Discussion

The proposed method is based on martingales properties. Our results for estimating the martingales covariance under null hypothesis are similar to those of [PRE92] when there is no censoring, but differ in the censored case, because their estimator is expressed with an estimator of the joint survival function of the two times to failure. In particular, their estimator of E {dMkji(u)dMk'ji(v)} for k = k' leads to

E{dMl(u)} = F k (u)dAk (u), that tends to under-estimate the classical variance of a martingale as the survival function estimate for event k is necessarily lower than 1. We also would like to point out that the Wei and Lachin variance covariance matrix estimator of vector (LR1,LR2)' under null hypothesis does not use the fact that under Ho the marginal survival functions are equal in groups A and B, since their estimator is derived from averaging martingale residuals over subjects in each group and not over the whole sample.

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