Emerging national patient claims and electronic health record databases offer a rich frontier for learning about treatment effectiveness and clinical decision making. However, these resources present statistical and computational challenges commensurate with their promise, requiring innovative approaches for practically and efficiently extracting meaningful results. In this dissertation, I seek to address some of these challenges. First, I present a hierarchical model for learning about the relationship between treatments and multiple related adverse outcomes simultaneously, showing that this approach can reduce bias in relative risk estimates. Second, I develop a novel minorization-maximization (MM) algorithm for uncoupling the sequential Newton steps that arise within the state of the art model fitting procedure for the conditional models popular for observational studies, allowing faster, parallelized model fitting. Third, I develop a birth-death model for treatment trajectories among patients with diabetes mellitus type II. In these sections, I discuss applications to observational healthcare datasets, demonstrating how these methods work at scale.

Inferring dependencies between complex biological traits while accounting for evolutionary relationships among specimens is of great scientific interest, yet remains infeasible when trait and specimen counts grow large. I aim to develop a scalable Bayesian inference framework to assess correlation between complex traits along the evolutionary tree relating the specimens and informed by molecular sequences. To accommodate discrete and continuous traits, I posit a phylogenetic multivariate probit model that uses a latent variable framework. Posterior computation under this model requires integrating many latent variables, or equivalently making many computationally expensive draws from a high-dimensional multivariate truncated normal distribution (MTN). To tackle this challenge, I propose an inference scheme that exploits 1) representative cutting-edge Markov chain Monte Carlo (MCMC) methods including the bouncy particle sampler (BPS), the Markovian Zigzag sampler (ZZ), and the Zigzag Hamiltonian Monte Carlo (Zigzag-HMC) that can simultaneously sample all truncated normal dimensions, and 2) novel dynamic programming strategies that reduce the cost of likelihood and gradient evaluations for all three samplers to linear in sample size. Compared to the previous best practices that employ multiple-try rejection sampling, my approach achieves an order-of-magnitude speedup, allowing us to tackle previously unworkable large-scale problems. In an application with 535 HIV-1 viruses and 24 traits that necessitates sampling from a 11,235-dimensional MTN, my method makes it possible to examine the conditional dependencies between 21 immune escape mutations and 3 virulence measurements. In a second application I study the evolution of influenza H1N1 glycosylations using around 900 viruses. Lastly, I extend the phylogenetic probit model to incorporate categorical traits and demonstrate its use to investigate Aquilegia flower and pollinator coevolution. In summary, the contribution of this dissertation is two-fold. First, I develop a state-of-the-art solution for the long-standing problem in Bayesian phylogenetics | learning correlation among complex biological traits with joint tree modeling. Second, further empirical and theoretical investigation of BPS, ZZ, and Zigzag-HMC yield insight into the differences and similarities between these recently developed MCMC samplers. As Zigzag-HMC outperforms the other two on MTNs, I also implement this approach in a standalone R package, aiming to provide a general efficient tool for high-dimensional MTN simulation.

Objective

We used a novel Sensing At-Risk Population (SARP) system to monitor patients’ physical activity and locations during post-acute rehabilitation; To (1) examine the correlation between SARP measurements and standard physical (PT) and occupational therapists (OT) and nurse (RN) evaluations; (2) examine the effectiveness of SARP to discriminate discharge dispositions.

Methods

Participants were instructed to wear the smartwatch and receive physical and occupational therapy. Spearman correlations were used to determine the associations between SARP measurements and in-person evaluations. Univariate logistic regression was used to identify predictors of discharge dispositions.�

Results

SARP measurements and PT/OT/RN evaluations were correlated significantly. SARP indicated that participants were active for only 5 minutes/hour during post-acute rehabilitation. SARP significantly predicted hospital readmission (AUC>70%).

Conclusions

SARP provides physical activity information during post-acute rehabilitation in real-time. Not only is SARP significantly correlated with PT/OT/RN evaluations, but it also helps to discern discharge dispositions.

Phylogenetic models with lineage-specific parameter characterizations provide a flexible framework to model ancestral changes in diffusion and evolution processes. However, increased taxonomic sampling challenges inference under these models as the number of unknown parameters grows with the number of taxa. To solve this problem, I develop scalable inference machinery as well as scalable models to permit the study of increasingly massive trees within a Bayesian phylogenetic framework. First, I introduce a method to compute the gradient of the trait data log-likelihood of the popular relaxed random walk model of trait diffusion with computational complexity that is linear with the number of tips in the tree. I use this gradient to build an efficient Hamiltonian Monte Carlo (HMC) sampler that simultaneously samples all branch-specific model parameters with high acceptance probability. Next, I propose a new, auto-correlated molecular clock rate model together with scalable inference methods. My approach permits estimating both the presence and location of local clocks without a priori knowledge of their placement and avoids inordinately shrinking clock-rates. Finally, I develop a shrinkage-based adaptive shift model that automatically detect the number and placement of shifts in adaptive trait optima along a tree. Leveraging recent fast closed-form gradient calculations, I build an efficient HMC sampler that scales inference under this new model. I demonstrate the speed and utility of each method via a range of applications, including the study of viral evolution and phenotypic trait data.

Objective: To determine if timely treatment within 60 minutes of confirmed diagnosis of severe maternal hypertension with antihypertensive medications was associated with reduction in severe maternal morbidity.

Methods: Medical records of women with severe hypertension (at least two severe blood pressures, systolic ≥160mmHg and/or diastolic ≥110mmHg, within 60 minutes) were accessed for timing of severe blood pressures, timing of treatment, and blood pressure response to treatment. Severe maternal morbidity was confirmed by multidisciplinary case review. We compared the incidence of severe maternal morbidity between women who received timely (within 60 minutes of diagnosis) vs. not-timely treatment.

Results: Of 465 women with severe hypertension, 29 (6.2%) experienced severe maternal morbidity. Fifty-six percent of women received timely treatment, of whom 1.9% had severe maternal morbidity, compared with 6.4% of women who did not receive timely treatment (p=0.02). Timely treatment was associated with a 72% reduction in relative odds of severe maternal morbidity (p=0.02). No significant difference was seen in median pre-treatment systolic pressures (p=0.20) between the groups.

Conclusion: Antihypertensive treatment within 60 minutes of confirmed diagnosis of severe hypertension was associated with reduction in severe maternal morbidity. Our findings support current recommendations to treat all women with severe hypertension with antihypertensive medications in a timely fashion.

Longitudinal observational health data are rapidly becoming standardized and consolidated at massive scale. However, the large size and observational nature of this data create infrastructural, statistical, and computational challenges to their utilization for generating reliable clinical evidence. I first review principles of observational research and various methodological and statistical tools used to conduct modern observational studies. I then discuss methodological advancements and their clinical implementations in large scale observational health analytics. I introduce a framework for evaluating propensity score methods that are a central tool in addressing confounding in non-randomized studies. This framework incorporates simulations that model real-world survival data and negative control experiments. I adapt my evaluation framework to probe the real-world prevalence and consequences of "instrumental variables" that unduly dominate propensity score models and bias clinical effect size estimates. I then compare propensity score adjustment methods in research evaluating spline functions for multiple treatment settings. Next, I turn to statistical computing challenges that hinder the application of high-quality methods in large data. I utilize graphics processing unit (GPU) programming to accelerate logistic regression, a staple statistical regression used for propensity score estimation, in the high-dimensional regimes necessitated by the largest health databases. Finally, I conduct clinical studies using tools developed through the Observational Health Data Sciences and Informatics (OHDSI) community that allow large-scale and high-quality observational studies to be conducted with previously unattainable efficiency. In one study, I analyze the comparative effectiveness of two popular osteoporosis drugs in preventing fractures and in regards to concerning drug-related adverse events. In a second study, I address the highly controversial use of recombinant human bone morphogenetic protein 2 in spinal fusion surgeries. In a third study, I report on the comparative effectiveness of antidepressant treatments in preventing suicide and suicidal ideation within a novel all-by-all paradigm of conducting many hypothesis simultaneously within a medical domain. In a final study, I evaluate the effectiveness of generic vs branded medications of many drugs across three medical domains with regards to death and major cardiovascular events. I conclude with thoughts about future research and progress in observational medical science.

A birth-death process is a continuous-time Markov chain that counts the number of particles in a system over time. Each particle can give birth to another particle or die, and the rate of births and deaths at any given time depends on how many extant particles there are. Birth-death processes are popular modeling tools in evolution, population biology, genetics, epidemiology, and ecology. Despite the widespread interest in birth-death models, no efficient method exists to evaluate the finite-time transition probabilities in a process with arbitrary birth and death rates. Statistical inference of the instantaneous particle birth and death rates also remains largely limited to continuously-observed processes in which per-particle birth and death rates are constant. The lack of theoretical progress in developing statistical tools for dealing with data from birth-death processes has hindered their adoption by applied researchers, and represents a major research frontier in statistical inference for stochastic processes. In this dissertation, I seek to fill this apparent void in three ways. First, I develop mathematical theory and computational tools for computing transition probabilities for general birth-death processes. Second, I develop algorithms for maximum likelihood estimation of rate parameters in discretely observed processes. Third, I derive probability distributions for characteristics of certain birth-death models that are fundamental in macroevolutionary studies. In each case, I give practical applications of the methodology, and show how unsolved problems can be attacked using these techniques.

Background: Spinal cord compression may lead to numerous symptoms and decreased functional capabilities. Causes include spinal stenosis, herniated disks, tumors, and spinal cord injury. Surgical outcomes are difficult to predict, especially those related to changes in patient functional capabilities. In this study, we sought to: 1) determine the predictors of change in disability and pain for spinal surgery patients, and 2) evaluate the relationship between pain and disability outcomes.

Methods: A single arm, 24-month cohort, repeated measures study of spinal surgery patient outcomes was performed in adult patients with spinal cord compression for which a surgical procedure was performed between June 2013 and December 2015, and with at least six months post-surgery data (N=76). Using linear regression, clinical and demographic parameters were evaluated as predictors of reduction in functional disability and pain, as measured by Oswestry Disability Index (ODI) and Visual Analog Scale (VAS) for Pain, respectively. The interaction between change in pain and functional disability was also evaluated.

Results: Changes from baseline were significant (p<0.05) for both the Oswestry Disability Index score (-0.13, 0.086-0.178), and Visual Analog Scale for Pain (-0.20, 0.129-0.268). Significant predictors for reduction in pain were pre-surgery pain and disability, prior spinal surgery history, age, alcoholic consumption, and microdiscectomy intervention. Predictors for reduction in disability were pre-surgery pain and disability, duration of symptoms, weight, resection, instrumentation, and laminectomy. Additionally, reduction in pain was found to be a significant confounder (>10% change in effect estimate with and without confounder) in the analysis, strongly affecting the impact of some predictors.

Conclusions: The results of this study suggest that postsurgical reduction in pain may be more amenable to prediction than reduction in disability. In addition, the relationship between spinal surgery disability and pain outcomes may be one of the factors that make prediction of surgical outcomes difficult. We recommend that future research, seeking to identify predictors of spinal surgery outcomes, be carefully designed to take into account the impact of pain on disability.

The emerging observational health data, such as electronic health records and administrative claims, provide a rich resource for learning about treatment effects and risks. However, computational challenges arise when fitting statistical models to such large-scale and high-dimensional data. In this dissertation, I employ parallel computing techniques to address the computational bottlenecks associated widely used statistical models in observational studies. First, I present a novel parallel scan algorithm to scale up the Cox proportional hazards model and the Fine-Gray model. This advancement significantly accelerates the execution of large-scale comparative effectiveness and safety studies involving millions of patients and thousands of patient characteristics by an order of magnitude. Second, I apply an efficient parallel segmented-scan algorithm to accelerate the computational intensive parts shared by the stratified Cox model, the Cox model with time-varying covariates, and the Cox model with time-varying coefficients. This innovation enables efficient large-scale and high-dimensional Cox modeling with stratification or time-varying effect, delivering an order of magnitude speedup over traditional central processing unit-based methods. Third, I introduce a memory-efficient approach for fitting pooled logistic regression models with massive sample-size data. This approach offers a valuable tool, allowing for pooled logistic regression analysis on massive sample sizes, even when computational resources are limited. I have implemented all of the above work in the open-source R package Cyclops.