Browsing by Subject "Survival analysis"
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Item A collection of Bayesian models of stochastic failure processes(2013-05) Kirschenmann, Thomas Harold; Damien, Paul, 1960-; Press, William H.Risk managers currently seek new advances in statistical methodology to better forecast and quantify uncertainty. This thesis comprises a collection of new Bayesian models and computational methods which collectively aim to better estimate parameters and predict observables when data arise from stochastic failure processes. Such data commonly arise in reliability theory and survival analysis to predict failure times of mechanical devices, compare medical treatments, and to ultimately make well-informed risk management decisions. The collection of models proposed in this thesis advances the quality of those forecasts by providing computational modeling methodology to aid quantitative based decision makers. Through these models, a reliability expert will have the ability: to model how future decisions affect the process; to impose his prior beliefs on hazard rate shapes; to efficiently estimate parameters with MCMC methods; to incorporate exogenous information in the form of covariate data using Cox proportional hazard models; to utilize nonparametric priors for enhanced model flexibility. Managers are often forced to make decisions that affect the underlying distribution of a stochastic process. They regularly make these choices while lacking a mathematical model for how the process may itself depend significantly on their decisions. The first model proposed in this thesis provides a method to capture this decision dependency; this is used to make an optimal decision policy in the future, utilizing the interactions of the sequences of decisions. The model and method in this thesis is the first to directly estimate decision dependency in a stochastic process with the flexibility and power of the Bayesian formulation. The model parameters are estimated using an efficient Markov chain Monte Carlo technique, leading to predictive probability densities for the stochastic process. Using the posterior distributions of the random parameters in the model, a stochastic optimization program is solved to determine the sequence of decisions that minimise a cost-based objective function over a finite time horizon. The method is tested with artificial data and then used to model maintenance and failure time data from a condenser system at the South Texas Project Nuclear Operating Company (STPNOC). The second and third models proposed in this thesis offer a new way for survival analysts and reliability engineers to utilize their prior beliefs regarding the shape of hazard rate functions. Two generalizations of Weibull models have become popular recently, the exponentiated Weibull and the modified Weibull densities. The popularity of these models is largely due to the flexible hazard rate functions they can induce, such as bathtub, increasing, decreasing, and unimodal shaped hazard rates. These models are more complex than the standard Weibull, and without a Bayesian approach, one faces difficulties using traditional frequentist techniques to estimate the parameters. This thesis develops stylized families of prior distributions that should allow engineers to model their beliefs based on the context. Both models are first tested on artificial data and then compared when modeling a low pressure switch for a containment door at the STPNOC in Bay City, TX. Additionally, survival analysis is performed with these models using a famous collection of censored data about leukemia treatments. Two additional models are developed using the exponentiated and modified Weibull hazard functions as a baseline distribution to implement Cox proportional hazards models, allowing survival analysts to incorporate additional covariate information. Two nonparametric methods for estimating survival functions are compared using both simulated and real data from cancer treatment research. The quantile pyramid process is compared to Polya tree priors and is shown to have a distinct advantage due to the need for choosing a distribution upon which to center a Polya tree. The Polya tree and the quantile pyramid appear to have effectively the same accuracy when the Polya tree has a very well-informed choice of centering distribution. That is rarely the case, however, and one must conclude that the quantile pyramid process is at least as effective as Polya tree priors for modeling unknown situations.Item Parametric inference with density-free variance in censored regression models(Texas Tech University, 2000-05) Hummer, Amanda J.Survival analysis describes the analysis of data that corresponds to the time from a well-defined time origin until the occurrence of the some particular event, the endpoint. In medical research the time origin may be the time at which the patient is recruited and the end-point may be death or recurrence of symptoms. Often patients are lost to follow-up for some reason. For example, the individual may be relocated after being recruited in a clinical trial, or may have died due to reasons unrelated to the study. For these reasons, survival times are frequently censored. Censoring occurs when the end-point of interest has not been observed for an individual participating in the trial. There are several types of censoring; right censoring, left censoring, interval censoring, etc. Right censoring, the most common type, takes place when the actual survival time is greater than the censored survival time [1]. This happens when the patient died of causes other than those under study, or when the patient withdraws from the study.Item A quantitative analysis of the production, selection, and career paths of Texas public school administrators(2012-08) Davis, Bradley Walter; Gooden, Mark A.; Cantu, Norma V; Feng, Li; O'Doherty, Ann; Powers, Daniel A; Young, Michelle D; Reyes, PedroUsing state-wide, longitudinal data on Texas public school educators employed between the 1991-1991 and 2010-2011 school years, this study explores the disproportionate selection of campus leaders based on ethnicity and gender. Through a combination of descriptive and inferential techniques, this study illustrates how trends in the production, selection, and career paths of administratively-certified educators at the various intersections of ethnicity and gender have changed over time. Controlling for a variety of individual work history and campus characteristics, this study also explores how an administratively-certified educator’s ethnicity and gender affect their probability of procuring a campus leadership position.Item Statistical Inference for Costs and Incremental Cost-Effectiveness Ratios with Censored Data(2012-07-16) Chen, ShuaiCost-effectiveness analysis is widely conducted in the economic evaluation of new treatment options. In many clinical and observational studies of costs, data are often censored. Censoring brings challenges to both medical cost estimation and cost-effectiveness analysis. Although methods have been proposed for estimating the mean costs with censored data, they are often derived from theory and it is not always easy to understand how these methods work. We provide an alternative method for estimating the mean cost more efficiently based on a replace-from-the-right algorithm, and show that this estimator is equivalent to an existing estimator based on the inverse probability weighting principle and semiparametric efficiency theory. Therefore, we provide an intuitive explanation to a theoretically derived mean cost estimator. In many applications, it is also important to estimate the survival function of costs. We propose a generalized redistribute-to-the right algorithm for estimating the survival function of costs with censored data, and show that it is equivalent to a simple weighted survival estimator of costs based on inverse probability weighting techniques. Motivated by this redistribute-to-the-right principle, we also develop a more efficient survival estimator for costs, which has the desirable property of being monotone, and more efficient, although not always consistent. We conduct simulation to compare our method with some existing survival estimators for costs, and find the bias seems quite small. Thus, it may be considered as a candidate for survival estimator for costs in a real setting when the censoring is heavy and cost history information is available. Finally, we consider one special situation in conducting cost-effectiveness analysis, when the terminating events for survival time and costs are different. Traditional methods for statistical inference cannot deal with such data. We propose a new method for deriving the confidence interval for the incremental cost-effectiveness ratio under this situation, based on counting process and the general theory for missing data process. The simulation studies show that our method performs very well for some practical settings. Our proposed method has a great potential of being applied to a real setting when different terminating events exist for survival time and costs.Item The over-winter ecology of lesser prairie-chickens (Tympanuchus pallidicinctus) in the northeast Texas Panhandle(2010-12) Kukal, Curtis A.; Ballard, Warren B.; Wallace, Mark C.; Butler, Matthew J.; Gipson, Philip S.; Whitlaw, Heather A.; Fish, Ernest B.Since the 1800s, lesser prairie-chicken (Tympanuchus pallidicinctus; LPC) populations have exhibited range-wide declines. Most aspects of the LPC?s over-winter ecology are poorly understood across the species? range, but especially in the northeast Texas Panhandle. We investigated space-use, habitat selection, and survival patterns for over-wintering LPCs between 1 September 2008 and 28 February 2010. We captured and monitored 41 LPCs (34 males and 7 hens) from 8 leks during the course of the study. We collected 1,229 locations from 19 LPCs during the over-winter of 2008?2009, and 1,984 locations from 29 LPCs during the over-winter of 2009?2010. We observed that ?98% of LPC locations were within 5.0 km of their leks-of-capture and ?98% were within 2.4 km of a known lek. We did not observe LPCs utilizing agricultural fields, possibly because most agriculture near leks was dominated by wheat (Triticum aestivum). Both genders consistently selected grassland landcover over shrubland landcover types. Our results underscore the need to conserve grassland landcover for over-wintering LPCs. We agree with previous management recommendations that rangelands within 5.0 km should be managed for over-wintering LPCs, but we further recommend prioritizing rangeland within 2.4 km of all the leks in an area. We found that cause-specific mortality rates were equally attributable to mammalian (M = 0.133, SE = 0.056) and avian (M = 0.198, SE = 0.063) predators. We evaluated 22 competing survival models using the second-order Akaike?s Information Criterion (AICc). Model selection indicated that mean patch size of shinnery oak (Quercus havardii) rangelands best explained over-winter survival. However, limited sample size likely contributed to uncertainty in our models. Our results suggested that managing for large, contiguous patches of shinnery oak could be counter-productive for LPC over-winter survival.Item Use of statins and the development of incident diabetes mellitus : a retrospective cohort study(2015-05) Olotu, Busuyi Sunday; Shepherd, Marvin D.; Lawson, Kenneth A; Wilson, James P; Richards, Kristin M; Novak, SuzanneStatins are pharmaceutical agents used in lowering blood cholesterols levels. Several landmark statin trials have demonstrated the beneficial effects of statins in both primary and secondary prevention of cardiovascular disease. Although statins are generally safe and well tolerated, several studies have suggested that statins are associated with a moderate increase in risk of new-onset diabetes. These observations prompted the FDA to revise statin labels to now include a warning of an increased risk of incident diabetes mellitus as a result of increases in glycosylated hemoglobin (A1C) and fasting plasma glucose (FPG). However, few studies have used US-based data to investigate this statin-associated increased risk of diabetes. Thus, the purpose of this study was to evaluate whether statin use was associated with an increased risk of new-onset diabetes. In addition, this study evaluated whether diabetes risk was increased when patients received intensive statin doses. This study was a retrospective cohort analysis that utilized data from the Thomson Reuters MarketScan® Commercial Claims Database for the period of 2003 - 2004. The study population included new statin users who were aged 20 - 63 years at index and who do not have a history of diabetes. Among the study population (N=116,224), 6.5% (or N=7,593) had incident diabetes. Compared to no statin use, statin use was significantly associated with increased risk of incident diabetes (HR=2.752; 99% C.I.=2.535 - 2.987; p<0.0001). In addition, each statin type (i.e., atorvastatin, fluvastatin, lovastatin, pravastatin, rosuvastatin, and simvastatin) was associated with about a two-fold increase in risk of diabetes. Diabetes risk was highest among lovastatin users and lowest among rosuvastatin users. Furthermore, diabetes risk was higher among intensive-dose statin users compared to moderate-dose statin users (HR=1.540; 99% C.I.=1.393 – 1.704; p<0.0001). Because of the proven benefits of statins in both primary and secondary prevention of cardiovascular disease, and because the potential for diabetogenicity differs among statins, health care professionals should individualize statin therapy by identifying patients who would benefit from less diabetogenic statin types. This could help optimize treatment by providing the highest benefit achievable while reducing the number of patients developing diabetes under statin therapy.