Testing the Independence of Competing Risks: An Application to the Analysis of Breast Cancer Recurrence

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Abstract
As evidenced by the results of data analysis the contralateral breast cancer recurrence is most likely to originate from subclinical tumor foci that preexist at the time of treatment This raises the natural question as to whether the rtcumnas in the contralateral breast evolve independently of those in the ipsilateral breast It is common knowledge in the theory of competing risks that this problem can not be solved within the nonparaoretric framework. To overcome the obstacle om needs to proceed from a biologically‐based parametric model of tumor latency. We explore this possibility with a model proposed earlier (HOANG et al., 1992). When incorporated into a family of joint distributions with given marginal distributions for the tumor latency times, the model allows testing the independencc hypothesis by the likelihood ratio test Our analysis of data on the ipsilateral and contralateral breast recurrence, though being conclusive only under the model assumptions, suggests that the dependence of risks is negligible for the two typcs of local failure.AMS 1980 subject classification