There is broad agreement that medicine ought to be `evidence based' and `personalized' and that data should play a large role in achieving both these goals. But the path from data to improved medical decision making is not clear. This thesis presents three methods that hopefully help in small ways to clear the path. Personalized medicine depends almost entirely on understanding variation in treatment effect. Chapter 1 describes latent class mixture models for treatment effect heterogeneity that distinguish between continuous and discrete heterogeneity, use hierarchical shrinkage priors to mitigate overfitting and multiple comparisons concerns, and employ flexible error distributions to improve robustness. We apply different versions of these models to reanalyze a clinical trial comparing HIV treatments and a natural experiment on the effect of Medicaid on emergency department utilization. Medical decisions often depend on observational studies performed on large longitudinal health insurance claims databases. These studies usually claim to identify a causal effect, but empirical evaluations have demonstrated that standard methods for causal discovery perform poorly in this context, most likely in large part due to the presence of unobserved confounding. Chapter 2 proposes an algorithm called Ensembles of Granger Graphs (EGG) that does not rely on the assumption that unobserved confounding is absent. In a simulation and experiments on a real claims database, EGG is robust to confounding, has high positive predictive value, and has high power to detect strong causal effects. While decision making inherently involves causal inference, purely predictive models aid many medical decisions in practice. Predictions from health histories are challenging because the space of possible predictors is so vast. Not only are there thousands of health events to consider, but also their temporal interactions. In Chapter 3, we adapt a method originally developed for speech recognition that greedily constructs informative labeled graphs representing temporal relations between multiple health events at the nodes of randomized decision trees. We use this method to predict strokes in patients with atrial fibrillation using data from a Medicaid claims database. I hope the ideas illustrated in these three projects inspire work that someday genuinely improves healthcare. I also include a short `bonus' chapter on an improved estimate of effective sample size in importance sampling. This chapter is not directly related to medicine, but finds a home in this thesis nonetheless.

Real-world evidence (RWE) plays a crucial role in understanding the impact of medical interventions and uncovering disparities in clinical practice. However, confounding bias, especially unmeasured confounding, poses challenges to inferring causal relationships from observational data, such as estimating treatment effects and treatment responses. Various methods have been developed to reduce confounding bias, including methods specific for detecting and adjusting for unmeasured confounding. However, these methods typically rely on assumptions that are either untestable or too strong to hold in practice. Some methods also require domain knowledge that is rarely available in medicine. Despite recent advances in method development, the challenge of unmeasured confounding in observational studies persists. This dissertation provides insights in adjusting for unmeasured confounding by exploiting correlations within electronic health records (EHRs). In Aim 1, we demonstrate a novel use of probabilistic model for inferring unmeasured confounders from drug co-prescription pattern. In Aim 2, we provide theoretical justifications and empirical evidence that adjusting for all (pre-treatment) covariates without explicitly selecting for confounders, as implemented in the large-scale propensity score (LSPS) method, offers a more robust approach to mitigating unmeasured confounding. In Aim 3, we shift focus to the problem of evaluating fairness of treatment allocation in clinical practice from a causal perspective. We develop a causal fairness algorithm for assessing treatment allocation. By applying this fairness analysis method to a cohort of patients with coronary artery disease from EHR data, we uncover disparities in treatment allocation based on gender and race, highlighting the importance of addressing fairness concerns in clinical practice. Furthermore, we demonstrate that social determinants of health, variables that are often unavailable in EHR databases and are potential unmeasured confounders, do not significantly impact the estimation of treatment responses when conditioned on clinical features from EHR data, shedding light on the intricate relationship between EHR features and social determinants of health. Collectively, this dissertation contributes valuable insights into addressing unmeasured confounding in the context of evidence generation from EHRs. These findings have significant implications for improving the reliability of observational studies and promoting equitable healthcare practices.