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If Cox's proportional hazards regression model is used in the presence of non-proportional hazards, i.e., with underlying time-dependent hazard ratios of prognostic factors, the average relative risk for such a factor is under- or overestimated and testing power for the corresponding regression parameter is reduced. While non-proportional hazards can be accommodated by including interactions of prognostic factors with survival time, weighted estimation provides a parsimonious alternative. Weighted estimation in Cox regression extends the tests by Breslow and Prentice to a multi-covariate situation as does the Cox model to Mantel's logrank test. Weighted Cox regression can also be seen as a robust alternative to the standard Cox estimator, reducing the influence of outlying survival times on parameter estimates. Schemper (1992) first demonstrated the suitability of weighted Cox regression for estimating average hazard ratios when hazards are non-proportional,  and Sasieni (1993) extensively investigated its favorable properties.

Recent developments in this area of research by Schemper et al. (2009) have been implemented in a SAS macro WCM, which is described in a Technical Report (WCM), and in the R package coxphw (Dunkler et al, submitted), available at CRAN.



Dunkler,D., Ploner,M., Schemper, M., Heinze,G. (submitted): "Weighted Cox Regression using the R Package coxphw".

Schemper, M., Wakounig, S., Heinze, G. (2009): "The estimation of average hazard ratios by weighted Cox regression", Statistics in Medicine 28, 2473 - 2489
Sasieni, P. (1993): "Maximum Weighted Partial Likelihood Estimators for the Cox Model", Journal of the American Statistical Association 88, 144 - 152
Schemper, M. (1992): "Cox analysis of survival data with non-proportional hazard functions", The Statistician 41, 455 - 465


The R package coxphw is available under a General Public License Version 2 (GPL-2) on CRAN.

The SAS-version of WCM is free of charge. However, before download, we would like you to supply your name and e-mail address here; we may then notify you if a new version is published:


WCM: SAS macro