In teaching some students about survival analysis methods this week, I wanted to demonstrate why we need to use statistical methods that properly allow for right censoring. This post is a brief introduction, via a simulation in R, to why such methods are needed.
Survival analysis
Testing equality of two survival distributions: log-rank/Cox versus RMST
Cox’s proportional hazards model is by far the most common approach used to model survival or time to event data. For a simple two group comparison, such as in a randomised controlled trial, the model says that the hazard of failure in one group is a constant ratio (over time) of the hazard of failure in the other group. A test that this hazard ratio equals 1 is a test of the null hypothesis of equality of the survival functions of the two groups. The log rank test is essentially equivalent to the score test that the HR=1 in the Cox model, and is commonly used as the primary analysis hypothesis test in randomised trials.
Handling competing risks in randomized trials
Peter Austin and Jason Fine (of Fine & Gray fame) have just published a nice review article in Statistics in Medicine on handling competing risks in randomized trials. They reviewed RCTs published in four top medical journals in the last three months of 2015. Of the 40 trials found with time to event outcomes, Austin & Gray determined that 31 were potentially susceptible to competing risks.