In survival analysis or time-to-event analysis, one of the primary goals of analysis is to predict the occurrence of an event of interest for subjects within the study. Even though survival analysis methods were originally developed and used in medical re- search, those methods are also commonly used nowadays in other areas as well, such as in predicting the default of a loan and in estimating of the failure of a system. To include covariates in the analysis, the most widely used models are the propor- tional hazard model developed by Cox (1972) and the accelerated failure time model developed by Buckley and James (1979). The proportional hazard (PH) model as- sumes subjects from different groups have their hazard functions proportionally, while the accelerated failure time (AFT) model assumes the effect of covariates is to accel- erate or decelerate the occurrence of event of interest. In some survival analyses, not all subjects in the study will experience the event. Such a group of individuals is referred to `cured' group. To analyze a data set with a cured fraction, Boag (1948) and Berkson and Gage (1952) discussed a mixture cure model. Since then, the cure model and associated inferential methods have been widely stud- ied in the literature. It has also been recognized that subjects in the study are often correlated within clusters or groups; for example, patients in a hospital would have similar conditions and environment. For this reason, Vaupel et al. (1979) proposed a frailty model to model the correlation among subjects within clusters and conse- quently the presence of heterogeneity in the data set. Hougaard (1989), McGilchrist and Aisbett (1991), and Klein (1992) all subsequently developed parametric frailty models. Balakrishnan and Peng (2006) proposed a Generalized Gamma frailty model, which includes many common frailty models, and discussed model fitting and model selection based on it. To combine the key components and distinct features of the mixture cure model and the frailty model, a mixture cure frailty model is discussed here for modelling correlated survival data when not all the subjects under study would experience the occurrence of the event of interest. Longini and Halloran (1996) and Price and Manatunga (2001) developed several parametric survival models and employed the Likelihood Ratio Test (LRT) to perform a model discrimination among cure, frailty and mixture cure frailty models. In this thesis, we first describe the components of a mixture cure frailty model, wherein the flexibility of the frailty distributions and lifetime survival functions are discussed. Both proportional hazard and accelerated failure time models are considered for the distribution of lifetimes of susceptible (or non-cured) individuals. Correlated ran- dom effect is modelled by using a Generalized Gamma frailty term, and an EM-like algorithm is developed for the estimation of model parameters. Some Monte Carlo simulation studies and real-life data sets are used to illustrate the models as well as the associated inferential methods. / Thesis / Doctor of Philosophy (PhD)

PROPHAZ is a computer program created for the analysis of survival data using the general proportional hazards model. It was designed specifically for the situation in which the underlying hazard function may be estimated from the mortality experience of a large reference population, but may be used for other problems as well. Input for the program includes the variables of interest as well as the information necessary for estimating the hazard function (demographic and mortality data). Regression coefficients for the variables of interest are obtained iteratively using the Newton-Raphson method. Utilizing large sample asymptotic theory, χ2 statistics are derived which may be used to test hypotheses of the form Cβ = 0. Input format is completely flexible for the variables of interest as well as the mortality data.

A Logspline method of estimating an unknown density function f based on sample data is studied. Our approach is to use maximum likelihood estimation to estimate the unknown density function from a space of linear splines that have a finite number of fixed uniform knots. In the end of this thesis, the method is applied to a real survival data set of lung cancer patients.

Patients who were previously diagnosed with prostate cancer usually undergo a routine clinical monitoring that involves measuring the Prostate-specific antigen (PSA). The trajectory of this biomarker over time serves as an indication of cancer recurrence. If the PSA value begins to increase, the cancer is said to be more likely to recur and thus, the patient is advised to start a treatment. There are two reasons for stopping the patient follow-up and this poses a certain challenge. One of them is starting a salvage hormone therapy and another is actual recurrence of cancer. When analyzing such data, we need to account for informative dropout, otherwise, neglecting it may lead to increased bias in estimation of the PSA trajectory. Thus, hormone therapy serves as a censoring event, which is a defining feature of survival analysis. Motivated by the PSA data, we need to efficiently describe the dropout mechanism using the joint model. The survival submodel is based on the Weibull distribution and we use the Bayesian inference to fit this model, more specifically, we use the R-INLA package, which is a much faster alternative to MCMC-based inference. The fact that our joint model with a linear bivariate Gaussian association structure is a latent Gaussian model (LGM) allows us to use this inferential tool. Based on this work, we are then able to develop dynamic predictions of prostate cancer recurrence. Making accurate prognosis for cancer data is clinically impactful and could ultimately contribute to the development of precision medicine.

In survival analysis, the Cox model is one of the most widely used tools. However, up to now there has not been any published work on the Cox model with complicated types of censored data, such as doubly censored data, partly-interval censored data, etc., while these types of censored data have been encountered in important medical studies, such as cancer, heart disease, diabetes, etc. In this dissertation, we first derive the bivariate nonparametric maximum likelihood estimator (BNPMLE) F[subscript n](t,z) for joint distribution function F[sub 0](t,z) of survival time T and covariate Z, where T is subject to right censoring, noting that such BNPMLE F[subscript n] has not been studied in statistical literature. Then, based on this BNPMLE F[subscript n] we derive empirical likelihood-based (Owen, 1988) confidence interval for the conditional survival probabilities, which is an important and difficult problem in statistical analysis, and also has not been studied in literature. Finally, with this BNPMLE F[subscript n] as a starting point, we extend the weighted empirical likelihood method (Ren, 2001 and 2008a) to the multivariate case, and obtain a weighted empirical likelihood-based estimation method for the Cox model. Such estimation method is given in a unified form, and is applicable to various types of censored data aforementioned.

The Accelerated Life Model is one of the most commonly used tools in the analysis of survival data which are frequently encountered in medical research and reliability studies. In these types of studies we often deal with complicated data sets for which we cannot observe the complete data set in practical situations due to censoring. Such difficulties are particularly apparent by the fact that there is little work in statistical literature on the Accelerated Life Model for complicated types of censored data sets, such as doubly censored data, interval censored data, and partly interval censored data. In this work, we use the Weighted Empirical Likelihood approach (Ren, 2001) [33] to construct tests, confidence intervals, and goodness-of-fit tests for the Accelerated Life Model in a unified way for various types of censored data. We also provide algorithms for implementation and present relevant simulation results. I began working on this problem with Dr. Jian-Jian Ren. Upon Dr. Ren’s departure from the University of Central Florida I completed this dissertation under the supervision of Dr. Marianna Pensky.

Survival Analysis is the collection of statistical techniques used to model the time of occurrence, i.e. survival time, of an event of interest such as death, marriage, the lifespan of a consumer product or the onset of a disease. Traditional survival analysis methods rely on assumptions that make it difficult, if not impossible to learn complex non-linear relationships between the covariates and survival time that is inherent in many real world applications. We first demonstrate that a recurrent neural network (RNN) is better suited to model problems with non-linear dependencies in synthetic time-dependent and non-time-dependent experiments.

Hydraulic fracturing has been increasingly used in the USA to economically extract natural gas and oil from newly discovered shale plays. Despite new, more severe, and long term impacts of hydraulic fracturing compared to conventional drilling, regulatory practices are mostly implemented by states that regulate with older regulations that were were written before the widespread use of hydraulic fracturing. This dissertation presents three essays on the economics of hydraulic fracturing. A standard renewable lease in hydraulic fracturing runs for a five-year primary term. The first essay examines the effect of initial contract length on extraction behavior and social costs. It finds that the rate of extraction decreases over time for both, the social planner and the private extractor. In addition, the social planner has a more stable extraction path compared to the private extractor. Holding other things equal, if the social planner seeks to induce a private extractor to leave a higher in situ stock un-extracted, then the optimal contract duration is longer. Simulations illustrate the magnitude of social costs inherent in hydraulic fracturing and non-optimal fixed contract lengths. The second essay investigates the impact of the significantly increased bonding requirements for horizontal wells introduced in West Virginia in December, 2011, on the probability of violation committed by those wells. Results suggest that the increased bonding requirement has reduced the probability of violation by 2.6 to 3.2 percentage points. Moreover, it slightly reduces the number of violations done by horizontal wells. Finally, the third essay explores several aspects of Act-13, introduced on February 14, 2012, by Pennsylvania. This act imposes new fees that are assessed annually for fifteen years, on all unconventional gas wells in Pennsylvania. This chapter explores the impacts of Act-13 on the likelihood of an unconventional well's shut-down, rate of extraction, and probability of violation. Results suggest that wells incurring this increased fee schedule have a significantly higher likelihood (more than three times) of shut-down. Also, Act-13 have reduced the extraction rate, and the probability of violation committed by unconventional wells in Pennsylvania. / Ph. D.

Objective: The present study examined the potential roles of externalizing and depressive co-occurring psychopathology on the time-course to anxiety treatment response among youth receiving different treatment conditions. Method: Participants were 488 youth (aged 7-17 years) who received either Cognitive-Behavioral Therapy (CBT) (N = 139), sertraline (SRT) (N = 133), CBT+sertraline (COMB; N = 140), or pill placebo (PLB; N = 76) in the Child/Adolescent Anxiety Multimodal Study (CAMS; Walkup et al., 2008). Results: Findings did not demonstrate a significant relation of comorbid psychopathology with treatment response time-course. Participants in CBT and SRT had significantly different overall treatment response trajectories, though comorbid psychopathology did not significantly relate to the observed treatment response trajectories. Exploratory analyses revealed that parental treatment assignment reaction to CBT was positively associated with more favorable treatment response time course, whereas parental treatment assignment reaction to SRT did not significantly relate to treatment response time course. Conclusions: Our results are consistent with the notion that current interventions (CBT, SRT) produce improvements that generalize across co-occurring depressive and externalizing psychopathology. Clinical implications for the treatment of anxious youth with regard to comorbidity and contextual factors are discussed and suggestions for future research are offered. / Psychology

no abstract provided by author / Master of Science