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 this paper, we consider the deterministic trend model where the error process is allowed to be weakly or strongly correlated and subject to non‐stationary volatility. Extant estimators of the trend coefficient are analysed. We find that under heteroskedasticity, the Cochrane–Orcutt‐type estimator (with some initial condition) could be less efficient than Ordinary Least Squares (OLS) when the process is highly persistent, whereas it is asymptotically equivalent to OLS when the process is less persistent. An efficient non‐parametrically weighted Cochrane–Orcutt‐type estimator is then proposed. The efficiency is uniform over weak or strong serial correlation and non‐stationary volatility of unknown form. The feasible estimator relies on non‐parametric estimation of the volatility function, and the asymptotic theory is provided. We use the data‐dependent smoothing bandwidth that can automatically adjust for the strength of non‐stationarity in volatilities. The implementation does not require pretesting persistence of the process or specification of non‐stationary volatility. Finite‐sample evaluation via simulations and an empirical application demonstrates the good performance of proposed estimators. 相似文献
The widely used empirical Bayes (EB) and full Bayes (FB) methods for before–after safety assessment are sometimes limited because of the extensive data needs from additional reference sites. To address this issue, this study proposes a novel before–after safety evaluation methodology based on survival analysis and longitudinal data as an alternative to the EB/FB method. A Bayesian survival analysis (SARE) model with a random effect term to address the unobserved heterogeneity across sites is developed. The proposed survival analysis method is validated through a simulation study before its application. Subsequently, the SARE model is developed in a case study to evaluate the safety effectiveness of a recent red‐light‐running photo enforcement program in New Jersey. As demonstrated in the simulation and the case study, the survival analysis can provide valid estimates using only data from treated sites, and thus its results will not be affected by the selection of defective or insufficient reference sites. In addition, the proposed approach can take into account the censored data generated due to the transition from the before period to the after period, which has not been previously explored in the literature. Using individual crashes as units of analysis, survival analysis can incorporate longitudinal covariates such as the traffic volume and weather variation, and thus can explicitly account for the potential temporal heterogeneity. 相似文献