Cox Proportional Hazards Regression Model: Applications and Case Studies

Survival analysis, a popular feature of survival studies, this study also examines the Cox Proportional Hazard Regression Model developed by David Cox in 1972, one of the “foundational models” in survival studies, especially those with time-to-event outcomes. The objective of this paper will be to try to grasp how the mechanism of the model works and how it can be used to analyze the impact of different variables on the time to an event, ultimately death or a cure, in diverse medical settings. A literature review on the use of the Cox model in medical research, such as cancer, heart diseases, and psychiatric disorders, is contained in the paper. It also covers how this model is applied to study the risk factors that influence when events occur, as well as the treatment of censored data using Maximum Likelihood Estimation techniques. The model was utilized on data of COVID-19 patients, studying how different variables such as age, gender, blood pressure, diabetes, etc., influence the time until death. Both gender and age were highly significant in their effect on the hazard ratio, with females surviving longer than males, and age having a positive relationship with the risk of death. Also, the model’s use when independent variables’ effects are time dependent, utilizing time-dependent covariates in the extended Cox model, is discussed. To sum up, this study confirms the utility of the Cox Model in a variety of medical and scientific fields and suggests future enhancements and the need for improved, accurate alternatives to the analysis of time-to-event data.