Time-to-event data are often subject to left-truncation. Lack of consideration of the sampling condition will introduce bias and loss in efficiency of the estimation. While auxiliary information from the same or similar cohorts may be available, challenges arise due to the practical issue of accessibility of individual-level data and taking account of various sampling conditions for different cohorts. In this paper, we introduce a likelihood-based method to incorporate information from auxiliary data to eliminate the left-truncation problem and improve efficiency. A one-step Monte-Carlo Expectation-Maximization algorithm is developed to calculate an augmented likelihood through creating pseudo-data sets which extend the form and conditions of the observed sample. The method is illustrated by both a real dataset and simulation studies.

时间到事件数据通常会被左截断。不考虑采样条件会导致估计效率的偏差和损失。虽然来自相同或相似队列的辅助信息可能可用，但由于个人层面数据的可访问性和考虑到不同队列的各种采样条件的实际问题，挑战出现了。在本文中，我们引入了一种基于似然的方法来合并来自辅助数据的信息，以消除左截断问题并提高效率。开发了一种一步蒙特卡罗期望最大化算法，通过创建扩展观察样本的形式和条件的伪数据集来计算增强的可能性。该方法通过真实数据集和模拟研究来说明。