An Overview of Introductory and Advanced Survival Analysis Methods in Clinical Applications: Where Have we Come so far?

The time-to-event relationship for survival modeling is considered when designing a study in clinical trials. However, because time-to-event data are mostly not normally distributed, survival analysis uses non-parametric data processing and analysis methods, mainly Kaplan-Meier (KM) estimation models and Cox proportional hazards (CPH) regression models. At the same time, the log-rank test can be applied to compare curves from different groups. However, resorting to conventional survival analysis when fundamental assumptions, such as the Cox PH assumption, are not met can seriously affect the results, rendering them flawed. Consequently, it is necessary to examine and report more sophisticated statistical methods related to the processing of survival data, but at the same time, able to adequately respond to the contemporary real problems of clinical applications. On the other hand, the frequent misinterpretation of survival analysis methodology, combined with the fact that it is a complex statistical tool for clinicians, necessitates a better understanding of the basic principles underlying this analysis to effectively interpret medical studies in making treatment decisions. In this review, we first consider the basic models and mechanisms behind survival analysis. Then, due to common errors arising from the inappropriate application of conventional models, we revise more demanding statistical extensions of survival models related to data manipulation to avoid wrong results. By providing a structured review of the most representative statistical methods and tests covering contemporary survival analysis, we hope this review will assist in solving problems that arise in clinical applications