Given the following output from R, the p-values from the likelihood ratio test and wald test are quite different. There is a warning message "Ran out of iterations and did not converge". Can someone help explain this situation?

> summary(coxph(Surv(years,status) ~ feature, data=tmp))
coxph(formula = Surv(years, status) ~ feature, data = tmp)

  n= 74, number of events= 30 

              coef  exp(coef)   se(coef)      z Pr(>|z|)
feature -7.662e+01  5.326e-34  1.365e+04 -0.006    0.996

        exp(coef) exp(-coef) lower .95 upper .95
feature 5.326e-34  1.877e+33         0       Inf

Concordance= 0.547  (se = 0.027 )
Rsquare= 0.078   (max possible= 0.962 )
Likelihood ratio test= 5.99  on 1 df,   p=0.01442
Wald test            = 0  on 1 df,   p=0.9955
Score (logrank) test = 1.71  on 1 df,   p=0.1909

Warning message:
In fitter(X, Y, strats, offset, init, control, weights = weights,  :
  Ran out of iterations and did not converge

The information below may help. The feature variable is not normally distributed.

table(tmp[,"status"], tmp[,"feature"])

              3.32193 3.5223 3.55332 4.04619 4.56255 4.67836 7.10919
  0=censored       38      1       1       1       1       1       1
  1=event          30      0       0       0       0       0       0 

1 Answer 1


Before you start worrying about which one is more reliable, you need to deal with the convergence problem itself.

What's happening is that the algorithm that is estimating the regression coefficients is running out of "tries" to find the maximum of the likelihood function (this is what converging means). This, in turn, means the regression coefficients themselves aren't reliable - there's no promise that these are anywhere near the actual estimates that would have been produced if the algorithm had converged.

As for which method of calculating a p-value is more reliable, there's not necessarily a single answer to that question - otherwise people would only use one of them. I found this to be a decent treatment of situations where log-rank tests are potentially flawed.


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