If you have a binary or categorical covariate in the model and there are no events associated with one level of this covariate, the parameter estimates for this covariate do not converge. The general phenomenon, due to specific conditions of the data, is known as 'monotone likelihood'. The estimation method of maximizing the likelihood cannot appropriately deal with this problem.

Typically, the estimated standard error for the affected covariate becomes very large. Adding the MAXITER=50 (or 100), ITPRINT and XCONV=1e-9 options in the MODEL statement and examining the Iteration History table might enable you to determine that the parameter estimate for the affected covariate does not converge. No warnings or error messages are issued.

You can use PROC FREQ to help identify binary or categorical variables with no events in some categories. For example, if STATUS=1 indicates an event and STATUS=0 indicates a censored observation then a crosstabulation as follows can be helpful:

proc freq data=sasdsname; 
     tables (list of binary/categorical covariates)*status / norow nocol nocum nopercent; 
run; 

There are other data situations where the phenomenon of monotone likelihood is observed in which the likelihood converges to a finite value while the parameter estimate diverges. When the model has only 1 parameter, Tsiatis (1981) has identified the sufficient conditions for monotone likelihood. Beginning in SAS 9.2, a potential workaround for these other data situations is to use the FIRTH option in the MODEL statement, which maximizes a penalized likelihood. The FIRTH option might solve the monotone likelihood problem. See Example 85.4 Firth’s Correction for Monotone Likelihood in the SAS9.4 PHREG documentation. Note that the FIRTH option is available only for the TIES=BRESLOW likelihood..

-------------

Bryson, C.B. and Johnson, M. (1981) "The Incidence of Monotone Likelihood in the Cox Model", Technometrics, Vol. 23, No. 4, 381-383.

Firth, D. (1993), "Bias Reduction of Maximum Likelihood Estimates", Biometrika, 80, 27–38.

Heinze, G. and Schemper, M. (2001), "A Solution to the Problem of Monotone Likelihood in Cox Regression", Biometrics, 57, 114-119.

Tsiatis, A. (1981), "A Large Sample Study of the Estimates for the Integrated Hazard Function in Cox's Regression Model for Survival Data", Annals of Statistics, 9, 93 - 108.

Operating System and Release Information