We consider the nonparametric maximum likelihood estimation for the underlying event time based on mixed-case interval-censored data, under a log-concavity assumption on its distribution function. This generalized framework relaxes the assumptions of a log-concave density function or a concave distribution function considered in the literature. A log-concave distribution function is fulfilled by many common parametric families in survival analysis and also allows for multi-modal and heavy-tailed distributions. We establish the existence, uniqueness and consistency of the log-concave nonparametric maximum likelihood estimator. A computationally efficient procedure that combines an active set algorithm with the iterative convex minorant algorithm is proposed. Numerical studies demonstrate the advantages of incorporating additional shape constraint compared to the unconstrained nonparametric maximum likelihood estimator. The results also show that our method achieves a balance between efficiency and robustness compared to assuming log-concavity in the density. An R package iclogcondist is developed to implement our proposed method.

翻译：我们考虑在分布函数满足对数凹性假设下，基于混合型区间删失数据对潜在事件时间进行非参数极大似然估计。这一广义框架放宽了现有文献中考虑的对数凹密度函数或凹分布函数的假设条件。对数凹分布函数被生存分析中的许多常见参数族所满足，同时也允许多峰分布和重尾分布。我们证明了对数凹非参数极大似然估计量的存在性、唯一性和相合性。提出了一种结合主动集算法与迭代凸小值算法的计算高效流程。数值研究表明，相较于无约束的非参数极大似然估计量，引入额外形状约束具有显著优势。结果还显示，与假设密度函数对数凹性的方法相比，我们的方法在效率与稳健性之间取得了平衡。我们开发了R软件包iclogcondist以实现所提出的方法。