Modern approach to Survival Analysis

Survival analysis is a branch of statistics that focuses on analyzing and predicting the time until an event of interest occurs. It is commonly applied in fields where events are censored and may not be directly observed within the monitoring period. The Cox proportional hazards model is the most widely used technique in this domain due to its semi-parametric nature, allowing it to estimate the effects of covariates on survival outcomes without assuming a specific baseline hazard function. However, this model is constrained by relatively strict assumptions. The goal of this work is to assess whether the field of survival analysis can benefit from the adoption of algorithms based on machine learning, which are generally not constrained by strong assumptions. These algorithms include tree-based methods such as random survival forests, conditional inference forests, and oblique random survival forests, as well as enhancements to the Cox model that incorporate machine learning techniques like boosting and penalization. For this purpose, real data were used as well as simulated data in order to make comparison between the predictive power of traditional and machine learning algorithms. Comparison of the algorithms was done on data, which the models were not trained on. For real-world data, the study utilized a dataset about patients admitted to the intensive care unit at Beth Israel Deaconess Medical Center in Boston. The analysis was divided into two parts: one focusing on time-independent covariates and the other on time-dependent covariates. In the time-independent analysis, emphasis was placed on understanding how specific diagnoses, along with patient demographics, impact survival. Additionally, significant attention was given to techniques that facilitate explanations of specific predictions made by the model and the model’s overall behavior. The analysis with time-dependent covariates aimed to explore additional opportunities and abilities of the described models to work with these data. The simulation was conducted to generate nine different datasets, varying in the number of observations and levels of censoring. However, all simulated datasets had common set of 32 covariates, out of which only 8 had a real impact on the outcome. This approach was designed to explore abilities of the model to perform under the prevalence of noisy variables. This time, apart from predictive power of individual models, the ability to recognize important covariates under different scenarios was investigated as well. The results from the simulations aligned with those from the real data analysis, with the best-performing algorithms being CoxBoost and the Cox model with elastic net regularization. The Cox model with elastic net regularization was particularly effective in scenarios with a limited number of observations, outperforming the other models. These findings demonstrate that enhancing the traditional Cox model with boosting and regularization techniques can lead to improvements. However, the tree-based methods did not show superior predictive power compared to the traditional Cox model.