AI 中文总结
本文针对 promotion time 治愈率模型的单调似然问题，提出基于 Firth 偏差减少方法的修正得分函数，经模拟与真实数据集应用验证，可得到有限稳定的参数估计，使有丝分裂因子具统计显著性。
AI 中文摘要
纳入治愈比例的生存模型为联合建模治愈分布与生存分布提供了灵活框架。然而当数据包含高比例删失观测或高度不平衡的二元协变量时，极大似然估计可能变得不稳定，导致参数估计值发散至无穷大。该现象在文献中通常被称为单调似然，因不存在有限的极大似然估计而破坏了统计推断。具体而言，似然函数在参数空间的某些方向上单调递增，故不存在有限的最大化值。据作者所知，单调似然问题在涉及 promotion time 模型的情境中几乎未受到关注。本文针对这一空白，基于 Firth 偏差减少方法提出修正得分函数，调整估计过程以确保得到有限且稳定的参数估计。通过广泛的蒙特卡洛模拟研究评估所提方法的性能，对真实数据集的应用进一步证明其实际优势：在该方法下，已确立的预后标志物有丝分裂因子具有统计显著性。
英文摘要
Survival models that incorporate a cure fraction provide a flexible framework for jointly modeling the cure and the survival distributions. However, when the data comprise a high proportion of censored observations or highly unbalanced binary covariates, maximum likelihood estimation may become unstable, leading to parameter estimates that diverge to infinity. This phenomenon, commonly referred to in the literature as monotone likelihood, compromises statistical inference by precluding the existence of finite maximum likelihood estimates. Specifically, the likelihood function increases monotonically along certain directions in the parameter space, so no finite maximizer exists. To the best of our knowledge, the monotone likelihood problem has received little or no attention in the context involving the promotion time model. This paper addresses this gap by proposing a modified score function based on Firth's bias-reduction method, which adjusts the estimation procedure to ensure finite and stable parameter estimates. The performance of the proposed approach is evaluated through extensive Monte Carlo simulation studies. An application to a real dataset further demonstrates its practical advantages, showing that the mitosis factor, an established prognostic marker, becomes statistically significant under the proposed methodology.
