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.

Genetic variants underlying risk of endometriosis: Insights from meta-analysis of eight genome-wide association and replication datasets

BACKGROUND Endometriosis is a heritable common gynaecological condition influenced by multiple genetic and environmental factors. Genome-wide association studies (GWASs) have proved successful in identifying common genetic variants of moderate effects for various complex diseases. To date, eight GWAS and replication studies from multiple populations have been published on endometriosis. In this review, we investigate the consistency and heterogeneity of the results across all the studies and their implications for an improved understanding of the aetiology of the condition. METHODS Meta-analyses were conducted on four GWASs and four replication studies including a total of 11 506 cases and 32 678 controls, and on the subset of studies that investigated associations for revised American Fertility Society (rAFS) Stage III/IV including 2859 cases. The datasets included 9039 cases and 27 343 controls of European (Australia, Belgium, Italy, UK, USA) and 2467 cases and 5335 controls of Japanese ancestry. Fixed and Han and Elkin random-effects models, and heterogeneity statistics (Cochran's Q test), were used to investigate the evidence of the nine reported genome-wide significant loci across datasets and populations. RESULTS Meta-analysis showed that seven out of nine loci had consistent directions of effect across studies and populations, and six out of nine remained genome-wide significant (P < 5 × 10(-8)), including rs12700667 on 7p15.2 (P = 1.6 × 10(-9)), rs7521902 near WNT4 (P = 1.8 × 10(-15)), rs10859871 near VEZT (P = 4.7 × 10(-15)), rs1537377 near CDKN2B-AS1 (P = 1.5 × 10(-8)), rs7739264 near ID4 (P = 6.2 × 10(-10)) and rs13394619 in GREB1 (P = 4.5 × 10(-8)). In addition to the six loci, two showed borderline genome-wide significant associations with Stage III/IV endometriosis, including rs1250248 in FN1 (P = 8 × 10(-8)) and rs4141819 on 2p14 (P = 9.2 × 10(-8)). Two independent inter-genic loci, rs4141819 and rs6734792 on chromosome 2, showed significant evidence of heterogeneity across datasets (P < 0.005). Eight of the nine loci had stronger effect sizes among Stage III/IV cases, implying that they are likely to be implicated in the development of moderate to severe, or ovarian, disease. While three out of nine loci were inter-genic, the remaining were in or near genes with known functions of biological relevance to endometriosis, varying from roles in developmental pathways to cellular growth/carcinogenesis. CONCLUSIONS Our meta-analysis shows remarkable consistency in endometriosis GWAS results across studies, with little evidence of population-based heterogeneity. They also show that the phenotypic classifications used in GWAS to date have been limited. Stronger associations with Stage III/IV disease observed for most loci emphasize the importance for future studies to include detailed sub-phenotype information. Functional studies in relevant tissues are needed to understand the effect of the variants on downstream biological pathways.

Bayesian statistics in oncology: a guide for the clinical investigator

The rise of evidence-based medicine as well as important progress in statistical methods and computational power have led to a second birth of the >200-year-old Bayesian framework. The use of Bayesian techniques, in particular in the design and interpretation of clinical trials, offers several substantial advantages over the classical statistical approach. First, in contrast to classical statistics, Bayesian analysis allows a direct statement regarding the probability that a treatment was beneficial. Second, Bayesian statistics allow the researcher to incorporate any prior information in the analysis of the experimental results. Third, Bayesian methods can efficiently handle complex statistical models, which are suited for advanced clinical trial designs. Finally, Bayesian statistics encourage a thorough consideration and presentation of the assumptions underlying an analysis, which enables the reader to fully appraise the authors' conclusions. Both Bayesian and classical statistics have their respective strengths and limitations and should be viewed as being complementary to each other; we do not attempt to make a head-to-head comparison, as this is beyond the scope of the present review. Rather, the objective of the present article is to provide a nonmathematical, reader-friendly overview of the current practice of Bayesian statistics coupled with numerous intuitive examples from the field of oncology. It is hoped that this educational review will be a useful resource to the oncologist and result in a better understanding of the scope, strengths, and limitations of the Bayesian approach.

Nonlinear tests for genetic studies of complex disease

Linkage and association studies are major analytical tools to search for susceptibility genes for complex diseases. With the availability of large collection of single nucleotide polymorphisms (SNPs) and the rapid progresses for high throughput genotyping technologies, together with the ambitious goals of the International HapMap Project, genetic markers covering the whole genome will be available for genome-wide linkage and association studies. In order not to inflate the type I error rate in performing genome-wide linkage and association studies, multiple adjustment for the significant level for each independent linkage and/or association test is required, and this has led to the suggestion of genome-wide significant cut-off as low as 5 × 10 −7. Almost no linkage and/or association study can meet such a stringent threshold by the standard statistical methods. Developing new statistics with high power is urgently needed to tackle this problem. This dissertation proposes and explores a class of novel test statistics that can be used in both population-based and family-based genetic data by employing a completely new strategy, which uses nonlinear transformation of the sample means to construct test statistics for linkage and association studies. Extensive simulation studies are used to illustrate the properties of the nonlinear test statistics. Power calculations are performed using both analytical and empirical methods. Finally, real data sets are analyzed with the nonlinear test statistics. Results show that the nonlinear test statistics have correct type I error rates, and most of the studied nonlinear test statistics have higher power than the standard chi-square test. This dissertation introduces a new idea to design novel test statistics with high power and might open new ways to mapping susceptibility genes for complex diseases. ^

Gene-gene interaction and gene-pathway analysis of genome-wide association for schizophrenia

Schizophrenia (SZ) is a complex disorder with high heritability and variable phenotypes that has limited success in finding causal genes associated with the disease development. Pathway-based analysis is an effective approach in investigating the molecular mechanism of susceptible genes associated with complex diseases. The etiology of complex diseases could be a network of genetic factors and within the genes, interaction may occur. In this work we argue that some genes might be of small effect that by itself are neither sufficient nor necessary to cause the disease however, their effect may induce slight changes to the gene expression or affect the protein function, therefore, analyzing the gene-gene interaction mechanism within the disease pathway would play crucial role in dissecting the genetic architecture of complex diseases, making the pathway-based analysis a complementary approach to GWAS technique. ^ In this study, we implemented three novel linkage disequilibrium based statistics, the linear combination, the quadratic, and the decorrelation test statistics, to investigate the interaction between linked and unlinked genes in two independent case-control GWAS datasets for SZ including participants of European (EA) and African (AA) ancestries. The EA population included 1,173 cases and 1,378 controls with 729,454 genotyped SNPs, while the AA population included 219 cases and 288 controls with 845,814 genotyped SNPs. We identified 17,186 interacting gene-sets at significant level in EA dataset, and 12,691 gene-sets in AA dataset using the gene-gene interaction method. We also identified 18,846 genes in EA dataset and 19,431 genes in AA dataset that were in the disease pathways. However, few genes were reported of significant association to SZ. ^ Our research determined the pathways characteristics for schizophrenia through the gene-gene interaction and gene-pathway based approaches. Our findings suggest insightful inferences of our methods in studying the molecular mechanisms of common complex diseases.^

Novel therapeutics for complex diseases from genome-wide association data

The development of novel therapies is essential to lower the burden of complex diseases. The purpose of this study is to identify novel therapeutics for complex diseases using bioinformatic methods. Bioinformatic tools such as candidate gene prediction tools allow identification of disease genes by identifying the potential candidate genes linked to genetic markers of the disease. Candidate gene prediction tools can only identify candidates for further research, and do not identify disease genes directly. Integration of drug-target datasets with candidate gene data-sets can identify novel potential therapeutics suitable for repositioning in clinical trials. Drug repositioning can save valuable time and money spent in therapeutic development of complex diseases.

Application of a Bayesian Network complex system model to a successful community electricity demand reduction program

Utilities worldwide are focused on supplying peak electricity demand reliably and cost effectively, requiring a thorough understanding of all the factors influencing residential electricity use at peak times. An electricity demand reduction project based on comprehensive residential consumer engagement was established within an Australian community in 2008, and by 2011, peak demand had decreased to below pre-intervention levels. This paper applied field data discovered through qualitative in-depth interviews of 22 residential households at the community to a Bayesian Network complex system model to examine whether the system model could explain successful peak demand reduction in the case study location. The knowledge and understanding acquired through insights into the major influential factors and the potential impact of changes to these factors on peak demand would underpin demand reduction intervention strategies for a wider target group.

Case Studies in Bayesian Statistical Modelling and Analysis

Provides an accessible foundation to Bayesian analysis using real world models This book aims to present an introduction to Bayesian modelling and computation, by considering real case studies drawn from diverse fields spanning ecology, health, genetics and finance. Each chapter comprises a description of the problem, the corresponding model, the computational method, results and inferences as well as the issues that arise in the implementation of these approaches. Case Studies in Bayesian Statistical Modelling and Analysis: •Illustrates how to do Bayesian analysis in a clear and concise manner using real-world problems. •Each chapter focuses on a real-world problem and describes the way in which the problem may be analysed using Bayesian methods. •Features approaches that can be used in a wide area of application, such as, health, the environment, genetics, information science, medicine, biology, industry and remote sensing. Case Studies in Bayesian Statistical Modelling and Analysis is aimed at statisticians, researchers and practitioners who have some expertise in statistical modelling and analysis, and some understanding of the basics of Bayesian statistics, but little experience in its application. Graduate students of statistics and biostatistics will also find this book beneficial.

Genome-wide association analysis identifies 13 new risk loci for schizophrenia

Schizophrenia is an idiopathic mental disorder with a heritable component and a substantial public health impact. We conducted a multi-stage genome-wide association study (GWAS) for schizophrenia beginning with a Swedish national sample (5,001 cases and 6,243 controls) followed by meta-Analysis with previous schizophrenia GWAS (8,832 cases and 12,067 controls) and finally by replication of SNPs in 168 genomic regions in independent samples (7,413 cases, 19,762 controls and 581 parent-offspring trios). We identified 22 loci associated at genome-wide significance; 13 of these are new, and 1 was previously implicated in bipolar disorder. Examination of candidate genes at these loci suggests the involvement of neuronal calcium signaling. We estimate that 8,300 independent, mostly common SNPs (95% credible interval of 6,300-10,200 SNPs) contribute to risk for schizophrenia and that these collectively account for at least 32% of the variance in liability. Common genetic variation has an important role in the etiology of schizophrenia, and larger studies will allow more detailed understanding of this disorder.

A mega-analysis of genome-wide association studies for major depressive disorder

Prior genome-wide association studies (GWAS) of major depressive disorder (MDD) have met with limited success. We sought to increase statistical power to detect disease loci by conducting a GWAS mega-analysis for MDD. In the MDD discovery phase, we analyzed more than 1.2 million autosomal and X chromosome single-nucleotide polymorphisms (SNPs) in 18 759 independent and unrelated subjects of recent European ancestry (9240 MDD cases and 9519 controls). In the MDD replication phase, we evaluated 554 SNPs in independent samples (6783 MDD cases and 50 695 controls). We also conducted a cross-disorder meta-analysis using 819 autosomal SNPs with P<0.0001 for either MDD or the Psychiatric GWAS Consortium bipolar disorder (BIP) mega-analysis (9238 MDD cases/8039 controls and 6998 BIP cases/7775 controls). No SNPs achieved genome-wide significance in the MDD discovery phase, the MDD replication phase or in pre-planned secondary analyses (by sex, recurrent MDD, recurrent early-onset MDD, age of onset, pre-pubertal onset MDD or typical-like MDD from a latent class analyses of the MDD criteria). In the MDD-bipolar cross-disorder analysis, 15 SNPs exceeded genome-wide significance (P<5 x 10(-8)), and all were in a 248 kb interval of high LD on 3p21.1 (chr3:52 425 083-53 822 102, minimum P=5.9 x 10(-9) at rs2535629). Although this is the largest genome-wide analysis of MDD yet conducted, its high prevalence means that the sample is still underpowered to detect genetic effects typical for complex traits. Therefore, we were unable to identify robust and replicable findings. We discuss what this means for genetic research for MDD. The 3p21.1 MDD-BIP finding should be interpreted with caution as the most significant SNP did not replicate in MDD samples, and genotyping in independent samples will be needed to resolve its status.

A complex system perspective on the emergence and spread of infectious diseases: integrating economic and ecological aspects

The emergence and spread of infectious diseases reflects the interaction of ecological and economic factors within an adaptive complex system. We review studies that address the role of economic factors in the emergence and spread of infectious diseases and identify three broad themes. First, the process of macro-economic growth leads to environmental encroaching, which is related to the emergence of infectious diseases. Second, there are a number of mutually reinforcing processes associated with the emergence/spread of infectious diseases. For example, the emergence and spread of infectious diseases can cause significant economic damages, which in turn may create the conditions for further disease spread. Also, the existence of a mutually reinforcing relationship between global trade and macroeconomic growth amplifies the emergence/spread of infectious diseases. Third, microeconomic approaches to infectious disease point to the adaptivity of human behavior, which simultaneously shapes the course of epidemics and responds to it. Most of the applied research has been focused on the first two aspects, and to a lesser extent on the third aspect. With respect to the latter, there is a lack of empirical research aimed at characterizing the behavioral component following a disease outbreak. Future research should seek to fill this gap and develop hierarchical econometric models capable of integrating both macro and micro-economic processes into disease ecology.

Training pharmacists to deliver a complex information technology intervention (PINCER) using the principles of educational outreach and root cause analysis

Objective: To describe the training undertaken by pharmacists employed in a pharmacist-led information technology-based intervention study to reduce medication errors in primary care (PINCER Trial), evaluate pharmacists’ assessment of the training, and the time implications of undertaking the training. Methods: Six pharmacists received training, which included training on root cause analysis and educational outreach, to enable them to deliver the PINCER Trial intervention. This was evaluated using self-report questionnaires at the end of each training session. The time taken to complete each session was recorded. Data from the evaluation forms were entered onto a Microsoft Excel spreadsheet, independently checked and the summary of results further verified. Frequencies were calculated for responses to the three-point Likert scale questions. Free-text comments from the evaluation forms and pharmacists’ diaries were analysed thematically. Key findings: All six pharmacists received 22 hours of training over five sessions. In four out of the five sessions, the pharmacists who completed an evaluation form (27 out of 30 were completed) stated they were satisfied or very satisfied with the various elements of the training package. Analysis of free-text comments and the pharmacists’ diaries showed that the principles of root cause analysis and educational outreach were viewed as useful tools to help pharmacists conduct pharmaceutical interventions in both the study and other pharmacy roles that they undertook. The opportunity to undertake role play was a valuable part of the training received. Conclusions: Findings presented in this paper suggest that providing the PINCER pharmacists with training in root cause analysis and educational outreach contributed to the successful delivery of PINCER interventions and could potentially be utilised by other pharmacists based in general practice to deliver pharmaceutical interventions to improve patient safety.

Tumor necrosis factor-alpha-308G/A single nucleotide polymorphism and red-complex periodontopathogens are independently associated with increased levels of tumor necrosis factor-alpha in diseased periodontal tissues

Background and Objective: Inflammatory cytokines such as tumor necrosis factor-alpha are involved in the pathogenesis of periodontal diseases. A high between-subject variation in the level of tumor necrosis factor-alpha mRNA has been verified, which may be a result of genetic polymorphisms and/or the presence of periodontopathogens such as Porphyromonas gingivalis, Tannerella forsythia, Treponema denticola (called the red complex) and Aggregatibacter actinomycetemcomitans. In this study, we investigated the effect of the tumor necrosis factor-alpha (TNFA) -308G/A gene polymorphism and of periodontopathogens on the tumor necrosis factor-alpha levels in the periodontal tissues of nonsmoking patients with chronic periodontitis (n = 127) and in control subjects (n = 177). Material and Methods: The TNFA-308G/A single nucleotide polymorphism was investigated using polymerase chain reaction-restriction fragment length polymorphism analysis, whereas the tumor necrosis factor-alpha levels and the periodontopathogen load were determined using real-time polymerase chain reaction. Results: No statistically significant differences were found in the frequency of the TNFA-308 single nucleotide polymorphism in control and chronic periodontitis groups, in spite of the higher frequency of the A allele in the chronic periodontitis group. The concomitant analyses of genotypes and periodontopathogens demonstrated that TNFA-308 GA/AA genotypes and the red-complex periodontopathogens were independently associated with increased levels of tumor necrosis factor-alpha in periodontal tissues, and no additive effect was seen when both factors were present. P. gingivalis, T. forsythia and T. denticola counts were positively correlated with the level of tumor necrosis factor-alpha. TNFA-308 genotypes were not associated with the periodontopathogen detection odds or with the bacterial load. Conclusion: Our results demonstrate that the TNFA-308 A allele and red-complex periodontopathogens are independently associated with increased levels of tumor necrosis factor-alpha in diseased tissues of nonsmoking chronic periodontitis patients and consequently are potentially involved in determining the disease outcome.

Parameter recovery for a skew-normal IRT model under a Bayesian approach: hierarchical framework, prior and kernel sensitivity and sample size

Item response theory (IRT) comprises a set of statistical models which are useful in many fields, especially when there is an interest in studying latent variables (or latent traits). Usually such latent traits are assumed to be random variables and a convenient distribution is assigned to them. A very common choice for such a distribution has been the standard normal. Recently, Azevedo et al. [Bayesian inference for a skew-normal IRT model under the centred parameterization, Comput. Stat. Data Anal. 55 (2011), pp. 353-365] proposed a skew-normal distribution under the centred parameterization (SNCP) as had been studied in [R. B. Arellano-Valle and A. Azzalini, The centred parametrization for the multivariate skew-normal distribution, J. Multivariate Anal. 99(7) (2008), pp. 1362-1382], to model the latent trait distribution. This approach allows one to represent any asymmetric behaviour concerning the latent trait distribution. Also, they developed a Metropolis-Hastings within the Gibbs sampling (MHWGS) algorithm based on the density of the SNCP. They showed that the algorithm recovers all parameters properly. Their results indicated that, in the presence of asymmetry, the proposed model and the estimation algorithm perform better than the usual model and estimation methods. Our main goal in this paper is to propose another type of MHWGS algorithm based on a stochastic representation (hierarchical structure) of the SNCP studied in [N. Henze, A probabilistic representation of the skew-normal distribution, Scand. J. Statist. 13 (1986), pp. 271-275]. Our algorithm has only one Metropolis-Hastings step, in opposition to the algorithm developed by Azevedo et al., which has two such steps. This not only makes the implementation easier but also reduces the number of proposal densities to be used, which can be a problem in the implementation of MHWGS algorithms, as can be seen in [R.J. Patz and B.W. Junker, A straightforward approach to Markov Chain Monte Carlo methods for item response models, J. Educ. Behav. Stat. 24(2) (1999), pp. 146-178; R. J. Patz and B. W. Junker, The applications and extensions of MCMC in IRT: Multiple item types, missing data, and rated responses, J. Educ. Behav. Stat. 24(4) (1999), pp. 342-366; A. Gelman, G.O. Roberts, and W.R. Gilks, Efficient Metropolis jumping rules, Bayesian Stat. 5 (1996), pp. 599-607]. Moreover, we consider a modified beta prior (which generalizes the one considered in [3]) and a Jeffreys prior for the asymmetry parameter. Furthermore, we study the sensitivity of such priors as well as the use of different kernel densities for this parameter. Finally, we assess the impact of the number of examinees, number of items and the asymmetry level on the parameter recovery. Results of the simulation study indicated that our approach performed equally as well as that in [3], in terms of parameter recovery, mainly using the Jeffreys prior. Also, they indicated that the asymmetry level has the highest impact on parameter recovery, even though it is relatively small. A real data analysis is considered jointly with the development of model fitting assessment tools. The results are compared with the ones obtained by Azevedo et al. The results indicate that using the hierarchical approach allows us to implement MCMC algorithms more easily, it facilitates diagnosis of the convergence and also it can be very useful to fit more complex skew IRT models.