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:

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:

```
Call:
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

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.

Makes sense, see also here.

Confidence intervals on blue variable neither look great, though!