Question: Cox proportional hazards - how to interpret summary output
gravatar for adampennycuick
2.3 years ago by
UCL, London
adampennycuick130 wrote:

Hi all,

I've been using a cox proportional hazard model to do survival analysis in R. I am looking for some advice interpreting the p-values produced by this model. I came across the interesting case where I stratified my data into two groups and the survival curve looked like this:

Survival curve

This was generated with code of the form shown below, where var is a binary variable:

km_fit <- survfit(Surv(time, status) ~ var, data=data)
cox <- coxph(Surv(time, status) ~ var, data=data)

When I run summary(cox) I get the following output:

cox <- coxph(Surv(time, status) ~ var, data=data)

n= 93, number of events= 32 

         coef exp(coef)  se(coef)     z Pr(>|z|)
varTRUE 1.991e+01 4.449e+08 4.441e+03 0.004    0.996

    exp(coef) exp(-coef) lower .95 upper .95
varTRUE 444911382  2.248e-09         0       Inf

Concordance= 0.696  (se = 0.047 )
Rsquare= 0.305   (max possible= 0.935 )
Likelihood ratio test= 33.79  on 1 df,   p=6e-09
Wald test            = 0  on 1 df,   p=1
Score (logrank) test = 22.29  on 1 df,   p=2e-06

I was quite surprised that using a Wald test, there was no difference between the groups (p=1) - presumably due to the absence of events in one group. I wonder if anyone could advise me when it is appropriate to use each of these different statistical tests to generate a p-value? What are the underlying assumptions? Is there a good reference on this that you could direct me towards?

Many thanks

R • 2.9k views
ADD COMMENTlink modified 2.3 years ago by Biostar ♦♦ 20 • written 2.3 years ago by adampennycuick130
gravatar for Devon Ryan
2.3 years ago by
Devon Ryan98k
Freiburg, Germany
Devon Ryan98k wrote:

The wald test produced a p-value of 1 because the fit was really really poor. You can see that in the coef field, where it's 19.91+/-4441. That's then leading to the really low Z value (19.91/4441 ~= 0.004) and thus the poor p-value.

I don't know why the fit was so poor, but at least that's the reason for p=1.

ADD COMMENTlink written 2.3 years ago by Devon Ryan98k

Indeed, when you are testing a dichotomous variable and one has no events, Wald test will invariably be 1 due to convergence, and should not be used. Take the log rank or LRT p-values.

ADD REPLYlink written 2.3 years ago by Kevin Blighe69k

Makes sense, see also here.

ADD REPLYlink written 2.3 years ago by Devon Ryan98k

Confidence intervals on blue variable neither look great, though!

ADD REPLYlink written 2.3 years ago by Kevin Blighe69k
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