The Effects of the Earth's Rotation on Internal Wave Near-resonant Triads and Weakly Nonlinear Models

This thesis investigates the effects of the earth's rotation on internal waves from two perspectives of nonlinear internal wave theory: near-resonant triads and weakly nonlinear models. We apply perturbation theory (multiple scale analysis) to the governing equations of internal waves and develop a near-resonant internal wave triad theory. This theory explains a resonant-like phenomenon in the numerical results obtained from simulating internal waves generated by tide topography interaction. Furthermore, we find that the inclusion of the earth's rotation (nonzero $f$) in the numerical runs leads to a very special type of resonance: parametric subharmonic instability. Through using perturbation expansion to solve separable solutions to the governing equations of internal waves, we derive a new rotation modified KdV equation (RMKdV). Of particular interest, the dispersion relation of the new equation obeys the exact dispersion relation for internal waves for both small and moderate wavenumbers ($k$). Thus this new RMKdV is able to model wea kly nonlinear internal waves with various wavenumbers ($k$), better than the Ostrovsky equation which fails at describing waves of small $k$

Genome-Wide Association Analyses in 128,266 Individuals Identifies New Morningness and Sleep Duration Loci

Disrupted circadian rhythms and reduced sleep duration are associated with several human diseases, particularly obesity and type 2 diabetes, but until recently, little was known about the genetic factors influencing these heritable traits. We performed genome-wide association studies of self-reported chronotype (morning/evening person) and self-reported sleep duration in 128,266 white British individuals from the UK Biobank study. Sixteen variants were associated with chronotype (P<5x10(-8)), including variants near the known circadian rhythm genes RGS16 (1.21 odds of morningness, 95% CI [1.15, 1.27], P = 3x10(-12)) and PER2 (1.09 odds of morningness, 95% CI [1.06, 1.12], P = 4x10(-10)). The PER2 signal has previously been associated with iris function. We sought replication using self-reported data from 89,283 23andMe participants;thirteen of the chronotype signals remained associated at P<5x10(-8) on meta-analysis and eleven of these reached P< 0.05 in the same direction in the 23andMe study. We also replicated 9 additional variants identified when the 23andMe study was used as a discovery GWAS of chronotype (all P<0.05 and meta-analysis P<5x10(-8)). For sleep duration, we replicated one known signal in PAX8 (2.6 minutes per allele, 95% CI [1.9, 3.2], P = 5.7x10(-16)) and identified and replicated two novel associations at VRK2 (2.0 minutes per allele, 95% CI [1.3, 2.7], P = 1.2x10(-9);and 1.6 minutes per allele, 95% CI [1.1, 2.2], P = 7.6x10(-9)). Although we found genetic correlation between chronotype and BMI (rG = 0.056, P = 0.05);undersleeping and BMI (rG = 0.147, P = 1x10(-5)) and over-sleeping and BMI (rG = 0.097, P = 0.04), Mendelian Randomisation analyses, with limited power, provided no consistent evidence of causal associations between BMI or type 2 diabetes and chronotype or sleep duration. Our study brings the total number of loci associated with chronotype to 22 and with sleep duration to three, and provides new insights into the biology of sleep and circadian rhythms in humans

Identification of a Rare Coding Variant in Complement 3 Associated with Age-related Macular Degeneration

Macular degeneration is a common cause of blindness in the elderly. To identify rare coding variants associated with a large increase in risk of age-related macular degeneration (AMD), we sequenced 2,335 cases and 789 controls in 10 candidate loci (57 genes). To increase power, we augmented our control set with ancestry-matched exome sequenced controls. An analysis of coding variation in 2,268 AMD cases and 2,268 ancestry matched controls revealed two large-effect rare variants; previously described R1210C in the CFH gene (fcase = 0.51%, fcontrol = 0.02%, OR = 23.11), and newly identified K155Q in the C3 gene (fcase = 1.06%, fcontrol = 0.39%, OR = 2.68). The variants suggest decreased inhibition of C3 by Factor H, resulting in increased activation of the alternative complement pathway, as a key component of disease biology

Whole-Exome Sequencing Identifies Rare and Low-Frequency Coding Variants Associated with LDL Cholesterol

Elevated low-density lipoprotein cholesterol (LDL-C) is a treatable, heritable risk factor for cardiovascular disease. Genome-wide association studies (GWASs) have identified 157 variants associated with lipid levels but are not well suited to assess the impact of rare and low-frequency variants. To determine whether rare or low-frequency coding variants are associated with LDL-C, we exome sequenced 2,005 individuals, including 554 individuals selected for extreme LDL-C (>98th or <2nd percentile). Follow-up analyses included sequencing of 1,302 additional individuals and genotype-based analysis of 52,221 individuals. We observed significant evidence of association between LDL-C and the burden of rare or low-frequency variants in PNPLA5, encoding a phospholipase-domain-containing protein, and both known and previously unidentified variants in PCSK9, LDLR and APOB, three known lipid-related genes. The effect sizes for the burden of rare variants for each associated gene were substantially higher than those observed for individual SNPs identified from GWASs. We replicated the PNPLA5 signal in an independent large-scale sequencing study of 2,084 individuals. In conclusion, this large whole-exome-sequencing study for LDL-C identified a gene not known to be implicated in LDL-C and provides unique insight into the design and analysis of similar experiments

Statistical Methods on Emerging Medical Studies.

Many areas of medical research can benefit from the application of new statistical methods. In this dissertation, we demonstrate the possibilities in some emerging medical studies. In chapter 2, we describe the design of longitudinal trials with dichotomized outcomes. Longitudinal studies are often analyzed using Generalized Estimating Equations (GEE) or Quadratic Inference Functions (QIF). We explore QIF-based analysis for study design: (i) we derive and compared sample size and power for QIF and GEE; (ii) we propose an optimal scheme of sample size determination to overcome the difficulty of unknown true correlation matrix; and (iii) we show that QIF based analysis become more efficient as the number of follow-up visits increases. We illustrate that without sacrificing power, the QIF design leads to sample size an study cost savings than the GEE analysis. In chapter 3, we focus on the analysis of exome sequencing studies. These studies focus sequencing resources on the exome but often yield many reads outside the targeted regions. These reads are almost always discarded but we propose our method SEQMIX to incorporate genotype likelihoods of off-targeted reads and show that it can decipher the local ancestry with resolution similar to that obtained with modern genome-wide association studies (GWAS) arrays. Our estimates are useful for analysis of human population history and disease gene mapping studies with exome and targeted sequence data. In chapter 4, we develop a general framework to explore benefits of incorporating genetic risk into prevention trial designs. We consider screening, recruitment and follow-up costs and current genetic findings in diseases. We consider type 1 diabetes (T1D), type 2 diabetes (T2D), myocardial infarction (MI) and age-related macular degeneration (AMD) as examples as they have distinct genetic architecture: many small effect markers are associated with T2D and MI; whilst loci with large effect size have been identified for T1D and AMD. We quantify the benefits by illustrating settings where reduction of trial cost or duration is up to 70% and settings where savings are modest. The benefits depend on the disease genetic architecture, but we also project that benefits will increase.PHDBiostatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/96090/1/youna_1.pd

The benefits of using genetic information to design prevention trials.

Clinical trials for preventative therapies are complex and costly endeavors focused on individuals likely to develop disease in a short time frame, randomizing them to treatment groups, and following them over time. In such trials, statistical power is governed by the rate of disease events in each group and cost is determined by randomization, treatment, and follow-up. Strategies that increase the rate of disease events by enrolling individuals with high risk of disease can significantly reduce study size, duration, and cost. Comprehensive study of common, complex diseases has resulted in a growing list of robustly associated genetic markers. Here, we evaluate the utility--in terms of trial size, duration, and cost--of enriching prevention trial samples by combining clinical information with genetic risk scores to identify individuals at greater risk of disease. We also describe a framework for utilizing genetic risk scores in these trials and evaluating the associated cost and time savings. With type 1 diabetes (T1D), type 2 diabetes (T2D), myocardial infarction (MI), and advanced age-related macular degeneration (AMD) as examples, we illustrate the potential and limitations of using genetic data for prevention trial design. We illustrate settings where incorporating genetic information could reduce trial cost or duration considerably, as well as settings where potential savings are negligible. Results are strongly dependent on the genetic architecture of the disease, but we also show that these benefits should increase as the list of robustly associated markers for each disease grows and as large samples of genotyped individuals become available

Whole-exome sequencing of 2,000 Danish individuals and the role of rare coding variants in type 2 diabetes.

It has been hypothesized that, in aggregate, rare variants in coding regions of genes explain a substantial fraction of the heritability of&nbsp;common diseases. We sequenced the exomes of 1,000 Danish cases with common forms of type 2 diabetes (including body mass index&nbsp;&gt; 27.5&nbsp;kg/m(2) and hypertension) and 1,000 healthy controls to an average depth of 56×. Our simulations suggest that our study had the statistical power to detect at least one causal gene (a gene containing causal mutations) if the heritability of these common diseases was explained by rare variants in the coding regions of a limited number of genes. We applied a series of gene-based tests to detect such susceptibility genes. However, no gene showed a significant association with disease risk after we corrected for the number of genes analyzed. Thus, we could reject a model for the genetic architecture of type 2 diabetes where rare nonsynonymous variants clustered in a modest number of genes (fewer than 20) are responsible for the majority of disease risk