In past years, measurements of the solar wind plasma have advanced our understanding of MHD turbulence tremendously. At small scales, the solar wind is believed to be very multifractal with nonlinear interactions causing an intermittent energy dissipation, leading to possible current-sheet structures. In this Letter, we propose a systematic data analysis procedure to examine the existence of current sheets in the solar wind. We show that by studying the integrated distribution function F(v, z) of the angle between two unit magnetic fields b(t) and, as well as its z-dependence, one can unambiguously identify the existence of current-sheet–like structures b(t z) in the solar wind. Using this procedure, we analyze magnetic field data from the VHM/FGM instrument on board the spacecraft Ulysses for two periods, one in solar maximum and the other in solar minimum. In both cases, current sheets are clearly inferred. Furthermore, we also outline a procedure that allows the identification of the actual locations of these current sheets. Results from our analysis and the implications of the existence of current sheets in the solar wind are discussed.

This dissertation develops joint inferential methods for the cause specific hazard function and the cumulative incidence function of a specific type of failure to assess the effects of a variable on the type of failure of interest in the presence of competing risks. Joint inference for the two functions are needed in practice because 1) they describe different characteristics of a particular type of failure, 2) they do not uniquely determine each other, and 3) the effects of a variable on the two functions can be different and one often does not know which effects are to be expected. We study both the group comparison problem and the Cox's regression problem. We also develop joint inference for other equivalent pairs of functions. Our simulation shows that the derived joint tests can be considerably more powerful than the Bonferroni method, which has important practical implications to the analysis and design of clinical studies with competing risks data. We illustrate our methods using a Hodgkin disease data and a lymphoma data. We also develop sample size calculation methods based on nonparametric two sample joint tests of the cause-specfic hazard and the all-cause hazard. A user friendly R-function is developed to implement the method. We illustrate the implementation of our method and the potential saving on the required sample size over the Bonferroni method through simulations and the 4-D (Die Deutsche Diabetes Dialyse Studie) clinical trial designed to compare a lipid lowering treatment with placebo in type 2 diabetic patients on hemodialysis.

It is often of interest to study the temporal patterns of longitudinal biomarker(s) that are potentially correlated and predictive of time-to-event outcomes in biomedical studies. In this dissertation, I develop new approaches for joint modeling of longitudinal and time-to-event data. My dissertation consists of three projects. In Chapter 2, I develop customized linear scan algorithms to speed up the computation of semi-parametric joint models by linearizing the computational burden of the estimation procedure from $O(n^2)$ or $O(n^3)$ to $O(n)$. Compared to the existing software and packages on semi-parametric joint models, our implementations can provide more than thousands of speed-ups when the sample size goes large. In Chapter 3, motivated by the Multi-Ethnic Study of Atherosclerosis (MESA), I propose a novel joint model to account for the heterogeneity of within-subject variability of a longitudinal outcome and demonstrate that it improves the dynamic prediction accuracy of predicting the future event probabilities of both heart failure and death across MESA individuals. In Chapter 4, I extend the joint model described in Chapter 3 to handle interval-censored covariates as missing data due to the unknown initial event time. Using age at diagnosis of diabetes as an interval-censored covariate, we revisit the UK-Biobank data to illustrate that our proposed joint model can yield clinically meaningful parameter estimates, compared to the existing methods such as midpoint imputation, which can lead to problematic conclusion on the effect of covariates on the outcomes.

The method of instrumental variable (IV) analysis has been widely used in economics, epidemiology, and other fields to estimate the causal effects of intermediate covariates on outcomes, in the presence of unobserved confounders and/or measurement errors in covariates. Consistent estimation of the effect has been developed when the outcome is continuous, while methods for binary outcome produce inconsistent estimation. In this dissertation, we examine two IV methods in the literature for binary outcome and show the bias in parameter estimate by a simulation study. The identifiability problem of IV analysis with binary outcome is discussed. Moreover, IV methods for time-to-event outcome with censored data remain underdeveloped. We propose two Bayesian approaches for IV analysis with censored time-to-event outcome by using a two-stage linear model: One is a parametric Bayesian model with normal and non-normal elliptically contoured error distributions, and the other is a semiparametric Bayesian model with Dirichlet process mixtures for the random errors, in order to relax the parametric assumptions and address heterogeneous clustering problems. Markov Chain Monte Carlo sampling methods are developed for both parametric and semiparametric Bayesian models to estimate the endogenous parameter. Performance of our methods is examined by simulation studies. Both methods largely reduce bias in estimation and greatly improve coverage probability of the endogenous parameter, compared to the regular method where the unobserved confounders and/or measurement errors are ignored. We illustrate our methods on the Women's Health Initiative Observational Study and the Atherosclerosis Risk in Communities Study.

Introduction: Enlargement of the remnant gastric pouch and gastro-jejunal (GJ) stoma are associated with weight regain after RYGB surgery. Current evidence suggests an excess weight loss (%EWL) of 12-25% with GJ outlet reduction (TORe) alone. However, the efficacy of a combined approach using endoscopic trans-oral outlet reduction (TORe) in combination with Gastroplasty of the entire gastric pouch from the gastro-esophageal (GE) junction to the GJ stoma (TORe-G) is unknown.

Methods: Patients who experienced inadequate weight loss (<50% EWL) or weight regain (>25% EWL from nadir) post-RYGB along with evidence of dilated GJ stoma and gastric pouch underwent a combined GJ stoma reduction and gastroplasty. The procedure involved ablation of the peristomal mucosa and gastric pouch using APC and placement of interrupted and running full-thickness plications (Overstitch, Apollo Endosurgery, Austin Tx) for a targeted GJ diameter of ~5-8 mm and significant reduction of gastric pouch volume.

Results: 40 patients (78% females) with age 53?10 years, BMI 41?9 kg/m2, and time since RYGB 10?4 years were prospectively studied. Significant weight loss (>5% TBWL) was seen in 90% patients. Post Tore-G, mean (95% CI) %TBWL observed at 1, 3, 6, 9 and 12 months follow up was 7.6 (5-10.1), 10.4 (8.1-12.8), 12.3 (9.6-14.9), 13.3 (10.4-16.2), and 14.1 (10.9-17.2) respectively. Corresponding %EWL was 24.1 (15.9-32.3), 31.3 (23.7-38.9), 35.9 27.3-44.4), 38.5 (29.1-47.9), and 40.4 (30.2-50.6); and %RWL was 39.6 (22.1-57), 52.1 (35.5 -68.8), 60.1 (41.9-78.3), 64.7 (45-84.5), and 68 (47-89) respectively. No covariates including age, sex, interval time since RYGB, % weight regained were significantly associated with weight loss over time. No serious adverse events were observed.

Conclusions: We demonstrate for the first time the efficacy and safety of TORe-G to re-establish weight loss in patients with failed RYGB using a full thickness endoscopic suturing device. TORe-G resulted in robust weight loss and superior outcomes compared with published data with TORe alone.

Computational advancements and cost efficiency over the recent years have made big data readily available to researchers. In the biomedical and public health fields analyzing time-to-event data, where the outcome of interest is a time-to-event endpoint, is of particular interest. However, big time-to-event data poses many challenges to currently-available statistical methods due to the large number of covariates and/or observations one can observe. In this dissertation we propose scalable sparse regression methods for both big right-censored and competing risks time-to-event data. We extend the recently-introduced broken adaptive ridge (BAR) regression procedure to both the Cox (1972) proportional hazards for right-censored data and the Fine and Gray (1999) proportional subdistribution hazards model for competing risks data, establish its large-sample properties under diverging dimension, and develop computational software that is scalable to big time-to-event data.

Collection of large amounts of genetic data and advancements in computational genetics over the recent years provide us with tools to explore epigenetic mechanisms that lead to aging and lifespan. In the context of continuous DNA methylation data, with a novel cross-species DNA methylation microarray targeting conserved CpG sites across mammalian species, we are able to leverage readily available statistical models to extensively study important life history traits such as lifespan, gestation time, and time to sexual maturity across various species. DNA methylation data are often high dimensional and require regularized regression frameworks to construct practical prediction models. Based on an unprecedented mammalian DNA methylation data set, we have developed methylation-based epigenetic life history traits predictors using regularized linear regressions. The estimators can accurately predict maximum lifespan using cytosine methylation patterns collected from over 13,000 samples derived from 348 mammalian species. To extend our future inferential analyses into diverse data sources such as RNA-seq data, we have proposed an L0-regularized Poisson graphical model for exploring gene-to-gene relations. The superior theoretical properties that the L0 sparse graphical model enjoys will more effectively assist the future work of clustering and grouping large numbers of DNA methylation sites and genes. Both the applied research and methodological work will aid in the aging research goals of integrating various layers of multiomics data.

In this paper we obtain first a gap theorem for a class of conformally compact Einstein manifolds with a renormalized volume that is close to its maximum value. We also use a blow-up method to derive curvature estimates for conformally compact Einstein manifolds with large renormalized volume. The major part of this paper is the study of how a property of the conformal infinity influences the geometry of the interior of a conformally compact Einstein manifold. Specifically we are interested in conformally compact Einstein manifolds with conformal infinity whose Yamabe invariant is close to that of the round sphere. Based on the approach initiated by Dutta and Javaheri we present a complete proof of the relative volume inequality \[ ( Y ( ∂ X , [ g ^ ] ) Y ( S n − 1 , [ g S ] ) ) n − 1 2 ≤ V o l ( ∂ B g + ( p , t ) ) V o l ( ∂ B g H ( 0 , t ) ) ≤ V o l ( B g + ( p , t ) ) V o l ( B g H ( 0 , t ) ) ≤ 1 , \left (\frac {Y(\partial X, [\hat {g}])}{Y(\mathbb {S}^{n-1}, [g_{\mathbb {S}}])}\right )^{\frac {n-1}{2}}\leq \frac {Vol(\partial B_{g^+}(p, t))} {Vol(\partial B_{g_{\mathbb {H}}}(0, t))} \leq \frac {Vol(B_{g^+}(p, t))} {Vol(B_{g_{\mathbb {H}}}(0, t))}\leq 1, \] for conformally compact Einstein manifolds. This leads not only to the complete proof of the rigidity theorem for conformally compact Einstein manifolds in arbitrary dimension without spin assumption but also a new curvature pinching estimate for conformally compact Einstein manifolds with conformal infinities having large Yamabe invariant. We also derive curvature estimates for such manifolds.