生存分析Cox回归 生存数据不符合应用条件怎么办？

Cox回归，全称为Cox比例风险模型，主要用于带有时间的生存结局的影响因素研究，或评价某个临床治疗措施对患者生存的影响。

Cox对因变量和自变量要求都不高，只要求结局指标既要有生存的二分类结局，也要有生存时间，对生存时间也没有分布的要求，对自变量要求更低，什么类型的自变量都可以。此外，Cox回归要求观察值残差分布同样满足独立性的要求(一般情况下都不成问题，开展回归分析可以基本忽略本要求)。

1. 等比例风险(Proportional hazards)假定；
2. 当自变量是连续型变量时，Cox回归中自变量与因变量的关系——一种转换后线性关系，也必须满足。

1. 等比例风险假定

1.1 什么是等比例风险？

Cox回归有一个重大规定，虽然各组生存率下降，各个时间点死亡速度不一致，但是要求下降的速率比是一样，比如第2年，处理组死亡速率是10%，那么对照组死亡速率5%，第3年术中放疗组风险率20%，那么对照组应该也是10%左右。如此，死亡速率之比，也就是HR值保持一致,这便是等比例风险

1.2 等比例风险判断

1.2.4 其它方法

1. Proportionality of hazards was assessed for each variable and Schoenfeld residuals were visually inspected for potential time–variant biases. Our assessment of the proportionality of hazards assumption and visual inspection of Schoenfeld residuals showed that none were significant based on a p value threshold of 0·05.
2. The proportional hazards assumption was confirmedby residual plots
3. We examined the proportional hazards assumption by testing statistical significance of interactions between follow-up time and exposures.
4. We used the Schoenfeld residual test to verify the assumption of proportional hazards in the Cox analysis, which was fulfilled for the end points of death from any causeand further bleeding.
5. We examined the assumption ofproportional hazards by using a Wald test of the interaction between treatment status and time.
6. To assess the validity of the proportional hazards assumption, the assumption was assessed by log-minus-log-survival function and found to hold. To confirm the assumption of proportionality, time-dependent covariate analysis was used.

2. 线性关系是经常被忽略的条件

Cox回归对线性条件的诊断，常见的方式是通过建立自变量与鞅残差(martingale residual)的散点图，看是否存在着线性趋势。

``````install.packages("survival")
library(survival)
resCox<-coxph(Surv(time,censor)~age+sex+bui+ch+p+stage+trt,data=p1)
summary(resCox)
p1\$resid<-residuals(resCox,type = "martingale",data=p1)
plot(p1\$age,p1\$resid)
lines(lowess(p1\$age,p1\$resid))
``````

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