Computer software for performing likelihood tests of pedigree relationship using genetic markers

Molecular techniques are making ever more genetic markers available for use in parentage assignment, and measures of relatedness. We present a program, Kinship, designed to use likelihood techniques to test for any non-inbred pedigree relationship between pairs of individuals, using single-locus codominant genetic markers. Kinship calculates the likelihood that each pair of individuals in a data set are related by a given pedigree hypothesis, and likelihood ratios for any pair of hypotheses. The program also uses a simulation routine to attach statistical significance to its results.     

Retrospective versus prospective score tests for genetic association with case‐control data

Since the seminal work of Prentice and Pyke, the prospective logistic likelihood has become the standard method of analysis for retrospectively collected case‐control data, in particular for testing the association between a single genetic marker and a disease outcome in genetic case‐control studies. In the study of multiple genetic markers with relatively small effects, especially those with rare variants, various aggregated approaches based on the same prospective likelihood have been developed to integrate subtle association evidence among all the markers considered. Many of the commonly used tests are derived from the prospective likelihood under a common‐random‐effect assumption, which assumes a common random effect for all subjects. We develop the locally most powerful aggregation test based on the retrospective likelihood under an independent‐random‐effect assumption, which allows the genetic effect to vary among subjects. In contrast to the fact that disease prevalence information cannot be used to improve efficiency for the estimation of odds ratio parameters in logistic regression models, we show that it can be utilized to enhance the testing power in genetic association studies. Extensive simulations demonstrate the advantages of the proposed method over the existing ones. A real genome‐wide association study is analyzed for illustration.     

Likelihood estimation of quantitative genetic parameters when selection occurs: models and problems

Conceptual aspects of estimation of genetic components of variance and covariance under selection are discussed, with special attention to likelihood methods. Certain selection processes are described and alternative likelihoods that can be used for analysis are specified. There is a mathematical relationship between the likelihoods that permits comparing the relative amount of information contained in them. Theoretical arguments and evidence indicate that point inferences made from likelihood functions are not affected by some forms of selection.     

Statistical analysis of multilocus recombination

A general formula for the frequency of different recombinant gamete types, in terms of the underlying distribution of crossovers, is derived. This formula may be applied to any theoretical model of recombination in which it is assumed that there is no chromatid interference. Multiple-locus recombination data may be evaluated by using this formula in conjunction with a maximum likelihood procedure. The validity of any model of recombination may be tested in such a fashion. The possibilities are demonstrated through application to a generalized noninterference model of crossing over described in a previous paper (Risch and Lange, 1979, Annals of Human Genetics 43, 61-70).     

Statistical basis for positive identification in forensic anthropology

Forensic scientists are often expected to present the likelihood of DNA identifications in US courts based on comparative population data, yet forensic anthropologists tend not to quantify the strength of an osteological identification. Because forensic anthropologists are trained first and foremost as physical anthropologists, they emphasize estimation problems at the expense of evidentiary problems, but this approach must be reexamined. In this paper, the statistical bases for presenting osteological and dental evidence are outlined, using a forensic case as a motivating example. A brief overview of Bayesian statistics is provided, and methods to calculate likelihood ratios for five aspects of the biological profile are demonstrated. This paper emphasizes the definition of appropriate reference samples and of the "population at large," and points out the conceptual differences between them. Several databases are introduced for both reference information and to characterize the "population at large," and new data are compiled to calculate the frequency of specific characters, such as age or fractures, within the "population at large." Despite small individual likelihood ratios for age, sex, and stature in the case example, the power of this approach is that, assuming each likelihood ratio is independent, the product rule can be applied. In this particular example, it is over three million times more likely to obtain the observed osteological and dental data if the identification is correct than if the identification is incorrect. This likelihood ratio is a convincing statistic that can support the forensic anthropologist's opinion on personal identity in court.     

An explicit formula for frequency changes in genetic algebras

Summary A general situation in population genetics is considered with any hereditary system described by a genetic algebra. It is assumed that there is random mating, no selection, and infinite population size. A formula is derived for the distribution of genetic types in the general jth generation given the distribution in the initial generation. Special attention is paid to the case of one locus with polyploidy and chromosome segregation. The calculations are carried out as far as possible in the situation with triploid gametes.Work supported by the Alexander von Humboldt Foundation.     

Testing separate families of segregation hypotheses: bootstrap methods.

Aspects of the statistical modeling and assessment of hypotheses concerning quantitative traits in genetics research are discussed. It is suggested that a traditional approach to such modeling and hypothesis testing, whereby competing models are "nested" in an effort to simplify their probabilistic assessment, can be complimented by an alternative statistical paradigm - the separate-families-of-hypotheses approach to segregation analysis. Two bootstrap-based methods are described that allow testing of any two, possibly non-nested, parametric genetic hypotheses. These procedures utilize a strategy in which the unknown distribution of a likelihood ratio-based test statistic is simulated, thereby allowing the estimation of critical values for the test statistic. Though the focus of this paper concerns quantitative traits, the strategies described can be applied to qualitative traits as well. The conceptual advantages and computational ease of these strategies are discussed, and their significance levels and power are examined through Monte Carlo experimentation. It is concluded that the separate-families-of-hypotheses approach, when carried out with the methods described in this paper, not only possesses some favorable statistical properties but also is well suited for genetic segregation analysis.     

Multifactorial genetic models for quantitative traits in humans.

Quantitative traits measured in human families can be analyzed to partition the total population variance into genetic and environmental components, or to elucidate the genetic mechanism involved. We review the estimation of variance components directly from human pedigree data, or in the form of path coefficients from correlations between pairs of relatives. To elucidate genetic mechanisms, a mixed model that allows for segregation at a major locus, a polygenic effect and a sibling environmental correlation is described for nuclear families. In each case appropriate likelihoods are derived as a basis, using numerical maximum likelihood methods, for parameter estimation and hypothesis testing. A general model is then described that allows for several familial sources of environmental variation, assortative mating, and both major gene and polygenic effects; and an algorithm for calculating the likelihood of a pedigree under this model is indicated. Finally, some of the remaining problems in this area of biometric analysis are pointed out.     

A Likelihood Ratio Test for the Nonparametric Behrens‐Fisher Problem

The nonparametric Behrens‐Fisher hypothesis is the most appropriate null hypothesis for the two‐sample comparison when one does not wish to make restrictive assumptions about possible distributions. In this paper, a numerical approach is described by which the likelihood ratio test can be calculated for the nonparametric Behrens‐Fisher problem. The approach taken here effectively reduces the number of parameters in the score equations to one by using a recursive formula for the remaining parameters. The resulting single dimensional problem can be solved numerically. The power of the likelihood ratio test is compared by simulation to that of a generalized Wilcoxon test of Brunner and Munzel. The tests have similar power for all alternatives considered when a simulated null distribution is used to generate cutoff values for the tests. The methods are illustrated on data on shoulder pain from a clinical trial.     

Failed refutations: further comments on parsimony and likelihood methods and their relationship to Popper's degree of corroboration

Kluge's (2001, Syst. Biol. 50:322-330) continued arguments that phylogenetic methods based on the statistical principle of likelihood are incompatible with the philosophy of science described by Karl Popper are based on false premises related to Kluge's misrepresentations of Popper's philosophy. Contrary to Kluge's conjectures, likelihood methods are not inherently verificationist; they do not treat every instance of a hypothesis as confirmation of that hypothesis. The historical nature of phylogeny does not preclude phylogenetic hypotheses from being evaluated using the probability of evidence. The low absolute probabilities of hypotheses are irrelevant to the correct interpretation of Popper's concept termed degree of corroboration, which is defined entirely in terms of relative probabilities. Popper did not advocate minimizing background knowledge; in any case, the background knowledge of both parsimony and likelihood methods consists of the general assumption of descent with modification and additional assumptions that are deterministic, concerning which tree is considered most highly corroborated. Although parsimony methods do not assume (in the sense of entailing) that homoplasy is rare, they do assume (in the sense of requiring to obtain a correct phylogenetic inference) certain things about patterns of homoplasy. Both parsimony and likelihood methods assume (in the sense of implying by the manner in which they operate) various things about evolutionary processes, although violation of those assumptions does not always cause the methods to yield incorrect phylogenetic inferences. Test severity is increased by sampling additional relevant characters rather than by character reanalysis, although either interpretation is compatible with the use of phylogenetic likelihood methods. Neither parsimony nor likelihood methods assess test severity (critical evidence) when used to identify a most highly corroborated tree(s) based on a single method or model and a single body of data; however, both classes of methods can be used to perform severe tests. The assumption of descent with modification is insufficient background knowledge to justify cladistic parsimony as a method for assessing degree of corroboration. Invoking equivalency between parsimony methods and likelihood models that assume no common mechanism emphasizes the necessity of additional assumptions, at least some of which are probabilistic in nature. Incongruent characters do not qualify as falsifiers of phylogenetic hypotheses except under extremely unrealistic evolutionary models; therefore, justifications of parsimony methods as falsificationist based on the idea that they minimize the ad hoc dismissal of falsifiers are questionable. Probabilistic concepts such as degree of corroboration and likelihood provide a more appropriate framework for understanding how phylogenetics conforms with Popper's philosophy of science. Likelihood ratio tests do not assume what is at issue but instead are methods for testing hypotheses according to an accepted standard of statistical significance and for incorporating considerations about test severity. These tests are fundamentally similar to Popper's degree of corroboration in being based on the relationship between the probability of the evidence e in the presence versus absence of the hypothesis h, i.e., between p(e|hb) and p(e|b), where b is the background knowledge. Both parsimony and likelihood methods are inductive in that their inferences (particular trees) contain more information than (and therefore do not follow necessarily from) the observations upon which they are based; however, both are deductive in that their conclusions (tree lengths and likelihoods) follow necessarily from their premises (particular trees, observed character state distributions, and evolutionary models). For these and other reasons, phylogenetic likelihood methods are highly compatible with Karl Popper's philosophy of science and offer several advantages over parsimony methods in this context.     

The structure of allelic diversity in the presence of purifying selection

In the absence of selection, the structure of equilibrium allelic diversity is described by the elegant sampling formula of Ewens. This formula has helped to shape our expectations of empirical patterns of molecular variation. Along with coalescent theory, it provides statistical techniques for rejecting the null model of neutrality. However, we still do not fully understand the statistics of the allelic diversity expected in the presence of natural selection. Earlier work has described the effects of strongly deleterious mutations linked to many neutral sites, and allelic variation in models where offspring fitness is unrelated to parental fitness, but it has proven difficult to understand allelic diversity in the presence of purifying selection at many linked sites. Here, we study the population genetics of infinitely many perfectly linked sites, some neutral and some deleterious. Our approach is based on studying the lineage structure within each class of individuals of similar fitness in the deleterious mutation-selection balance. Consistent with previous observations, we find that for moderate and weak selection pressures, the patterns of allelic diversity cannot be described by a neutral model for any choice of the effective population site. We compute precisely how purifying selection at many linked sites distorts the patterns of allelic diversity, by developing expressions for the likelihood of any configuration of allelic types in a sample analogous to the Ewens sampling formula.     

Bayes框架下DNA证据的量化研究

针对DNA（脱氧核糖核酸）证据的量化过程中常用的插入算法存在的缺陷，即量化结果与样本大小无关，小样本时过分量化了DNA证据，本文考虑了样本大小的影响，引入了Bayes模型。给出了基于Bayes模型下的似然比的计算公式，结合实际案例，对比了两种方法下的计算结果，数据结果表明基于Bayes模型下的算法比插入算法更加精确和合理。     

A general program for estimation of haplotype frequencies from population diploid data.

The program which is written in FORTRAN estimates haplotype frequencies in two-locus and three-locus genetic systems from population diploid data. It is based on the gene counting method which leads to maximum likelihood estimates, and can be used whenever the possible antigens (one or more) on each chromosome can be specified for each person and for each locus, i.e., ABO-like systems and inclusions are permitted. The number of alleles per locus may be rather large, and both grouped and ungrouped data can be used. Log likelihoods are calculated on the basis of various assumptions, so that likelihood ratio tests can be carried out.     

Plant Taxonomy Today

A computer program for genetic models which has some useful and labour saving features is described. The program allows students with only a rudimentary knowledge of programming to cope easily with complex genetic models. Some applications of the program are discussed.     

Case report: Intestinal perforation and secondary peritonitis due to Acanthocephala infection in a black-bellied pangolin (Phataginus tetradactyla)

A case of Acanthocephala infection in a 5-year-old female rehabilitated and released black-bellied pangolin (Phataginus tetradactyla), which was part of a post-release monitoring program of a pangolin research operation in the Central African Republic, is described. This represents the first report of Acanthocephala infection in this species, which lead to intestinal perforation, secondary peritonitis and ultimately to the death of the animal concerned. It is of relevance to alert the pangolin conservation and research community to a so far unreported cause of death. A case history and necropsy findings, as well as preliminary parasite identification and genetic characterization which potentially revealed a new gigantorhynchid taxon are presented.     

Relationships between familial risks of cancer and the effects of heritable genes and their SNP variants

Familial risks for cancer can be used in many ways in guiding gene identification efforts and, more broadly, in understanding cancer etiology. Gene identification efforts may be properly designed and targeted if the familial risks are well characterized and the mode of inheritance is identified. Single nucleotide polymorphisms (SNPs) are extensively used in case-control studies of practically all cancer types. They are used for the identification of inherited cancer susceptibility genes and those that may interact with environmental factors. However, being genetic markers, they are applicable only on heritable conditions, which is often a neglected fact. Based on the data in the nationwide Swedish Family-Cancer Database, we review familial risks for all main cancers and discuss the evidence for a heritable component in cancer. The available evidence, including differences in cancer incidence between regions and temporal changes within regions, indicates that cancer is mainly an environmental disease, with a minor heritable etiology. The large environmental component will hamper the success of SNP-based genetic association studies. Empirical familial risks should be used to evaluate the feasibility of such studies. We develop figures for the assessment of genetic parameters based on familial risks. Such data are helpful in the estimation of the expected genetic effects in cancer. Overall, we consider the likelihood of a successful application of SNPs in gene-environment studies small, unless established environmental risk factors are tested on proven candidate genes.     

A computer program for stepwise logistic regression using maximum likelihood estimation

A computer program has been written which performs a stepwise selection of variables for logistic regression using maximum likelihood estimation. The selection procedure is based on likelihood ratio tests for the coefficients. These tests are used in a forward selection and a backward elimination at each step. The use of the program is illustrated by several examples.     

Mixture models for continuous data in dose-response studies when some animals are unaffected by treatment.

A mixture model is described for dose-response studies where measurements on a continuous variable suggest that some animals are not affected by treatment. The model combines a logistic regression on dose for the probability an animal will "respond" to treatment with a linear regression on dose for the mean of the responders. Maximum likelihood estimation via the EM algorithm is described and likelihood ratio tests are used to distinguish between the full model and meaningful reduced-parameter versions. Use of the model is illustrated with three real-data examples.