The Cox proportional hazards model allows data to be analyzed with a concept of survival and death over time. Unlike a lot of other traditional models, there is a clear relationship of how the risk of death is affected by time and the features of the data. The model is equivalent to a generalized linear model, and the L1 regularized Cox model can be solved by coordinate descent. In addition, a condition to eliminate features is explored to save computational time in solving the maximization of the partial log likelihood. The Cox model can be applied to many tasks because of its unique survival aspect. The probabilities of surviving past a certain time are used to predict loan defaults. Understanding which characteristics correlate with survival for dogs and cats in animal shelters is also possible through creating survival curves.