No Event Issue at Cox Regression?

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I am trying to do a cox-regression on a data set with patients treated for meningioma (a kind of brain tumor). I have varying follow-up times after surgery (time variable), whether the tumor recurred (status variable) and a number of predictors. My sample size is about 40 patients, nicely distributed over categorical variables (treatment, gender)

When I run the analysis I get the error message "since coefficients did not converge, no further model will be fitted."

I think the problem is that the most important predictor (treatment strategy) has no events in the new treatment strategy. As a clinician it's a huge success because the recurrence rate in the patients receiving standard treatment is quite high, so we're obviously doing the right thing, but I can't get the cox regression to work.. If I enter one event in the treatment group that has no events, the analysis works fine..

I'm suspecting that this outcome is inherently logical from the way the cox regression works, but still curious if there's anything I could do - I mean, there's an obvious difference between the groups! Wait for an event in the treatment group? :)

Any suggestions greatly appreciated!

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关键词：regression regressio regress issue Event receiving important standard patients question

SAS and SPLUS programs to perform Cox regression without convergence problems

Abstract
When analyzing survival data, the parameter estimates and consequently the relative risk estimates of a Cox model
sometimes do not converge to finite values. This phenomenon is due to special conditions in a data set and is known
as ‘monotone likelihood’. Statistical software packages for Cox regression using the maximum likelihood method
cannot appropriately deal with this problem. A new procedure to solve the problem has been proposed by G. Heinze,
M. Schemper, A solution to the problem of monotone likelihood in Cox regression, Biometrics 57 (2001). It has been
shown that unlike the standard maximum likelihood method, this method always leads to finite parameter estimates.
We developed a SAS macro and an SPLUS library to make this method available from within one of these widely
used statistical software packages. Our programs are also capable of performing interval estimation based on profile
penalized log likelihood (PPL) and of plotting the PPL function as was suggested by G. Heinze, M. Schemper, A
solution to the problem of monotone likelihood in Cox regression, Biometrics 57 (2001). © 2002 Elsevier Science
Ireland Ltd. All rights reserved.
http://cemsiis.meduniwien.ac.at/fileadmin/msi_akim/CeMSIIS/KB/volltexte/Heinze_Ploner_2002_CompMethProgBiom.pdf