coxphf-package {coxphf}R Documentation

Cox Regression with Firth's Penalized Likelihood

Description

Implements Firth's penalized maximum likelihood bias reduction method for Cox regression which has been shown to provide a solution in case of monotone likelihood (nonconvergence of likelihood function). The program fits profile penalized likelihood confidence intervals which were proved to outperform Wald confidence intervals.

Details

The phenomenon of monotone likelihood in a sample causes parameter estimates of a Cox model to diverge, with infinite standard errors. Therefore, classical maximum likelihood analysis fails; the usual Wald confidence intervals cover the whole range of real numbers. Monotone likelihood appears if there is single covariate or a linear combination of covariates such that at each event time, out of all individuals being at risk at that time, the individual with the highest (or at each event time the individual with the lowest) value for that covariate or linear combination experiences the event. It was shown that analysis by Firth's penalized likelihood method, particularly in conjunction with the computation of profile likelihood confidence intervals and penalized likelihood ratio tests is superior to maximum likelihood analysis. It completely removes the convergence problem mentioned in the paragraph on CONVERGENCE of the description of the function coxph. The formula may involve time-dependent effects or time-dependent covariates. The response may be given in counting process style, but it cannot be used for multivariate failure times, as the program has no option to fit a robust covariance matrix. The user is responsible for the independency of observations within each risk set, i.e., the same individual should not appear twice within the same risk set.

The package coxphf provides a comprehensive tool to facilitate the application of Firth's penalized likelihood method to Cox regression analysis. The core routines are written in Fortran 90, (and to our knowledge this is the first package written in Fortran 90). Some description of the problem of monotone likelihood and Firth's penalized likelihood method as a solution can be found the web page https://cemsiis.meduniwien.ac.at/en/kb/science-research/software/statistical-software/fccoxphf/.

Version 1.13 now includes a convergence check and issues a warning in case of non-convergence. Profile likelihood confidence intervals or the estimation of the penalized likelihood ratio $p$-values can be vulnerable non-convergence for numerical issues. In case of non-convergence problems, we suggest to first compare the output values iter.ci with the input parameter maxit. Then, set maxstep to a smaller value, e.g., 0.1 and increase the number of allowed iterations to e.g. 500. This setting may slow down convergence for some of the confidence limits, but proved robust also in extreme data sets.

Author(s)

Georg Heinze <georg.heinze@meduniwien.ac.at> and Meinhard Ploner

References

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(1):114–119. Heinze G (1999). Technical Report 10/1999: The application of Firth's procedure to Cox and logistic regression. Section of Clinical Biometrics, Department of Medical Computer Sciences, University of Vienna, Vienna.

See Also

Useful links:

[Package coxphf version 1.13.4 Index]