Interval-censored failure time data arise in a number of fields and many authors have recently paid more attention to their analysis. However, regression analysis of interval-censored data under the additive risk model can be challenging in maximizing the complex likelihood, especially when there exists a non-ignorable cure fraction in the population. For the problem, we develop a sieve maximum likelihood estimation approach based on Bernstein polynomials. To relieve the computational burden, an expectation–maximization algorithm by exploiting a Poisson data augmentation is proposed. Under some mild conditions, the asymptotic properties of the proposed estimator are established. The finite sample performance of the proposed method is evaluated by extensive simulations, and is further illustrated through a real data set from the smoking cessation study.

间隔删失的失效时间数据出现在许多领域，许多作者最近更加关注他们的分析。然而，在加性风险模型下对区间删失数据进行回归分析在最大化复杂可能性方面可能具有挑战性，尤其是当人群中存在不可忽略的治愈分数时。对于这个问题，我们开发了一种基于伯恩斯坦多项式的筛子最大似然估计方法。为了减轻计算负担，提出了一种利用泊松数据增强的期望最大化算法。在一些温和的条件下，所提出的估计量的渐近性质成立。通过广泛的模拟评估了所提出方法的有限样本性能，