KM曲线交叉解决方法

COX Assumption

The hazards from different covariates values including treatments are proportional over time. 

Survival Curves Cross

The proportional hazards assumption can be examined visually in the Kaplan– Meier curve: when two survival curves cross, the proportional hazards assumption is violated.

解决方法：

1. Alternatively, one can plot the negative log of survival functions of two groups to examine whether they are parallel.
2. Another approach is to examine and test whether the Schoenfeld residuals from Cox regression model are independent of time.If independent, the proportional hazards assumption is acceptable. Otherwise, the assumption is violated and the hazard ratio is not the best statistic of the treatment difference because the benefit and harm can change over time.
3. Recently, there was a call to move beyond the use of hazard ratio in quantifying the between-group difference in survival analysis.The restricted mean survival time (RSMT) has been proposed as one of the alternatives. 

RMST

A RMST measures the mean survival time up to a clinically relevant time point, such as the mean survival time up to 5 years. The interpretation is the mean survival time if we follow the participants to 5 years in this case. Mathematically, a 5-year RMST is the area under the Kaplan–Meier survival curve up to 5 years. The choice of the time window depends on clinical relevance. The difference of two RMSTs measures the difference of two areas under the two survival curves. 

The main advantages of RMST are the following: (1) it is easier to communicate the meaning among clinicians, patients, and statisticians; (2) It is estimable even for rare events where the median survival time cannot be achieved; (3) It is nonparametric and free from assumptions such as the proportional hazards; (4) comparison of survival difference via RMSTs can be more powerful than the log-rank test when the proportional hazards assumption is not true; (5) comparison of survival difference via RMSTs integrates difference in survival probabilities from the beginning to the end of the follow-up time, thus a more meaningful difference.