Central to the goals of public health are obtaining and interpreting timely and relevant information for the benefit of humanity. In this dissertation, we propose methods to monitor and assess the spread HIV in a more rapid manner, as well as to improve decisions regarding patient treatment options. In Chapter 1, we propose a method, extending the previously proposed dual-testing algorithm and augmented cross-sectional design, for estimating the HIV incidence rate in a particular community. Compared to existing methods, our proposed estimator allows for shorter follow-up time and does not require estimation of the mean window period, a crucial, but often unknown, parameter. The estimator performs well in a wide range of simulation settings. We discuss when this estimator would be expected to perform well and offer design considerations for the implementation of such a study. Chapters 2 and 3 are concerned with obtaining a more complete understanding of the impact of treatment in randomized clinical trials in which multiple patient outcomes are recorded. Chapter 2 provides an illustration of methods that may be used to address concerns of both risk-benefit analysis and personalized medicine simultaneously, with a goal of successfully identifying patients who will be ideal candidates for future treatment. Riskbenefit analysis is intended to address the multivariate nature of patient outcomes, while “personalized medicine” is concerned with patient heterogeneity, both of which complicate the determination of a treatment’s usefulness. A third complicating factor is the duration of treatment use. Chapter 3 features proposed methods for assessing the impact of treatment as a function of time, as well as methods for summarizing the impact of treatment across a range of follow-up times. Chapter 4 addresses the issue of meta-analysis, a commonly used tool for combining information for multiple independent studies, primarily for the purpose of answering a clinical question not suitably addressed by any one single study. This approach has proven highly useful and attractive in recent years, but often relies on parametric assumptions that cannot be verified. We propose a non-parametric approach to meta-analysis, valid in a wider range of scenarios, minimizing concerns over compromised validity.

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<p>The aim of this study is to illustrate, adapt and develop methods of survival analysis in analysing and estimating customer survival time in subscription-based businesses. Two particular objectives are studied. The rst objective is to redene the existing survival analysis techniques in business terms and to discuss their uses in order to understand various issues related to the customer-rm relationship.</p>

This paper analyzes the effect of political and economic factors on the risk of regime change in countries between 1975 and 2010, using survival analysis with time-dependent covariates. The findings show that negative economic growth increases the risk of regime change in the following year, and that a higher level of GDP per Capita, as well as international trade, has an inhibiting effect on the risk of regime change in democracies. The results also show that countries with young regimes are more likely to experience a regime change, and that countries with a long tradition of democratic governance suffer virtually no risk of experiencing a regime failure. These findings lend heavy support to the democratic consolidation theory, while giving mixed support to other theories of economic and political causes of regime change. The more generalized approach to regime change used in this paper provides a stepping stone for opening up a greater understanding of the mechanisms which cause regime change in all types of governments, and regardless of the direction of the change in relation to democracy.

Acute Myocardial Infarction (AMI), commonly known as heart attack, is a leading cause of death for adult men and women in the world. Studying mortality after AMI is therefore an important problem in epidemiology. This thesis develops statistical methodology for examining geographic patterns in mortality following AMI. Specifically, we develop parametric Accelerated Failure Time (AFT) models for censored survival data, where space-varying regression is used to investigate spatial patterns of mortality after AMI. In addition to important covariates such as age and gender, the regression models proposed here also incorporate spatial random e ects that describe the residual heterogeneity associated with di erent local health geographical units. We conduct model inference under a hierarchical Bayesian modeling framework using Markov Chain Monte Carlo algorithms for implementation. We compare an array of models and address the goodness-of- t of the parametric AFT model through simulation studies and an application to a longitudinal AMI study in Quebec. The application of our AFT model to the Quebec AMI data yields interesting ndings concerning aspects of AMI, including spatial variability. This example serves as a strong case for considering the parametric AFT model developed here as a useful tool for the analysis of spatially correlated survival data.

This research carries out a survival analysis for patients with breast cancer. The influence of clinical and pathologic features, as well as molecular markers on survival time are investigated. Special attention focuses on whether the molecular markers can provide additional information in helping predict clinical outcome and guide therapies for breast cancer patients. Three outcomes, breast cancer specific survival (BCSS), local relapse survival (LRS) and distant relapse survival (DRS), are examined using two datasets, the large dataset with missing values in markers (n=1575) and the small (complete) dataset consisting of patient records without any missing values (n=910). Results show that some molecular markers, such as YB1, could join ER, PR and HER2 to be integrated into cancer clinical practices. Further clinical research work is needed to identify the importance of CK56. The 10 year survival probability at the mean of all the covariates (clinical variables and markers) for BCSS, LRS, and DRS is 77%, 91%, and 72% respectively. Due to the presence of a large portion of missing values in the dataset, a sophisticated multiple imputation method is needed to estimate the missing values so that an unbiased and more reliable analysis can be achieved. In this study, three multiple imputation (MI) methods, data augmentation (DA), multivariate imputations by chained equations (MICE) and AREG, are employed and compared. Results shows that AREG is the preferred MI approach. The reliability of MI results are demonstrated using various techniques. This work will hopefully shed light on the determination of appropriate MI methods for other similar research situations.

Linear assets are among the largest and most important engineered systems; their reliability is of the utmost importance. This thesis presents an overview of the reliability estimation methods used for the various types of linear assets, both observation- and statistically-based. While observation-based reliability monitoring and estimation methods are necessarily particular to a certain type of asset, statistically-based methods developed for one type can potentially inform those used for another. Therefore, this thesis looks to point out commonalities in the methods for the statistical evaluation of the reliability of various types of linear assets, develop and extend reliability models and methods with this knowledge, and suggest how maintenance strategies may be improved. To help illustrate and test the models described in this paper a case study was conducted with a utility operator; this thesis shows the modelling results from the study, and demonstrates the model’s use in a maintenance decision model.

Linear assets are among the largest and most important engineered systems; their reliability is of the utmost importance. This thesis presents an overview of the reliability estimation methods used for the various types of linear assets, both observation- and statistically-based. While observation-based reliability monitoring and estimation methods are necessarily particular to a certain type of asset, statistically-based methods developed for one type can potentially inform those used for another. Therefore, this thesis looks to point out commonalities in the methods for the statistical evaluation of the reliability of various types of linear assets, develop and extend reliability models and methods with this knowledge, and suggest how maintenance strategies may be improved. To help illustrate and test the models described in this paper a case study was conducted with a utility operator; this thesis shows the modelling results from the study, and demonstrates the model’s use in a maintenance decision model.

This thesis considers a variety of statistical issues related to the design and analysis of clinical trials involving multiple lifetime events. The use of composite endpoints, multivariate survival methods with dependent censoring, and recurrent events with dependent termination are considered. Much of this work is based on problems arising in oncology research. Composite endpoints are routinely adopted in multi-centre randomized trials designed to evaluate the effect of experimental interventions in cardiovascular disease, diabetes, and cancer. Despite their widespread use, relatively little attention has been paid to the statistical properties of estimators of treatment effect based on composite endpoints. In Chapter 2 we consider this issue in the context of multivariate models for time to event data in which copula functions link marginal distributions with a proportional hazards structure. We then examine the asymptotic and empirical properties of the estimator of treatment effect arising from a Cox regression model for the time to the first event. We point out that even when the treatment effect is the same for the component events, the limiting value of the estimator based on the composite endpoint is usually inconsistent for this common value. The limiting value is determined by the degree of association between the events, the stochastic ordering of events, and the censoring distribution. Within the framework adopted, marginal methods for the analysis of multivariate failure time data yield consistent estimators of treatment effect and are therefore preferred. We illustrate the methods by application to a recent asthma study. While there is considerable potential for more powerful tests of treatment effect when marginal methods are used, it is possible that problems related to dependent censoring can arise. This happens when the occurrence of one type of event increases the risk of withdrawal from a study and hence alters the probability of observing events of other types. The purpose of Chapter 3 is to formulate a model which reflects this type of mechanism, to evaluate the effect on the asymptotic and finite sample properties of marginal estimates, and to examine the performance of estimators obtained using flexible inverse probability weighted marginal estimating equations. Data from a motivating study are used for illustration. Clinical trials are often designed to assess the effect of therapeutic interventions on occurrence of recurrent events in the presence of a dependent terminal event such as death. Statistical methods based on multistate analysis have considerable appeal in this setting since they can incorporate changes in risk with each event occurrence, a dependence between the recurrent event and the terminal event and event-dependent censoring. To date, however, there has been limited methodology for the design of trials involving recurrent and terminal events, and we addresses this in Chapter 4. Based on the asymptotic distribution of regression coefficients from a multiplicative intensity Markov regression model, we derive sample size formulae to address power requirements for both the recurrent and terminal event processes. Superiority and non-inferiority trial designs are dealt with. Simulation studies confirm that the designs satisfy the nominal power requirements in both settings, and an application to a trial evaluating the effect of a bisphosphonate on skeletal complications is given for illustration.

Aquesta tesi s'emmarca en l'anàlisi de la supervivència. A la primera part es proposa una metodologia per estimar els coeficients d'un model lineal amb censura a la resposta i error de mesura a les covariants. Es proposa un estimador consistent que combina les metodologies per estimar models lineals de resposta censurada i, les utilitzades per als models amb variables explicatives mesurades amb error. Els errors estàndard de l'estimador es calculen numèricament mitjançant bootstrap. Algunes simulacions mostren les propietats de l'estimador.A la segona part s'analitzen històries laborals espanyoles. Hi ha tres tipus d'episodis: de treball autònom, per compte d'altri i sense treballar. Es duen a terme els següents estudis: estimació no paramètrica de la funció de supervivència pels diferents episodis; anàlisi de la durada del primer episodi de la història laboral; models de competing risk per a cada tipus d'episodis; i una anàlisi longitudinal dels cinc primers episodis tractats conjuntament. / This thesis is about survival analysis. The first part is focused on linear regression models with a censored dependent variable and, the explanatory variable contaminated with measurement error. A methodology which produces consistent estimates of the regression coefficients is proposed. It combines the procedures for fitting linear models with censoring and, the estimation methods for linear models with measurement error. Standard errors of the estimator are computed using the bootstrap method. The performance of the estimator is evaluated by Monte Carlo studies.The second part analyzes data about Spanish labor market histories. We study the duration of three types of labor spells (self-employment, wage-earner and non-working). We carry out several analyses: non-parametric approaches of the survival functions for several sets of spells a standard duration analysis for the first spells of the labor history a competing risk analysis for each type of spell; and a longitudinal analysis for the five early spells of the labor histories.