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Survival Analysis in the context of Political Science is frequently used to study the duration of agreements, political party influence, wars, senator term lengths, etc. This paper surveys a collection of methods implemented on a modified version of the Power-Sharing Event Dataset (which documents civil war peace agreement durations in the Post-Cold War era) in order to identify the research questions that are optimally addressed by each method. A primary comparison will be made between a Cox Proportional Hazards Model using some advanced capabilities in the glmnet package, a Survival Random Forest Model, and a Survival SVM. En route to this comparison, issues including Cox Model variable selection using the LASSO, identification of clusters using Hierarchal Clustering, and discretizing the response for Classification Analysis will be discussed. The results of the analysis will be used to justify the need and accessibility of the Survival Random Forest algorithm as an additional tool for survival analysis.

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Indiana University-Purdue University Indianapolis (IUPUI) / Survival analysis has broad applications in diverse research areas. In this dissertation, we consider an innovative application of survival analysis approach to phase I dose-finding design and the modeling of multivariate survival data. In the first part of the dissertation, we apply time to event analysis in an innovative dose-finding design. To account for the unique feature of a new class of oncology drugs, T-cell engagers, we propose a phase I dose-finding method incorporating systematic intra-subject dose escalation. We utilize survival analysis approach to analyze intra-subject dose-escalation data and to identify the maximum tolerated dose. We evaluate the operating characteristics of the proposed design through simulation studies and compare it to existing methodologies. The second part of the dissertation focuses on multivariate survival data with semi-competing risks. Time-to-event data from the same subject are often correlated. In addition, semi-competing risks are sometimes present with correlated events when a terminal event can censor other non-terminal events but not vice versa. We use a semiparametric frailty model to account for the dependence between correlated survival events and semi-competing risks and adopt penalized partial likelihood (PPL) approach for parameter estimation. In addition, we investigate methods for variable selection in semi-parametric frailty models and propose a double penalized partial likelihood (DPPL) procedure for variable selection of fixed effects in frailty models. We consider two penalty functions, least absolute shrinkage and selection operator (LASSO) and smoothly clipped absolute deviation (SCAD) penalty. The proposed methods are evaluated in simulation studies and illustrated using data from Indianapolis-Ibadan Dementia Project.

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Objective: The project aimed to compare marginal structural models, and propensity score adjusted models with Cox Proportional Hazards models to address confounding by indication due to time-dependent confounders. These methods were applied to data from approximately 120,000 women in the Women’s Health Initiative to evaluate the causal effect of antidepressant medication with respect to diabetes risk. Methods: Four approaches were compared. Three Cox Models were used. The first used baseline covariates. The second used time-varying antidepressant medication use, BMI and presence of elevated depressive symptoms and adjusted for other baseline covariates. The third used time-varying antidepressant medication use, BMI and presence of elevated depressive symptoms and adjusted for other baseline covariates and propensity to taking antidepressants at baseline. Our fourth method used a Marginal Structural Cox Model with Inverse Probability of Treatment Weighting that included time-varying antidepressant medication, BMI and presence of elevated depressive symptoms and adjusted for other baseline covariates. Results: All approaches showed an increase in diabetes risk for those taking antidepressants. Diabetes risk increased with adjustment for time-dependent confounding and results for these three approaches were similar. All models were statistically significant. Ninety-five percent confidence intervals overlapped for all approaches showing they were not different from one another. Conclusions: Our analyses did not find a difference between Cox Proportional Hazards Models and Marginal Structural Cox Models in the WHI cohorts. Estimates of the Inverse Probability of Treatment Weights were very close to 1 which explains why we observed similar results.