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Partially exact alternatives to regularization in proportional hazards regression models with monotone likelihood

 John E Kolassa

Proportional hazards regression models are very commonly used to model time to events in the presence of censoring. In some cases, particularly when sample sizes are moderate and covariates are discrete, maximum partial likelihood estimates are infinite. This lack of finite estimators complicates the use of profile methods for estimating and testing the remaining parameters. This presentation provides a method for inference in such cases. The method builds on similar techniques in use in logistic and multinomial regression and avoids arbitrary regularization. The phenomenon of monotone likelihood is observed in the fitting process of a Cox model if the likelihood converges to a finite value while at least one parameter estimate diverges to ±∞. Monotone likelihood primarily occurs in small samples with substantial censoring of survival times and several highly predictive covariates. Previous options to deal with monotone likelihood have been unsatisfactory.