Motivated by a breast cancer research program, this paper is concerned with the joint survivor function of multiple event times when their observations are subject to informative censoring caused by a terminating event. We formulate the correlation of the multiple event times together with the time to the terminating event by an Archimedean copula to account for the informative censoring. Adapting the widely used two-stage procedure under a copula model, we propose an easy-to-implement pseudo-likelihood based procedure for estimating the model parameters. The approach yields a new estimator for the marginal distribution of a single event time with semicompeting-risks data. We conduct both asymptotics and simulation studies to examine the proposed approach in consistency, efficiency, and robustness. Data from the breast cancer program are employed to illustrate this research.
In many real-world scenarios, an individual accepts a new piece of information based on her intrinsic interest as well as friends’ influence. However, in most of the previous works, the factor of individual’s interest does not receive great attention from researchers. Here, we propose a new model which attaches importance to individual’s interest including friends’ influence. We formulate the problem of maximizing the acceptance of information (MAI) as: launch a seed set of acceptors to trigger a cascade such that the number of final acceptors under a time constraint T in a social network is maximized. We then prove that MAI is NP-hard, and for time \(T = 1,2\), the objective function for information acceptance is sub-modular when the function for friends’ influence is sub-linear in the number of friends who have accepted the information (referred to as active friends). Therefore, an approximation ratio \((1-\frac{1}{e})\) for MAI problem is guaranteed by the greedy algorithm. Moreover, we also prove that when the function for friends’ influence is not sub-linear in the number of active friends, the objective function is not sub-modular. 相似文献