再探生存分析：理解并统一跌倒风险分析中的 Poisson、Exponential 与 Cox 模型
Survival Analysis Revisited: Understanding and Unifying Poisson, Exponential, and Cox Models in Fall Risk Analysis
AI总结：
本文以跌倒风险评估为例，梳理并统一 logistic、Poisson、Exponential 与 Cox 生存模型，证明生存情境下 Poisson 回归是 Cox 模型特例，突出经典模型的可解释性与医疗实用价值。
摘要：
本文探讨生存分析的基础与应用层面，并以跌倒风险评估作为案例研究。文中重新审视了与时间相关的关键概率分布和统计方法，包括 logistic 回归、Poisson 回归、Exponential 回归以及 Cox 比例风险模型，并在生存分析框架内对它们之间的关系提出统一视角。这项工作的一个贡献是逐步推导并阐明这些模型之间的关系，特别证明了在生存情境下，Poisson 回归是 Cox 模型的一个特例。这些洞见弥补了理解上的空白，并强化了生存模型的简洁性与可解释性。本文还通过将理论洞见与现实世界应用相联系，强调生存分析的实用价值。在跌倒检测情境中，文中展示了这些模型如何能够在单一精简框架内同时预测跌倒风险、分析促成因素并估计至事件发生时间的结果。相比之下，先进的深度学习方法往往需要复杂的事后解释，并且需要针对不同任务分别训练，尤其是在处理结构化数值数据时。这凸显了经典统计框架持久的现实意义，也使生存模型在医疗环境中尤其具有价值，因为在这些环境中，可解释性和稳健性至关重要。通过统一基础概念，并对至事件发生时间分析提供连贯一致的视角，本工作成为理解生存模型并将其有效应用于各类分析挑战的易读资源。
英文摘要：
This paper explores foundational and applied aspects of survival analysis, using fall risk assessment as a case study. It revisits key time-related probability distributions and statistical methods, including logistic regression, Poisson regression, Exponential regression, and the Cox Proportional Hazards model, offering a unified perspective on their relationships within the survival analysis framework. A contribution of this work is the step-by-step derivation and clarification of the relationships among these models, particularly demonstrating that Poisson regression in the survival context is a specific case of the Cox model. These insights address gaps in understanding and reinforce the simplicity and interpretability of survival models. The paper also emphasizes the practical utility of survival analysis by connecting theoretical insights with real-world applications. In the context of fall detection, it demonstrates how these models can simultaneously predict fall risk, analyze contributing factors, and estimate time-to-event outcomes within a single streamlined framework. In contrast, advanced deep learning methods often require complex post-hoc interpretation and separate training for different tasks particularly when working with structured numerical data. This highlights the enduring relevance of classical statistical frameworks and makes survival models especially valuable in healthcare settings, where explainability and robustness are critical. By unifying foundational concepts and offering a cohesive perspective on time-to-event analysis, this work serves as an accessible resource for understanding survival models and applying them effectively to diverse analytical challenges.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
