Novel Statistical Methods in Quantitative Genetics : Modeling Genetic Variance for Quantitative Trait Loci Mapping and Genomic Evaluation

This thesis develops and evaluates statistical methods for different types of genetic analyses, including quantitative trait loci (QTL) analysis, genome-wide association study (GWAS), and genomic evaluation. The main contribution of the thesis is to provide novel insights in modeling genetic variance, especially via random effects models. In variance component QTL analysis, a full likelihood model accounting for uncertainty in the identity-by-descent (IBD) matrix was developed. It was found to be able to correctly adjust the bias in genetic variance component estimation and gain power in QTL mapping in terms of precision.  Double hierarchical generalized linear models, and a non-iterative simplified version, were implemented and applied to fit data of an entire genome. These whole genome models were shown to have good performance in both QTL mapping and genomic prediction. A re-analysis of a publicly available GWAS data set identified significant loci in Arabidopsis that control phenotypic variance instead of mean, which validated the idea of variance-controlling genes.  The works in the thesis are accompanied by R packages available online, including a general statistical tool for fitting random effects models (hglm), an efficient generalized ridge regression for high-dimensional data (bigRR), a double-layer mixed model for genomic data analysis (iQTL), a stochastic IBD matrix calculator (MCIBD), a computational interface for QTL mapping (qtl.outbred), and a GWAS analysis tool for mapping variance-controlling loci (vGWAS).

Likelihood estimate of treatment effects under selection bias

We consider methods for estimating causal effects of treatment in the situation where the individuals in the treatment and the control group are self selected, i.e., the selection mechanism is not randomized. In this case, simple comparison of treated and control outcomes will not generally yield valid estimates of casual effects. The propensity score method is frequently used for the evaluation of treatment effect. However, this method is based onsome strong assumptions, which are not directly testable. In this paper, we present an alternative modeling approachto draw causal inference by using share random-effect model and the computational algorithm to draw likelihood based inference with such a model. With small numerical studies and a real data analysis, we show that our approach gives not only more efficient estimates but it is also less sensitive to model misspecifications, which we consider, than the existing methods.

Likelihood prediction for generalized linear mixed models under covariate uncertainty

This paper presents the techniques of likelihood prediction for the generalized linear mixed models. Methods of likelihood prediction is explained through a series of examples; from a classical one to more complicated ones. The examples show, in simple cases, that the likelihood prediction (LP) coincides with already known best frequentist practice such as the best linear unbiased predictor. The paper outlines a way to deal with the covariate uncertainty while producing predictive inference. Using a Poisson error-in-variable generalized linear model, it has been shown that in complicated cases LP produces better results than already know methods.

Performance of fluorescence methods, radiographic examination and ICDAS II on occlusal surfaces in vitro

This study compared the performance of fluorescence-based methods, radiographic examination, and International Caries Detection and Assessment System (ICDAS) II on occlusal surfaces. One hundred and nineteen permanent human molars were assessed twice by 2 experienced dentists using the laser fluorescence (LF and LFpen) and fluorescence camera (FC) devices, ICDAS II and bitewing radiographs (BW). After measuring, the teeth were histologically prepared and assessed for caries extension. The sensitivities for dentine caries detection were 0.86 (FC), 0.78 (LFpen), 0.73 (ICDAS II), 0.51 (LF) and 0.34 (BW). The specificities were 0.97 (BW), 0.89 (LF), 0.65 (ICDAS II), 0.63 (FC) and 0.56 (LFpen). BW presented the highest values of likelihood ratio (LR)+ (12.47) and LR- (0.68). Rank correlations with histology were 0.53 (LF), 0.52 (LFpen), 0.41 (FC), 0.59 (ICDAS II) and 0.57 (BW). The area under the ROC curve varied from 0.72 to 0.83. Inter- and intraexaminer intraclass correlation values were respectively 0.90 and 0.85 (LF), 0.93 and 0.87 (LFpen) and 0.85 and 0.76 (FC). The ICDAS II kappa values were 0.51 (interexaminer) and 0.61 (intraexaminer). The BW kappa values were 0.50 (interexaminer) and 0.62 (intraexaminer). The Bland and Altman limits of agreement were 46.0 and 38.2 (LF), 55.6 and 40.0 (LFpen) and 1.12 and 0.80 (FC), for intra- and interexaminer reproducibilities. The posttest probability for dentine caries detection was high for BW and LF. In conclusion, LFpen, FC and ICDAS II presented better sensitivity and LF and BW better specificity. ICDAS II combined with BW showed the best performance and is the best combination for detecting caries on occlusal surfaces. Copyright (C) 2008 S. Karger AG, Basel.

Likelihood approximations and discrete models for tied survival data

Ties among event times are often recorded in survival studies. For example, in a two week laboratory study where event times are measured in days, ties are very likely to occur. The proportional hazards model might be used in this setting using an approximated partial likelihood function. This approximation works well when the number of ties is small. on the other hand, discrete regression models are suggested when the data are heavily tied. However, in many situations it is not clear which approach should be used in practice. In this work, empirical guidelines based on Monte Carlo simulations are provided. These recommendations are based on a measure of the amount of tied data present and the mean square error. An example illustrates the proposed criterion.

Methods to verify parameter equality in nonlinear regression models

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Bayesian and multivariate methods applied to favorability quantification in recôncavo Basin and Ribeira Belt, Brazil

A methodology to define favorable areas in petroleum and mineral exploration is applied, which consists in weighting the exploratory variables, in order to characterize their importance as exploration guides. The exploration data are spatially integrated in the selected area to establish the association between variables and deposits, and the relationships among distribution, topology, and indicator pattern of all variables. Two methods of statistical analysis were compared. The first one is the Weights of Evidence Modeling, a conditional probability approach (Agterberg, 1989a), and the second one is the Principal Components Analysis (Pan, 1993). In the conditional method, the favorability estimation is based on the probability of deposit and variable joint occurrence, with the weights being defined as natural logarithms of likelihood ratios. In the multivariate analysis, the cells which contain deposits are selected as control cells and the weights are determined by eigendecomposition, being represented by the coefficients of the eigenvector related to the system's largest eigenvalue. The two techniques of weighting and complementary procedures were tested on two case studies: 1. Recôncavo Basin, Northeast Brazil (for Petroleum) and 2. Itaiacoca Formation of Ribeira Belt, Southeast Brazil (for Pb-Zn Mississippi Valley Type deposits). The applied methodology proved to be easy to use and of great assistance to predict the favorability in large areas, particularly in the initial phase of exploration programs. © 1998 International Association for Mathematical Geology.

Precision of yule-walker methods for the arma spectral model

In this work a new method is proposed of separated estimation for the ARMA spectral model based on the modified Yule-Walker equations and on the least squares method. The proposal of the new method consists of performing an AR filtering in the random process generated obtaining a new random estimate, which will reestimate the ARMA model parameters, given a better spectrum estimate. Some numerical examples will be presented in order to ilustrate the performance of the method proposed, which is evaluated by the relative error and the average variation coefficient.

Improving methods in gap ecology: Revisiting size and shape distributions using a model selection approach

Questions: We assess gap size and shape distributions, two important descriptors of the forest disturbance regime, by asking: which statistical model best describes gap size distribution; can simple geometric forms adequately describe gap shape; does gap size or shape vary with forest type, gap age or the method used for gap delimitation; and how similar are the studied forests and other tropical and temperate forests? Location: Southeastern Atlantic Forest, Brazil. Methods: Analysing over 150 gaps in two distinct forest types (seasonal and rain forests), a model selection framework was used to select appropriate probability distributions and functions to describe gap size and gap shape. The first was described using univariate probability distributions, whereas the latter was assessed based on the gap area-perimeter relationship. Comparisons of gap size and shape between sites, as well as size and age classes were then made based on the likelihood of models having different assumptions for the values of their parameters. Results: The log-normal distribution was the best descriptor of gap size distribution, independently of the forest type or gap delimitation method. Because gaps became more irregular as they increased in size, all geometric forms (triangle, rectangle and ellipse) were poor descriptors of gap shape. Only when small and large gaps (> 100 or 400m2 depending on the delimitation method) were treated separately did the rectangle and isosceles triangle become accurate predictors of gap shape. Ellipsoidal shapes were poor descriptors. At both sites, gaps were at least 50% longer than they were wide, a finding with important implications for gap microclimate (e.g. light entrance regime) and, consequently, for gap regeneration. Conclusions: In addition to more appropriate descriptions of gap size and shape, the model selection framework used here efficiently provided a means by which to compare the patterns of two different types of forest. With this framework we were able to recommend the log-normal parameters μ and σ for future comparisons of gap size distribution, and to propose possible mechanisms related to random rates of gap expansion and closure. We also showed that gap shape varied highly and that no single geometric form was able to predict the shape of all gaps, the ellipse in particular should no longer be used as a standard gap shape. © 2012 International Association for Vegetation Science.

Geostatistics and remote sensing methods in the classification of images of areas cultivated with citrus

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Computer intensive methods for controlling bias in a generalized species diversity index

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Do pets reduce the likelihood of sudden unexplained death in epilepsy?

Purpose: To assess the relationship between the presence of pets in homes of epilepsy patients and the occurrence of sudden unexpected death in epilepsy (SUDEP). Methods: Parents or relatives of SUDEP patients collected over a ten-year period (2000-2009) in a large epilepsy unit were asked if the patient lived together with any domestic pet at the time of death or not. Patients who did not experience SUDEP served as controls. Results and conclusions: Eleven out of the 1092 included patients (1%) experienced SUDEP, all with refractory symptomatic epilepsy, but none of them had pets in their homes at the time of death. In contrast, the frequency of pet-ownership in the control group (n = 1081) was 61%. According to previous studies there are some indications that human health is directly related to companionship with animals in a way that domestic animals prevent illness and facilitate recovery of patients. Companion animals can buffer reactivity against acute stress, diminish stress perception and improve physical health. These factors may reduce cardiac arrhythmias and seizure frequency, factors related to SUDEP. Companion animals may have a positive effect on well-being, thus irnproving epilepsy outcome. (c) 2012 British Epilepsy Association. Published by Elsevier Ltd. All rights reserved.

The performance of four molecular methods for the laboratory diagnosis of congenital toxoplasmosis in amniotic fluid samples

Introduction Toxoplasmosis may be life-threatening in fetuses and in immune-deficient patients. Conventional laboratory diagnosis of toxoplasmosis is based on the presence of IgM and IgG anti-Toxoplasma gondii antibodies; however, molecular techniques have emerged as alternative tools due to their increased sensitivity. The aim of this study was to compare the performance of 4 PCR-based methods for the laboratory diagnosis of toxoplasmosis. One hundred pregnant women who seroconverted during pregnancy were included in the study. The definition of cases was based on a 12-month follow-up of the infants. Methods Amniotic fluid samples were submitted to DNA extraction and amplification by the following 4 Toxoplasma techniques performed with parasite B1 gene primers: conventional PCR, nested-PCR, multiplex-nested-PCR, and real-time PCR. Seven parameters were analyzed, sensitivity (Se), specificity (Sp), positive predictive value (PPV), negative predictive value (NPV), positive likelihood ratio (PLR), negative likelihood ratio (NLR) and efficiency (Ef). Results Fifty-nine of the 100 infants had toxoplasmosis; 42 (71.2%) had IgM antibodies at birth but were asymptomatic, and the remaining 17 cases had non-detectable IgM antibodies but high IgG antibody titers that were associated with retinochoroiditis in 8 (13.5%) cases, abnormal cranial ultrasound in 5 (8.5%) cases, and signs/symptoms suggestive of infection in 4 (6.8%) cases. The conventional PCR assay detected 50 cases (9 false-negatives), nested-PCR detected 58 cases (1 false-negative and 4 false-positives), multiplex-nested-PCR detected 57 cases (2 false-negatives), and real-time-PCR detected 58 cases (1 false-negative). Conclusions The real-time PCR assay was the best-performing technique based on the parameters of Se (98.3%), Sp (100%), PPV (100%), NPV (97.6%), PLR (â^ž), NLR (0.017), and Ef (99%).

Squared Extrapolation Methods (SQUAREM): A New Class of Simple and Efficient Numerical Schemes for Accelerating the Convergence of the EM Algorithm

We derive a new class of iterative schemes for accelerating the convergence of the EM algorithm, by exploiting the connection between fixed point iterations and extrapolation methods. First, we present a general formulation of one-step iterative schemes, which are obtained by cycling with the extrapolation methods. We, then square the one-step schemes to obtain the new class of methods, which we call SQUAREM. Squaring a one-step iterative scheme is simply applying it twice within each cycle of the extrapolation method. Here we focus on the first order or rank-one extrapolation methods for two reasons, (1) simplicity, and (2) computational efficiency. In particular, we study two first order extrapolation methods, the reduced rank extrapolation (RRE1) and minimal polynomial extrapolation (MPE1). The convergence of the new schemes, both one-step and squared, is non-monotonic with respect to the residual norm. The first order one-step and SQUAREM schemes are linearly convergent, like the EM algorithm but they have a faster rate of convergence. We demonstrate, through five different examples, the effectiveness of the first order SQUAREM schemes, SqRRE1 and SqMPE1, in accelerating the EM algorithm. The SQUAREM schemes are also shown to be vastly superior to their one-step counterparts, RRE1 and MPE1, in terms of computational efficiency. The proposed extrapolation schemes can fail due to the numerical problems of stagnation and near breakdown. We have developed a new hybrid iterative scheme that combines the RRE1 and MPE1 schemes in such a manner that it overcomes both stagnation and near breakdown. The squared first order hybrid scheme, SqHyb1, emerges as the iterative scheme of choice based on our numerical experiments. It combines the fast convergence of the SqMPE1, while avoiding near breakdowns, with the stability of SqRRE1, while avoiding stagnations. The SQUAREM methods can be incorporated very easily into an existing EM algorithm. They only require the basic EM step for their implementation and do not require any other auxiliary quantities such as the complete data log likelihood, and its gradient or hessian. They are an attractive option in problems with a very large number of parameters, and in problems where the statistical model is complex, the EM algorithm is slow and each EM step is computationally demanding.