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.