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.

本研究针对生存分析中的关键时间相关概率分布和统计方法进行了全面探讨，特别是在跌倒风险评估的背景下。通过逐步推导和澄清泊松回归与考克斯模型之间的关系，研究强调了生存模型的可解释性和实用性，表明这些模型可以有效地预测跌倒风险并分析影响因素，尤其在医疗健康领域具有重要价值。

生存分析的再审视：理解和统一在跌倒风险分析中的泊松、指数和考克斯模型