We study parametric inference on a rich class of hazard regression models in the presence of right-censoring. Previous literature has reported some inferential challenges, such as multimodal or flat likelihood surfaces, in this class of models for some particular data sets. We formalize the study of these inferential problems by linking them to the concepts of near-redundancy and practical non-identifiability of parameters. We show that the maximum likelihood estimators of the parameters in this class of models are consistent and asymptotically normal. Thus, the inferential problems in this class of models are related to the finite-sample scenario, where it is difficult to distinguish between the fitted model and a nested non-identifiable (i.e., parameter-redundant) model. We propose a method for detecting near-redundancy, based on distances between probability distributions. We also employ methods used in other areas for detecting practical non-identifiability and near-redundancy, including the inspection of the profile likelihood function and the Hessian method. For cases where inferential problems are detected, we discuss alternatives such as using model selection tools to identify simpler models that do not exhibit these inferential problems, increasing the sample size, or extending the follow-up time. We illustrate the performance of the proposed methods through a simulation study. Our simulation study reveals a link between the presence of near-redundancy and practical non-identifiability. Two illustrative applications using real data, with and without inferential problems, are presented.

翻译：在右删失数据背景下，本文研究了一类丰富参数危险回归模型的推断问题。现有文献报告了此类模型在处理特定数据集时出现的推断困难，例如似然面存在多峰或平坦现象。我们通过将这些问题与参数的近冗余性和实际不可辨识性概念建立联系，对这类推断问题进行了形式化研究。本文证明该类模型中参数的最大似然估计量具有一致性和渐近正态性，因此推断问题仅存在于有限样本场景——此时难以区分拟合模型与嵌套的不可辨识（即参数冗余）模型。我们提出了一种基于概率分布距离的近冗余性检测方法，同时借鉴其他领域的技术（包括轮廓似然函数分析和Hessian矩阵方法）来检测实际不可辨识性与近冗余性。针对检测到推断问题的情形，我们探讨了替代方案：使用模型选择工具识别不存在此类问题的简约模型、增加样本量或延长随访时间。通过模拟研究验证了提出方法的有效性，该模拟揭示了近冗余性与实际不可辨识性之间的关联。最终展示了两组分别存在和不存在推断问题的真实数据应用案例。