I have trouble understanding how do I compare multiple groups in a single survival analysis. When I only have two groups of patients, I simply perform the Kaplan-Meier estimator. However, if there are more than 2 exposure levels, the inference is not so straightforward.
If you look at the colon data (available in R, survival plot below), you will find 3 different cohorts (rx column): Obs (observation), Lev (Levamisole treatment) and Lev+5FU (Levamisole + 5-FU treatment).
The plot demonstrates clear evidence that:
- Obs and Lev cohorts have similar survival levels
- Lev+5FU cohort has higher survival level than Obs and Lev ones
However, since a single P is given (a single value is usually given in multiple online tutorials), I guess that this P represents the higher survival in Lev+5FU compared to others, just like the P given with an ANOVA test states that data is, somehow, different and you need to do additional tests to figure out what is different. Is my thought correct? I actually would like a better measurement of this. What test can I perform to measure survival differences between:
- Obs versus Lev
- Obs versus Lev+FU
- Lev versus Lev+FU
Should I just perform multiple Kaplan-Meier estimators and then adjust P for multiple tests (Bonferroni, BH or whatever) or is there any alternate solution?
I also experienced that if I perform a Cox PH, I do not get full information.
coxph(Surv(time,status) ~ rx, data = colon)
Call: coxph(formula = Surv(time, status) ~ rx, data = colon) coef exp(coef) se(coef) z p rxLev -0.0209 0.9793 0.0768 -0.27 0.79 rxLev+5FU -0.4410 0.6434 0.0839 -5.26 1.5e-07 Likelihood ratio test=35.2 on 2 df, p=2.23e-08 n= 1858, number of events= 920
I guess that the two given P compare Obs versus Lev and Obs versus Lev+5FU right? I my case, no "control" cohort can be used as a survival reference.
Can someone help me with that?