In the last decade, genome-wide association studies have helped to advance our understanding of the genetic architecture of many important traits, including diseases. However, the statistical analysis of genotype-phenotype associations remains challenging due to multiple factors. First, many traits have polygenic architectures, which means that they are controlled by a large number of variants with small individual effects. Second, as increasingly deep phenotype data are being generated there is a need for multivariate analysis approaches to leverage multiple related phenotypes while retaining computational efficiency. Additionally, genetic analyses are confronted by strong confounding factors that can create spurious associations when not properly accounted for in the statistical model. We here derive more flexible methods that allow integrating genetic effects across variants and multiple quantitative traits. To do so, we build on the classical linear mixed model (LMM), a widely adopted framework for genetic studies. The first contribution of this thesis is mtSet, an efficient mixed-model approach that enables genome-wide association testing between sets of genetic variants and multiple traits while accounting for confounding factors. In both simulations and real-data applications we demonstrate that mtSet effectively combines the advantages of variant-set and multi-trait analyses. Next, we present a new model for gene-context interactions that builds on mtSet. The proposed interaction set test (iSet) yields increased statistical power for detecting polygenic interactions. Additionally, iSet enables the identification of genetic loci that are associated with different configurations of causal variants across contexts. After benchmarking the proposed method using simulated data, we consider two applications to real datasets, where we investigate genetic effects on gene expression across different cellular contexts and sex-specific genetic effects on lipid levels. Finally, we describe LIMIX, a software framework for the flexible implementation of different LMMs. Most of the models considered in this thesis, including mtSet and iSet, are implemented and available in LIMIX. A unique aspect of the software is an inference framework that allows a large class of genetic models to be defined and, in many cases, to be efficiently fitted by exploiting specific algebraic properties. We demonstrate the utility of this software suite in two applied collaboration projects. Taken together, this thesis demonstrates the value of flexible and integrative modelling in genetics and contributes new statistical methods for genetic analysis. These approaches generalise previous models, yet retain the computational efficiency that is needed to tackle large genetic datasets.

We collected the data for decomposition of spruce litter to determine the limit values of mass loss and to find both chemical and climate factors that influence limit values. Our data contained 28 sequences of spruce which mainly in Sweden and a small part in other places. We choose mean annual temperature (MAT) and mean annual precipitation (MAP) as climate factors and water solubles, lignin, N, P, K, Ca, Mg and Mn as chemical factors. Then we got the estimated limit values by performing a nonlinear model with mass loss and time spots, and found out the influential factors by using another linear mixed model. At the end we knew that linear mixed model is a proper and efficient approach for determining the factors, P and MAP are the significant factors and Species is a good random effect to explain the variance within groups.

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In this study, I investigated how proficiently seventh-grade students enrolled in two Southwestern schools solve algebra word problems. I analyzed various factors that could affect this proficiency and explored the differences between English Learners (ELs) and native English Primary students (EPs). I collected the data as part of the Animal Watch project, a computer-based initiative designed to improve the mathematical skills of children from grades 5-8 in the Southwest. A sample of 86 students (26 ELs and 60 EPs), clustered in four different classes, was used for this project. A Generalized Linear Mixed Model (GLMM) approach with the GLIMMIX procedure in SAS 9.3 showed that students from the classes that had a higher percentage of EL students performed better than those in the classes where the EL concentration was lower. Classes with more EL males were better at learning mathematics than classes with more EP females. The results also indicated: (a) a positive correlation between the students' ability to solve algebra word problems on their first attempt and their success ratio in solving all problems, and (b) a negative correlation between the percentage of problems solved correctly and those considered too hard from the very beginning. I conclude my dissertation by making specific recommendations for further research.

Master of Science / Department of Statistics / Christopher Vahl / In animal health research, it is quite common for a clinical trial to be designed to demonstrate the efficacy of a new drug where a binary response variable is measured on an individual experimental animal (i.e., the observational unit). However, the investigational treatments are applied to groups of animals instead of an individual animal. This means the experimental unit is the group of animals and the response variable could be modeled with the binomial distribution. Also, the responses of animals within the same experimental unit may then be statistically dependent on each other. The usual logit model for a binary response assumes that all observations are independent. In this report, a logit model with a random error term representing the group of animals is considered. This is model belongs to a class of models referred to as generalized linear mixed models and is commonly fit using the SAS System procedure PROC GLIMMIX. Furthermore, practitioners often adjust the denominator degrees of freedom of the test statistic produced by PROC GLIMMIX using one of several different methods. In this report, a simulation study was performed over a variety of different parameter settings to compare the effects on the type I error rate and power of two methods for adjusting the denominator degrees of freedom, namely “DDFM = KENWARDROGER” and “DDFM = NONE”. Despite its reputation for fine performance in linear mixed models with normally distributed errors, the “DDFM = KENWARDROGER” option tended to perform poorly more often than the “DDFM = NONE” option in the logistic regression model with one random effect.

Cystic fibrosis (CF) is the most common life-restricting, genetically inherited disease among Caucasians affecting approximately 30,000 people in the United States. Lung disease is the major cause of morbidity and mortality in CF. A number of oral, inhaled, and intravenous therapies are available to combat CF lung disease. Of these, this research project focused on inhaled dornase alfa, oral azithromycin, inhaled tobramycin, and inhaled aztreonam. Data to address three research aims were requested and obtained from the Cystic Fibrosis Foundation Patient Registry (CFFPR). The first aim examined the use of inhaled dornase alfa in younger children with CF. With no clinical efficacy data of dornase alfa in children ≤ 6 years of age, the study utilized subsequent forced expiratory volume in 1 second (FEV₁) measured between 6 - 7 years of age, to assess the effectiveness of long-term dornase alfa use ≤ 6 years of age. Propensity score methods were used to reduce the likelihood of treatment indication bias. The results suggested that receiving treatment with dornase alfa before 6 years of age did not improve FEV₁ between 6 - 7 years. Unmeasured covariates leading to treatment indication bias were likely one of the key explanations for these results. Additionally, lack of a more sensitive outcome than FEV₁ to assess lung function in young patients with early lung damage was thought to be another reason for the failure to reject the null hypothesis. The second aim assessed the long-term clinical effectiveness of chronic azithromycin use on the rate of FEV₁ decline in CF patients between 6 - 20 years of age. This study was novel in that the rate of FEV₁ decline, rather than change in FEV₁ from baseline, was the primary outcome, which was characterized using propensity score matching followed by a linear mixed model analysis. The results of the analysis suggested that the rate of FEV₁ decline was slower in patients who did not receive chronic treatment with azithromycin. Treatment indication bias was thought to play an important role in the direction of the association between treatment and outcome. Associations between FEV₁ % predicted and many of the other study variables included in the analysis were consistent with previous studies. The final aim compared the clinical effectiveness of a combination of inhaled tobramycin and aztreonam with inhaled tobramycin alone on the rate of FEV₁ decline in CF patients between 6 - 20 years of age. This aim was novel in that the effect of this combination treatment on rate of decline in FEV₁ has never been assessed. A linear mixed model analysis was used after matching patients in the two treatment groups on their propensity scores. Once again, the results were contrary to the alternative hypothesis with the combination group having a steeper rate of FEV₁ decline than the group that was treated with tobramycin alone. An important reason for this result was thought to be unresolved treatment indication bias that could not be eliminated even with the use of the propensity score methods used to test the associated hypothesis. The use of validated methods of analysis, i.e., propensity scores, to counter treatment indication bias using the largest available observational dataset for CF, was one of the key strengths of this study. Moreover, this study highlighted important weaknesses in the CFFPR with regards to lack of data on patient and physician-level variables - an area of active interest for the Cystic Fibrosis Foundation.

Background: By 2050, it is estimated that 14 million older Americans will live with Alzheimer’s disease (AD), a progressive form of dementia with unknown cause or cure. Persons with AD and related dementias (ADRD) become increasingly dependent on others as they experience cognitive decline, which concomitantly undermines individuals’ functional skills, social initiative, and quality of life. The Alzheimer’s Association advocates for interventions that address cognition, mood, behavior, social engagement, and by extension, quality of life – goals music therapists often address. Although a small but growing body of literature suggests that clinical music therapy may be effective, the evidentiary support for the use and appropriate application of music as a form of treatment with this population is currently limited. Objectives: This thesis consisted of the development of a Clinical Practice Model of music therapy for persons with ADRD. It also examined the effectiveness of a specific, protocol-based music therapy intervention, grounded in this model, relative to a verbal discussion activity. Methods: The Clinical Practice Model is theoretically grounded in the biopsychosocial model of healthcare (Engel, 1980) and Kitwood’s (1997) personhood framework, and I developed it through extensive literature review and expert input. It includes an organizational schema for applying intervention strategies, per six themes: cognition, attention, familiarity, audibility, structure, and autonomy. The initial model predicts that an intervention built upon this schema will influence social-affective responses, quality of life, and in turn, psychosocial symptoms of ADRD. I tested a singing-based music therapy intervention, grounded in this model, through a randomized clinical crossover trial. I compared participants’ responses to music therapy to a non-music verbal discussion activity, and both conditions followed a protocol. Dependent variables included: (1) affective responses (self-reported feelings, observed emotions, and observed mood), (2) social engagement, and (3) observed quality of life. Thirty-two individuals with ADRD (n = 6 men, n = 26 women) ages 65-97 years old (μ̂ = 84.13) participated in this study. I randomly assigned treatment order; each treatment occurred in small-group format, three times per week in the afternoon (25 minutes each session), for two consecutive weeks. A two-week “wash-out” period occurred between conditions. Credentialed music therapists led both study conditions. This study followed recommendations from the National Institutes of Health Behavior Change Consortium (Bellg et al., 2004) to enhance quality assurance in protocol administration and data collection. Results and Significance: I used a linear mixed model approach to analysis. Music therapy exacted a significant, positive effect on self-reported feelings, observed emotions, and constructive engagement, particularly for individuals with moderate dementia. Results also suggested that men’s feelings improved in response to music therapy only, whereas women responded positively to both conditions. Weekly observations failed to indicate a significant change in mood or quality of life across the eight-week study. Based on these findings, I revised the Clinical Practice Model to include wellbeing (an outcome more concordant with psychosocial change in response to music intervention) rather than global quality of life (affected by numerous aspects of the care milieu). In addition to the Clinical Practice Model to the music therapy profession, contributions of this thesis include a rigorous clinical study and practical implications for music therapy practice, including the importance of considering patient characteristics and careful selection and implementation of music in a music therapy intervention.

Although the captive reproduction of non-avian reptiles has increased steadily since the 1970’s, a dearth of information exists on successful management practices for large captive populations of these species. The data reported here come from a captive population of ball pythons (Python regius) maintained by a commercial breeding company, The Snake Keeper, Inc. (Spanish Fork, UT). Reproductive data are available for 6,480 eggs from 937 ball python clutches. The data presented suggest that proper management practices should include the use of palpation and/or ultrasound to ensure breeding occurs during the proper time of the female reproductive cycle, and that maintenance of proper humidity during the incubation of eggs is vitally important. Ball python reproduction traits (clutch size, clutch mass, relative clutch mass, egg mass, hatch rate, egg length, egg width, hatchling mass, healthy offspring per clutch, week laid, and days of incubation) were recorded for the clutches laid during this study. For the 937 clutches, the identity of the dam and sire were known for 862 (92%) and 777 (83%) of the clutches, respectively. A multivariate model that included nine of the 11 traits listed above was compiled. Heritability and genetic and phenotypic correlations were calculated from the multivariate analysis. The trait that showed the most promise for use in artificial selection to increase reproduction rates was clutch size due to considerable genetic variation, high heritability, and favorable genetic correlations with other reproduction traits. Although large datasets have been published for twinning in avian species, relatively few are available for non-avian reptiles. Reported here are 14 sets of twins produced from 6,480 eggs from 937 ball python clutches. The survival rate for twins during the first 3 months of life in our study was 97%. Interestingly, 11 of the sets of twins were identical in sex and phenotype, and additional genetic data suggested the rate of monozygotic twinning within this captive population of ball pythons was higher than that of dizygotic twinning. Further, using microsatellite analysis we were able to generate data that shows three sets of python twins were genetically identical.

Linear mixed models (LMMs) provide a still underused methodological perspective on combining experimental and individual-differences research. Here we illustrate this approach with two-rectangle cueing in visual attention (Egly et al., 1994). We replicated previous experimental cue-validity effects relating to a spatial shift of attention within an object (spatial effect), to attention switch between objects (object effect), and to the attraction of attention toward the display centroid (attraction effect), also taking into account the design-inherent imbalance of valid and other trials. We simultaneously estimated variance/covariance components of subject-related random effects for these spatial, object, and attraction effects in addition to their mean reaction times (RTs). The spatial effect showed a strong positive correlation with mean RT and a strong negative correlation with the attraction effect. The analysis of individual differences suggests that slow subjects engage attention more strongly at the cued location than fast subjects. We compare this joint LMM analysis of experimental effects and associated subject-related variances and correlations with two frequently used alternative statistical procedures

This research paper creates a comprehensive statistical model, relating financial impact of risk engineering activity, and insurance claims costs. Specifically, the model shows important statistical relationships among six variables including: types of risk engineering activity, risk engineering dollar cost, duration of risk engineering service, and type of customer by industry classification, dollar premium amounts, and dollar claims costs. We accomplish this by using a large data sample of approximately 15,000 customer-years of insurance coverage, and risk engineering activity. Data sample is from an international casualty/property insurance company and covers four years of operations, 2006-2009. The choice of statistical model is the linear mixed model, as presented in SAS 9.2 software. This method provides essential capabilities, including the flexibility to work with data having missing values, and the ability to reveal time-dependent statistical associations.