Multiple imputation methods for modelling relative survival data

In population-based cancer survival studies, the cause-specific survival measures the net survival (excess mortality) due to cancer when the cause of death information is available and reliable. In contrast, when the cause of death is uncertain or unavailable, relative survival, the ratio of the survival rate due to all causes to the expected survival rate, is more appropriate. There is a large body of work on the modelling and hypothesis testing of cause-specific survival, but many of these methods are not directly applicable to relative survival. In this paper, we extend the multiple imputation (MI) methods (Stat. Methods Med. Res. 1999; 8:3-15) to the case of relative survival data. The MI methodology is combined with relative survival to estimate the net survival by changing relative survival data to cause-specific data. This facilitates the direct application to statistical methods developed for the cause-specific survival to the special situation of relative survival. The parameter estimates and the log-rank statistics are obtained by combining the results from multiple imputed cause-specific data. The likelihood-based methods for modelling relative survival data have been implemented by a Windows application called CANSURV (Comput. Meth. Prog. Biomed 2005). Although these methods produce accurate parameter estimates, the choice for models and diagnostic tools is limited. The MI method is presented as a simpler alternative. The relative survival data for the colorectal cancer patients from Surveillance, Epidemiology, and End Results (SEER) program (SEER Cancer Statistics Review, 1973-1999. National Cancer Institute: Bethesda, 2002) is used as an illustration. The results are compared with those obtained from the likelihood-based relative survival analysis methods. A sample SAS macro for the MI method is provided.