk factor with high familial correlation can result in a strong family history. In this paper, family history refers to the number of first‐degree relatives affected with the disease. Cui and Hopper (Journal of Epidemiology and Biostatistics 2001; 6 : 331–342) proposed an analytical relationship between family history and relevant genetic parameters. In this paper we expand the relationship to both genetic and environmental risk factors. We established a closed‐form formula for family history as a function of genetic and environmental parameters which include genetic and environmental relative risks, genotype frequency, prevalence and familial correlation of the environmental risk factor. The relationship is illustrated by an example of female breast cancer in Australia. For genetic and environmental relative risks less than 10, most of the female breast cancer cases occur between the age of 40 and 60 years. A higher genetic or environmental relative risk will move the peak of the distribution to a younger age. A more common disease allele or more prevalent environmental risk factor will move the peak to an older age. For a proband with breast cancer, it is most likely (with probability ≥80%) that none of her first‐degree relatives is affected with the disease. To enable the probability of having a positive family history to reach 50%, the environmental relative risks must be extremely as high as 100, the familial correlation as high as 0.8 and the prevalence as low as 0.1. For genetic risk alone, even the relative risk is as high as 100, the probability of having a positive family history can only reach about 30%. This suggests that the environmental risk factor seems to play a more important role in determining a strong family history than the genetic risk factor. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Genetic factors affecting HDL levels, structure, metabolism and function

PURPOSE OF REVIEW: HDL is a recognized negative risk factor for the cardiovascular diseases. Establishing the genetic determinants of HDL concentration and functions would add to the prediction of cardiovascular risk and point to the biochemical mechanisms underlying this risk. The present review focuses on various approaches to establish genetic determinants of the HDL concentration, structure and function. RECENT FINDINGS: While many genes contribute to the HDL concentration and collectively account for half of the variability, polymorphism of individual candidate genes contributes little. There are strong interactions between environmental and genetic influences. Recent findings have confirmed that APOA1 and ABCA1 exert the strongest influence on HDL concentrations and risk of atherosclerosis. CETP and lipases also affect the HDL concentration and functionality, but their connection to the atherosclerosis risk is conditional on the interaction between environmental and genetic factors. SUMMARY: Analysis of genetic determinants of HDL-cholesterol in patients with specific disease states or in response to the environmental condition may be a more accurate way to assess variations in HDL concentration. This may result in defining the rules of interaction between genetic and environmental factors and lead to understanding the mechanisms responsible for the variations in HDL concentration and functionality.     

Power Analysis for Population-Based Longitudinal Studies Investigating Gene-Environment Interactions in Chronic Diseases: A Simulation Study

Conventional methods for sample size calculation for population-based longitudinal studies tend to overestimate the statistical power by overlooking important determinants of the required sample size, such as the measurement errors and unmeasured etiological determinants, etc. In contrast, a simulation-based sample size calculation, if designed properly, allows these determinants to be taken into account and offers flexibility in accommodating complex study design features. The Canadian Longitudinal Study on Aging (CLSA) is a Canada-wide, 20-year follow-up study of 30,000 people between the ages of 45 and 85 years, with in-depth information collected every 3 years. A simulation study, based on an illness-death model, was conducted to: (1) investigate the statistical power profile of the CLSA to detect the effect of environmental and genetic risk factors, and their interaction on age-related chronic diseases; and (2) explore the design alternatives and implementation strategies for increasing the statistical power of population-based longitudinal studies in general. The results showed that the statistical power to identify the effect of environmental and genetic risk exposures, and their interaction on a disease was boosted when: (1) the prevalence of the risk exposures increased; (2) the disease of interest is relatively common in the population; and (3) risk exposures were measured accurately. In addition, the frequency of data collection every three years in the CLSA led to a slightly lower statistical power compared to the design assuming that participants underwent health monitoring continuously. The CLSA had sufficient power to detect a small (1<hazard ratio (HR)≤1.5) or moderate effect (1.5< HR≤2.0) of the environmental risk exposure, as long as the risk exposure and the disease of interest were not rare. It had enough power to detect a moderate or large (2.0<HR≤3.0) effect of the genetic risk exposure when the prevalence of the risk exposure was not very low (≥0.1) and the disease of interest was not rare (such as diabetes and dementia). The CLSA had enough power to detect a large effect of the gene-environment interaction only when both risk exposures had relatively high prevalence (0.2) and the disease of interest was very common (such as diabetes). The minimum detectable hazard ratios (MDHR) of the CLSA for the environmental and genetic risk exposures obtained from this simulation study were larger than those calculated according to the conventional sample size calculation method. For example, the MDHR for the environmental risk exposure was 1.15 according to the conventional method if the prevalence of the risk exposure was 0.1 and the disease of interest was dementia. In contrast, the MDHR was 1.61 if the same exposure was measured every 3 years with a misclassification rate of 0.1 according to this simulation study. With a given sample size, higher statistical power could be achieved by increasing the measuring frequency in participants with high risk of declining health status or changing risk exposures, and by increasing measurement accuracy of diseases and risk exposures. A properly designed simulation-based sample size calculation is superior to conventional methods when rigorous sample size calculation is necessary.     

Epidemiological evaluation of the use of genetics to improve the predictive value of disease risk factors.

The prevention of common diseases relies on identifying risk factors and implementing intervention in high-risk groups. Nevertheless, most known risk factors have low positive predictive value (PPV) and low population-attributable fraction (PAF) for diseases (e.g., cholesterol and coronary heart disease). With advancing genetic technology, it will be possible to refine the risk-factor approach to target intervention to individuals with risk factors who also carry disease-susceptibility allele(s). We provide an epidemiological approach to assess the impact of genetic testing on the PPV and PAF associated with risk factors. Under plausible models of interaction between a risk factor and a genotype, we derive values of PPV and PAF associated with the joint effects of a risk factor and a genotype. The use of genetic testing can markedly increase the PPV of a risk factor. PPV increases with increasing genotype-risk factor interaction and increasing marginal relative risk associated with the factor, but it is inversely proportional to the prevalences of the genotype and the factor. For example, for a disease with lifetime risk of 1%, if all the risk-factor effect is confined to individuals with a susceptible genotype, a risk factor with 10% prevalence and disease relative risk of 2 in the population will have a disease PPV of 1.8%, but it will have a PPV of 91.8% among persons with a genotype of 1% prevalence. On the other hand, genetic testing and restriction of preventive measures to those susceptible may decrease the PAF of the risk factor, especially at low prevalences of the risk factor and genotype.(ABSTRACT TRUNCATED AT 250 WORDS)     

Evidence for major gene inheritance of Alzheimer disease in families of patients with and without apolipoprotein E epsilon 4.

Apolipoprotein E (APOE) genotype is the single most important determinant to the common form of Alzheimer disease (AD) yet identified. Several studies show that family history of AD is not entirely accounted for by APOE genotype. Also, there is evidence for an interaction between APOE genotype and gender. We carried out a complex segregation analysis in 636 nuclear families of consecutively ascertained and rigorously diagnosed probands in the Multi-Institutional Research in Alzheimer Genetic Epidemiology study in order to derive models of disease transmission which account for the influences of APOE genotype of the proband and gender. In the total group of families, models postulating sporadic occurrence, no major gene effect, random environmental transmission, and Mendelian inheritance were rejected. Transmission of AD in families of probands with at least one epsilon 4 allele best fit a dominant model. Moreover, single gene inheritance best explained clustering of the disorder in families of probands lacking epsilon 4, but a more complex genetic model or multiple genetic models may ultimately account for risk in this group of families. Our results also suggest that susceptibility to AD differs between men and women regardless of the proband's APOE status. Assuming a dominant model, AD appears to be completely penetrant in women, whereas only 62%-65% of men with predisposing genotypes develop AD. However, parameter estimates from the arbitrary major gene model suggests that AD is expressed dominantly in women and additively in men. These observations, taken together with epidemiologic data, are consistent with the hypothesis of an interaction between genes and other biological factors affecting disease susceptibility.     

Gene-environment interaction and affected sib pair linkage analysis

OBJECTIVES: Gene-environment (GxE) interaction influences risk for many complex disease traits. However, genome screens using affected sib pair linkage techniques are typically conducted without regard for GxE interaction. We propose a simple extension of the commonly used mean test and evaluate its power for several forms of GxE interaction. METHODS: We compute expected IBD sharing by sibling exposure profile, that is by whether two sibs are exposed (EE), unexposed (UU), or are discordant for exposure (EU). We describe a simple extension of the mean test, the "mean-interaction" test that utilizes heterogeneity in IBD sharing across EE, EU, and UU sib pairs in a test for linkage. RESULTS: The mean-interaction test provides greater power than the mean test for detecting linkage in the presence of moderate or strong GxE interaction, typically when the interaction relative risk (R(ge)) exceeds 3 or is less than 1/3. In the presence of strong interaction (R(ge) = 10), the required number of affected sib pairs to achieve 80% power for detecting linkage is approximately 30% higher when the environmental factor is ignored in the mean test, than when it is utilized in the mean-interaction test. CONCLUSION: Linkage methods that incorporate environmental data and allow for interaction can lead to increased power for localizing a disease gene involved in a GxE interaction.     

甘蔗品种主要性状的基因型与环境及其互作效应分析

用AMMI模型双标图对国家第六轮甘蔗品种区域试验5个试点的12个甘蔗品种试验数据进行分析,研究甘蔗区试中不同品种的产量稳定性问题。结果表明,参试品种的6个产量性状在品种间和地点间差异显著,品种与地点的互作效应差异显著;FN30、YG16蔗茎产量和含糖量高,稳定性强,属于高产、稳产性较好的品种。AMMI模型很好地解释了甘蔗品种产量性状的基因型效应、环境效应和GE互作效应。     

Estimation and testing of gene-environment interactions in family-based association studies

Gene-environment interactions are of interest in genetic association studies for several reasons. First, the power to detect genetic effects may be substantially decreased if those effects differ according to environmental exposure and if no account is taken of this interaction with environmental exposure in the analysis. Second, such interactions may indicate a phenomenon of genuine biological interest (whereby a particular genetic effect operates only in the presence of an environmental trigger, or vice versa), understanding of which can lead us to a greater understanding of possible mechanisms and pathways in disease progression. Here I discuss the testing and estimation of gene-environment interactions via the case/pseudocontrol and related approaches. As originally proposed, the case/pseudocontrol approach applies to case/parents trios with no missing genotype data. I discuss some recent extensions that allow larger pedigree structures with some missing genotype data and present computer simulations to compare the performance of several competing approaches.     

Causes and consequences of variation in competitive ability in plant communities

Abstract. Several factors may define the cause and pattern of variation in competitive ability among individuals within a plant community. Variation may be a consequence of genetic or environmental variability. These two sources of variation may vary in their relative magnitudes. The relevant scale of genetic variation may occur at the individual genotype level or at the species level. The relevant scale of environmental variation may occur at the individual plant level or at the neighbourhood (or community) level. Relative competitive abilities may be effected by genotype-environment interaction or by genotype-genotype (or species-species) interaction. The complex relationship among these factors reveals the mechanistic basis for establishing a clear distinction among five specific hypotheses for species coexistence and diversity that are all variations of the general hypothesis that competitive abilities do not differ sufficiently among coexisting species to cause any competitive exclusion at the community level. These hypotheses are compared in terms of the degree to which they are restricted by assumptions and supported by existing data, and in the extent to which they involve evolutionary consequences of competition.     

Integrating Bacterial and Viral Water Quality Assessment to Predict Swimming-Associated Illness at a Freshwater Beach: A Cohort Study

Background & Objective

Recreational waters impacted by fecal contamination have been linked to gastrointestinal illness in swimmer populations. To date, few epidemiologic studies examine the risk for swimming-related illnesses based upon simultaneous exposure to more than one microbial surrogate (e.g. culturable E. coli densities, genetic markers). We addressed this research gap by investigating the association between swimming-related illness frequency and water quality determined from multiple bacterial and viral genetic markers.

Methods

Viral and bacterial genetic marker densities were determined from beach water samples collected over 23 weekend days and were quantified using quantitative polymerase chain reaction (qPCR). These genetic marker data were paired with previously determined human exposure data gathered as part of a cohort study carried out among beach users at East Fork Lake in Ohio, USA in 2009. Using previously unavailable genetic marker data in logistic regression models, single- and multi-marker/multi-water quality indicator approaches for predicting swimming-related illness were evaluated for associations with swimming-associated gastrointestinal illness.

Results

Data pertaining to genetic marker exposure and 8- or 9-day health outcomes were available for a total of 600 healthy susceptible swimmers, and with this population we observed a significant positive association between human adenovirus (HAdV) exposure and diarrhea (odds ratio  = 1.6; 95% confidence interval: 1.1–2.3) as well as gastrointestinal illness (OR  = 1.5; 95% CI: 1.0–2.2) upon adjusting for culturable E. coli densities in multivariable models. No significant associations between bacterial genetic markers and swimming-associated illness were observed.

Conclusions

This study provides evidence that a combined measure of recreational water quality that simultaneously considers both bacterial and viral densities, particularly HAdV, may improve prediction of disease risk than a measure of a single agent in a beach environment likely influenced by nonpoint source human fecal contamination.     

Use of the correlation of liability in twins and siblings in the study of birth defects

The epidemiologic approach to determining the etiology of disease involves identification of potential risk factors and then comparison of disease incidence among people with varying levels of exposure to the potential risk factors. This paper defines risk factors which correspond to different levels of genetic and environmental proximity to index cases of birth defects. Genetic proximity is estimated by the coefficient of relationship (R): 0.5 for siblings and dizygotic twins and 1.0 for monozygotic twins. Environmental proximity is measured by a combination of two variables: one variable for those potentially preventable risk factors common to siblings (S) and another for those common only to twins (T). Discordance in identical twins is attributed to a third type of environmental factors (U) that are unshared by twins and include random (stochastic) factors. The association between these risk factors and birth defects is estimated by using a linear model of the correlation of liability for different relatives. The coefficients derived from the model reflect the relative importance of genetic and different types of environmental risk factors as causes for the defects and can be used to identify birth defects most likely to be caused by measurable and possibly preventable risk factors. These defects could then be assigned high priority for future studies and preventive efforts.     

GENOTYPE-ENVIRONMENT INTERACTION FOR CLIMATE AND COMPETITION IN A NATURAL POPULATION OF FLOUR BEETLES,TRIBOLIUM CASTANEUM

The norm of reaction, the set of average phenotypes produced by a genotype in different environments, can be affected by spatial variation in natural selection especially when there exists genotype-environment interaction. In subdivided populations, the greater the genotype-environment interaction variance and the lower the migration rate, the more independent are the possible evolutionary trajectories for local adaptation. I examined genotype-environment interaction in the rate of population increase for lineages randomly derived from a wild population of Tribolium castaneum across a series of ecologically important environments. The lineages were derived from an outbred, wild-caught population by 14 generations of random genetic drift, during which the effective size of each lineage was approximately 22 breeding adults. The environments studied were the classic temperate-wet and cold-dry climates of Park (1954) in factorial combination with two genetic strains of a congeneric competitor, T. confusum. Much among-lineage genetic variation for rate of population increase was found for each of these ecologically important environments of climate and competition. Genotype-environment interaction accounted for 40.5% of the total among-lineage variance in rate of population increase signifying that the performance of a lineage in one environment is not necessarily a good predictor of its performance in another. Changing the genetic identity of the competitor changed the rate of increase of some lineages as much or more than changing the climatic conditions of temperature and humidity. This is the first empirical study to characterize the genotype-environment interaction variance associated with genetic variation in a competing congeneric species. This competitor-specific genetic variation in competitive ability may play an important role in coevolution in subdivided populations.     

GENOTYPE-ENVIRONMENT INTERACTION FOR JUVENILE GROWTH IN THE HARD CLAM MERCENARIA MERCENARIA (L.)

Offspring from half-sib and full-sib families of the hard clam, Mercenaria mercenaria were reared in five locations along the Atlantic Coast to test for the presence of genotype-environment interaction for juvenile growth rate. Location effects upon growth rate variation were prevalent; of the genetic effects, the additive genetic by location variance was predominant with the nonadditive genetic by location component contributing to a lesser degree to the interaction variance. The additive and nonadditive variation over all environments was negligible. Genotype-environment interaction was found to be at least partially due to a change in the amount of genetic variation expressed at each location; with significant additive variation detected at Charleston and Georgetown, SC sites and significant nonadditive variation at Millsboro, DE. Genetic covariance/correlation analysis indicated that reversals in relative family performance across locations were prevalent, implying the possibility of habitat specialization among genotypes. In addition, graphical analysis produced no evidence of a ubiquitously superior genotype. These analyses suggest that genotype-environment interaction should act to constrain the evolution of juvenile growth rate in Mercenaria, preserve any heritable variation associated with this trait and may lead to the development of phenotypic plasticity for growth.     

Parent–child pair design for detecting gene–environment interactions in complex diseases

It is becoming clear that the etiology of complex diseases involves not only genetic and environmental factors but also gene–environment (GE) interactions. Therefore, it is important to take account of all these factors to improve the power of an epidemiological study design. We propose here a novel parent–child pair (PCP) design for this purpose. In comparison with conventional designs, this approach has the following advantages: (a) PCP is a 4 × 16 design consisting of pairs of parent–child (PC) genotype statuses, PC exposure statuses and PC disease statuses. Therefore, it utilizes more information than the traditional approaches in association studies; (b) It can determine whether findings in studies of association between disease and genetic or environmental factors and their interaction are spurious, arising from Hardy–Weinberg disequilibrium or the other factors; (c) Since the information from both parents and children of the PC pairs are used in this design, it has high power for detecting association of candidate gene, exposure with a complex disease and GE interaction. We also present a set of estimates of relative risks of candidate genes, exposures and GE interactions under the multiplicative model and a method for computing the sample size requirements to test for these relative risks in the context of the PCP design.     

Genetics and epidemiology of gallbladder disease in New World native peoples.

Native peoples of the New World, including Amerindians and admixed Latin Americans such as Mexican-Americans, are highly susceptible to diseases of the gallbladder. These include cholesterol cholelithiasis (gallstones) and its complications, as well as cancer of the gallbladder. Although there is clearly some necessary dietary or other environmental risk factor involved, the pattern of disease prevalence is geographically associated with the distribution of genes of aboriginal Amerindian origin, and levels of risk generally correspond to the degree of Amerindian admixture. This pattern differs from that generally associated with Westernization, which suggests a gene-environment interaction, and that within an admixed population there is a subset whose risk is underestimated when admixture is ignored. The risk that an individual of a susceptible New World genotype will undergo a cholecystectomy by age 85 can approach 40% in Mexican-American females, and their risk of gallbladder cancer can reach several percent. These are heretofore unrecognized levels of risk, especially of the latter, because previous studies have not accounted for admixture or for the loss of at-risk individuals due to cholecystectomy. A genetic susceptibility may, thus, be as "carcinogenic" in New World peoples as any known major environmental exposure; yet, while the risk has a genetic basis, its expression as gallbladder cancer is so delayed as to lead only very rarely to multiply-affected families. Estimates in this paper are derived in part from two studies of Mexican-Americans in Starr County and Laredo, Texas.     

Challenges and opportunities in genome-wide environmental interaction (GWEI) studies

The interest in performing gene-environment interaction studies has seen a significant increase with the increase of advanced molecular genetics techniques. Practically, it became possible to investigate the role of environmental factors in disease risk and hence to investigate their role as genetic effect modifiers. The understanding that genetics is important in the uptake and metabolism of toxic substances is an example of how genetic profiles can modify important environmental risk factors to disease. Several rationales exist to set up gene-environment interaction studies and the technical challenges related to these studies-when the number of environmental or genetic risk factors is relatively small-has been described before. In the post-genomic era, it is now possible to study thousands of genes and their interaction with the environment. This brings along a whole range of new challenges and opportunities. Despite a continuing effort in developing efficient methods and optimal bioinformatics infrastructures to deal with the available wealth of data, the challenge remains how to best present and analyze genome-wide environmental interaction (GWEI) studies involving multiple genetic and environmental factors. Since GWEIs are performed at the intersection of statistical genetics, bioinformatics and epidemiology, usually similar problems need to be dealt with as for genome-wide association gene-gene interaction studies. However, additional complexities need to be considered which are typical for large-scale epidemiological studies, but are also related to "joining" two heterogeneous types of data in explaining complex disease trait variation or for prediction purposes.     

A latent variable approach to study gene-environment interactions in the presence of multiple correlated exposures

Many existing cohort studies initially designed to investigate disease risk as a function of environmental exposures have collected genomic data in recent years with the objective of testing for gene-environment interaction (G × E) effects. In environmental epidemiology, interest in G × E arises primarily after a significant effect of the environmental exposure has been documented. Cohort studies often collect rich exposure data; as a result, assessing G × E effects in the presence of multiple exposure markers further increases the burden of multiple testing, an issue already present in both genetic and environment health studies. Latent variable (LV) models have been used in environmental epidemiology to reduce dimensionality of the exposure data, gain power by reducing multiplicity issues via condensing exposure data, and avoid collinearity problems due to presence of multiple correlated exposures. We extend the LV framework to characterize gene-environment interaction in presence of multiple correlated exposures and genotype categories. Further, similar to what has been done in case-control G × E studies, we use the assumption of gene-environment (G-E) independence to boost the power of tests for interaction. The consequences of making this assumption, or the issue of how to explicitly model G-E association has not been previously investigated in LV models. We postulate a hierarchy of assumptions about the LV model regarding the different forms of G-E dependence and show that making such assumptions may influence inferential results on the G, E, and G × E parameters. We implement a class of shrinkage estimators to data adaptively trade-off between the most restrictive to most flexible form of G-E dependence assumption and note that such class of compromise estimators can serve as a benchmark of model adequacy in LV models. We demonstrate the methods with an example from the Early Life Exposures in Mexico City to Neuro-Toxicants Study of lead exposure, iron metabolism genes, and birth weight.     

Epidemiology of childhood leukemia in the presence and absence of Down syndrome

Down syndrome (DS) is a common congenital anomaly, and children with DS have a substantially higher risk of leukemia. Although understanding of genetic and epigenetic changes of childhood leukemia has improved, the causes of childhood leukemia and the potential role of environmental exposures in leukemogenesis remain largely unknown. Although many epidemiologic studies have examined a variety of environmental exposures, ionizing radiation remains the only generally accepted environmental risk factor for childhood leukemia. Among suspected risk factors, infections, exposure to pesticides, and extremely low frequency magnetic fields are notable. While there are well-defined differences between leukemia in children with and without DS, studies of risk factors for leukemia among DS children are generally consistent with trends seen among non-DS (NDS) children.We provide background on DS epidemiology and review the similarities and differences in biological and epidemiologic features of leukemia in children with and without DS. We propose that both acute lymphoblastic and acute myeloblastic leukemia among DS children can serve as an informative model for development of childhood leukemia. Further, the high rates of leukemia among DS children make it possible to study this disease using a cohort approach, a powerful method that is unfeasible in the general population due to the rarity of childhood leukemia.     

Measures of association between disease and genotype.

This paper is concerned with the statistical aspects of the phenomenon of disease occurring more frequently in individuals with some genotypes than in individuals with others. A correlation coefficient is defined to quantify association between disease and genotype. A distinction is made between the concepts of independence of allele and disease and independence of genotype and disease. This distinction is used to define two components of association which describe separate aspects of association of disease with genotype. One component is a measure of the association of disease with allele; the other a measure of the effect of allele interaction on association of disease and genotype. One aspect of the usefulness of the partition into components which is discussed is in expressing the recurrence risk of disease for a relative of an affected individual. A chi-squared analysis is provided to test hypotheses about the components of association and other hypotheses of genetic interest. This analysis is illustrated using a study done to determine the effect of the sex-linked dwarfing gene in male chickens on resistance to E. coli infection. This analysis shows a significant allele interaction effect on resistance to disease but no association of disease with alleles. In conclusion, some extensions and limitations of the proposed concepts and procedures are discussed.