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It is shown, using the results of Slud and Rubinstein (1983, Biometrika 70, 643-649) in a specially constructed theoretical example, that competing latent failure times Ti and Ci and a two-level covariate Vi, if analyzed as though Ti and Ci are independent for each Vi level, can lead to exactly the wrong conclusion about the ordering of Pr(Ti greater than or equal to t[Vi = 1) and Pr(Ti greater than or equal to t[Vi = 0) for every t. This phenomenon can never be excluded on purely statistical grounds using such data and should be considered when interpreting data analyses involving competing risks.
Slud et al. (Tue,) studied this question.