[R] Coxph and loglik converged before variable X

Terry Therneau therneau at mayo.edu
Thu Sep 18 14:49:13 CEST 2008

> Loglik converged before variable  1,2 ; beta may be infinite.
> I have two (related) questions:
> 1. Can I in general ignore this kind of warning and just pay attention to
>     predictors which produce significant p values?
> 2. In the specific case of stepAIC, can I ignore this warning and trust
>    that stepAIC will remove predictors that aren't useful contributors
>    to the model.

  Usually you can ignore the message, it is mostly for your information.  The 
key things to note are
   a. When one of the coefficients goes to infinity in a Cox model, the Wald 
test of significance beta/se(beta) breaks down, and is no longer reliable.  
     The LR test however is still valid.  Hence routines like stepAIC are ok.
So are predicted values, residuals, etc etc.  In fact it is pretty much only the 
Wald test that needs to be ignored: it is based on a Taylor series that simply 
doesn't work that far from zero.  Oops -- confidence intervals based on the se 
are also useless.

   b. The actual value of beta that is reported depends on the convergence 
criteria for the routine.  So this is one case where different Cox model 
functions can give results that look different.  I work in medical research, and 
view these differences as unimportant: if I were to tell you that your relative 
risk of death was exp(11) = 59,774 fold greater than your compatriots, would the 
message be substantially changed for beta of 10 or 12?
  There is a statistical literature under the heading of "monotone likelihood 
ratio" that worries about these coefficients and tries to fix them.  Much ado 
about nothing, IMHO.  
   c. For a large beta and a very skewed covariate the message can sometimes be 
wrong.  Beta is finite, just unstable. I might still prefer the LR to the Wald 
in this case.  Spline fits based on the truncated power basis (which Frank 
Harrell uses) are one way to generate such spurious messages.  
   Frank has argued with me that these messages may be shedding more confusion 
than illumination.  He has a point.
   	Terry Therneau

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