Longitudinal familial analysis of blood pressure involving parametric (co)variance functions

Abstract Background For analyzing longitudinal familial data we adopted a log-linear form to incorporate heterogeneity in genetic variance components over the time, and additionally a serial correlation term in the genetic effects at different levels of ages. Due to the availability of multiple measures on the same individual, we permitted environmental correlations that may change across time. Results Systolic blood pressure from family members from the first and second cohort was used in the current analysis. Measures of subjects receiving hypertension treatment were set as censored values and they were corrected. An initial check of the variance and covariance functions proposed for analyzing longitudinal familial data, using empirical semi-variogram plots, indicated that the observed trait dispersion pattern follows the assumptions adopted. Conclusion The corrections for censored phenotypes based on ordinary linear models may be an appropriate simple model to correct the data, ensuring that the original variability in the data was retained. In addition, empirical semi-variogram plots are useful for diagnosis of the (co)variance model adopted.

Mean dynamic topography and oceanographic parameters estimated from an inverse model and satellite geodesy, with link to model result in one single NetCDF file (392 MB), including the inverse data error covariance

Geostrophic surface velocities can be derived from the gradients of the mean dynamic topography-the difference between the mean sea surface and the geoid. Therefore, independently observed mean dynamic topography data are valuable input parameters and constraints for ocean circulation models. For a successful fit to observational dynamic topography data, not only the mean dynamic topography on the particular ocean model grid is required, but also information about its inverse covariance matrix. The calculation of the mean dynamic topography from satellite-based gravity field models and altimetric sea surface height measurements, however, is not straightforward. For this purpose, we previously developed an integrated approach to combining these two different observation groups in a consistent way without using the common filter approaches (Becker et al. in J Geodyn 59(60):99-110, 2012, doi:10.1016/j.jog.2011.07.0069; Becker in Konsistente Kombination von Schwerefeld, Altimetrie und hydrographischen Daten zur Modellierung der dynamischen Ozeantopographie, 2012, http://nbn-resolving.de/nbn:de:hbz:5n-29199). Within this combination method, the full spectral range of the observations is considered. Further, it allows the direct determination of the normal equations (i.e., the inverse of the error covariance matrix) of the mean dynamic topography on arbitrary grids, which is one of the requirements for ocean data assimilation. In this paper, we report progress through selection and improved processing of altimetric data sets. We focus on the preprocessing steps of along-track altimetry data from Jason-1 and Envisat to obtain a mean sea surface profile. During this procedure, a rigorous variance propagation is accomplished, so that, for the first time, the full covariance matrix of the mean sea surface is available. The combination of the mean profile and a combined GRACE/GOCE gravity field model yields a mean dynamic topography model for the North Atlantic Ocean that is characterized by a defined set of assumptions. We show that including the geodetically derived mean dynamic topography with the full error structure in a 3D stationary inverse ocean model improves modeled oceanographic features over previous estimates.

A reassessment of genetic limits to evolutionary change

An absence of genetic variance in traits under selection is perhaps the oldest explanation for a limit to evolutionary change, but has also been the most easily dismissed. We review a range of theoretical and empirical results covering single traits to more complex multivariate systems, and show that an absence of genetic variance may be more common than is currently appreciated. From a single-trait perspective, we highlight that it is becoming clear that some trait types do not display significant levels of genetic variation, and we raise the possibility that species with restricted ranges may differ qualitatively from more widespread species in levels of genetic variance in ecologically important traits. A common misconception in many life-history studies is that a lack of genetic variance in single traits, and genetic constraints as a consequence of bivariate genetic correlations, are different causes of selection limits. We detail how interpretations of bivariate patterns are unlikely to demonstrate genetic limits to selection in many cases. We advocate a multivariate definition of genetic constraints that emphasizes the presence (or otherwise) of genetic variance in the multivariate direction of selection. For multitrait systems, recent results using longer term studies of organisms, in which more is understood concerning what traits may be under selection, have indicated that selection may exhaust genetic variance, resulting in a limit to the selection response.

Studying phenotypic evolution using multivariate quantitative genetics

Quantitative genetics provides a powerful framework for studying phenotypic evolution and the evolution of adaptive genetic variation. Central to the approach is G, the matrix of additive genetic variances and covariances. G summarizes the genetic basis of the traits and can be used to predict the phenotypic response to multivariate selection or to drift. Recent analytical and computational advances have improved both the power and the accessibility of the necessary multivariate statistics. It is now possible to study the relationships between G and other evolutionary parameters, such as those describing the mutational input, the shape and orientation of the adaptive landscape, and the phenotypic divergence among populations. At the same time, we are moving towards a greater understanding of how the genetic variation summarized by G evolves. Computer simulations of the evolution of G, innovations in matrix comparison methods, and rapid development of powerful molecular genetic tools have all opened the way for dissecting the interaction between allelic variation and evolutionary process. Here I discuss some current uses of G, problems with the application of these approaches, and identify avenues for future research.

The stability of P in coral reef fishes

The constancy of phenotypic variation and covariation is an assumption that underlies most recent investigations of past selective regimes and attempts to predict future responses to selection. Few studies have tested this assumption of constancy despite good reasons to expect that the pattern of phenotypic variation and covariation may vary in space and time. We compared phenotypic variance-covariance matrices (P) estimated for Populations of six species of distantly related coral reef fishes sampled at two locations on Australia's Great Barrier Reef separated by more than 1000 km. The intraspecific similarity between these matrices was estimated using two methods: matrix correlation and common principal component analysis. Although there was no evidence of equality between pairs of P, both statistical approaches indicated a high degree of similarity in morphology between the two populations for each species. In general, the hierarchical decomposition of the variance-covariance structure of these populations indicated that all principal components of phenotypic variance-covariance were shared but that they differed in the degree of variation associated with each of these components. The consistency of this pattern is remarkable given the diversity of morphologies and life histories encompassed by these species. Although some phenotypic instability was indicated, these results were consistent with a generally conserved pattern of multivariate selection between populations.

Population Monte Carlo Algorithm in High Dimensions

The population Monte Carlo algorithm is an iterative importance sampling scheme for solving static problems. We examine the population Monte Carlo algorithm in a simplified setting, a single step of the general algorithm, and study a fundamental problem that occurs in applying importance sampling to high-dimensional problem. The precision of the computed estimate from the simplified setting is measured by the asymptotic variance of estimate under conditions on the importance function. We demonstrate the exponential growth of the asymptotic variance with the dimension and show that the optimal covariance matrix for the importance function can be estimated in special cases.

Bayesian hybrid algorithms and models : implementation and associated issues

This thesis addresses computational challenges arising from Bayesian analysis of complex real-world problems. Many of the models and algorithms designed for such analysis are ‘hybrid’ in nature, in that they are a composition of components for which their individual properties may be easily described but the performance of the model or algorithm as a whole is less well understood. The aim of this research project is to after a better understanding of the performance of hybrid models and algorithms. The goal of this thesis is to analyse the computational aspects of hybrid models and hybrid algorithms in the Bayesian context. The first objective of the research focuses on computational aspects of hybrid models, notably a continuous finite mixture of t-distributions. In the mixture model, an inference of interest is the number of components, as this may relate to both the quality of model fit to data and the computational workload. The analysis of t-mixtures using Markov chain Monte Carlo (MCMC) is described and the model is compared to the Normal case based on the goodness of fit. Through simulation studies, it is demonstrated that the t-mixture model can be more flexible and more parsimonious in terms of number of components, particularly for skewed and heavytailed data. The study also reveals important computational issues associated with the use of t-mixtures, which have not been adequately considered in the literature. The second objective of the research focuses on computational aspects of hybrid algorithms for Bayesian analysis. Two approaches will be considered: a formal comparison of the performance of a range of hybrid algorithms and a theoretical investigation of the performance of one of these algorithms in high dimensions. For the first approach, the delayed rejection algorithm, the pinball sampler, the Metropolis adjusted Langevin algorithm, and the hybrid version of the population Monte Carlo (PMC) algorithm are selected as a set of examples of hybrid algorithms. Statistical literature shows how statistical efficiency is often the only criteria for an efficient algorithm. In this thesis the algorithms are also considered and compared from a more practical perspective. This extends to the study of how individual algorithms contribute to the overall efficiency of hybrid algorithms, and highlights weaknesses that may be introduced by the combination process of these components in a single algorithm. The second approach to considering computational aspects of hybrid algorithms involves an investigation of the performance of the PMC in high dimensions. It is well known that as a model becomes more complex, computation may become increasingly difficult in real time. In particular the importance sampling based algorithms, including the PMC, are known to be unstable in high dimensions. This thesis examines the PMC algorithm in a simplified setting, a single step of the general sampling, and explores a fundamental problem that occurs in applying importance sampling to a high-dimensional problem. The precision of the computed estimate from the simplified setting is measured by the asymptotic variance of the estimate under conditions on the importance function. Additionally, the exponential growth of the asymptotic variance with the dimension is demonstrated and we illustrates that the optimal covariance matrix for the importance function can be estimated in a special case.

Reliability of partial ambiguity fixing with multiple GNSS constellations

Reliable ambiguity resolution (AR) is essential to Real-Time Kinematic (RTK) positioning and its applications, since incorrect ambiguity fixing can lead to largely biased positioning solutions. A partial ambiguity fixing technique is developed to improve the reliability of AR, involving partial ambiguity decorrelation (PAD) and partial ambiguity resolution (PAR). Decorrelation transformation could substantially amplify the biases in the phase measurements. The purpose of PAD is to find the optimum trade-off between decorrelation and worst-case bias amplification. The concept of PAR refers to the case where only a subset of the ambiguities can be fixed correctly to their integers in the integer least-squares (ILS) estimation system at high success rates. As a result, RTK solutions can be derived from these integer-fixed phase measurements. This is meaningful provided that the number of reliably resolved phase measurements is sufficiently large for least-square estimation of RTK solutions as well. Considering the GPS constellation alone, partially fixed measurements are often insufficient for positioning. The AR reliability is usually characterised by the AR success rate. In this contribution an AR validation decision matrix is firstly introduced to understand the impact of success rate. Moreover the AR risk probability is included into a more complete evaluation of the AR reliability. We use 16 ambiguity variance-covariance matrices with different levels of success rate to analyse the relation between success rate and AR risk probability. Next, the paper examines during the PAD process, how a bias in one measurement is propagated and amplified onto many others, leading to more than one wrong integer and to affect the success probability. Furthermore, the paper proposes a partial ambiguity fixing procedure with a predefined success rate criterion and ratio-test in the ambiguity validation process. In this paper, the Galileo constellation data is tested with simulated observations. Numerical results from our experiment clearly demonstrate that only when the computed success rate is very high, the AR validation can provide decisions about the correctness of AR which are close to real world, with both low AR risk and false alarm probabilities. The results also indicate that the PAR procedure can automatically chose adequate number of ambiguities to fix at given high-success rate from the multiple constellations instead of fixing all the ambiguities. This is a benefit that multiple GNSS constellations can offer.

A genetic analysis of cortical thickness in 372 twins

Imaging genetics is a new field of neuroscience that blends methods from computational anatomy and quantitative genetics to identify genetic influences on brain structure and function. Here we analyzed brain MRI data from 372 young adult twins to identify cortical regions in which gray matter volume is influenced by genetic differences across subjects. Thickness maps, reconstructed from surface models of the cortical gray/white and gray/CSF interfaces, were smoothed with a 25 mm FWHM kernel and automatically parcellated into 34 regions of interest per hemisphere. In structural equation models fitted to volume values at each surface vertex, we computed components of variance due to additive genetic (A), shared (C) and unique (E) environmental factors, and tested their significance. Cortical regions in the vicinity of the perisylvian language cortex, and at the frontal and temporal poles, showed significant additive genetic variance, suggesting that volume measures from these regions may provide quantitative phenotypes to narrow the search for quantitative trait loci that influence brain structure.

Efficient estimation for rank-based regression with clustered data

Rank-based inference is widely used because of its robustness. This article provides optimal rank-based estimating functions in analysis of clustered data with random cluster effects. The extensive simulation studies carried out to evaluate the performance of the proposed method demonstrate that it is robust to outliers and is highly efficient given the existence of strong cluster correlations. The performance of the proposed method is satisfactory even when the correlation structure is misspecified, or when heteroscedasticity in variance is present. Finally, a real dataset is analyzed for illustration.

Induced smoothing for rank regression with censored survival times

Adaptions of weighted rank regression to the accelerated failure time model for censored survival data have been successful in yielding asymptotically normal estimates and flexible weighting schemes to increase statistical efficiencies. However, for only one simple weighting scheme, Gehan or Wilcoxon weights, are estimating equations guaranteed to be monotone in parameter components, and even in this case are step functions, requiring the equivalent of linear programming for computation. The lack of smoothness makes standard error or covariance matrix estimation even more difficult. An induced smoothing technique overcame these difficulties in various problems involving monotone but pure jump estimating equations, including conventional rank regression. The present paper applies induced smoothing to the Gehan-Wilcoxon weighted rank regression for the accelerated failure time model, for the more difficult case of survival time data subject to censoring, where the inapplicability of permutation arguments necessitates a new method of estimating null variance of estimating functions. Smooth monotone parameter estimation and rapid, reliable standard error or covariance matrix estimation is obtained.

Standard errors and covariance matrices for smoothed rank estimators

A 'pseudo-Bayesian' interpretation of standard errors yields a natural induced smoothing of statistical estimating functions. When applied to rank estimation, the lack of smoothness which prevents standard error estimation is remedied. Efficiency and robustness are preserved, while the smoothed estimation has excellent computational properties. In particular, convergence of the iterative equation for standard error is fast, and standard error calculation becomes asymptotically a one-step procedure. This property also extends to covariance matrix calculation for rank estimates in multi-parameter problems. Examples, and some simple explanations, are given.

A Phenomic Scan of the Norfolk Island Genetic Isolate Identifies a Major Pleiotropic Effect Locus Associated with Metabolic and Renal Disorder Markers

Multiphenotype genome-wide association studies (GWAS) may reveal pleiotropic genes, which would remain undetected using single phenotype analyses. Analysis of large pedigrees offers the added advantage of more accurately assessing trait heritability, which can help prioritise genetically influenced phenotypes for GWAS analysis. In this study we performed a principal component analysis (PCA), heritability (h2) estimation and pedigree-based GWAS of 37 cardiovascular disease -related phenotypes in 330 related individuals forming a large pedigree from the Norfolk Island genetic isolate. PCA revealed 13 components explaining >75% of the total variance. Nine components yielded statistically significant h2 values ranging from 0.22 to 0.54 (P<0.05). The most heritable component was loaded with 7 phenotypic measures reflecting metabolic and renal dysfunction. A GWAS of this composite phenotype revealed statistically significant associations for 3 adjacent SNPs on chromosome 1p22.2 (P<1x10-8). These SNPs form a 42kb haplotype block and explain 11% of the genetic variance for this renal function phenotype. Replication analysis of the tagging SNP (rs1396315) in an independent US cohort supports the association (P = 0.000011). Blood transcript analysis showed 35 genes were associated with rs1396315 (P<0.05). Gene set enrichment analysis of these genes revealed the most enriched pathway was purine metabolism (P = 0.0015). Overall, our findings provide convincing evidence for a major pleiotropic effect locus on chromosome 1p22.2 influencing risk of renal dysfunction via purine metabolism pathways in the Norfolk Island population. Further studies are now warranted to interrogate the functional relevance of this locus in terms of renal pathology and cardiovascular disease risk.

Genetic Impacts of the Hull on Barley Grain Quality

Barley hull plays an important role in malt and feed quality and processing. In this study we measured the variation in hull con-tent along with other grain quality traits namely, kernel discolouration and degree of pre-harvest sprouting, in a single map-ping population. There were significant (p < 0.05) genetic as well as environment effects. In addition, heritability was calculated for hull content to be 29% and 47% for two years’ data. From the analysis, major QTL markers were identified in con-trolling the expression of hull content on chromosomes 2 (2H), and 6 (6H) with significant (P < 0.05) LOD scores of 5.4 and 3.46 respectively. Minor QTLs were identified on 1 (7H), 4 (4H), 5 (1H) and 7 (5H). The region at marker Bmac310 on 4(4H) could be associated with dormancy gene SD4. A number of the QTLs also coincided with regions for either kernel discolouration or preharvest sprouting resistance (dormancy). The results indicate that variation exists for hull content, which is influenced by both growing environment as well as genetically, although the genetic variance explained less than half of the total variance. Further, hull content also impacts on other grain quality attributes including dormancy, sprouting resistance and kernel appearance.

Nicotine Dependence and Smoking Behaviour : A genetic and epidemiological study

The worldwide health burden caused by the tobacco epidemic highlights the importance of study-ing determinants of smoking behaviour and key factors sustaining nicotine dependence. Despite vast-ranging preventive efforts, smoking remains one of the most deleterious health behaviours, and its genetic and environmental factors warrant continuous investigation. The heritability of smoking behaviour and nicotine dependence has been suggested to be relatively high. Earlier smoking behaviour, nicotine dependence, socio-economic position and demographic factors have all been shown to be associated with smoking cessation. This thesis aimed to examine various aspects of smoking behaviour and nicotine dependence from an epidemiological and genetic per-spective. Data for Studies I and IV were obtained from the Older Finnish Twin Cohort, a postal health sur-vey conducted in 1975, 1981 and 1990 on same-sexed pairs and in 1996-1997 on male-female adult pairs. The number of ever-smoking participants was 8941 in Study I and 3069 in Study IV. Data for Studies II and III came from the Family Study of Cigarette Smoking - Vulnerability to Nicotine Addiction. This study is linked to the Older Finnish Twin Cohort with new data collec-tion during 2001-2006 that focused on smoking twin pairs and their family members. The meas-ures included intensive telephone interviews, blood samples and additional postal questionnaires. The numbers of ever-smoking participants was 1370 in Study II and 529 in Study III. Study I examined whether a genetic component underlies smoking behaviour among Finnish adults. Genetic factors were important in the amount smoked and smoking cessation, with about half of the phenotypic differences explained by genetic variance. A novel finding was that genetic influences on amount smoked and smoking cessation were largely independent of genetic influ-ences on age at initiation. This result has implications for defining phenotypes in the search for genes underlying smoking behaviour. Furthermore, even if smoking initiation is postponed to a later age, potential vulnerability to subsequent nicotine dependence cannot be completely inhib-ited. Study II investigated the effect of genetic and environmental factors on nicotine dependence, as measured by the novel multidimensional Nicotine Dependence Syndrome Scale (NDSS). This scale was validated in the Finnish data. The NDSS correlated highly with other established nico-tine dependence scales (FTND and DSM-IV), suggesting that this new scale would be a feasible and valid measure for identifying nicotine-dependent smokers among the ever-smoking popula-tion. About one-third of the phenotypic variation in nicotine dependence in this sample was ex-plained by genetic influences. Study III aimed at identifying chromosomal regions harbouring genes that influence smoking be-haviour and nicotine dependence. Linkage analysis of family data revealed that for smoker and nicotine dependence phenotypes as well as for co-morbidity between nicotine dependence and alcohol use signals on specific chromosome regions (chromosomes 2q33, 5q12, 5q34 7q21, 7q31, 10q25, 11p15, 20p13) exist. Results further support the hypothesis that smoking behaviour phe-notypes have a genetic background. Study IV examined associations of smoking behaviour, socio-economic position and transition of marital status with smoking cessation. Indicators of socio-economic position were important pre-dictors of smoking cessation even when adjusted for previous smoking behaviour. Getting married was associated with an increased probability of cessation in men, a finding confirmed among dis-cordant twin pairs. Thus, having a partner appears to have a positive impact on smoking cessation. In conclusion, nicotine dependence and smoking behaviour demonstrate significant genetic liabil-ity, but also substantial environmental influences among Finnish adults. Smoking initiation should be prevented or at least postponed to a later age. Although genetic factors are important in nicotine dependence and smoking behaviour, societal actions still have a primary role in tobacco control and smoking prevalence. Future studies should examine the complex interactions between genetic and environmental factors in nicotine dependence.