A Model for Analysis of Population Structure

Arguments have been presented for the appropriateness of a multinomial Dirichlet distribution for describing single-locus genotypic frequencies in a subdivided population. This distribution is defined as a function of allele frequency, the average (over the entire population) inbreeding coefficient and the correlation between genotypes within a subdivision. Alternative parameterizations and their genetic interpretations are given.-We then show how information from a sample drawn from this subdivided population, in the absence of pedigrees, can be combined with the multinomial Dirichlet model to form a likelihood function. This likelihood function is then used as the basis for estimation and testing hypotheses concerning the genetic parameters of the model. Comparisons of this approach to the alternative procedure of Cockerham (1969) and (1973) are made using human data obtained from Tecumseh, Michigan and Monte Carlo simulations.-Finally, implications of these results to statistical inference and to mutation rates are presented.     

Using Lifetime Risk Estimates in Personal Genomic Profiles: Estimation of Uncertainty

Personal genome tests are now offered direct-to-consumer (DTC) via genetic variants identified by genome-wide association studies (GWAS) for common diseases. Tests report risk estimates (age-specific and lifetime) for various diseases based on genotypes at multiple loci. However, uncertainty surrounding such risk estimates has not been systematically investigated. With breast cancer as an example, we examined the combined effect of uncertainties in population incidence rates, genotype frequency, effect sizes, and models of joint effects among genetic variants on lifetime risk estimates. We performed simulations to estimate lifetime breast cancer risk for carriers and noncarriers of genetic variants. We derived population-based cancer incidence rates from Surveillance, Epidemiology, and End Results (SEER) Program and comparative international data. We used data for non-Hispanic white women from 2003 to 2005. We derived genotype frequencies and effect sizes from published GWAS and meta-analyses. For a single genetic variant in FGFR2 gene (rs2981582), combination of uncertainty in these parameters produced risk estimates where upper and lower 95% simulation intervals differed by more than 3-fold. Difference in population incidence rates was the largest contributor to variation in risk estimates. For a panel of five genetic variants, estimated lifetime risk of developing breast cancer before age 80 for a woman that carried all risk variants ranged from 6.1% to 21%, depending on assumptions of additive or multiplicative joint effects and breast cancer incidence rates. Epidemiologic parameters involved in computation of disease risk have substantial uncertainty, and cumulative uncertainty should be properly recognized. Reliance on point estimates alone could be seriously misleading.     

Multivariate approach to calculating the recurrence risk in families with multifactorial diseases

To resolve one of the main theoretical problems of genetic counselling, namely, calculation of the recurrence risk for common diseases, a multivariate approach is suggested, based on the multifactorial model. The model suggests partially different liability for several diseases or various forms of a disease. The specified recurrence risk for each family can be calculated with the account of different morbidity rates for different sexes and the degree of kinship to proband. The input data for computer calculations are: population incidence of diseases, their heritabilities as well as genetical and environmental correlations between the diseases. Our method is illustrated by calculation of the recurrence risk for diabetes mellitus (DM) and bronchial asthma (BA), each of which may be subdivided into several forms. It is proposed that the nature of genetic correlations is different for two diseases. The phenotypic forms of DM are genetically independent, whereas the forms of BA have a common genetic basis.     

A Regression Modeling Approach for Describing Patterns of HIV Genetic Variation

We introduce a novel approach for describing patterns of HIV genetic variation using regression modeling techniques. Parameters are defined for describing genetic variation within and between viral populations by generalizing Simpson's index of diversity. Regression models are specified for these variation parameters and the generalized estimating equation framework is used for estimating both the regression parameters and their corresponding variances. Conditions are described under which the usual asymptotic approximations to the distribution of the estimators are met. This approach provides a formal statistical framework for testing hypotheses regarding the changing patterns of HIV genetic variation over time within an infected patient. The application of these methods for testing biologically relevant hypotheses concerning HIV genetic variation is demonstrated in an example using sequence data from a subset of patients from the Multicenter AIDS Cohort Study.     

Poisson Regression with Change‐Point Prior in the Modelling of Disease Risk around a Point Source

Bayesian estimation of the risk of a disease around a known point source of exposure is considered. The minimal requirements for data are that cases and populations at risk are known for a fixed set of concentric annuli around the point source, and each annulus has a uniquely defined distance from the source. The conventional Poisson likelihood is assumed for the counts of disease cases in each annular zone with zone‐specific relative risk and parameters and, conditional on the risks, the counts are considered to be independent. The prior for the relative risk parameters is assumed to be piecewise constant at the distance having a known number of components. This prior is the well‐known change‐point model. Monte Carlo sampling from the posterior results in zone‐specific posterior summaries, which can be applied for the calculation of a smooth curve describing the variation in disease risk as a function of the distance from the putative source. In addition, the posterior can be used in the calculation of posterior probabilities for interesting hypothesis. The suggested model is suitable for use in geographical information systems (GIS) aimed for monitoring disease risks. As an application, a case study on the incidence of lung cancer around a former asbestos mine in eastern Finland is presented. Further extensions of the model are discussed.     

BRCA1 and BRCA2 pathways and the risk of cancers other than breast or ovarian

OBJECTIVE: Germline mutations in the tumor suppressor genes BRCA1 and BRCA2 predispose women to breast and ovarian cancer. Female carriers of BRCA1 or BRCA2 gene mutations have very high lifetime risks for breast and ovarian cancers. Genetic abnormalities occur in all cancers, so BRCA-related pathways are critical because they serve to safeguard genetic content. Although protecting genetic information is a general function, BRCA-related pathways seem largely specific to preventing breast and ovarian cancer. The objective of this study was to resolve this difference between the theoretical functions of BRCA genes and their specific clinical effects. DATA SOURCES, DATA EXTRACTION, DATA SYNTHESIS: The author collected data published in > 30 epidemiologic studies on the incidence of cancers other than breast or ovarian in mutation carriers and in large populations eligible for mutation testing. Data were extracted and used directly as published whenever possible with a minimum of statistical manipulation. CONCLUSIONS: Although mutations target breast and ovary, a broader spectrum of cancers also occur with statistically significant elevated frequencies. Risks for "all cancers except breast or ovary" are elevated, with some population subgroups differing with regard to how frequently elevated risks were found at individual sites. Additional sites at risk included stomach, pancreas, prostate, and colon. The increased risk ranged from about 20% to 60%, with the greatest increases in risk in stomach and pancreas. The collected data show BRCA-pathway functions are probably required at multiple sites, not just in breast or ovary. Known interactions and relationships among BRCA-related pathways strongly support the idea that their inactivation provides growth or survival advantages for a variety of cancers. The data suggest applying an increased level of clinical alertness to those with defects in BRCA-related pathways. Identifying molecules that confer growth or survival advantages to BRCA-related cancers may provide broadly useful targets for chemotherapy or chemoprevention.     

A method for determining weights for excess relative risk and excess absolute risk when applied in the calculation of lifetime risk of cancer from radiation exposure

Radiation-related risks of cancer can be transported from one population to another population at risk, for the purpose of calculating lifetime risks from radiation exposure. Transfer via excess relative risks (ERR) or excess absolute risks (EAR) or a mixture of both (i.e., from the life span study (LSS) of Japanese atomic bomb survivors) has been done in the past based on qualitative weighting. Consequently, the values of the weights applied and the method of application of the weights (i.e., as additive or geometric weighted means) have varied both between reports produced at different times by the same regulatory body and also between reports produced at similar times by different regulatory bodies. Since the gender and age patterns are often markedly different between EAR and ERR models, it is useful to have an evidence-based method for determining the relative goodness of fit of such models to the data. This paper identifies a method, using Akaike model weights, which could aid expert judgment and be applied to help to achieve consistency of approach and quantitative evidence-based results in future health risk assessments. The results of applying this method to recent LSS cancer incidence models are that the relative EAR weighting by cancer solid cancer site, on a scale of 0–1, is zero for breast and colon, 0.02 for all solid, 0.03 for lung, 0.08 for liver, 0.15 for thyroid, 0.18 for bladder and 0.93 for stomach. The EAR weighting for female breast cancer increases from 0 to 0.3, if a generally observed change in the trend between female age-specific breast cancer incidence rates and attained age, associated with menopause, is accounted for in the EAR model. Application of this method to preferred models from a study of multi-model inference from many models fitted to the LSS leukemia mortality data, results in an EAR weighting of 0. From these results it can be seen that lifetime risk transfer is most highly weighted by EAR only for stomach cancer. However, the generalization and interpretation of radiation effect estimates based on the LSS cancer data, when projected to other populations, are particularly uncertain if considerable differences exist between site-specific baseline rates in the LSS and the other populations of interest. Definitive conclusions, regarding the appropriate method for transporting cancer risks, are limited by a lack of knowledge in several areas including unknown factors and uncertainties in biological mechanisms and genetic and environmental risk factors for carcinogenesis; uncertainties in radiation dosimetry; and insufficient statistical power and/or incomplete follow-up in data from radio-epidemiological studies.     

Genetic analysis of the predisposition to uterine myoma. Prevalence and morbidity

Prevalence of uterine myoma (MU) was estimated in several Moscow districts. The overall average estimate of the MU prevalence is 2.45% among women of all groups. The prevalence MU estimates increase with the age, its maximum value reaching 8.31% at the age of 50 years. The morbidity risk estimates increased with the age as well, the maximum value being 2.98% at the age of 40-44 years. The value of "cumulative" morbidity risks, i. e. the probability to be affected, is 9.74% for a population living long enough, this value being based on the age-specific estimates of morbidity risks. Taking into consideration the autopsy data, indicating that frequency of MU, including small myomatous nodes, is 20%, the conclusion is made that MU is manifested by clinically expressed disturbances (urging a woman to address to a doctor) in 50% of cases only. Epidemiological data obtained are to be used later for genetic analysis of familial data on MU.     

A reanalysis of liver cancer incidence in Danish patients administered thorotrast using a two-mutation carcinogenesis model

In recent years, a two-mutation carcinogenesis (TMC) model has been used to analyze epidemiological data and estimate the radiation risks at low doses for the organs affected. Here the TMC model was used to reanalyze the liver cancer incidence in the Danish population in general and in patients administered Thorotrast, and to estimate the radiation risks for the liver. The data for 807 patients for whom sufficient data on the injected volumes of Thorotrast were available were used in this reanalysis. These data were combined with data on liver cancer incidence in the Danish population as the baseline or background incidence. Because males and females show different baseline liver cancer incidences, separate fits were made for males and females. The fits showed that the radiation effect could be ascribed entirely to the radiation dependence of the first mutation rate of the TMC model, which was higher for females than for males. The second mutation rate was not significantly dependent on dose. The radiation risks for the liver were calculated on the basis of the model parameters. These risks for lifetime exposures are about the same for males and females and are between a factor of 2 and 10 higher than current estimates. The discrepancy between the model results and previous risk estimates probably arises because the model calculations give more complete lifetime radiation risk estimates. For short-term exposures of the liver to ionizing radiation, the maximum radiation-induced excess liver cancer risk per unit dose applies to exposures at the age of about 10; exposures at ages above 35 have a radiation effect of less than approximately 15% of this maximum.     

A computer model to simulate family history of breast/ovarian cancer in BRCA1 mutation carriers

The BRCA1 gene and its relationship to family history of breast/ovarian cancer are difficult to study in a population because of practical and ethical issues. The paucity of information on BRCA1 in the general population was a major theme in a recent review of genetic testing in Canada. We develop a simulation model to mimic genetic inheritance and cancer incidence in the family of someone with a germline BRCA1 mutation. Given someone's age and family structure, our model simulates his or her family history in three steps: (1) determine which family members have the mutation, (2) determine the ages of family members and (3) determine which family members have breast/ovarian cancer. Each step involves random variation. Some parameters in our model are estimated using local (British Columbia, Canada) population data. The breast/ovarian cancer risk associated with BRCA1 mutations is estimated using values published in the literature. An example is provided to illustrate the model's application. The model incorporates results from genetics, demography and epidemiology, but requires several additional assumptions. Research to address these assumptions is recommended.     

Risk prediction of complex diseases from family history and known susceptibility loci, with applications for cancer screening

Risk prediction based on genomic profiles has raised a lot of attention recently. However, family history is usually ignored in genetic risk prediction. In this study we proposed a statistical framework for risk prediction given an individual's genotype profile and family history. Genotype information about the relatives can also be incorporated. We allow risk prediction given the current age and follow-up period and consider competing risks of mortality. The framework allows easy extension to any family size and structure. In addition, the predicted risk at any percentile and the risk distribution graphs can be computed analytically. We applied the method to risk prediction for breast and prostate cancers by using known susceptibility loci from genome-wide association studies. For breast cancer, in the population the 10-year risk at age 50 ranged from 1.1% at the 5th percentile to 4.7% at the 95th percentile. If we consider the average 10-year risk at age 50 (2.39%) as the threshold for screening, the screening age ranged from 62 at the 20th percentile to 38 at the 95th percentile (and some never reach the threshold). For women with one affected first-degree relative, the 10-year risks ranged from 2.6% (at the 5th percentile) to 8.1% (at the 95th percentile). For prostate cancer, the corresponding 10-year risks at age 60 varied from 1.8% to 14.9% in the population and from 4.2% to 23.2% in those with an affected first-degree relative. We suggest that for some diseases genetic testing that incorporates family history can stratify people into diverse risk categories and might be useful in targeted prevention and screening.     

Flexible dose-response models for Japanese atomic bomb survivor data: Bayesian estimation and prediction of cancer risk

Generalised absolute risk models were fitted to the latest Japanese atomic bomb survivor cancer incidence data using Bayesian Markov Chain Monte Carlo methods, taking account of random errors in the DS86 dose estimates. The resulting uncertainty distributions in the relative risk model parameters were used to derive uncertainties in population cancer risks for a current UK population. Because of evidence for irregularities in the low-dose dose response, flexible dose-response models were used, consisting of a linear-quadratic-exponential model, used to model the high-dose part of the dose response, together with piecewise-linear adjustments for the two lowest dose groups. Following an assumed administered dose of 0.001 Sv, lifetime leukaemia radiation-induced incidence risks were estimated to be 1.11 x 10(-2) Sv(-1) (95% Bayesian CI -0.61, 2.38) using this model. Following an assumed administered dose of 0.001 Sv, lifetime solid cancer radiation-induced incidence risks were calculated to be 7.28 x 10(-2) Sv(-1) (95% Bayesian CI -10.63, 22.10) using this model. Overall, cancer incidence risks predicted by Bayesian Markov Chain Monte Carlo methods are similar to those derived by classical likelihood-based methods and which form the basis of established estimates of radiation-induced cancer risk.     

Statistical analysis of occupancy rates for overdispersed populations by redistribution procedures: Application to the european corn borer EGG masses distribution

Standard statistical analyses of distributions of individuals from contingency tables are generally invalid if the individuals are not distributed independently of each other. In this paper, we discuss a method of testing hypotheses about classification category occupancy rates for overdispersed population or for population whose individuals are distributed by groups rather than lonely. These methods are based on population redistribution simulations and provide valid, exact and powerful tests in situations for which classical methods are not appropriate. Illustrations are given from the European Corn Borer eggs data.     

An efficient algorithm for estimation of functions of a pedigree with short inbred loops

The study is a further development of the methods for genetic analysis using pedigree data. Methods for approximation of the likelihood based on cutting of all loops are often used in analysis of large pedigrees with multiple loops. In this study, a fast efficient algorithm for calculating likelihood is proposed. This algorithm allows short inbred loops to be processed without cutting them and, hence, prevents the loss of genetic information. The approach proposed may be important for analysis of the pedigrees of farm and laboratory animals, where inbred crosses resulting in short inbred loops are common. The results of a stochastic genetic experiment agree with this suggestion: the use of the algorithm proposed considerably increases the accuracy of estimation of model parameters and testing of genetic hypotheses.     

Representing genetic variation as continuous surfaces: an approach for identifying spatial dependency in landscape genetic studies

Landscape genetics, an emerging field integrating landscape ecology and population genetics, has great potential to influence our understanding of habitat connectivity and distribution of organisms. Whereas typical population genetics studies summarize gene flow as pairwise measures between sampling localities, landscape characteristics that influence population genetic connectivity are often continuously distributed in space. Thus, there are currently gaps in both the ability to analyze genotypic data in a continuous spatial context and our knowledge of expected of landscape genetic structure under varying conditions. We present a framework for generating continuous “genetic surfaces”, evaluate their statistical properties, and quantify statistical behavior of landscape genetic structure in a simple landscape. We simulated microsatellite genotypes under varying parameters (time since vicariance, migration, effective population size) and used ancestry (q) values from STRUCTURE to interpolate a genetic surface. Using a spatially adjusted Pearson's correlation coefficient to test the significance of landscape variable(s) on genetic structure we were able to detect landscape genetic structure on a contemporary time scale (≥5 generations post vicariance, migration probability ≤0.10) even when population differentiation was minimal (F_ST≥0.00015). We show that genetic variation can be significantly correlated with geographic distance even when genetic structure is due to landscape variable(s), demonstrating the importance of testing landscape influence on genetic structure. Finally, we apply genetic surfacing to analyze an empirical dataset of black bears from northern Idaho USA. We find black bear genetic variation is a function of distance (autocorrelation) and habitat patch (spatial dependency), consistent with previous results indicating genetic variation was influenced by landscape by resistance. These results suggest genetic surfaces can be used to test competing hypotheses of the influence of landscape characteristics on genetic structure without delineation of categorical groups.     

Hypothesis-Based Analysis of Gene-Gene Interactions and Risk of Myocardial Infarction

The genetic loci that have been found by genome-wide association studies to modulate risk of coronary heart disease explain only a fraction of its total variance, and gene-gene interactions have been proposed as a potential source of the remaining heritability. Given the potentially large testing burden, we sought to enrich our search space with real interactions by analyzing variants that may be more likely to interact on the basis of two distinct hypotheses: a biological hypothesis, under which MI risk is modulated by interactions between variants that are known to be relevant for its risk factors; and a statistical hypothesis, under which interacting variants individually show weak marginal association with MI. In a discovery sample of 2,967 cases of early-onset myocardial infarction (MI) and 3,075 controls from the MIGen study, we performed pair-wise SNP interaction testing using a logistic regression framework. Despite having reasonable power to detect interaction effects of plausible magnitudes, we observed no statistically significant evidence of interaction under these hypotheses, and no clear consistency between the top results in our discovery sample and those in a large validation sample of 1,766 cases of coronary heart disease and 2,938 controls from the Wellcome Trust Case-Control Consortium. Our results do not support the existence of strong interaction effects as a common risk factor for MI. Within the scope of the hypotheses we have explored, this study places a modest upper limit on the magnitude that epistatic risk effects are likely to have at the population level (odds ratio for MI risk 1.3-2.0, depending on allele frequency and interaction model).     

景观遗传学：概念与方法

全球变化下的物种栖息地丧失和破碎化给生物多样性保护带来了新的问题和挑战,生物多样性保护必须由单纯的物种保护上升到栖息地景观的保护。景观遗传学是定量确定栖息地景观特征对种群遗传结构影响的一门交叉学科,在生物保护及自然保护区管理方面有巨大的潜力。从生物多样性保护的角度评述了景观结构与遗传多样性的关系,介绍了景观遗传学的基本概念,研究尺度和方法,并对景观遗传学当前的研究焦点及面临的挑战做了总结。     

Deciphering host migrations and origins by means of their microbes

Mitochondrial DNA and microsatellite sequences are powerful genetic markers for inferring the genealogy and the population genetic structure of animals but they have only limited resolution for organisms that display low genetic variability due to recent strong bottlenecks. An alternative source of data for deciphering migrations and origins in genetically uniform hosts can be provided by some of their microbes, if their evolutionary history correlates closely with that of the host. In this review, we first discuss how a variety of viruses, and the bacterium Helicobacter pylori, can be used as genetic tracers for one of the most intensively studied species, Homo sapiens. Then, we review statistical problems and limitations that affect the calculation of particular population genetic parameters for these microbes, such as mutation rates, with particular emphasis on the effects of recombination, selection and mode of transmission. Finally, we extend the discussion to other host-parasite systems and advocate the adoption of an integrative approach to both sampling and analysis.     

Seasonality comparisons among groups using incidence data

A new test using incidence data is developed for testing whether two or more groups have the same seasonal pattern. The method fits sine waves to the data with a fundamental period of one cycle per year, and has the possibility of using higher harmonics, when necessary, to adequately model the data. The seasonal pattern can, therefore, have an arbitrary shape. The method allows for different length time intervals and different size populations at risk in the time intervals. Maximum likelihood estimation, based on the Poisson distribution, is used to determine the parameters of the model. Likelihood ratio tests and Akaike's information criterion (AIC) are used to determine the number of harmonics, and to test hypotheses. This method has been used to test for seasonal patterns in the incidence of insulin-dependent diabetes mellitus (IDDM) in Colorado among persons aged 0-17 years. Comparisons of seasonal patterns are made between males and females, and three age groups, each controlling for the other effect as in analysis of variance. Other potential applications of this approach are also discussed. A basic program is available for an IBM-PC to carry out these analyses.