Association Analysis for Multivariate Time-to-event Data

Association analyses are performed for two types of multivariate time-to-event data: multivariate clustered competing risks data and bivariate recurrent events data. In the first part, we extend the bivariate hazard ratio [Cheng and Fine, 2008] to multivariate competing risks data and show it is equivalent to the cause-specific cross hazard ratio in Cheng et al. [2010]. Two nonparametric approaches are proposed. One extends the plug-in estimator in Cheng and Fine [2008] and the other adapts the pseudo likelihood estimator for bivariate survival data [Clayton, 1978] to multivariate competing risks data. The asymptotic properties are established by using empirical process techniques. We compare the extended plug-in and pseudo likelihood estimators with the existing U statistic Cheng et al. [2010] by simulations and show that the three methods have comparable performance when no tied events exist. However, the plug-in estimator underestimate and the other two overestimate positive associations in the presence of rounding errors. Hence, we propose a modified U statistic for tied observations, which outperforms the other estimators by simulation studies. All methods are applied to the Cache County Study to examine mother-child and sibship associations in dementia among this aging population. The modified U essentially lies between the plug-in estimate and the original U statistic. We therefore recommend using the straightforward plug-in estimator for untied data, and using the modified U statistic when there are rounding errors. In the second part, bivariate recurrent events data are modeled by a compound Poisson process, whose dependence structure is then modeled by a Levy copula. When only the parameter of dependence structure is of primary interest, we proposed two methods to estimate the dependence parameter of the Levy copula. One uses Kendall's tau assuming the Clayton Levy copula while the other uses two-stage strategy to propose a semiparametric estimator. Consistency and asymptotic normality are also established. Simulation studies show that the proposed semi-parametric estimator is less efficient than the full likelihood estimator but superior to the nonparametric one. The proposed methods are also applied to Danish fire data to examine the relationship between loss to a building and loss to its contents