Multivariate variance-components analysis in DTI

Twin studies are a major research direction in imaging genetics, a new field, which combines algorithms from quantitative genetics and neuroimaging to assess genetic effects on the brain. In twin imaging studies, it is common to estimate the intraclass correlation (ICC), which measures the resemblance between twin pairs for a given phenotype. In this paper, we extend the commonly used Pearson correlation to a more appropriate definition, which uses restricted maximum likelihood methods (REML). We computed proportion of phenotypic variance due to additive (A) genetic factors, common (C) and unique (E) environmental factors using a new definition of the variance components in the diffusion tensor-valued signals. We applied our analysis to a dataset of Diffusion Tensor Images (DTI) from 25 identical and 25 fraternal twin pairs. Differences between the REML and Pearson estimators were plotted for different sample sizes, showing that the REML approach avoids severe biases when samples are smaller. Measures of genetic effects were computed for scalar and multivariate diffusion tensor derived measures including the geodesic anisotropy (tGA) and the full diffusion tensors (DT), revealing voxel-wise genetic contributions to brain fiber microstructure.

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.

Comparison of three-dimensional profiles over time

In this paper, we describe an analysis for data collected on a three-dimensional spatial lattice with treatments applied at the horizontal lattice points. Spatial correlation is accounted for using a conditional autoregressive model. Observations are defined as neighbours only if they are at the same depth. This allows the corresponding variance components to vary by depth. We use the Markov chain Monte Carlo method with block updating, together with Krylov subspace methods, for efficient estimation of the model. The method is applicable to both regular and irregular horizontal lattices and hence to data collected at any set of horizontal sites for a set of depths or heights, for example, water column or soil profile data. The model for the three-dimensional data is applied to agricultural trial data for five separate days taken roughly six months apart in order to determine possible relationships over time. The purpose of the trial is to determine a form of cropping that leads to less moist soils in the root zone and beyond.We estimate moisture for each date, depth and treatment accounting for spatial correlation and determine relationships of these and other parameters over time.

A Bayesian analysis of an agricultural field trial with three spatial dimensions

Modern technology now has the ability to generate large datasets over space and time. Such data typically exhibit high autocorrelations over all dimensions. The field trial data motivating the methods of this paper were collected to examine the behaviour of traditional cropping and to determine a cropping system which could maximise water use for grain production while minimising leakage below the crop root zone. They consist of moisture measurements made at 15 depths across 3 rows and 18 columns, in the lattice framework of an agricultural field. Bayesian conditional autoregressive (CAR) models are used to account for local site correlations. Conditional autoregressive models have not been widely used in analyses of agricultural data. This paper serves to illustrate the usefulness of these models in this field, along with the ease of implementation in WinBUGS, a freely available software package. The innovation is the fitting of separate conditional autoregressive models for each depth layer, the ‘layered CAR model’, while simultaneously estimating depth profile functions for each site treatment. Modelling interest also lay in how best to model the treatment effect depth profiles, and in the choice of neighbourhood structure for the spatial autocorrelation model. The favoured model fitted the treatment effects as splines over depth, and treated depth, the basis for the regression model, as measured with error, while fitting CAR neighbourhood models by depth layer. It is hierarchical, with separate onditional autoregressive spatial variance components at each depth, and the fixed terms which involve an errors-in-measurement model treat depth errors as interval-censored measurement error. The Bayesian framework permits transparent specification and easy comparison of the various complex models compared.

Mapping quantitative trait loci in a wild population using linkage and linkage disequilibrium analyses

Historical information can be used, in addition to pedigree, traits and genotypes, to map quantitative trait locus (QTL) in general populations via maximum likelihood estimation of variance components. This analysis is known as linkage disequilibrium (LD) and linkage mapping, because it exploits both linkage in families and LD at the population level. The search for QTL in the wild population of Soay sheep on St. Kilda is a proof of principle. We analysed the data from a previous study and confirmed some of the QTLs reported. The most striking result was the confirmation of a QTL affecting birth weight that had been reported using association tests but not when using linkage-based analyses. Copyright © Cambridge University Press 2010.

Linkage mapping of CVD risk traits in the isolated Norfolk Island population

To understand the underlying genetic architecture of cardiovascular disease (CVD) risk traits, we undertook a genome-wide linkage scan to identify CVD quantitative trait loci (QTLs) in 377 individuals from the Norfolk Island population. The central aim of this research focused on the utilization of a genetically and geographically isolated population of individuals from Norfolk Island for the purposes of variance component linkage analysis to identify QTLs involved in CVD risk traits. Substantial evidence supports the involvement of traits such as systolic and diastolic blood pressures, high-density lipoprotein-cholesterol, low-density lipoprotein-cholesterol, body mass index and triglycerides as important risk factors for CVD pathogenesis. In addition to the environmental inXuences of poor diet, reduced physical activity, increasing age, cigarette smoking and alcohol consumption, many studies have illustrated a strong involvement of genetic components in the CVD phenotype through family and twin studies. We undertook a genome scan using 400 markers spaced approximately 10 cM in 600 individuals from Norfolk Island. Genotype data was analyzed using the variance components methods of SOLAR. Our results gave a peak LOD score of 2.01 localizing to chromosome 1p36 for systolic blood pressure and replicated previously implicated loci for other CVD relevant QTLs.

Susceptibility to ankylosing spondylitis in twins: The role of genes, HLA, and the environment

Objective To determine the relative effects of genetic and environmental factors in susceptibility to ankylosing spondylitis (AS). Methods Twins with AS were identified from the Royal National Hospital for Rheumatic Diseases database. Clinical and radiographic examinations were performed to establish diagnoses, and disease severity was assessed using a combination of validated scoring systems. HLA typing for HLA-B27, HLA-B60, and HLA-DR1 was performed by polymerase chain reaction with sequence- specific primers, and zygosity was assessed using microsatellite markers. Genetic and environmental variance components were assessed with the program Mx, using data from this and previous studies of twins with AS. Results Six of 8 monozygotic (MZ) twin pairs were disease concordant, compared with 4 of 15 B27-positive dizygotic (DZ) twin pairs (27%) and 4 of 32 DZ twin pairs overall (12.5%). Nonsignificant increases in similarity with regard to age at disease onset and all of the disease severity scores assessed were noted in disease-concordant MZ twins compared with concordant DZ twins. HLA-B27 and B60 were associated with the disease in probands, and the rate of disease concordance was significantly increased among DZ twin pairs in which the co- twin was positive for both B27 and DR1. Additive genetic effects were estimated to contribute 97% of the population variance. Conclusion Susceptibility to AS is largely genetically determined, and the environmental trigger for the disease is probably ubiquitous. HLA-B27 accounts for a minority of the overall genetic susceptibility to AS.

Is disease severity in ankylosing spondylitis genetically determined?

Objective. To assess the role of genes and the environment in determining the severity of ankylosing spondylitis. Methods: One hundred seventy-three families with >1 case of ankylosing spondylitis were recruited (120 affected sibling pairs, 26 affected parent-child pairs, 20 families with both first- and second-degree relatives affected, and 7 families with only second-degree relatives affected), comprising a total of 384 affected individuals. Disease severity was assessed by the Bath Ankylosing Spondylitis Disease Activity Index (BASDAI) and functional impairment was determined using the Bath Ankylosing Spondylitis Functional Index (BASFI). Disease duration and age at onset were also studied. Variance-components modeling was used to determine the genetic and environmental components Contributing to familiality of the traits examined, and complex segregation analysis was performed to assess different disease models. Results. Both the disease activity and functional capacity as assessed by the BASDAI and the BASFI, respectively, were found to be highly familial (BASDAI familiality 0.51 [P = 10-4], BASFI familiality 0,68 [P = 3 × 10-7]). No significant shared environmental component was demonstrated to be associated with either the BASDAI or the BASFI. Including age at disease onset and duration of disease as covariates made no difference in the heritability assessments. A strong correlation was noted between the BASDAI and the BASFI (genetic correlation 0.9), suggesting the presence of shared determinants of these 2 measures. However, there was significant residual heritability for each measure independent of the other (BASFI residual heritability 0.48, BASDAI 0,36), perhaps indicating that not all genes influencing disease activity influence chronicity. No significant heritability of age at disease onset was found (heritability 0.18; P = 0.2). Segregation studies suggested the presence of a single major gene influencing the BASDAI and the BASFI. Conclusion. This study demonstrates a major genetic contribution to disease severity in ankylosing spondylitis. As with susceptibility to ankylosing spondylitis, shared environmental factors play little role in determining the disease severity.

Suggestive linkage of the parathyroid receptor type 1 to osteoporosis

We have investigated the role of 23 candidate genes in the control of bone mineral density (BMD) by linkage studies in families of probands with osteoporosis (lumbar spine [LS] or femoral neck [FN] BMD T score < -2.5) and low BMD relative to an age- and gender-matched cohort (Z score < -2.0). One hundred and fifteen probands (35 male, 80 female) and 499 of their first- or second-degree relatives (223 males and 276 females) were recruited for the study. BMD was measured at the LS and FN using dual-energy X-ray absorptiometry and expressed as age- and gender-matched Z scores corrected for body mass index. The candidate genes studied were the androgen receptor, type I collagen A1 (COLIA1), COLIA2, COLIIA1, vitamin D receptor (VDR), colony-stimulating factor 1, calcium-sensing receptor, epidermal growth factor (EGF), estrogen receptor 1 (ESR1), fibrillin type 1, insulin-like growth factor 1, interleukin-1 alpha (IL-1α), interleukin-4 (IL-4), interleukin-6 (IL-6), interleukin-11 (IL-11), osteopontin, parathyroid hormone (PTH), PTH-related peptide, PTH receptor type 1 (PTHR1), transforming growth factor-beta 1, and tumor necrosis factors alpha and beta. Sixty-four microsatellites lying close to or within these genes were investigated for linkage with BMD. Using the program MapMaker/Sibs there was suggestive evidence of linkage between BMD and PTHR1 (maximum LOD score obtained [MLS] 2.7-3.5). Moderate evidence of linkage was also observed with EGF (MLS 1.8), COLIA1 (MLS 1.7), COLIIA1/VDR (MLS 1.7), ESR1 (MLS 1.4), IL-1α (MLS 1.4), IL-4 (MLS 1.2), and IL-6 (MLS 1.2). Variance components analysis using the program ACT, correcting for proband-wise ascertainment, also showed evidence of linkage (p ≤0.05) at markers close to or within the candidate genes IL- 1α, PTHR1, IL-6, and COLIIA1/VDR. Further studies will be required to confirm these findings, to refine the location of gene responsible for the observed linkage, and to screen the candidate genes targeted at these loci for mutations.

Estimation of growth parameters from multiple-recapture data

This article develops a method for analysis of growth data with multiple recaptures when the initial ages for all individuals are unknown. The existing approaches either impute the initial ages or model them as random effects. Assumptions about the initial age are not verifiable because all the initial ages are unknown. We present an alternative approach that treats all the lengths including the length at first capture as correlated repeated measures for each individual. Optimal estimating equations are developed using the generalized estimating equations approach that only requires the first two moment assumptions. Explicit expressions for estimation of both mean growth parameters and variance components are given to minimize the computational complexity. Simulation studies indicate that the proposed method works well. Two real data sets are analyzed for illustration, one from whelks (Dicathais aegaota) and the other from southern rock lobster (Jasus edwardsii) in South Australia.

Replication of the association of common rs9939609 variant of FTO with increased BMI in an Australian adult twin population but no evidence for gene by environment (G x E) interaction

OBJECTIVE: To further investigate a common variant (rs9939609) in the fat mass- and obesity-associated gene (FTO), which recent genome-wide association studies have shown to be associated with body mass index (BMI) and obesity. DESIGN: We examined the effect of this FTO variant on BMI in 3353 Australian adult male and female twins. RESULTS: The minor A allele of rs9939609 was associated with an increased BMI (P=0.0007). Each additional copy of the A allele was associated with a mean BMI increase of approximately 1.04 kg/m(2) (approximately 3.71 kg). Using variance components decomposition, we estimate that this single-nucleotide polymorphism accounts for approximately 3% of the genetic variance in BMI in our sample (approximately 2% of the total variance). By comparing intrapair variances of monozygotic twins of different genotypes we were able to perform a direct test of gene by environment (G x E) interaction in both sexes and gene by parity (G x P) interaction in women, but no evidence was found for either. CONCLUSIONS: In addition to supporting earlier findings that the rs9939609 variant in the FTO gene is associated with an increased BMI, our results indicate that the associated genetic effect does not interact with environment or parity.

Principle components analysis with covariance matrix on regional differences for mortality and percentages of cancers in Shandong province [山东省恶性肿瘤死亡率和构成比地区差异协方差矩阵主成分分析]

Objective To explore the characteristics of regional distribution of cancer deaths in Shandong Province with the principle components analysis. Methods The principle components analysis with co-variance matrix for age-adjusted mortality rates and percentages of 20 types of cancer in 22 counties （cities） were carried out using SAS Software. Results Over 90% of the total information could be reflected by the top 3 principle components and the first principle component alone represented more than half of the overall regional variances. The first component mainly reflected the area differences of esophageal cancer. The second component mainly reflected the area differences of lung cancer， stomach cancer and liver cancer. The value of the first principal component scores showed a clear trend that the west areas possessed higher values and the east the lower values. Based on the top two components，the 22 counties （cities） could be divided into several geographical clusters. Conclusion The overall difference of regional distribution of cancers in Shandong is dominated by several major cancers including esophageal cancer， lung cancer， stomach cancer and liver cancer. Among them，esophageal cancer makes the largest contribution. If the range of counties （cities） analyzed could be further widened， the characteristics of regional distribution of cancer mortality would be better examined. Abstract in Chinese 目的 利用主成分分析探讨山东省恶性肿瘤死亡的地区分布特征. 方法 利用SAS软件对山东省22个县市区2004～2006午的20种恶性肿瘤标化死亡率和构成比分别进行协方差矩阵主成分分析. 结果 前3个主成分就反映了总体差异90%以上的信息,其中仅第1主成分就提供了总体差异一半以上的信息.第1主成分主要反映了食管癌的地区差异,第2主成分主要反映肺癌的地区差异,兼顾胃癌和肝癌.各地区第1主成分得分呈现西高东低的趋势,根据第1和第2主成分可以将调查地区分为若干类别,表现为明显的地理聚集性. 结论 山东省各地区恶性肿瘤死亡的总体差异主要取决于少数高发肿瘤,包括食管癌、肺癌、胃癌、肝癌等,其中以食管癌地位最为突出.如能进一步扩大分析范围,可更好地查明恶性肿瘤死亡的地区特征.