Cure rate survival models with missing covariates: a simulation study

Abstract

In this paper we study the cure rate survival model involving a competitive risk structure with missing categorical covariates. A parametric distribution that can be written as a sequence of one-dimensional conditional distributions is specified for the missing covariates. We consider the missing data at random situation so that the missing covariates may depend only on the observed ones. Parameter estimates are obtained by using the EM algorithm via the method of weights. Extensive simulation studies are conducted and reported to compare estimates efficiency with and without missing data. As expected, the estimation approach taking into consideration the missing covariates presents much better efficiency in terms of mean square errors than the complete case situation. Effects of increasing cured fraction and censored observations are also reported. We demonstrate the proposed methodology with two real data sets. One involved the length of time to obtain a BS degree in Statistics, and another about the time to breast cancer recurrence.

Keywords:

• survival analysis
• cure rate
• missing data
• EM algorithm

Acknowledgements

We wish to thank the associate editor and the referee for their interest and insightful comments on earlier drafts of the paper. This research was supported in part by the CAPES and CNPq, Brazil.