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.

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