Solved – Survival analyses: how to relevel contrasts for multiple group comparisons

bioinformaticsbiostatisticsrsurvival

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).

Survival plot
From: https://www.visualcinnamon.com/2013/07/plotting-survival-analysis-results-in-r.html

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)

OUT:

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?

Best Answer

You can compare the three Kaplan-Meier survival curves. One of your curves is clearly statistically superior to the other two. Those other two are not distinguishable. Another statistical approach could be to use parametric survival distributions such as Weibull or Negative Exponential et cetera. The alternative approach would be to produce smooth curves but not lead to a statistically significant difference between the lower two curves. The fit would be by maximum likelihood, taking account of any right censoring

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