The majority of current smokers in the United States want to quit smoking; however, long-term abstinence rates do not improve beyond 30%, despite the availability of effective pharmaco-behavioral treatments and increased outreach of awareness programs on quitting benefits. One of the reasons is non-adherence to pharmacological treatment. Pharmacological treatments are developed to alleviate withdrawal symptoms experienced during a quit attempt. However, without continued treatment adherence, especially in the first few weeks of a quit attempt (when withdrawal symptoms fluctuate the most), the chances of relapse peak. Thus, adherence to pharmacological treatments must be improved to sustain long-term smoking abstinence. Moreover, smoking cessation is a complex and time-varying process. Therefore, the time-varying causal structure of adherence and smoking cessation must be studied carefully.The time-varying mechanisms underlying the smoking cessation process can be captured efficiently through intensive longitudinal data and quantified through appropriate methods. Mediation analysis is an efficient tool for studying such mechanisms. However, despite the time-varying nature of the data, existing approaches for assessing mediation provide overall average (in)direct effects over time and omit describing the temporal characteristic of the dynamic effect. This dissertation research aims to develop a new approach to estimating time-varying causal (in)direct effects of pharmacological treatments on daily smoking cessation outcome(s) mediated via daily treatment adherence. Additionally, it is hypothesized that adherence is influenced by daily stress events related to social contextual factors, not treatment-induced. The purpose of this research is to derive time-varying causal (in)direct effects. A local polynomial regression-based approach integrated with the mediational g-formula was proposed as a possible solution. Furthermore, since no other studies have studied time-specific mediation effects using a potential outcomes framework-based method, the performance of the proposed method was tested using two simulation studies. Finally, the optimum analytical approach (based on the findings from the simulation studies) was applied to answer the substantive research questions on smoking cessation using empirical data from a smoking cessation clinical trial. This dissertation is divided into six chapters. A brief overview of the chapters is as follows: Chapter 1 provides a comprehensive background and rationale for the methodological and substantive research that motivated this work. The chapter concludes with the three specific aims addressed in this research and a summary of the next steps. In Chapter 2, the longitudinal causal frameworks and the assumptions required to interpret the estimated time-varying (in)direct effects as causal are described in detail. These frameworks were further used in Chapters 3 and 4 for the two simulation studies that evaluated the performance of the proposed new approach. The simulation study in Chapter 3 evaluates the time-varying (in)direct effects in a longitudinal study in the absence of exposure-induced time-varying confounding of a mediator-outcome pathway. Four outcome scenarios with a binary exposure, a binary mediator, and a time-varying binary confounder of the mediator-outcome pathway were examined: 1) continuous outcome, 2) rare binary outcome, 3) common binary outcome, and 4) count outcome that is not zero-inflated. Two types of path-specific causal estimands are identifiable for these scenarios. The findings suggest good performance of the proposed analytical approach in producing accurate effect estimates (reduced bias and reasonable coverage) of these estimands for all the outcome scenarios. The simulation study in Chapter 4 evaluates the time-varying (in)direct effects in a longitudinal study in the presence of exposure-induced time-varying confounding of a mediator-outcome pathway. A zero-inflated count outcome scenario with a binary exposure, a binary mediator, and a time-varying binary confounder of the mediator-outcome pathway was examined. Four types of path-specific causal estimands are identifiable for this scenario, and the findings suggest good performance of the proposed analytical approach in producing accurate effect estimates. Chapter 5 uses the Wisconsin Smokers Health Study II data to assess the mechanisms via which pharmacological smoking cessation treatments affect the cessation-related outcome(s) in the presence of time-varying confounding that is not exposure induced. We found that individuals randomized to Nicotine Patch only group have better smoking cessation outcome(s) compared to individuals on Varenicline or combination Nicotine Replacement Therapy. This is due to better adherence among Nicotine Patch-only users. Finally, Chapter 6 presents the concluding remarks, including key findings from the three studies, limitations, and recommendations for future research. / Epidemiology

Challenges of financial forecasting, such as a dearth of independent samples and non- stationary underlying process, limit the relevance of conventional machine learning towards financial forecasting. Meta-learning approaches alleviate some of these is- sues by allowing the model to generalize across unrelated or loosely related tasks with few observations per task. The neural process family achieves this by con- ditioning forecasts based on a supplied context set at test time. Despite promise, meta-learning approaches remain underutilized in finance. To our knowledge, ours is the first application of neural processes to realized volatility (RV) forecasting and financial forecasting in general. We propose a hybrid temporal convolutional network attentive neural process (ANP- TCN) for the purpose of financial forecasting. The ANP-TCN combines a conven- tional and performant financial time series embedding model (TCN) with an ANP objective. We found ANP-TCN variant models outperformed the base TCN for equity index realized volatility forecasting. In addition, when stack-ensembled with a tree- based model to forecast a trading signal, the ANP-TCN outperformed the baseline buy-and-hold strategy and base TCN model in out-of-sample performance. Across four liquid US equity indices (incl. S&P 500) tested over ∼15 years, the best long-short models (reported by median trajectory) resulted in the following out-of-sample (∼3 years) performance ranges: directional accuracy of 58.65% to 62.26%, compound an- nual growth rate (CAGR) of 0.2176 to 0.4534, and annualized Sharpe ratio of 2.1564 to 3.3375. All project code can be found at: https://github.com/kpa28-git/thesis-code.

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Various approaches for discriminant analysis of longitudinal data are investigated, with some focus on model-based approaches. The latter are typically based on the modi ed Cholesky decomposition of the covariance matrix in a Gaussian mixture; however, non-Gaussian mixtures are also considered. Where applicable, the Bayesian information criterion is used to select the number of components per class. The various approaches are demonstrated on real and simulated data. / Thesis / Master of Science (MSc)

Doctor of Philosophy / Department of Statistics / Weixin Yao / This dissertation contains two projects that are related to varying coefficient models. The traditional least squares based kernel estimates of the varying coefficient model will lose some efficiency when the error distribution is not normal. In the first project, we propose a novel adaptive estimation method that can adapt to different error distributions and provide an efficient EM algorithm to implement the proposed estimation. The asymptotic properties of the resulting estimator is established. Both simulation studies and real data examples are used to illustrate the finite sample performance of the new estimation procedure. The numerical results show that the gain of the adaptive procedure over the least squares estimation can be quite substantial for non-Gaussian errors. In the second project, we propose a unified inference for sparse and dense longitudinal data in time-varying coefficient models. The time-varying coefficient model is a special case of the varying coefficient model and is very useful in longitudinal/panel data analysis. A mixed-effects time-varying coefficient model is considered to account for the within subject correlation for longitudinal data. We show that when the kernel smoothing method is used to estimate the smooth functions in the time-varying coefficient model for sparse or dense longitudinal data, the asymptotic results of these two situations are essentially different. Therefore, a subjective choice between the sparse and dense cases may lead to wrong conclusions for statistical inference. In order to solve this problem, we establish a unified self-normalized central limit theorem, based on which a unified inference is proposed without deciding whether the data are sparse or dense. The effectiveness of the proposed unified inference is demonstrated through a simulation study and a real data application.

In longitudinal studies, outcomes are measured repeatedly over time, but in reality clinical studies are full of missing data points of monotone and non-monotone nature. Often this missingness is related to the unobserved data so that it is non-ignorable. In such context, pattern-mixture model (PMM) is one popular tool to analyze the joint distribution of outcome and missingness patterns. Then the unobserved outcomes are imputed using the distribution of observed outcomes, conditioned on missing patterns. However, the existing methods suffer from model identification issues if data is sparse in specific missing patterns, which is very likely to happen with a small sample size or a large number of repetitions. We extend the existing methods using latent class analysis (LCA) and a shared-parameter PMM. The LCA groups patterns of missingness with similar features and the shared-parameter PMM allows a subset of parameters to be different among latent classes when fitting a model, thus restoring model identifiability. A novel imputation method is also developed using the distribution of observed data conditioned on latent classes. We develop this model for continuous response data and extend it to handle ordinal rating scale data. Our model performs better than existing methods for data with small sample size. The method is applied to two datasets from a phase II clinical trial that studies the quality of life for patients with prostate cancer receiving radiation therapy, and another to study the relationship between the perceived neighborhood condition in adolescence and the drinking habit in adulthood.