The field of survival analysis has experienced tremendous growth during the latter half of the 20th century. The methodological developments of survival analysis that have had the most profound impact are the Kaplan-Meier method for estimating the survival function, the log-rank test for comparing the equality of two or more survival distributions, and the Cox proportional hazards (PH) model for examining the covariate effects on the hazard function. The accelerated failure time (AFT) model was proposed but seldom used. In this thesis, we present the basic concepts, nonparametric methods (the Kaplan-Meier method and the log-rank test), semiparametric methods (the Cox PH model, and Cox model with time-dependent covariates) and parametric methods (Parametric PH model and the AFT model) for analyzing survival data.<p> We apply these methods to a randomized placebo-controlled trial to prevent Tuberculosis (TB) in Ugandan adults infected with Human Immunodificiency Virus (HIV). The objective of the analysis is to determine whether TB preventive therapies affect the rate of AIDS progression and survival in HIV-infected adults. Our conclusion is that TB preventive therapies appear to have no effect on AIDS progression, death and combined event of AIDS progression and death. The major goal of this paper is to support an argument for the consideration of the AFT model as an alternative to the PH model in the analysis of some survival data by means of this real dataset. We critique the PH model and assess the lack of fit. To overcome the violation of proportional hazards, we use the Cox model with time-dependent covariates, the piecewise exponential model and the accelerated failure time model. After comparison of all the models and the assessment of goodness-of-fit, we find that the log-logistic AFT model fits better for this data set. We have seen that the AFT model is a more valuable and realistic alternative to the PH model in some situations. It can provide the predicted hazard functions, predicted survival functions, median survival times and time ratios. The AFT model can easily interpret the results into the effect upon the expected median duration of illness for a patient in a clinical setting. We suggest that the PH model may not be appropriate in some situations and that the AFT model could provide a more appropriate description of the data.

In large-scale peer-assisted live streaming systems with hundreds of online channels, it becomes critically important to investigate the lifetime pattern of streaming sessions to have a better understanding of peer dynamics. Aiming to improve performance of the P2P streaming systems, the goal of this thesis is twofold: 1) for popular channels, we wish to identify superior peers, that contribute a higher percentage of upload capacities and stay for a longer period of time; 2) for unpopular channels, we seek to explore factors that affect the peer instability. Utilizing more than 130 GB worth of run-time traces from a large-scale real-world live streaming system, UUSee, we conduct a comprehensive and in-depth statistical analysis. Using survival analysis techniques, we discover critical factors that may influence the longevity. Based on the Cox regression models we built, we also discuss several interesting insights from our measurement results.

In large-scale peer-assisted live streaming systems with hundreds of online channels, it becomes critically important to investigate the lifetime pattern of streaming sessions to have a better understanding of peer dynamics. Aiming to improve performance of the P2P streaming systems, the goal of this thesis is twofold: 1) for popular channels, we wish to identify superior peers, that contribute a higher percentage of upload capacities and stay for a longer period of time; 2) for unpopular channels, we seek to explore factors that affect the peer instability. Utilizing more than 130 GB worth of run-time traces from a large-scale real-world live streaming system, UUSee, we conduct a comprehensive and in-depth statistical analysis. Using survival analysis techniques, we discover critical factors that may influence the longevity. Based on the Cox regression models we built, we also discuss several interesting insights from our measurement results.

We address the questions on what determines local government proliferation, specifically on the impact of intergovernmental transfers on proliferation. On exploring the determinants of proliferation, we provide a more elaborate empirical technique than exists in the literature by employing panel binary outcome, survival regression, as well as count analysis to capture the time varying effect from intergovernmental transfers. We also examine the impact of proliferation on service delivery outcomes and construct channels by which the policy may affect the outcomes in the education and health sectors. We apply panel difference-in-difference estimation and we uniquely identify the different treatment group and thus control for the plausible differential impact on outcomes in regards to changes in intergovernmental transfers. On the determinants of local government formation, there are likely competing effects across transfers on the decision to proliferate as well as on the extent of fragmentation given that we find (1) the lump-sum conditional grants positively influence the probability of proliferation, (2) a province with higher median share of equalization grants associates with higher number of local governments, (3) higher equalization grants implies a longer duration to the proliferation event, and (4) higher tax sharing in the proliferated local governments reflects higher stability where stability refers to the longer duration to the sequential proliferation event. The findings suggest the tactical central-local behavior may be present, however, the support of rent-seeking hypothesis on proliferation should not be generalized to overall system of transfers. On the impact from the proliferation policy, the education and health outcomes estimations provide mixed results within the treatment group. The findings shed light on the current practice of administrative or political decentralization, specifically on the competing local-central preferences within each sector on measured service delivery outcomes. The results from difference-in-difference (DID) estimations show support on attainment of education outcome in new local governments represented by a reduction in the dropout rate but not on the quality of education in terms of higher students’ tests scores even though there is a relatively higher conditional grants allocated to the proliferated local governments. Meanwhile, in terms of infant mortality rate, we only find evidence of improvement in infant mortality on the originating local government but not on the new local governments. Controlling for selectivity and production function covariates have not changed the pattern of the impact.

Context & Rationale: Individuals with similar CD4 cell counts and RNA levels can vary considerably with regards to clinical progression. This variation is likely the result of a complex interplay between viral, host and environmental factors. This study aimed to characterize and identify predictors associated with disease progression to AIDS or death in Saskatoon, Saskatchewan. Methods: This is a retrospective cohort study of 343 seroprevalent HIV positive patients diagnosed from Jan 2005 to Dec 2010. Of these, 73 had an estimated seroconversion date. Data was extracted from medical charts at two clinics specialized in HIV/AIDS care. Disease progression was measured as time from HIV diagnosis (or seroconversion) to immunological AIDS and death. The Cox hazard model was used. Results: The 3-year and 5-year immunological AIDS free probability was 53% and 33%, respectively. The 3-year and 5-year survival probability was 89% and 77%, respectively. Among the seroconversion cohort, the 3-year immunological AIDS free probability was 76%. Due to multicollinearity, separate models were built for IDU, hepatitis C and ethnicity. A history of IDU (HR, 3.0; 95%CI, 1.2-7.1), hepatitis C coinfection (HR, 2.9; 95%CI, 1.2-6.9), baseline CD4 counts (HR, 0.95; 95%CI, 0.92-0.98, per ever 10 unit increase), ever on ART, and year of diagnosis were significant predictors of progression to immunological AIDS among the seroprevalent cohort. Age at diagnosis, sex and ethnicity were not. For survival, only treatment use was a significant predictor (HR, 0.34; 95%CI, 0.1-0.8). Hepatitis C coinfection was marginally significant (p=0.067), while a history of IDU, ethnicity, gender, age at diagnosis, and year of diagnosis were not. Among the seroconversion cohort, no predictors of progression to immunological AIDS were identified. Ethnicity, hepatitis C coinfection and history of IDU could not be assessed. Conclusion: Our study found that IDU, HCV coinfections, baseline CD4 counts, and ART use were significant predictors of disease progression. This highlights the need for increased testing and early detection and for targeted interventions for these particularly vulnerable populations to slow disease progression.

Data obtained from longitudinal surveys using complex multi-stage sampling designs contain cross-sectional dependencies among units caused by inherent hierarchies in the data, and within subject correlation arising due to repeated measurements. The statistical methods used for analyzing such data should account for stratification, clustering and unequal probability of selection as well as within-subject correlations due to repeated measurements. <p>The complex multi-stage design approach has been used in the longitudinal National Population Health Survey (NPHS). This on-going survey collects information on health determinants and outcomes in a sample of the general Canadian population. <p>This dissertation compares the model-based and design-based approaches used to determine the risk factors of asthma prevalence in the Canadian female population of the NPHS (marginal model). Weighted, unweighted and robust statistical methods were used to examine the risk factors of the incidence of asthma (event history analysis) and of recurrent asthma episodes (recurrent survival analysis). Missing data analysis was used to study the bias associated with incomplete data. To determine the risk factors of asthma prevalence, the Generalized Estimating Equations (GEE) approach was used for marginal modeling (model-based approach) followed by Taylor Linearization and bootstrap estimation of standard errors (design-based approach). The incidence of asthma (event history analysis) was estimated using weighted, unweighted and robust methods. Recurrent event history analysis was conducted using Anderson and Gill, Wei, Lin and Weissfeld (WLW) and Prentice, Williams and Peterson (PWP) approaches. To assess the presence of bias associated with missing data, the weighted GEE and pattern-mixture models were used.<p>The prevalence of asthma in the Canadian female population was 6.9% (6.1-7.7) at the end of Cycle 5. When comparing model-based and design- based approaches for asthma prevalence, design-based method provided unbiased estimates of standard errors. The overall incidence of asthma in this population, excluding those with asthma at baseline, was 10.5/1000/year (9.2-12.1). For the event history analysis, the robust method provided the most stable estimates and standard errors. <p>For recurrent event history, the WLW method provided stable standard error estimates. Finally, for the missing data approach, the pattern-mixture model produced the most stable standard errors <p>To conclude, design-based approaches should be preferred over model-based approaches for analyzing complex survey data, as the former provides the most unbiased parameter estimates and standard errors.

Context & Rationale: Individuals with similar CD4 cell counts and RNA levels can vary considerably with regards to clinical progression. This variation is likely the result of a complex interplay between viral, host and environmental factors. This study aimed to characterize and identify predictors associated with disease progression to AIDS or death in Saskatoon, Saskatchewan. Methods: This is a retrospective cohort study of 343 seroprevalent HIV positive patients diagnosed from Jan 2005 to Dec 2010. Of these, 73 had an estimated seroconversion date. Data was extracted from medical charts at two clinics specialized in HIV/AIDS care. Disease progression was measured as time from HIV diagnosis (or seroconversion) to immunological AIDS and death. The Cox hazard model was used. Results: The 3-year and 5-year immunological AIDS free probability was 53% and 33%, respectively. The 3-year and 5-year survival probability was 89% and 77%, respectively. Among the seroconversion cohort, the 3-year immunological AIDS free probability was 76%. Due to multicollinearity, separate models were built for IDU, hepatitis C and ethnicity. A history of IDU (HR, 3.0; 95%CI, 1.2-7.1), hepatitis C coinfection (HR, 2.9; 95%CI, 1.2-6.9), baseline CD4 counts (HR, 0.95; 95%CI, 0.92-0.98, per ever 10 unit increase), ever on ART, and year of diagnosis were significant predictors of progression to immunological AIDS among the seroprevalent cohort. Age at diagnosis, sex and ethnicity were not. For survival, only treatment use was a significant predictor (HR, 0.34; 95%CI, 0.1-0.8). Hepatitis C coinfection was marginally significant (p=0.067), while a history of IDU, ethnicity, gender, age at diagnosis, and year of diagnosis were not. Among the seroconversion cohort, no predictors of progression to immunological AIDS were identified. Ethnicity, hepatitis C coinfection and history of IDU could not be assessed. Conclusion: Our study found that IDU, HCV coinfections, baseline CD4 counts, and ART use were significant predictors of disease progression. This highlights the need for increased testing and early detection and for targeted interventions for these particularly vulnerable populations to slow disease progression.

Considerable amounts of event history data are collected through longitudinal surveys. These surveys have many particularities or features that are the results of the dynamic nature of the population under study and of the fact that data collected through longitudinal surveys involve the use of complex survey designs, with clustering and stratification. These particularities include: attrition, seam-effect, censoring, left-truncation and complications in the variance estimation due to the use of complex survey designs. This thesis focuses on the last two points. Statistical methods based on the stratified Cox proportional hazards model that account for intra-cluster dependence, when the sampling design is uninformative, are proposed. This is achieved using the theory of estimating equations in conjunction with empirical process theory. Issues concerning analytic inference from survey data and the use of weighted versus unweighted procedures are also discussed. The proposed methodology is applied to data from the U. S. Survey of Income and Program Participation (SIPP) and data from the Canadian Survey of Labour and Income Dynamics (SLID). Finally, different statistical methods for handling left-truncated sojourns are explored and compared. These include the conditional partial likelihood and other methods, based on the Exponential or the Weibull distributions.

Data obtained from longitudinal surveys using complex multi-stage sampling designs contain cross-sectional dependencies among units caused by inherent hierarchies in the data, and within subject correlation arising due to repeated measurements. The statistical methods used for analyzing such data should account for stratification, clustering and unequal probability of selection as well as within-subject correlations due to repeated measurements. <p>The complex multi-stage design approach has been used in the longitudinal National Population Health Survey (NPHS). This on-going survey collects information on health determinants and outcomes in a sample of the general Canadian population. <p>This dissertation compares the model-based and design-based approaches used to determine the risk factors of asthma prevalence in the Canadian female population of the NPHS (marginal model). Weighted, unweighted and robust statistical methods were used to examine the risk factors of the incidence of asthma (event history analysis) and of recurrent asthma episodes (recurrent survival analysis). Missing data analysis was used to study the bias associated with incomplete data. To determine the risk factors of asthma prevalence, the Generalized Estimating Equations (GEE) approach was used for marginal modeling (model-based approach) followed by Taylor Linearization and bootstrap estimation of standard errors (design-based approach). The incidence of asthma (event history analysis) was estimated using weighted, unweighted and robust methods. Recurrent event history analysis was conducted using Anderson and Gill, Wei, Lin and Weissfeld (WLW) and Prentice, Williams and Peterson (PWP) approaches. To assess the presence of bias associated with missing data, the weighted GEE and pattern-mixture models were used.<p>The prevalence of asthma in the Canadian female population was 6.9% (6.1-7.7) at the end of Cycle 5. When comparing model-based and design- based approaches for asthma prevalence, design-based method provided unbiased estimates of standard errors. The overall incidence of asthma in this population, excluding those with asthma at baseline, was 10.5/1000/year (9.2-12.1). For the event history analysis, the robust method provided the most stable estimates and standard errors. <p>For recurrent event history, the WLW method provided stable standard error estimates. Finally, for the missing data approach, the pattern-mixture model produced the most stable standard errors <p>To conclude, design-based approaches should be preferred over model-based approaches for analyzing complex survey data, as the former provides the most unbiased parameter estimates and standard errors.

The field of survival analysis has experienced tremendous growth during the latter half of the 20th century. The methodological developments of survival analysis that have had the most profound impact are the Kaplan-Meier method for estimating the survival function, the log-rank test for comparing the equality of two or more survival distributions, and the Cox proportional hazards (PH) model for examining the covariate effects on the hazard function. The accelerated failure time (AFT) model was proposed but seldom used. In this thesis, we present the basic concepts, nonparametric methods (the Kaplan-Meier method and the log-rank test), semiparametric methods (the Cox PH model, and Cox model with time-dependent covariates) and parametric methods (Parametric PH model and the AFT model) for analyzing survival data.<p> We apply these methods to a randomized placebo-controlled trial to prevent Tuberculosis (TB) in Ugandan adults infected with Human Immunodificiency Virus (HIV). The objective of the analysis is to determine whether TB preventive therapies affect the rate of AIDS progression and survival in HIV-infected adults. Our conclusion is that TB preventive therapies appear to have no effect on AIDS progression, death and combined event of AIDS progression and death. The major goal of this paper is to support an argument for the consideration of the AFT model as an alternative to the PH model in the analysis of some survival data by means of this real dataset. We critique the PH model and assess the lack of fit. To overcome the violation of proportional hazards, we use the Cox model with time-dependent covariates, the piecewise exponential model and the accelerated failure time model. After comparison of all the models and the assessment of goodness-of-fit, we find that the log-logistic AFT model fits better for this data set. We have seen that the AFT model is a more valuable and realistic alternative to the PH model in some situations. It can provide the predicted hazard functions, predicted survival functions, median survival times and time ratios. The AFT model can easily interpret the results into the effect upon the expected median duration of illness for a patient in a clinical setting. We suggest that the PH model may not be appropriate in some situations and that the AFT model could provide a more appropriate description of the data.