A frequent problem that appears in practical survival data analysis is censoring. A censored observation occurs when the observation of the event time (duration or survival time) may be prevented by the occurrence of an earlier competing event (censoring time). Censoring may be due to different causes. For example, the loss of some subjects under study, the end of the follow-up period, drop out or the termination of the study and the limitation in the sensitivity of a measurement instrument. The literature about censored data focuses on the i.i.d. case. However in many real applications the data are collected sequentially in time or space and so the assumption of independence in such case does not hold. Here we only give some typical examples from the literature involving correlated data which are subject to censoring. In the clinical trials domain it frequently happens that the patients from the same hospital have correlated survival times due to unmeasured variables like the quality of the hospital equipment. Censored correlated data are also a common problem in the domain of environmental and spatial (geographical or ecological) statistics. In fact, due to the process being used in the data sampling procedure, e.g. the analytical equipment, only the measurements which exceed some thresholds, for example the method detection limits or the instrumental detection limits, can be included in the data analysis. Many other examples can also be found in other fields like econometrics and financial statistics. Observations on duration of unemployment e.g., may be right censored and are typically correlated. When the data are not independent and are subject to censoring, estimation and inference become more challenging mathematical problems with a wide area of applications. In this context, we propose here some new and flexible tools based on a nonparametric approach. More precisely, allowing dependence between individuals, our main contribution to this domain concerns the following aspects. First, we are interested in developing more suitable confidence intervals for a general class of functionals of a survival distribution via the empirical likelihood method. Secondly, we study the problem of conditional mean estimation using the local linear technique. Thirdly, we develop and study a new estimator of the conditional quantile function also based on the local linear method. In this dissertation, for each proposed method, asymptotic results like consistency and asymptotic normality are derived and the finite sample performance is evaluated in a simulation study.

A general time-to-event data analysis known as event history analysis is considered. The focus is on the analysis of time-to-event data using Cox's regression model when the time to the event may be measured from different origins giving several observable time scales and when longitudinal measurements are involved. For the multiple time scales problem, procedures to choose a basic time scale in Cox's regression model are proposed. The connections between piecewise constant hazards, time-dependent covariates and time-dependent strata in the dual time scales are discussed. For the longitudinal measurements problem, four methods known in the literature together with two proposed methods are compared. All quantitative comparisons are performed by means of simulations. Applications to the analysis of infant mortality, morbidity, and growth are provided.

An analysis of the effect of passing vehicles’ characteristics and their impact on other drivers’ velocities was investigated. Three experimental studies were proposed and likely outcomes were discussed. Experiment 1 focused on the effect of passing vehicle type (SUV, sedan or truck) on driver speed. Drivers were hypothesized as going faster when the same vehicle type as they were driving passed them versus when no vehicle or a different vehicle passed them. Experiment 2 focused on the effect of passing SUV age on driver’s speed. Evidence suggests passing older SUVs will increase the driver’s speed more than new SUVs. Experiment 3 focused on the effect of passing SUV color on speed. Drivers were hypothesized to go faster when brighter colors (red and yellow) rather than cooler colors (grey and black) were painted on the vehicle.

The purpose of this dissertation is threefold: to determine the differences in apparent prevalence and the antimicrobial susceptibility of Campylobacter spp. between antimicrobial-free and conventional swine farms; secondly, to introduce an appropriate statistical model to compare the minimum inhibitory concentration distributions of Escherichia coli and Campylobacter spp. isolated from both farm types; and thirdly, to examine the potential herd level risk factors that may be associated with antimicrobial resistance of Campylobacter spp. and E. coli isolates from finishers on antimicrobial-free and conventional farming systems. In addition, a critical review of studies that have compared the levels and patterns of antimicrobial resistance among animals from antimicrobial-free and conventional farming practices was performed. Fecal samples from 15 pigs were collected from each of 35 antimicrobial-free and 60 conventional farms in the Midwestern U.S. Campylobacter spp. was isolated from 464 of 1,422 fecal samples, and each isolate was tested for susceptibility to 6 antimicrobials. The apparent prevalence of Campylobacter spp. isolates was approximately 33 percent on both conventional and antimicrobial-free farms. The proportion of antimicrobial resistance among Campylobacter was higher for three antimicrobials within conventional compared to antimicrobial-free farms. The susceptibilities of populations of bacteria to antimicrobial drugs were summarized as minimum inhibitory concentration (MIC) frequency distributions. The use of MIC values removed the subjectivity associated with the choice of breakpoints which define an isolate as susceptible or resistant. A discrete-time survival analysis model was introduced as the recommended statistical model when MICs are the outcome. A questionnaire was completed by each farm manager on biosecurity, preventive medication, vaccines, disease history, and production management. Multivariable population-averaged statistical models were used to determine the relationships among antimicrobial susceptibility patterns and potential herd-level risk factors. Controlling for herd type (antimicrobial-free versus conventional), each antimicrobial-bacterial species combination yielded unique combinations of risk factors; however, housing type, history of rhinitis, farm ventilation, and history of swine flu were significant in more than one model. A variety of herd-level practices were associated with the prevalence of antimicrobial resistance on swine farms. Further studies are encouraged when considering interventions for antimicrobial resistance on both antimicrobial-free and conventional farms.

Empirical likelihood, which was pioneered by Thomas and Grunkemeier (1975) and Owen (1988), is a powerful nonparametric method of statistical inference that has been widely used in the statistical literature. In this thesis, we investigate the merits of empirical likelihood for various problems arising in ratio estimation. First, motivated by the smooth empirical likelihood (SEL) approach proposed by Zhou & Jing (2003), we develop empirical likelihood estimators for diagnostic test likelihood ratios (DLRs), and derive the asymptotic distributions for suitable likelihood ratio statistics under certain regularity conditions. To skirt the bandwidth selection problem that arises in smooth estimation, we propose an empirical likelihood estimator for the same DLRs that is based on non-smooth estimating equations (NEL). Via simulation studies, we compare the statistical properties of these empirical likelihood estimators (SEL, NEL) to certain natural competitors, and identify situations in which SEL and NEL provide superior estimation capabilities. Next, we focus on deriving an empirical likelihood estimator of a baseline cumulative hazard ratio with respect to covariate adjustments under two nonproportional hazard model assumptions. Under typical regularity conditions, we show that suitable empirical likelihood ratio statistics each converge in distribution to a 2 random variable. Through simulation studies, we investigate the advantages of this empirical likelihood approach compared to use of the usual normal approximation. Two examples from previously published clinical studies illustrate the use of the empirical likelihood methods we have described. Empirical likelihood has obvious appeal in deriving point and interval estimators for time-to-event data. However, when we use this method and its asymptotic critical value to construct simultaneous confidence bands for survival or cumulative hazard functions, it typically necessitates very large sample sizes to achieve reliable coverage accuracy. We propose using a bootstrap method to recalibrate the critical value of the sampling distribution of the sample log-likelihood ratios. Via simulation studies, we compare our EL-based bootstrap estimator for the survival function with EL-HW and EL-EP bands proposed by Hollander et al. (1997) and apply this method to obtain a simultaneous confidence band for the cumulative hazard ratios in the two clinical studies that we mentioned above. While copulas have been a popular statistical tool for modeling dependent data in recent years, selecting a parametric copula is a nontrivial task that may lead to model misspecification because different copula families involve different correlation structures. This observation motivates us to use empirical likelihood to estimate a copula nonparametrically. With this EL-based estimator of a copula, we derive a goodness-of-fit test for assessing a specific parametric copula model. By means of simulations, we demonstrate the merits of our EL-based testing procedure. We demonstrate this method using the data from Wieand et al. (1989). In the final chapter of the thesis, we provide a brief introduction to several areas for future research involving the empirical likelihood approach.

The paper uses data from 2003 Multiscopo Italian Survey to estimate education effects on fertility and in particular to determine how and to what degree does unobserved heterogeneity influence the estimated effects, that is to say how unobserved heterogeneity might bias estimates of effects of education on transition to 1st, 2nd and 3rd births. The peculiarity of this study is the implementation of a multiprocess approach, which allows for a broader and more efficient view of the phenomenon, studying jointly the transition to first, second and third or higher order births. In doing this I will use control variables, in particular educational level of the mother and her siblings (i.e. partner and grandmother), to detect possible influences of education in childbearing timing. Moreover, this topic has not yet been analysed using Italian data, in particular using Multiscopo Survey data and it may produce interesting comparisons with regard to other European countries, where the topic has already been addressed. In this study I will prove that number of siblings is the variable, which has a significative and relevant effect in all the models considered and that women partner’s education has an up-and-down effect on transition to childbearing. Moreover, the inclusion of unobserved characteristics of women has an important role in understanding transition to childbearing, being positive and significant.

Cost-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.

The objective of the present study is to investigate various problems associate with breast cancer and lung cancer patients. In this study, we compare the effectiveness of breast cancer treatments using decision tree analysis and come to the conclusion that although certain treatment shows overall effectiveness over the others, physicians or doctors should discretionally give different treatment to breast cancer patients based on their characteristics. Reoccurrence time of breast caner patients who receive different treatments are compared in an overall sense, histology type is also taken into consideration. To further understand the relation between relapse time and other variables, statistical models are applied to identify the attribute variables and predict the relapse time. Of equal importance, the transition between different breast cancer stages are analyzed through Markov Chain which not only gives the transition probability between stages for specific treatment but also provide guidance on breast cancer treatment based on stating information. Sensitivity analysis is conducted on breast cancer doubling time which involves two commonly used assumptions: spherical tumor and exponential growth of tumor and the analysis reveals that variation from those assumptions could cause very different statistical behavior of breast cancer doubling time. In lung cancer study, we investigate the mortality time of lung cancer patients from several different perspectives: gender, cigarettes per day and duration of smoking. Statistical model is also used to predict the mortality time of lung cancer patients.

The objective of the present study is to address some important questions related to prostate cancer treatments and survivorship among White and African American men. It is commonly understood that the risk of developing prostate cancer is higher in African American men than the other races. However, using parametric analysis, this study demonstrates that this perception is a "myth" not a "reality". The study further identifies the existence of racial/ethnic disparities by comparing the average mean tumor size, the median of survival time, and the survival function between White and African American men. These results underline the necessity of understanding the role of racial background in working towards improved clinical targeting, and thereby, improving clinical outcomes. Furthermore, parametric survival analysis was performed to estimate the survivorship of white men undergoing different treatments at each stage of prostate cancer. Additionally, to better understand the risk factors (age, tumor size, the interaction between age and tumor size) associated with survival time, an accelerated failure time model was developed that could accurately predict the rates of survivorship of white men at each stage of prostate cancer in accordance with whatever treatment they had received. Finally, the results of parametric survival analysis and the accelerated failure time model are compared among white men undergoing similar treatment at each stage of the disease.

Growth rate of prostate cancer tumor is an important aspect of understanding the natural history of prostate cancer. Using real prostate cancer data from the SEER database with tumor size as a response variable, we have clustered the cancerous tumor sizes into age groups to enhance its analytical behavior. The rate of change of the response variable as a function of age is given for each cluster. Residual analysis attests to the quality of the analytical model and the subject estimates. In addition, we have identified the probability distribution that characterize the behavior of the response variable and proceeded with basic parametric analysis. There are several remarkable treatment options available for prostate cancer patients. In this present study, we have considered the three commonly used treatment for prostate cancer: radiation therapy, surgery, and combination of surgery and radiation therapy. The study uses data from the SEER database to evaluate and rank the effectiveness of these treatment options using survival analysis in conjunction with basic parametric analysis. The evaluation is based on the stage of the prostate cancer classification. Improvement in prostate cancer disease can be measured by improvement in its mortality. Also, mortality projection is crucial for policy makers and the financial stability of insurance business. Our research applies a parametric model proposed by Renshaw et al. (1996) to project the force of mortality for prostate cancer. The proposed modeling structure can pick up both age and year effects.