This paper introduces a nonparametric approach for testing the equality of two or more survival distributions based on right censored failure times with missing population marks for the censored observations. The standard log-rank test is not applicable here because the population membership information is not available for the right censored individuals. We propose to use the imputed population marks for the censored observations leading to fractional at-risk sets that can be used in a two sample censored data log-rank test. We demonstrate with a simple example that there could be a gain in power by imputing population marks (the proposed method) for the right censored individuals compared to simply removing them (which also would maintain the right size). Performance of the imputed log-rank tests obtained this way is studied through simulation. We also obtain an asymptotic linear representation of our test statistic. Our testing methodology is illustrated using a real data set.
Bibliographical noteFunding Information:
The first author would like to acknowledge the research support from the University of Georgia for awarding him a Graduate School Dissertation Completion Fellowship. This research was supported in part by NIH/NCRR Grant P20 RR017696-04 and NSA Grant H98230-06-1-0062. We also thank an anonymous reviewer, the Associate Editor, and the Editor, for carefully reading the manuscript and for providing us with invaluable comments and suggestions which led to improvements.
- Equality of survival curves
- Fractional at-risk set
- Log-rank tests
- Multistate models