The use of modified maximum likelihood estimation in survival analysis and its comparisons with traditional statistical methods and machine learning algorithms

Aim: Aim of this thesis is to compare the performance of models obtained by analyzing survival times with traditional statistical and machine learning methods. Methods: Traditional statistical methods including Kaplan-Meier method with Log-rank test, Cox proportional hazard regression analysis and accelerated failure time model have been employed in survival analysis. It has been asummed that survival times follow a Weibull distribution in accelerated failure time model and modified maximum likelihood method has been used to make robust parameter estimates when deviating from this assumption. Additionally, random forest and gradient boosting machines have been used in survival analysis, and their performances have been compared with classical methods using C-index. Results: Model performances have been compared using both simulation studies and real data application. In simulation study, data were generated with sample sizes of n=500, n=1000, and censoring rates of 20%, 40%, 60%. Models obtained using random forest and gradient boosting machines showed higher performances compared to other models. In application study, random forest model has performed the best, followed by Weibull accelerated failure time model obtained using modified maximum likelihood estimates. Conclusion: In real-life, there are often numerous censored data and distribution assumption for survival times is often not met. Therefore, use of machine learning methods and robust estimation method for parametric statistical models in survival analysis are recommended. Keywords: Kaplan-Meier, Cox proportional hazard, machine learning, Weibull, modified maximum likelihood