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.

The fall descriptions and health characteristics of older adults with hip fracture : a mixed methods study

Background: In light of the multifactorial etiology of fall-related hip fracture, knowledge of fall circumstances may be especially valuable when placed in the context of the health of the person who falls. We aimed to investigate the circumstances surrounding fall-related hip fractures and to describe fall circumstances in relation to participants' health and functional characteristics. Methods: The fall circumstances of 125 individuals (age >= 50 years) with hip fracture were investigated using semi-structured interviews. Data concerning participants' health (comorbidities and medications) and function (self-reported performance of mobility, balance, personal activities of daily living and physical activity, previous falls and hand grip strength) were collected via medical records, questionnaires and dynamometry. Using a mixed methods design, both data sets were analysed separately and then merged in order to provide a comprehensive description of fall events and identify eventual patterns in the data. Results: Fall circumstances were described as i) Activity at the time of the fall: Positional change (n = 24, 19%); Standing (n = 16, 13%); Walking (n = 71, 57%); Balance challenging (n = 14, 11%) and ii) Nature of the fall: Environmental (n = 32, 26%); Physiological (n = 35, 28%); Activity-related indoor (n = 8, 6%) and outdoor (n = 8, 6%); Trips and slips on snow (n = 20, 16%) and in snow-free conditions (n = 12, 10%) and Unknown (n = 10, 8%). We observed the following patterns regarding fall circumstances and participants' health: those who fell i) during positional change had the poorest functional status; ii) due to environmental reasons (indoors) had moderate physical function, but high levels of comorbidity and fall risk increasing medications; iii) in snow-free environments (outdoors) appeared to have a poorer health and functional status than other outdoor groups. Conclusions: Our findings indicate that patterns exist in relation to the falls circumstances and health characteristics of people with hip fracture which build upon that previously reported. These patterns, when verified, can provide useful information as to the ways in which fall prevention strategies can be tailored to individuals of varying levels of health and function who are at risk for falls and hip fracture.

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).

Parameter estimation of Poisson generalized linear mixed models based on three different statistical principles : a simulation study

Generalized linear mixed models are flexible tools for modeling non-normal data and are useful for accommodating overdispersion in Poisson regression models with random effects. Their main difficulty resides in the parameter estimation because there is no analytic solution for the maximization of the marginal likelihood. Many methods have been proposed for this purpose and many of them are implemented in software packages. The purpose of this study is to compare the performance of three different statistical principles - marginal likelihood, extended likelihood, Bayesian analysis-via simulation studies. Real data on contact wrestling are used for illustration.