A method for analyzing disease-specific mortality with missing cause of death information

In this paper, we examine a method for analyzing competing risks data where the failure type of interest is missing or incomplete, but where there is an intermediate event, and only patients who experience the intermediate event can die of the cause of interest. In some applications, a method called "log-rank subtraction" has been applied to these problems. There has been no systematic study of this methodology, though. We investigate the statistical properties of the method and further propose a modified method by including a weight function in the construction of the test statistic to correct for potential biases. A class of tests is then proposed for comparing the disease-specific mortality in the two groups. The tests are based on comparing the difference of weighted log-rank scores for the failure type of interest. We derive the asymptotic properties for the modified test procedure. Simulation studies indicate that the tests are unbiased and have reasonable power. The results are also illustrated with data from a breast cancer study.