In biomedical research and lifetime data analysis, the comparison of two hazard functions usually plays an important role in practice. In this thesis, we consider the standard independent two-sample framework under right censoring. We construct efficient and useful confidence intervals for the ratio and difference of two hazard functions using smoothed empirical likelihood methods. The empirical log-likelihood ratio is derived and its asymptotic distribution is a chi-squared distribution. Furthermore, the proposed method can be applied to medical diagnosis research. Simulation studies show that the proposed EL confidence intervals have better performance in terms of coverage accuracy and average length than the traditional normal approximation method. Finally, our methods are illustrated with real clinical trial data. It is concluded that the empirical likelihood methods provide better inferential outcomes.

In this thesis, we study two independent samples under right censoring. Using a smoothed empirical likelihood method, we investigate the difference of quantiles in the two samples and construct the pointwise confidence intervals from it as well. The empirical log-likelihood ratio is proposed and its asymptotic limit is shown as a chi-squared distribution. In the simulation studies, in terms of coverage accuracy and average length of confidence intervals, we compare the empirical likelihood and the normal approximation method. It is concluded that the empirical likelihood method has a better performance. At last, a real clinical trial data is used for the purpose of illustration. Numerical examples to illustrate the efficacy of the method are presented.

We have constructed a response adaptive clinical trial to treat patients sequentially in order to maximize the total survival time of all patients. Typically the response adaptive design is based on the urn models or on sequential estimation procedures, but we used a bandit process in this dissertation. The objective of a bandit process is to optimize a measure of sequential selections from several treatments. Each treatment consist of a sequence of conditionally independent and identically distributed random variables, and some of these treatment have unknown distribution functions. For the purpose of this clinical trial, we are focusing on the bandit process with delayed response. These responses are lifetime variables which may be censored upon their observations. Following the Bayesian approach and dynamic programming technique, we formulated a controlled stochastic dynamic model. In addition, we used an example to illustrate the possible application of the main results as well as "R" to implement a model simulation.

The aim of this essay is to show the significant effect censoring Oscar Wilde’s The Picture of Dorian Gray had on the protagonist’s moral standing. I compare the original uncensored version of The Picture of Dorian Gray with the censored version. The uncensored version, published by the Belknap Press and edited by Nicholas Frankel, has only been available to the public for three years. My comparison proves that a great deal has been changed in terms of content between the two versions of the novel. This essay will outline and discusses the changes made in order to make the text acceptable in terms of late Victorian moral conventions. It also illustrates the changes by comparing quotes. The function of the censorship applied to the novel is to make Dorian seem more callous and immoral in the 1891 book version, since only then can Oscar Wilde’s story approach the standards of late Victorian morality. Indeed, a significant change has been effected in the character Dorian Gray’s morality between the two versions of the novel. / Syftet med den här uppsatsen är att visa vilken betydande effekt censureringen av Oscar Wildes The Picture of Dorian Gray hade på huvudkaraktärens moraliska ståndpunkter. Jag jämför den ocensurerade versionen av The Picture of Dorian Gray med den censurerade versionen. Den ocensurerade versionen som publicerades av Belknap Press och redigeradesav Nicholas Frankel, har bara varit tillgänglig för allmänheten i tre år. Min jämförelse visar att en stor del av innehållet har förändrats mellan de båda versionerna av romanen. Den här uppsatsen visar samt diskuterar förändringarna som har gjorts för att texten ska bli mer acceptabel i förhållande till senviktorianska moraliska konventioner. Uppsatsen illustrerar förändringarna genom att jämföra citat. Poängen med att censurera den här romanen var att få Dorian att verka mer hjärtlös och omoralisk  i bokversionen från 1891. Bara då kunde Oscar Wildes berättelse närma sig den viktorianska moralen. Man kan se en tydlig förändring av karaktären Dorian Grays moral mellan de två versionerna.

This thesis describes the survival analysis, exactly Kaplan-Meier estimate. A main part of the thesis deals with the problem of censored data, which is typical for survival analysis. The empirical part describes lenght of PhD studies at the Faculty of Informatics and Statistics and their "survival" in studies by Kaplan-Meier curves. First are analyzed uncensored data and then the whole data set (censored and uncensored data).

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.

<p> The estimators of the mean, standard deviation and group effects for one-way-classification experimental designs are obtained from type I censored samples. The bias and the variances and covariances of these estimators are evaluated. A test statistic is proposed for testing a linear contrast of the group-effects. Two numerical examples are presented.</p> / Thesis / Master of Science (MSc)

No description available.

Companies routinely perform life tests for their products. Typically, these tests involve running a set of products until the units fail. Most often, the data are censored according to different censoring schemes, depending on the particulars of the test. On occasion, tests are stopped at a predetermined time and the units that are yet to fail are suspended. In other instances, the data are collected through periodic inspection and only upper and lower bounds on the lifetimes are recorded. Reliability professionals use a number of non-normal distributions to model the resulting lifetime data with the Weibull distribution being the most frequently used. If one is interested in monitoring the quality and reliability characteristics of such processes, one needs to account for the challenges imposed by the nature of the data. We propose likelihood ratio based cumulative sum (CUSUM) control charts for censored lifetime data with non-normal distributions. We illustrate the development and implementation of the charts, and we evaluate their properties through simulation studies. We address the problem of interval censoring, and we construct a CUSUM chart for censored ordered categorical data, which we illustrate by a case study at Becton Dickinson (BD). We also address the problem of monitoring both of the parameters of the Weibull distribution for processes with right-censored data. / Ph. D.