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The cause and effect paradigm underlying medical research has led to an enhanced etiological understanding of many diseases and the development of many lifesaving drugs, but the paradigm does not always include an understanding of the pathways involved. Causal mediation analysis extends the cause and effect relationship to the cause and effect through a mediator, an intermediate variable on the causal pathway. The total effect of an exposure on an outcome is decomposed into two parts: 1) the indirect effect of the exposure on the outcome through the mediator and 2) the direct effect of the exposure on the outcome through all other pathways. In this dissertation, I describe various counterfactual causal mediation frameworks with identifiability assumptions that all lead to the Mediation Formula. The indirect and direct effects can be estimated from observable data using a semi-parametric algorithm derived from the Mediation Formula that I generalize to different types of mediators and outcomes. With an increased interest in causal mediation analysis, thoughtful consideration is necessary in the application of the Mediation Formula to real-world data challenges. Here, I consider three motivating causal mediation questions in the areas of HIV curative research and cardio-respiratory fitness. HIV curative treatments typically target the viral reservoir, cells infected with latent HIV. Quantifying the effect of an HIV curative treatment on viral rebound over a set time horizon mediated by reductions in the viral reservoir can inform future directions for improving curative treatments. In cardiorespiratory fitness research, metabolites, molecules involved with cellular respiration, are believed to mediate the effect of physical activity on cardiorespiratory fitness. I propose three novel adaptations to the semi-parametric estimation algorithm to address three data challenges: 1) Numerical integration and optimization of the observed data likelihood for mediators with an assay lower limit (left-censored mediators); 2) Pseudo-value approach for time-to-event outcomes on a restricted mean survival time scale; 3) Elastic net regression for high-dimensional mediators. My novel approaches provide estimation frameworks that can be applied to a broad spectrum of research questions. I provide simulation studies to assess the properties of the estimators and applications of the methodologies to the motivating data. / 2025-06-16T00:00:00Z

Most statistical methods to design and analyze randomized controlled trials with time-to-event data, and synthesize their results in meta-analyses, use the hazard ratio (HR) as the measure of treatment effect. However, the HR relies on the proportional hazard assumption which is often violated, especially in cancer trials. In addition, the HR might be challenging to interpret and is frequently misinterpreted as a risk ratio (RR). In meta-analysis, conventional methods ignore that HRs are estimated over different time supports when the component trials have different follow-up durations. These issues also pertain to advanced statistical methods, such as network meta-analysis and surrogate endpoints validation. Novel methods that rely on the difference in restricted mean survival times (RMST) would help addressing these issues. In this dissertation, I first developed a Bayesian network meta-analysis model using the difference in RMST. This model synthesizes all the available evidence from multiple time points and treatment comparisons simultaneously through within-study covariance and between-study covariance for the differences in RMST. I proposed an estimator of the within-study covariance and estimated the model under the Bayesian framework. The simulation studies showed adequate performance in terms of mean bias and mean squared error. I illustrated the model on a network of randomized trials of second-line treatments of advanced non-small-cell lung cancer. Second, I introduced a novel two-stage meta-analytical model to evaluate trial-level surrogacy. I measured trial-level surrogacy by the coefficient of determination at multiple time points based on the differences in RMST. The model borrows strength across data available at multiple time points and enables assessing how the strength of surrogacy changes over time. Simulation studies showed that the estimates of coefficients of determination are unbiased and have high precision in almost all of the scenarios we examined. I demonstrated my model in two individual patient data meta-analyses in gastric cancer. Both methods, for network meta-analysis and surrogacy evaluation, have the advantage of not involving extrapolation beyond the observed time support in component trials and of not relying on the proportional hazard assumption. Finally, motivated by the common misinterpretation of the HR as a RR, I investigated the theoretical relationship between the HR and the RR and compared empirically the treatment effects measured by the HR and the RR in a large sample of oncology RCTs. When there is evidence of superiority for experimental group, misinterpreting the HR as the RR leads to overestimating the benefits by about 20%. / 2026-02-08T00:00:00Z

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<p>This series of papers explores the value of and mechanisms for using a heterogeneity test to compare treatment differences between the individual outcomes included in a composite outcome. Trialists often combine a group of outcomes together into a single composite outcome based on the belief that all will share a common treatment effect. The question addressed here is how this assumption of homogeneity of treatment effect can be assessed in the analysis of a trial that uses this type of composite outcome. A class of models that can be used to form such a test involve the analysis of multiple outcomes per person, and adjust for the association due to repeated outcomes being observed on the same individuals. We compare heterogeneity tests from multiple models for binary and time-to-event composite outcomes, to determine which have the greatest power to detect treatment differences for the individual outcomes within a composite outcome. Generally both marginal and random effects models are shown to be reasonable choices for such tests. We show that a treatment heterogeneity test may be used to help design a study with a composite outcome and how it can help in the interpretation of trial results.</p> / Doctor of Philosophy (PhD)

Teacher turnover is a well-studied phenomenon, particularly in highly urbanized locales, but not well researched in a state as geographically and demographically diverse as Pennsylvania, which is a composition of two major metropolitan areas combined with smaller urban centers and expansive rural regions. Those retention studies that do exist have been mainly exclusive to the Philadelphia region, with limited research devoted to the remainder of the state. This lack of a comprehensive empirical approach that compares turnover in three distinct settings limits a nuanced understanding of the issue and, in turn, can lead to incomplete policy considerations. This study utilizes Pennsylvania Department of Education data from 2012-2017, which describes the entire public-school workforce in all local education agencies (LEAs), to study how compensation and auxiliary spending (per student spending sans instructional costs) influence teacher turnover using multiple, parallel Cox Proportional Hazards survival models. Findings suggest that despite a “one size fits all” approach to public school funding policy popular amongst politicians on both sides of the political aisle, the effects of a monetary increase in reducing the likelihood of turnover varies considerably when accounting for the region, Title I status, experience and subject matter. The study highlights how the lack of monetary investment can lead teachers to seek employment elsewhere since low pay functions as a strong demotivator. Additionally, the results suggest that while a pay raise may arrest turnover risk, it is a poor long-term motivator or cause of job satisfaction. The study concludes by offering state and LEA leaders with policy recommendations that may improve both retention and job satisfaction. To date, this is the only study in the current literature that explores teacher turnover extensively in the nation’s fifth most populous state. / Urban Education

In this dissertation, we are interested in studying processes which generate events repeatedly over the follow-up time of a given subject. Such processes are called recurrent event processes and the data they provide are referred to as recurrent event data. Examples include the cancer recurrences, recurrent infections or disease episodes, hospital readmissions, the filing of warranty claims, and insurance claims for policy holders. In particular, we focus on the multi-type recurrent event times which usually arise when two or more different kinds of events may occur repeatedly over a period of observation. Our main objectives are to describe features of each marginal process simultaneously and study the dependence among different types of events. We present applications to a real dataset collected from the Nutritional Prevention of Cancer Trial. The objective of the clinical trial was to evaluate the efficacy of Selenium in preventing the recurrence of several types of skin cancer among 1312 residents of the Eastern United States. Four chapters are involved in this dissertation. Chapter 1 introduces a brief background to the statistical techniques used to develop the proposed methodology. We cover some concepts and useful functions related to survival data analysis and present a short introduction to frailty distributions. The Monte Carlo expectation maximization (MCEM) algorithm and copula functions for the multivariate variables are also presented in this chapter. Chapter 2 develops a multi-type recurrent events model with multivariate Gaussian random effects (frailties) for the intensity functions. In this chapter, we present nonparametric baseline intensity functions and a multivariate Gaussian distribution for the multivariate correlated random effects. An MCEM algorithm with MCMC routines in the E-step is adopted for the partial likelihood to estimate model parameters. Equations for the variances of the estimates are derived and variances of estimates are computed by Louis' formula. Predictions of the individual random effects are obtained because in some applications the magnitude of the random effects is of interest for a better understanding and interpretation of the variability in the data. The performance of the proposed methodology is evaluated by simulation studies, and the developed model is applied to the skin cancer dataset. Chapter 3 presents copula-based semiparametric multivariate frailty models for multi-type recurrent event data with applications to the skin cancer data. In this chapter, we generalize the multivariate Gaussian assumption of the frailty terms and allow the frailty distributions to have more features than the symmetric, unimodal properties of the Gaussian density. More flexible approaches to modeling the correlated frailty, referred to as copula functions, are introduced. Copula functions provide tremendous flexibility especially in allowing taking the advantages of a variety of choices for the marginal distributions and correlation structures. Semiparametric intensity models for multi-type recurrent events based on a combination of the MCEM with MCMC sampling methods and copula functions are introduced. The combination of the MCEM approach and copula function is flexible and is a generally applicable approach for obtaining inferences of the unknown parameters for high dimension frailty models. Estimation procedures for fixed effects, nonparametric baseline intensity functions, copula parameters, and predictions for the subject-specific multivariate frailties and random effects are obtained. Louis' formula for variance estimates are derived and calculated. We investigate the impact of the specification of the frailty and random effect models on the inference of covariate effects, cumulative baseline intensity functions, prediction of random effects and frailties, and the estimation of the variance-covariance components. Performances of proposed models are evaluated by simulation studies. Applications are illustrated through the dataset collected from the clinical trial of patients with skin cancer. Conclusions and some remarks for future work are presented in Chapter 4. / Ph. D.

Maintenance of medical equipment plays an important role in ensuring the healthcare quality so that the care can be conducted with minimal risk. Preventive maintenance is performed to maintain the equipment in satisfactory operating condition, while corrective maintenance is made when there is an unpredicted maintenance requirement. This study aims to determine what effect preventive maintenance has on corrective maintenance. A correlation analysis, regression analysis and survival analysis are performed on work-order data from 2000-2021. The results obtained indicate that increasing the number of preventive maintenances made to medical equipment will decrease the number of corrective maintenances required for the medical equipment.