The Mean of Lifespan under Dependent Competing Risks with Application to Mice Data

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The aim of this article is to consider the property of the mean of the theoretical lifespan of an individual in the case where competing risks are not necessarily independent.We often encounter situations in which the lifespan of an individual dying from one cause may be correlated with that of the same individual dying from a different cause. Assuming that the underlying distribution is a bivariate Weibull, an estimator of the mean of lifespan and its asymptotic distribution can be derived. The test procedure concerning independence of competing risks is given, employing asymptotic distribution of a likelihood ratio statistic. As an alternative to the above test, we present a model selection approach based on an information criterion without use of the asymptotic theory. For a specified risk,we set forth a method to test the difference between the mean lifespan of dependent competing risks and that of independent ones. Then these findings are applied to the analysis of lifespan data of mice irradiated with X-rays. The resultant testing indicates that the theoretical mean lifespans related to some causes of death are significantly shortened due to the presence of dependent competing risks. A computational method for obtaining estimates of two scale parameters, two shape parameters and acorrelated parameter is proposed.
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