Conceptualizing human variation.

What is the relationship between the patterns of biological and sociocultural variation in extant humans? Is this relationship accurately described, or best explained, by the term 'race' and the schema of 'racial' classification? What is the relationship between 'race', genetics and the demographic groups of society? Can extant humans be categorized into units that can scientifically be called 'races'? These questions underlie the discussions that address the explanations for the observed differences in many domains between named demographic groups across societies. These domains include disease incidence and prevalence and other variables studied by biologists and social scientists. Here, we offer a perspective on understanding human variation by exploring the meaning and use of the term 'race' and its relationship to a range of data. The quest is for a more useful approach with which to understand human biological variation, one that may provide better research designs and inform public policy.

Ascertainment corrections based on smaller family units.

Ascertainment concerns the manner by which families are selected for genetic analysis and how to correct for it in likelihood models. Because such families are often neither drawn at random nor selected according to well-defined rules, the problem of ascertainment correction in the genetic analysis of family data has proved durable. This paper undertakes a systematic study of ascertainment corrections in terms of smaller distinct units, which will usually be sibships, nuclear families, or small pedigrees. Three principal results are presented. The first is that ascertainment corrections in likelihood models for family data can be made in terms of smaller units, without breaking up the pedigree. The second is that the appropriate correction for single ascertainment in a unit is the reciprocal of the sum of the marginal probabilities of all the persons relevant to its ascertainment, as if affected. The third result is a generalization of the single ascertainment-correction formula to k-plex ascertainment, in which each unit has k or more affecteds. The correction is the reciprocal of the sum of the joint probabilities of all distinct sets of k persons in the unit, as if they were all affected. In extended families, two additional ascertainment schemes will be considered and explicit formulas will be presented. One of these schemes is "uniform-proband-status ascertainment," in which nonmembers of a given unit have the same chance as members to become probands if they are affected; the other scheme is the "inverse law of ascertainment," in which the chance that nonmembers of a unit will become probands for that unit decreases with degree of relationship. Several specific recommendations are made for further study.

The use of logistic models for the analysis of codon frequencies of DNA sequences in terms of explanatory variables.

The development of the regressive logistic model applicable to the analysis of codon frequencies of DNA sequences in terms of explanatory variables is presented. A codon is a triplet of nucleotides that code for an amino acid, and may be considered as a trivariate response (B1, B2, B3), where Bi (i = 1, 2, 3) is a categorical random variable with values A, C, G, T. The linear order of bases in the DNA and possible statistical dependence of the bases in a given codon make the regressive logistic model a suitable tool for the analysis of codon frequencies. A problem of structural zeros arises from the fact that the stopping codons (terminators) do not code for amino acids; this is solved by normalizing the likelihood function. Codon frequencies may also depend on the function of the gene and they are known to differ between genes of the same genome. Differences also occur between synonymous codons for the same amino acid. Thus, the use of covariates that differ between synonymous codons as well as covariates that are constant within codons of the same amino acid may be useful in explaining the frequencies. As an illustration, the method is applied to the human mitochondrial genome using the following as explanatory variables: (1) TSCORE, a measure of the number of single base mutations required for a given codon to become a terminator; (2) AARISK, an indicator of a codon's ability of changing by a single base substitution to triplets coding for amino acids with very different characteristics; (3) AVDIST, a measure of the typicality of the amino acid coded for by the triplets. The results indicate that models that incorporate dependency structure and covariates are to be preferred to either the models comprising covariates alone or dependency structure alone.

Genetic analysis combining path analysis with regressive models: the TAU model of multifactorial transmission.

We have extended regressive models by incorporating a simple path model (the TAU model). This was achieved for both class A and class D regressive models by expressing the residual correlations in the regressive models in terms of parameters of the path model. We have presented explicit solutions for path coefficients in terms of the residual correlations. These methods were applied to a French-Canadian family study on body mass index. It was found that the estimate of pseudopolygenic heritability was robust under class A (t2 = 0.28) and class D (t2 = 0.26) models.

Investigating the genetic basis for ankylosing spondylitis. Linkage studies with the major histocompatibility complex region.

OBJECTIVE: To assess the hypothesis that B27 or a gene(s) in close proximity (e.g., within or near the major histocompatibility complex [MHC]) represents a disease-causing ankylosing spondylitis (AS) gene, and therefore contributes directly to the pathogenesis of this disorder. METHODS: MHC haplotypes were determined by both serologic and molecular analyses in 15 multiple-case AS families from Toronto and Newfoundland. Segregation of MHC haplotypes with AS within these families was examined by linkage and identity-by-descent analyses. Attributable risk estimates for various genetic markers and for sex were calculated. RESULTS: Linkage analyses established significant linkage between AS and the MHC, the maximal logarithm of odds (LOD) score being 3.48 at a recombination frequency (O) of 0.05. In a second analysis in which the population association of the MHC gene HLA-B27 with AS was taken into account, the maximal LOD score was 7.5 at O = 0.05. Identity-by-descent analyses showed a significant departure from random segregation among affected avuncular (P < 0.05) and cousin (P < 0.01) pairs. The presence of HLA-B40 in HLA-B27 positive individuals increased the risk for disease more than 3-fold, confirming previous reports. Disease susceptibility modeling suggested an autosomal dominant pattern of inheritance, with penetrance of approximately 20%. CONCLUSION: These data provide the first conclusive demonstration of linkage between the MHC region and AS, and confirm that genes within this region contribute directly to the genetic susceptibility for AS.

Genetic analysis combining path analysis with regressive models: the BETA path model of polygenic and familial environmental transmission.

We have extended the class D regressive model for the purpose of combined path and segregation analyses by incorporating the BETA path model. We have done this by expressing correlations among residuals from major genotype (RMGs) of family members under the class D regressive model as functions of path coefficients under the BETA path model. The likelihood function under the combined model was factorized into a product of conditional densities, which is dominated by bivariate normal densities. Statistical inferences under the combined model are analogous to those under the class D regressive model.

Breast cancer risk factors in African-American women: the Howard University Tumor Registry experience.

This retrospective case-control study examines risk factors for breast cancer in African-American women, who recently have shown an increase in the incidence of this malignancy, especially in younger women. Our study involves 503 cases from the Howard University Hospital and 539 controls from the same hospital, seen from 1978 to 1987. Using information culled from medical charts, an analysis of various factors for their effect on breast cancer risk was made. The source of data necessarily meant that some known risk factors were missing. Increases in risk were found for known risk factors such as decreased age at menarche and a family history of breast cancer. No change in risk was observed with single marital status, nulliparity, premenopausal status, or lactation. An increased odds ratio was found for induced abortions, which was significant in women diagnosed after 50 years of age. Spontaneous abortions had a small but significant protective effect in the same subgroup of women. Birth control pill usage conferred a significantly increased risk. It is of note that abortions and oral contraceptive usage, not yet studied in African Americans, have been suggested as possibly contributing to the recent increase in breast cancer in young African-American women.

Influence of genotype-dependent effects of covariates on the outcome of segregation analysis of the body mass index.

Several recent studies of the body mass index (BMI) have provided support for a recessive major gene influencing heaviness in humans. Segregation analysis of the BMI was carried out recently in a series of randomly sampled French-Canadian families to determine whether we could replicate the major gene finding by using a residual phenotype adjusted for the effects of age and sex. The best model included a recessive major effect for high BMI values with residual familial resemblance; however, Mendelian transmission could not be confirmed, and the no-transmission hypothesis (where all the tau's are constrained to be equal) was not rejected. Considering that the BMI is a complex phenotype affected by many factors and that there are known variations in body composition during growth and aging, we undertook a reanalysis of the data, using a model that allowed the estimation of genotype-specific age and gender effects. New tests on the transmission parameters satisfy the criteria for interfering Mendelian segregation. The results suggest that individuals with the "high" recessive genotype show the greatest degree of heaviness at birth, with a subsequent trend toward lower values throughout life, while individuals with the dominant "normal" genotypes show no appreciable trends with age. In addition, the "high" genotype appears to confer a greater degree of heaviness in females as compared with males. These results, along with other observations from the data, suggest that, while a recessive single gene influence may be discernible, the phenotypic expression of the BMI is likely to be complicated by genotype x environment interactions and, possibly, by the action of other loci. Further, the data also are consistent with the hypothesis that modifying factors may include the adoption of a more prudent life-style by individuals genetically predisposed to heaviness and a secular increase in the incidence, prevalence, and potency of environmentally based triggers leading to a higher penetrance of the "heavy" genotype in the young.

Compound regressive models for quantitative multivariate phenotypes: application to lipid and lipoprotein data.

In this paper we consider the compound version of the class D regressive models for a p variate phenotypic outcome. The likelihood function is noted and the results are illustrated with the Donner Laboratory data, without the assumption of a major gene for the brevity of presentation.

Familial aggregation of oesophageal cancer in Yangcheng County, Shanxi Province, China.

Oesophageal cancer is the second most common cause of cancer death in China and is particularly prevalent in northern China. Genetic factors have been studied less than environmental factors in the aetiology of this disease. This study was conducted to evaluate familial aggregation of oesophageal cancer. All households in Yangcheng County were interviewed in 1979 to determine family history of oesophageal cancer. In 1989, vital status for all family members from three Yangcheng villages was determined and re-interviews were conducted among families who reported a positive family history of oesophageal cancer in 1979. Risk of oesophageal cancer was evaluated by comparing family and individual rates of oesophageal cancer during the 1979-1989 interval stratified by the number of family members with oesophageal cancer prior to 1979. More families with prior oesophageal cancer history reported new oesophageal cancer deaths during the follow-up period than families without prior history (19% versus 5%). Oesophageal cancer rates increased with increasing positivity of family history, and adjustment for other risk factors did not substantially alter this result. We conclude that these data provide evidence for familial aggregation of oesophageal cancer.

Segregation analysis of esophageal cancer in 221 high-risk Chinese families.

BACKGROUND: Until recently, environmental factors were considered of greatest importance in the etiology of esophageal cancer. Recent studies, however, have suggested that genetic factors also have a role. PURPOSE: Since no formal genetic study of this cancer has been previously reported, we carried out a statistical analysis to determine how important genetic factors are in the etiology of esophageal cancer in high-incidence areas of North China. METHODS: Using a logistic regressive model, we performed a segregation analysis on 221 high-risk nuclear families from the Yaocun Commune, Linxian, Henan Province of China, with at least one affected family member and with all offspring aged 40 years or older. Three models, the mendelian, the environmental, and the no-transmission models, were each compared with the general-transmission model that incorporated both genetic and environmental factors. RESULTS: According to Akaike's Information Criterion, the mendelian model provided the best fit for the data. By the chi-square test, the mendelian inheritance model was not rejected, but the environmental and the no-transmission models were both rejected. CONCLUSION: The segregation analysis indicated an autosomal recessive mendelian inheritance, with the alleged mendelian gene present at a frequency of 19%, causing 4% of this population to be predisposed to develop esophageal cancer. Large, unmeasured, residual familial factors, however, were also significant. IMPLICATIONS: Both an autosomal recessive gene and unexplained environmental factors appear to be important in the etiology of esophageal cancer in the subpopulation studied.

Numerical comparisons of two formulations of the logistic regressive models with the mixed model in segregation analysis of discrete traits.

Segregation analysis of discrete traits can be conducted by the classical mixed model and the recently introduced regressive models. The mixed model assumes an underlying liability to the disease, to which a major gene, a multifactorial component, and random environment contribute independently. Affected persons have a liability exceeding a threshold. The regressive logistic models assume that the logarithm of the odds of being affected is a linear function of major genotype effects, the phenotypes of older relatives, and other covariates. A formulation of the regressive models, based on an underlying liability model, has been recently proposed. The regression coefficients on antecedents are expressed in terms of the relevant familial correlations and a one-to-one correspondence with the parameters of the mixed model can thus be established. Computer simulations are conducted to evaluate the fit of the two formulations of the regressive models to the mixed model on nuclear families. The two forms of the class D regressive model provide a good fit to a generated mixed model, in terms of both hypothesis testing and parameter estimation. The simpler class A regressive model, which assumes that the outcomes of children depend solely on the outcomes of parents, is not robust against a sib-sib correlation exceeding that specified by the model, emphasizing testing class A against class D. The studies reported here show that if the true state of nature is that described by the mixed model, then a regressive model will do just as well. Moreover, the regressive models, allowing for more patterns of family dependence, provide a flexible framework to understand gene-environment interactions in complex diseases.

Compound regressive models for family data.

The regressive models for the analysis of family data are extended to include cases in which the within-sibship covariation may exceed that implied by the class A regressive model, but for which birth order is not required. In addition to specified major genes, if any, and common parental phenotypes, the excess within-sibship covariation may come from a common cumulative risk from unspecified factors such as a shared environment, and other genes. The within-sibship cumulative risk has a probability distribution in the population. The sib-sib correlation (more generally within-sibship statistical dependence) is equal for all pairs within a given sibship. The compound regressive model is thus a version of the class D regressive model with the property of within-sibship interchangeability. The work is motivated here by comparing and contrasting the Elston-Stewart algorithm and the Morton-MacLean algorithm for the mixed model of inheritance. This points the way to derive practical algorithms for the compound regressive models proposed, with easy extensions to pedigrees of arbitrary structure, and to multilocus problems.

Combined segregation and linkage analysis of genetic hemochromatosis using affection status, serum iron, and HLA.

Characterizing the distribution of parameters of iron metabolism by hemochromatosis genotype remains an important goal vis-à-vis potential screening strategies to identify individuals at genetic risk, since a specific marker to detect the abnormal gene has not been identified as yet. In the present investigation, we analyze serum iron values in ascertained families using a method which incorporates both segregation of the clinical affection status and the HLA linkage information to identify the underlying genotypes. The analysis is performed using an extension of the model presented by Bonney et al., comprising regressive models for segregation analysis and the multipoint linkage strategy implemented in LINKAGE. The gene was found to be completely recessive with respect to both clinical manifestations and serum iron abnormalities, with significant differences in expression by sex. Clinical manifestations were present for all male homozygotes in this data set, suggesting that the recessive hemochromatosis genotype is fully penetrant at all ages in males. This was not the case for younger females. Significant genotype-specific age and sex effects were found for serum iron values. It is interesting that deletion of the HLA marker information did not affect our ability to resolve the genetic model when we analyzed a bivariate phenotype. This serves as a reminder that a search for relevant biological markers can be equally important in discerning the genetic etiology of a disease trait, as a search for linked genetic markers.

A multivariate method for detecting genetic linkage, with application to a pedigree with an adverse lipoprotein phenotype.

The robust or model-free method for detecting linkage developed by Haseman and Elston for data from sib pairs is extended to incorporate observations of multiple traits on each individual. A method is proposed that estimates the linear function that results in the strongest correlation between the squared pair differences in the trait measurements and identity by descent at a marker locus. The method is illustrated by the study of apolipoprotein and cholesterol levels in individuals from a large family that had many members diagnosed with coronary heart disease.

Search for faster methods of fitting the regressive models to quantitative traits.

The regressive models describe familial patterns of dependence of quantitative measures by specifying regression relationships among a person's phenotype and genotype and the phenotypes and genotypes of antecedents. When the number of sibs in the pattern of dependence increases, as in the class D regressive model, computation of the likelihood becomes time consuming, since the Elston-Stewart algorithm cannot be used generally. On the other hand, the simpler class A regressive model, which imposes a restriction on the sib-sib correlation, may lead to inference of a spurious major gene, as already observed in some instances. A simulation study is performed to explore the robustness of class A model with respect to false inference of a major gene and to search for faster methods of computing the likelihood under class D model. The class A model is not robust against the presence of a sib-sib correlation exceeding that specified by the model, unless tests on transmission probabilities are performed carefully: false detection of a major gene is reduced from a number of 26-30 to between 0 and 4 data sets out of 30 replicates after testing both the Mendelian transmission and the absence of transmission of a major effect against the general transmission model. Among various approximations of the likelihood formulation of the class D model, approximations 6 and 8 are found to work appropriately in terms of both the estimation of all parameters and hypothesis testing, for each generating model. These approximations lessen the computer time by allowing use of the Elston-Stewart algorithm.

A time-dependent logistic hazard function for modeling variable age of onset in analysis of familial diseases.

The paper presents an extension of the regressive logistic models proposed by Bonney [Biometrics 42:611-625, 1986], to address the problems of variable age-of-onset and time-dependent covariates in analysis of familial diseases. This goal is achieved by using failure time data analysis methods, and partitioning the time of follow up in K mutually exclusive intervals. The conditional probability of being affected within the kth interval (k = 1...K) given not affected before represents the hazard function in this discrete formulation. A logistic model is used to specify a regression relationship between this hazard function and a set of explanatory variables including genotype, phenotypes of ancestors, and other covariates which can be time dependent. The probability that a given person either becomes affected within the kth interval (i.e., interval k includes age of onset of the person) or remains unaffected by the end of the kth interval (i.e., interval k includes age at examination of the person) are derived from the general results of failure time data analysis and used for the likelihood formulation. This proposed approach can be used in any genetic segregation and linkage analysis in which a penetrance function needs to be defined. Application of the method to familial leprosy data leads to results consistent with our previous analysis performed using the unified mixed model [Abel and Demenais, Am J Hum Genet 42:256-266, 1988], i.e., the presence of a recessive major gene controlling susceptibility to leprosy. Furthermore, a simulation study shows the capability of the new model to detect major gene effects and to provide accurate parameter estimates in a situation of complete ascertainment.

A time-dependent logistic hazard function for modeling variable age of onset in analysis of familial diseases

This paper presents an extension of the regressive logistic model proposed by Bonney [Biometrics 42:611-625, 1986], to address the problems of variable age-of-onset and time-dependent covariates in analysis of familial diseases. The goal is achieved by using failure time data analysis methods, and partitioning the time of follow up in K mutually exclusive intervals. The conditional probability of being affected within the Kth interval (K=1...K) given not affected before represents the hazaard function in this discrete formulation. A logistic model is used to specify a regression relationship between this hazard function and a set of explanatory variables including genotype, phenotype of ancestors and other covariates which can be time independent. The probability that a given person either becomes affected within the Kth interval (ie. interval K includes age of onset of the person) or remains unaffected by the end of the Kth interval (ie. interval K includes age at examination of the person) are derived from the general result of failure time data analysis and used for the likelihood formulation. This proposed approach can be used in any genetic segregation and linkage analysis in which a penetrance function needs to be defined. Application of the method to familial leprosy data leads to results consistent with our previous analysis performed using the unified mixed model [Abel and Demenias, Am J Hum Genet 42:256-266, 1988], ie. the presence of a recessive major gene controlling susceptibility to leprosy. Furthermore, a simulation study shows the capability of the new method to detect major gene effects and to provide accurate parameter estimates in a situation of complete ascertainment. (AU)