Recent developments in statistical methods for detecting genetic loci affecting phenotypic variability

A number of recent works have introduced statistical methods for detecting genetic loci that affect phenotypic variability, which we refer to as variability-controlling quantitative trait loci (vQTL). These are genetic variants whose allelic state predicts how much phenotype values will vary about their expected means. Such loci are of great potential interest in both human and non-human genetic studies, one reason being that a detected vQTL could represent a previously undetected interaction with other genes or environmental factors. The simultaneous publication of these new methods in different journals has in many cases precluded opportunity for comparison. We survey some of these methods, the respective trade-offs they imply, and the connections between them. The methods fall into three main groups: classical non-parametric, fully parametric, and semi-parametric two-stage approximations. Choosing between alternatives involves balancing the need for robustness, flexibility, and speed. For each method, we identify important assumptions and limitations, including those of practical importance, such as their scope for including covariates and random effects. We show in simulations that both parametric methods and their semi-parametric approximations can give elevated false positive rates when they ignore mean-variance relationships intrinsic to the data generation process. We conclude that choice of method depends on the trait distribution, the need to include non-genetic covariates, and the population size and structure, coupled with a critical evaluation of how these fit with the assumptions of the statistical model.

A comparison of statistical methods for genomic selection in a mice population

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Epidemiology and genetics of endemic goiter. II. Genetic aspects

Complex genetic models and segregation analysis were applied to family data obtained in a hyperendemic goiter area in Brazil. The single locus and Falconer's models did not fit the data. Edward's model showed convergency, but statistical concordance has not been obtained. Although the genetic load model explains statistically the family data, it would be hard to imagine that endemic goiter could be explained by a model where synergism among genetic and environmental factors is not assumed.

Allelic frequencies and statistical data obtained from 12 codis STR loci in an admixed population of the Brazilian Amazon

The allelic frequencies of 12 short tandem repeat loci were obtained from a sample of 307 unrelated individuals living in Macapá, a city in the northern Amazon region, Brazil. These loci are the most commonly used in forensics and paternity testing. Based on the allele frequency obtained for the population of Macapá, we estimated an interethnic admixture for the three parental groups (European, Native American and African) of, respectively, 46%, 35% and 19%. Comparing these allele frequencies with those of other Brazilian populations and of the Iberian Peninsula population, no significant distances were observed. The interpopulation genetic distances (F_ST coefficients) to the present database ranged from F_ST = 0.0016 between Macapá and Belém to F_ST = 0.0036 between Macapá and the Iberian Peninsula.

Conservation genetics of European wildcat (Felis silvestris silvestris): a wide and integrating analysis protocol for admixture inferences and population structure

Introgression of domestic cat genes into European wildcat (Felis silvestris silvestris) populations and reduction of wildcats’ range in Europe, leaded by habitat loss and fragmentation, are considered two of the main conservation problems for this endangered feline. This thesis addressed the questions related with the artificial hybridization and populations’ fragmentation, using a conservation genetics perspective. We combined the use of highly polymorphic loci, Bayesian statistical inferences and landscape analyses tools to investigate the origin of the geographic-genetic substructure of European wildcats (Felis silvestris silvestris) in Italy and Europe. The genetic variability of microsatellites evidenced that European wildcat populations currently distributed in Italy differentiated in, and expanded from two distinct glacial refuges during the Last Glacial Maximum. The genetic and geographic substructure detected between the eastern and western sides of the Apennine ridge, resulted by adaptation to specific ecological conditions of the Mediterranean habitats. European wildcat populations in Europe are strongly structured into 5 geographic-genetic macro clusters corresponding to: the Italian peninsular & Sicily; Balkans & north-eastern Italy; Germany eastern; central Europe; and Iberian Peninsula. Central European population might have differentiated in the extra-Mediterranean Würm ice age refuge areas (Northern Alps, Carpathians, and the Bulgarian mountain systems), while the divergence among and within the southern European populations might have resulted by the Pleistocene bio geographical framework of Europe, with three southern refugia localized in the Balkans, Italian Peninsula and Iberia Peninsula. We further combined the use of most informative autosomal SNPs with uniparental markers (mtDNA and Y-linked) for accurately detecting parental genotypes and levels of introgressive hybridization between European wild and domestic cats. A total of 11 hybrids were identified. The presence of domestic mitochondrial haplotypes shared with some wild individuals led us to hypnotize the possibility that ancient introgressive events might have occurred and that further investigation should be recommended.

Appropriateness of reporting statistical results in orthodontics: the dominance of P values over confidence intervals

The purpose of this study was to search the orthodontic literature and determine the frequency of reporting of confidence intervals (CIs) in orthodontic journals with an impact factor. The six latest issues of the American Journal of Orthodontics and Dentofacial Orthopedics, the European Journal of Orthodontics, and the Angle Orthodontist were hand searched and the reporting of CIs, P values, and implementation of univariate or multivariate statistical analyses were recorded. Additionally, studies were classified according to the type/design as cross-sectional, case-control, cohort, and clinical trials, and according to the subject of the study as growth/genetics, behaviour/psychology, diagnosis/treatment, and biomaterials/biomechanics. The data were analyzed using descriptive statistics followed by univariate examination of statistical associations, logistic regression, and multivariate modelling. CI reporting was very limited and was recorded in only 6 per cent of the included published studies. CI reporting was independent of journal, study area, and design. Studies that used multivariate statistical analyses had a higher probability of reporting CIs compared with those using univariate statistical analyses. Misunderstanding of the use of P values and CIs may have important implications in implementation of research findings in clinical practice.

Population genetics of VNTR loci and their applications in evolutionary studies

Variable number of tandem repeats (VNTR) are genetic loci at which short sequence motifs are found repeated different numbers of times among chromosomes. To explore the potential utility of VNTR loci in evolutionary studies, I have conducted a series of studies to address the following questions: (1) What are the population genetic properties of these loci? (2) What are the mutational mechanisms of repeat number change at these loci? (3) Can DNA profiles be used to measure the relatedness between a pair of individuals? (4) Can DNA fingerprint be used to measure the relatedness between populations in evolutionary studies? (5) Can microsatellite and short tandem repeat (STR) loci which mutate stepwisely be used in evolutionary analyses?^ A large number of VNTR loci typed in many populations were studied by means of statistical methods developed recently. The results of this work indicate that there is no significant departure from Hardy-Weinberg expectation (HWE) at VNTR loci in most of the human populations examined, and the departure from HWE in some VNTR loci are not solely caused by the presence of population sub-structure.^ A statistical procedure is developed to investigate the mutational mechanisms of VNTR loci by studying the allele frequency distributions of these loci. Comparisons of frequency distribution data on several hundreds VNTR loci with the predictions of two mutation models demonstrated that there are differences among VNTR loci grouped by repeat unit sizes.^ By extending the ITO method, I derived the distribution of the number of shared bands between individuals with any kinship relationship. A maximum likelihood estimation procedure is proposed to estimate the relatedness between individuals from the observed number of shared bands between them.^ It was believed that classical measures of genetic distance are not applicable to analysis of DNA fingerprints which reveal many minisatellite loci simultaneously in the genome, because the information regarding underlying alleles and loci is not available. I proposed a new measure of genetic distance based on band sharing between individuals that is applicable to DNA fingerprint data.^ To address the concern that microsatellite and STR loci may not be useful for evolutionary studies because of the convergent nature of their mutation mechanisms, by a theoretical study as well as by computer simulation, I conclude that the possible bias caused by the convergent mutations can be corrected, and a novel measure of genetic distance that makes the correction is suggested. In summary, I conclude that hypervariable VNTR loci are useful in evolutionary studies of closely related populations or species, especially in the study of human evolution and the history of geographic dispersal of Homo sapiens. (Abstract shortened by UMI.) ^

A full pedigree based method for the statistical assessment of genetic anticipation

Genetic anticipation is defined as a decrease in age of onset or increase in severity as the disorder is transmitted through subsequent generations. Anticipation has been noted in the literature for over a century. Recently, anticipation in several diseases including Huntington's Disease, Myotonic Dystrophy and Fragile X Syndrome were shown to be caused by expansion of triplet repeats. Anticipation effects have also been observed in numerous mental disorders (e.g. Schizophrenia, Bipolar Disorder), cancers (Li-Fraumeni Syndrome, Leukemia) and other complex diseases. ^ Several statistical methods have been applied to determine whether anticipation is a true phenomenon in a particular disorder, including standard statistical tests and newly developed affected parent/affected child pair methods. These methods have been shown to be inappropriate for assessing anticipation for a variety of reasons, including familial correlation and low power. Therefore, we have developed family-based likelihood modeling approaches to model the underlying transmission of the disease gene and penetrance function and hence detect anticipation. These methods can be applied in extended families, thus improving the power to detect anticipation compared with existing methods based only upon parents and children. The first method we have proposed is based on the regressive logistic hazard model. This approach models anticipation by a generational covariate. The second method allows alleles to mutate as they are transmitted from parents to offspring and is appropriate for modeling the known triplet repeat diseases in which the disease alleles can become more deleterious as they are transmitted across generations. ^ To evaluate the new methods, we performed extensive simulation studies for data simulated under different conditions to evaluate the effectiveness of the algorithms to detect genetic anticipation. Results from analysis by the first method yielded empirical power greater than 87% based on the 5% type I error critical value identified in each simulation depending on the method of data generation and current age criteria. Analysis by the second method was not possible due to the current formulation of the software. The application of this method to Huntington's Disease and Li-Fraumeni Syndrome data sets revealed evidence for a generation effect in both cases. ^

A computerized statistical framework for coalescent analysis

Coalescent theory represents the most significant progress in theoretical population genetics in the past three decades. The coalescent theory states that all genes or alleles in a given population are ultimately inherited from a single ancestor shared by all members of the population, known as the most recent common ancestor. It is now widely recognized as a cornerstone for rigorous statistical analyses of molecular data from population [1]. The scientists have developed a large number of coalescent models and methods[2,3,4,5,6], which are not only applied in coalescent analysis and process, but also in today’s population genetics and genome studies, even public health. The thesis aims at completing a statistical framework based on computers for coalescent analysis. This framework provides a large number of coalescent models and statistic methods to assist students and researchers in coalescent analysis, whose results are presented in various formats as texts, graphics and printed pages. In particular, it also supports to create new coalescent models and statistical methods. ^

Statistical Methods for Differential Expressions of Genes Detected in Multiple-Condition Experiment of Microarray

Most studies of differential gene-expressions have been conducted between two given conditions. The two-condition experimental (TCE) approach is simple in that all genes detected display a common differential expression pattern responsive to a common two-condition difference. Therefore, the genes that are differentially expressed under the other conditions other than the given two conditions are undetectable with the TCE approach. In order to address the problem, we propose a new approach called multiple-condition experiment (MCE) without replication and develop corresponding statistical methods including inference of pairs of conditions for genes, new t-statistics, and a generalized multiple-testing method for any multiple-testing procedure via a control parameter C. We applied these statistical methods to analyze our real MCE data from breast cancer cell lines and found that 85 percent of gene-expression variations were caused by genotypic effects and genotype-ANAX1 overexpression interactions, which agrees well with our expected results. We also applied our methods to the adenoma dataset of Notterman et al. and identified 93 differentially expressed genes that could not be found in TCE. The MCE approach is a conceptual breakthrough in many aspects: (a) many conditions of interests can be conducted simultaneously; (b) study of association between differential expressions of genes and conditions becomes easy; (c) it can provide more precise information for molecular classification and diagnosis of tumors; (d) it can save lot of experimental resources and time for investigators.^

BAYESIAN STATISTICAL METHODS IN GENE-ENVIRONMENT AND GENE-GENE INTERACTION STUDIES

Complex diseases such as cancer result from multiple genetic changes and environmental exposures. Due to the rapid development of genotyping and sequencing technologies, we are now able to more accurately assess causal effects of many genetic and environmental factors. Genome-wide association studies have been able to localize many causal genetic variants predisposing to certain diseases. However, these studies only explain a small portion of variations in the heritability of diseases. More advanced statistical models are urgently needed to identify and characterize some additional genetic and environmental factors and their interactions, which will enable us to better understand the causes of complex diseases. In the past decade, thanks to the increasing computational capabilities and novel statistical developments, Bayesian methods have been widely applied in the genetics/genomics researches and demonstrating superiority over some regular approaches in certain research areas. Gene-environment and gene-gene interaction studies are among the areas where Bayesian methods may fully exert its functionalities and advantages. This dissertation focuses on developing new Bayesian statistical methods for data analysis with complex gene-environment and gene-gene interactions, as well as extending some existing methods for gene-environment interactions to other related areas. It includes three sections: (1) Deriving the Bayesian variable selection framework for the hierarchical gene-environment and gene-gene interactions; (2) Developing the Bayesian Natural and Orthogonal Interaction (NOIA) models for gene-environment interactions; and (3) extending the applications of two Bayesian statistical methods which were developed for gene-environment interaction studies, to other related types of studies such as adaptive borrowing historical data. We propose a Bayesian hierarchical mixture model framework that allows us to investigate the genetic and environmental effects, gene by gene interactions (epistasis) and gene by environment interactions in the same model. It is well known that, in many practical situations, there exists a natural hierarchical structure between the main effects and interactions in the linear model. Here we propose a model that incorporates this hierarchical structure into the Bayesian mixture model, such that the irrelevant interaction effects can be removed more efficiently, resulting in more robust, parsimonious and powerful models. We evaluate both of the 'strong hierarchical' and 'weak hierarchical' models, which specify that both or one of the main effects between interacting factors must be present for the interactions to be included in the model. The extensive simulation results show that the proposed strong and weak hierarchical mixture models control the proportion of false positive discoveries and yield a powerful approach to identify the predisposing main effects and interactions in the studies with complex gene-environment and gene-gene interactions. We also compare these two models with the 'independent' model that does not impose this hierarchical constraint and observe their superior performances in most of the considered situations. The proposed models are implemented in the real data analysis of gene and environment interactions in the cases of lung cancer and cutaneous melanoma case-control studies. The Bayesian statistical models enjoy the properties of being allowed to incorporate useful prior information in the modeling process. Moreover, the Bayesian mixture model outperforms the multivariate logistic model in terms of the performances on the parameter estimation and variable selection in most cases. Our proposed models hold the hierarchical constraints, that further improve the Bayesian mixture model by reducing the proportion of false positive findings among the identified interactions and successfully identifying the reported associations. This is practically appealing for the study of investigating the causal factors from a moderate number of candidate genetic and environmental factors along with a relatively large number of interactions. The natural and orthogonal interaction (NOIA) models of genetic effects have previously been developed to provide an analysis framework, by which the estimates of effects for a quantitative trait are statistically orthogonal regardless of the existence of Hardy-Weinberg Equilibrium (HWE) within loci. Ma et al. (2012) recently developed a NOIA model for the gene-environment interaction studies and have shown the advantages of using the model for detecting the true main effects and interactions, compared with the usual functional model. In this project, we propose a novel Bayesian statistical model that combines the Bayesian hierarchical mixture model with the NOIA statistical model and the usual functional model. The proposed Bayesian NOIA model demonstrates more power at detecting the non-null effects with higher marginal posterior probabilities. Also, we review two Bayesian statistical models (Bayesian empirical shrinkage-type estimator and Bayesian model averaging), which were developed for the gene-environment interaction studies. Inspired by these Bayesian models, we develop two novel statistical methods that are able to handle the related problems such as borrowing data from historical studies. The proposed methods are analogous to the methods for the gene-environment interactions on behalf of the success on balancing the statistical efficiency and bias in a unified model. By extensive simulation studies, we compare the operating characteristics of the proposed models with the existing models including the hierarchical meta-analysis model. The results show that the proposed approaches adaptively borrow the historical data in a data-driven way. These novel models may have a broad range of statistical applications in both of genetic/genomic and clinical studies.

A first trial of retrospective collaboration for positional cloning in complex inheritance: Assay of the cytokine region on chromosome 5 by the Consortium on Asthma Genetics (COAG)

The central problem of complex inheritance is to map oligogenes for disease susceptibility, integrating linkage and association over samples that differ in several ways. Combination of evidence over multiple samples with 1,037 families supports loci contributing to asthma susceptibility in the cytokine region on 5q [maximum logarithm of odds (lod) = 2.61 near IL-4], but no evidence for atopy. The principal problems with retrospective collaboration on linkage appear to have been solved, providing far more information than a single study. A multipoint lod table evaluated at commonly agreed reference loci is required for both collaboration and metaanalysis, but variations in ascertainment, pedigree structure, phenotype definition, and marker selection are tolerated. These methods are invariant with statistical methods that increase the power of lods and are applicable to all diseases, motivating collaboration rather than competition. In contrast to linkage, positional cloning by allelic association has yet to be extended to multiple samples, a prerequisite for efficient combination with linkage and the greatest current challenge to genetic epidemiology.

Journal of genetics.

Suspended 1977-1984. Cf. Letter from the publishing company dated July 1985; and page 1 of the July 1985 issue.