The Proper Use and Reporting of Survival Analysis and Cox Regression

Survival analyses are heavily used to analyze data in which the time to event is of interest. The purpose of this paper is to introduce some fundamental concepts for survival analyses in medical studies.

We comprehensively review current survival methodologies, such as the nonparametric Kaplan-Meier method used to estimate survival probability, the log-rank test, one of the most popular tests for comparing survival curves, and the Cox proportional hazard model, which is used for building the relationship between survival time and specific risk factors. More advanced methods, such as time-dependent receiver operating characteristic, restricted mean survival time, and time-dependent covariates are also introduced.

This tutorial is aimed toward covering the basics of survival analysis. We used a neurosurgical case series of surgically treated brain metastases from non-small cell lung cancer patients as an example. The survival time was defined from the date of craniotomy to the date of patient death.

This work is an attempt to encourage more investigators/medical practitioners to use survival analyses appropriately in medical research. We highlight some statistical issues, make recommendations, and provide more advanced survival modeling in this aspect.