Latent variable models in statistical genetics

Understanding the complexities that are involved in the genetics of multifactorial diseases is still a monumental task. In addition to environmental factors that can influence the risk of disease, there is also a number of other complicating factors. Genetic variants associated with age of disease onset may be different from those variants associated with overall risk of disease, and variants may be located in positions that are not consistent with the traditional protein coding genetic paradigm. Latent Variable Models are well suited for the analysis of genetic data. A latent variable is one that we do not directly observe, but which is believed to exist or is included for computational or analytic convenience in a model. This thesis presents a mixture of methodological developments utilising latent variables, and results from case studies in genetic epidemiology and comparative genomics. Epidemiological studies have identified a number of environmental risk factors for appendicitis, but the disease aetiology of this oft thought useless vestige remains largely a mystery. The effects of smoking on other gastrointestinal disorders are well documented, and in light of this, the thesis investigates the association between smoking and appendicitis through the use of latent variables. By utilising data from a large Australian twin study questionnaire as both cohort and case-control, evidence is found for the association between tobacco smoking and appendicitis. Twin and family studies have also found evidence for the role of heredity in the risk of appendicitis. Results from previous studies are extended here to estimate the heritability of age-at-onset and account for the eect of smoking. This thesis presents a novel approach for performing a genome-wide variance components linkage analysis on transformed residuals from a Cox regression. This method finds evidence for a dierent subset of genes responsible for variation in age at onset than those associated with overall risk of appendicitis. Motivated by increasing evidence of functional activity in regions of the genome once thought of as evolutionary graveyards, this thesis develops a generalisation to the Bayesian multiple changepoint model on aligned DNA sequences for more than two species. This sensitive technique is applied to evaluating the distributions of evolutionary rates, with the finding that they are much more complex than previously apparent. We show strong evidence for at least 9 well-resolved evolutionary rate classes in an alignment of four Drosophila species and at least 7 classes in an alignment of four mammals, including human. A pattern of enrichment and depletion of genic regions in the profiled segments suggests they are functionally significant, and most likely consist of various functional classes. Furthermore, a method of incorporating alignment characteristics representative of function such as GC content and type of mutation into the segmentation model is developed within this thesis. Evidence of fine-structured segmental variation is presented.

Bayesian methodology for genetics of complex diseases

Genetic research of complex diseases is a challenging, but exciting, area of research. The early development of the research was limited, however, until the completion of the Human Genome and HapMap projects, along with the reduction in the cost of genotyping, which paves the way for understanding the genetic composition of complex diseases. In this thesis, we focus on the statistical methods for two aspects of genetic research: phenotype definition for diseases with complex etiology and methods for identifying potentially associated Single Nucleotide Polymorphisms (SNPs) and SNP-SNP interactions. With regard to phenotype definition for diseases with complex etiology, we firstly investigated the effects of different statistical phenotyping approaches on the subsequent analysis. In light of the findings, and the difficulties in validating the estimated phenotype, we proposed two different methods for reconciling phenotypes of different models using Bayesian model averaging as a coherent mechanism for accounting for model uncertainty. In the second part of the thesis, the focus is turned to the methods for identifying associated SNPs and SNP interactions. We review the use of Bayesian logistic regression with variable selection for SNP identification and extended the model for detecting the interaction effects for population based case-control studies. In this part of study, we also develop a machine learning algorithm to cope with the large scale data analysis, namely modified Logic Regression with Genetic Program (MLR-GEP), which is then compared with the Bayesian model, Random Forests and other variants of logic regression.

The genetics of cutaneous melanoma

Although germline mutations in CDKN2A are present in approximately 25% of large multicase melanoma families, germline mutations are much rarer in the smaller melanoma families that make up most individuals reporting a family history of this disease. In addition, only three families worldwide have been reported with germline mutations in a gene other than CDKN2A (i.e., CDK4). Accordingly, current genomewide scans underway at the National Human Genome Research Institute hope to reveal linkage to one or more chromosomal regions, and ultimately lead to the identification of novel genes involved in melanoma predisposition. Both CDKN2A and PTEN have been identified as genes involved in sporadic melanoma development; however, mutations are more common in cell lines than uncultured tumors. A combination of cytogenetic, molecular, and functional studies suggests that additional genes involved in melanoma development are located to chromosomal regions 1p, 6q, 7p, 11q, and possibly also 9p and 10q. With the near completion of the human genome sequencing effort, combined with the advent of high throughput mutation analyses and new techniques including cDNA and tissue microarrays, the identification and characterization of additional genes involved in melanoma pathogenesis seem likely in the near future.

Quality of life and genetics in men with prostate cancer

As family history has been established as a risk factor for prostate cancer, attempts have been made to isolate predisposing genetic variants that are related to hereditary prostate cancer. With many genetic variants still to be identified and investigated, it is not yet possible to fully understand the impact of genetic variants on prostate cancer development. The high survival rates among men with prostate cancer have meant that other issues, such as quality of life (QoL), have also become important. Through their effect on a person’s health, a range of inherited genetic variants may potentially influence QoL in men with prostate cancer, even prior to treatment. Until now, limited research has been conducted on the relationship between genetics and QoL. Thus, this study contributes to an emerging field by aiming to identify certain genetic variants related to the QoL found in men with prostate cancer. It is hoped that this study may lead to future research that will identify men who have an increased risk of a poor QoL following prostate cancer treatment, which will aid in developing treatments that are individually tailored to support them. Previous studies have established that genetic variants of Vascular Endothelial Growth Factor (VEGF) and Insulin-like Growth Factor 1 (IGF-1) may play a role in prostate cancer development. VEGF and IGF-1 have also been reported to be associated with QoL in people with ovarian cancer and colorectal cancer, respectively. This study completed a series of secondary analyses using two major data-sets (from 850 men newly diagnosed with prostate cancer, and approximately 550 men from the general Queensland population), in which genetic variants of VEGF and IGF-1 were investigated for associations with prostate cancer susceptibility and QoL. The first aim of this research was to investigate genetic variants in the VEGF and IGF-I gene for an association with the risk of prostate cancer. It was found that one IGF-1 genetic variant (rs35765) had a statistically significant association with prostate cancer (p = 0.04), and one VEGF genetic variant (rs2146323) had a statistically significant association with advanced prostate cancer (p = 0.02). The estimates suggest that carriers of the CA and AA genotype for rs35765 may have a reduced risk of developing prostate cancer (Odds Ratio (OR) = 0.72, 95% Confidence Interval (CI) = 0.55, 0.95, OR = 0.60, 95% CI = 0.26, 1.39, respectively). Meanwhile, carriers of the CA and AA genotype for rs2146323 may be at increased risk of advanced prostate cancer, which was determined by a Gleason score of above 7 (OR = 1.72, 95% CI = 1.12, 2.63, OR = 1.90, 95% CI = 1.08, 3.34, respectively). Utilising the widely used short-form health survey, the SF-36v2, the second aim of this study was to investigate the relationship between prostate cancer and QoL prior to treatment. Assessing QoL at this time-point was important as little research has been conducted to evaluate if prostate cancer affects QoL regardless of treatment. The analyses found that mean SF-36v2 scale scores related to physical health were higher by at least 0.3 Standard Deviations (SD) among men with prostate cancer than the general population comparison group. This difference was considered clinically significant (defined by group differences in mean SF-36v2 scores by at least 0.3 SD). These differences were also statistically significant (p<0.05). Mean QoL scale scores related to mental health were similar between men with prostate cancer and those from the general population comparison group. The third aim of this study was to investigate genetic variants in the VEGF and IGF-1 gene for an association with QoL in prostate cancer patients prior to their treatment. It was essential to evaluate these relationships prior to treatment, before the involvement of these genes was potentially interrupted by treatment. The analyses found that some genetic variants had a small clinically significant association (0.3 SD) to some QoL domains experienced by these men. However, most relationships were not statistically significant (p>0.05). Most of the associations found identified that a small sub-group of men with prostate cancer (approximately 2%) reported, on average, a slightly better QoL than the majority of the prostate cancer patients. The fourth aim of this research was to investigate whether associations between genetic variants in VEGF and IGF-1 and QoL were specific to men with prostate cancer, or were also applicable to the general male population. It was found that twenty out of one-hundred relationships between the genetic variants of VEGF and IGF-1 and QoL health-measures and scales examined differed between these groups. In the majority of the relationships involving VEGF SNPs that differed, a clinically significant difference (0.3 or more SD) between mean scores among the genotype groups in prostate cancer patients was found, while mean scores among men from the general-population comparison group were similar. For example, prostate cancer participants who carried at least one T allele (CT or TT genotype) for rs3024994 had a clinically significant higher (0.3 SD) mean QoL score in terms of the role-physical scale, than participants who carried the CC genotype. This was not seen among men from the general population sample, as the mean score was similar between genotype groups. The opposite was seen in regards to the IGF-1 SNPs examined. Overall, these relationships were not considered to directly impact on the clinical options for men with prostate cancer. As this study utilised secondary data from two separate studies, there are a number of important limitations that should be acknowledged including issues of multiple comparisons, power, and missing or unavailable data. It is recommended that this study be replicated as a better-designed study that takes greater consideration of the many factors involved in prostate cancer and QoL. Investigation into other genetic variants of VEGF or IGF-1 is also warranted, as is consideration of other genes and their relationship with QoL. Through identifying certain genetic variants that have a modest association to prostate cancer, this project adds to the knowledge surrounding VEGF and IGF-1 and their role in prostate cancer susceptibility. Importantly, this project has also introduced the potential role genetics plays in QoL, through investigating the relationships between genetic variants of VEGF and IGF-1 and QoL.

Toward resolving deep neoaves phylogeny : data, signal enhancement, and priors

We report three developments toward resolving the challenge of the apparent basal polytomy of neoavian birds. First, we describe improved conditional down-weighting techniques to reduce noise relative to signal for deeper divergences and find increased agreement between data sets. Second, we present formulae for calculating the probabilities of finding predefined groupings in the optimal tree. Finally, we report a significant increase in data: nine new mitochondrial (mt) genomes (the dollarbird, New Zealand kingfisher, great potoo, Australian owlet-nightjar, white-tailed trogon, barn owl, a roadrunner [a ground cuckoo], New Zealand long-tailed cuckoo, and the peach-faced lovebird) and together they provide data for each of the six main groups of Neoaves proposed by Cracraft J (2001). We use his six main groups of modern birds as priors for evaluation of results. These include passerines, cuckoos, parrots, and three other groups termed “WoodKing” (woodpeckers/rollers/kingfishers), “SCA” (owls/potoos/owlet-nightjars/hummingbirds/swifts), and “Conglomerati.” In general, the support is highly significant with just two exceptions, the owls move from the “SCA” group to the raptors, particularly accipitrids (buzzards/eagles) and the osprey, and the shorebirds may be an independent group from the rest of the “Conglomerati”. Molecular dating mt genomes support a major diversification of at least 12 neoavian lineages in the Late Cretaceous. Our results form a basis for further testing with both nuclear-coding sequences and rare genomic changes.

Pedigree-free animal models : the relatedness matrix reloaded

Animal models typically require a known genetic pedigree to estimate quantitative genetic parameters. Here we test whether animal models can alternatively be based on estimates of relatedness derived entirely from molecular marker data. Our case study is the morphology of a wild bird population, for which we report estimates of the genetic variance-covariance matrices (G) of six morphological traits using three methods: the traditional animal model; a molecular marker-based approach to estimate heritability based on Ritland's pairwise regression method; and a new approach using a molecular genealogy arranged in a relatedness matrix (R) to replace the pedigree in an animal model. Using the traditional animal model, we found significant genetic variance for all six traits and positive genetic covariance among traits. The pairwise regression method did not return reliable estimates of quantitative genetic parameters in this population, with estimates of genetic variance and covariance typically being very small or negative. In contrast, we found mixed evidence for the use of the pedigree-free animal model. Similar to the pairwise regression method, the pedigree-free approach performed poorly when the full-rank R matrix based on the molecular genealogy was employed. However, performance improved substantially when we reduced the dimensionality of the R matrix in order to maximize the signal to noise ratio. Using reduced-rank R matrices generated estimates of genetic variance that were much closer to those from the traditional model. Nevertheless, this method was less reliable at estimating covariances, which were often estimated to be negative. Taken together, these results suggest that pedigree-free animal models can recover quantitative genetic information, although the signal remains relatively weak. It remains to be determined whether this problem can be overcome by the use of a more powerful battery of molecular markers and improved methods for reconstructing genealogies.

Snowy Owl

Poem.

Modeling as a means for making powerful ideas accessible to children at an early age

The SimCalc Vision and Contributions Advances in Mathematics Education 2013, pp 419-436 Modeling as a Means for Making Powerful Ideas Accessible to Children at an Early Age Richard Lesh, Lyn English, Serife Sevis, Chanda Riggs … show all 4 hide » Look Inside » Get Access Abstract In modern societies in the 21st century, significant changes have been occurring in the kinds of “mathematical thinking” that are needed outside of school. Even in the case of primary school children (grades K-2), children not only encounter situations where numbers refer to sets of discrete objects that can be counted. Numbers also are used to describe situations that involve continuous quantities (inches, feet, pounds, etc.), signed quantities, quantities that have both magnitude and direction, locations (coordinates, or ordinal quantities), transformations (actions), accumulating quantities, continually changing quantities, and other kinds of mathematical objects. Furthermore, if we ask, what kind of situations can children use numbers to describe? rather than restricting attention to situations where children should be able to calculate correctly, then this study shows that average ability children in grades K-2 are (and need to be) able to productively mathematize situations that involve far more than simple counts. Similarly, whereas nearly the entire K-16 mathematics curriculum is restricted to situations that can be mathematized using a single input-output rule going in one direction, even the lives of primary school children are filled with situations that involve several interacting actions—and which involve feedback loops, second-order effects, and issues such as maximization, minimization, or stabilizations (which, many years ago, needed to be postponed until students had been introduced to calculus). …This brief paper demonstrates that, if children’s stories are used to introduce simulations of “real life” problem solving situations, then average ability primary school children are quite capable of dealing productively with 60-minute problems that involve (a) many kinds of quantities in addition to “counts,” (b) integrated collections of concepts associated with a variety of textbook topic areas, (c) interactions among several different actors, and (d) issues such as maximization, minimization, and stabilization.

Prediction of IBD based on population history for fine gene mapping

A novel multiple regression method (RM) is developed to predict identity-by-descent probabilities at a locus L (IBDL), among individuals without pedigree, given information on surrounding markers and population history. These IBDL probabilities are a function of the increase in linkage disequilibrium (LD) generated by drift in a homogeneous population over generations. Three parameters are sufficient to describe population history: effective population size (Ne), number of generations since foundation (T), and marker allele frequencies among founders (p). IBD L are used in a simulation study to map a quantitative trait locus (QTL) via variance component estimation. RM is compared to a coalescent method (CM) in terms of power and robustness of QTL detection. Differences between RM and CM are small but significant. For example, RM is more powerful than CM in dioecious populations, but not in monoecious populations. Moreover, RM is more robust than CM when marker phases are unknown or when there is complete LD among founders or Ne is wrong, and less robust when p is wrong. CM utilises all marker haplotype information, whereas RM utilises information contained in each individual marker and all possible marker pairs but not in higher order interactions. RM consists of a family of models encompassing four different population structures, and two ways of using marker information, which contrasts with the single model that must cater for all possible evolutionary scenarios in CM.

Power of QTL detection using association tests with family controls

The power of testing for a population-wide association between a biallelic quantitative trait locus and a linked biallelic marker locus is predicted both empirically and deterministically for several tests. The tests were based on the analysis of variance (ANOVA) and on a number of transmission disequilibrium tests (TDT). Deterministic power predictions made use of family information, and were functions of population parameters including linkage disequilibrium, allele frequencies, and recombination rate. Deterministic power predictions were very close to the empirical power from simulations in all scenarios considered in this study. The different TDTs had very similar power, intermediate between one-way and nested ANOVAs. One-way ANOVA was the only test that was not robust against spurious disequilibrium. Our general framework for predicting power deterministically can be used to predict power in other association tests. Deterministic power calculations are a powerful tool for researchers to plan and evaluate experiments and obviate the need for elaborate simulation studies.