We propose a new method for the analysis of competing risks data with long term survivors. The proposed method enables us to estimate the overall survival probability and cure fraction simultaneously. We formulate the effect of covariates on cumulative incidence functions using linear transformation models. Estimating equations based on counting process are developed to estimate regression coefficients. The asymptotic properties of the estimators are studied using martingale theory. An extensive Monte Carlo simulation study is carried out to assess the finite sample performance of the proposed estimators. Finally, we illustrate our method using a real data set.

翻译：我们提出了与长期幸存者分析相互竞争的风险数据的新方法。拟议方法使我们能够同时估计总存活概率和治愈分数。我们用线性变换模型来制定共同变量对累积发生率功能的影响。根据计算过程来估计回归系数。使用马丁格尔理论来研究估计值的无症状特性。进行了广泛的蒙特卡洛模拟研究,以评估拟议的估计值的有限样本性能。最后,我们用一套真实的数据来说明我们的方法。