Survival Analysis Revisited: Understanding and Unifying Poisson, Exponential, and Cox Models in Fall Risk Analysis

• URL: http://arxiv.org/abs/2501.03058v1
• Date: Mon, 06 Jan 2025 14:48:30 GMT
• Title: Survival Analysis Revisited: Understanding and Unifying Poisson, Exponential, and Cox Models in Fall Risk Analysis
• Authors: Tianhua Chen,
• Abstract summary: This paper revisits key time-related probability distributions and statistical methods, including logistic regression, Poisson regression, Exponential regression, and the Cox Proportional Hazards model. Step-by-step derivation and clarification of the relationships among these models reinforce the simplicity and interpretability of survival models. 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.
• Score: 2.251754456289066
• License:
• Abstract: 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.

Related papers

• HACSurv: A Hierarchical Copula-based Approach for Survival Analysis with Dependent Competing Risks [51.95824566163554]
  HACSurv is a survival analysis method that learns structures and cause-specific survival functions from data with competing risks. By capturing the dependencies between risks and censoring, HACSurv achieves better survival predictions.
  arXiv  Detail & Related papers  (2024-10-19T18:52:18Z)
• Interpretable Survival Analysis for Heart Failure Risk Prediction [50.64739292687567]
  We propose a novel survival analysis pipeline that is both interpretable and competitive with state-of-the-art survival models. Our pipeline achieves state-of-the-art performance and provides interesting and novel insights about risk factors for heart failure.
  arXiv  Detail & Related papers  (2023-10-24T02:56:05Z)
• Contrastive Learning of Temporal Distinctiveness for Survival Analysis in Electronic Health Records [10.192973297290136]
  We propose a novel Ontology-aware Temporality-based Contrastive Survival (OTCSurv) analysis framework. OTCSurv uses survival durations from both censored and observed data to define temporal distinctiveness. We conduct experiments using a large EHR dataset to forecast the risk of hospitalized patients who are in danger of developing acute kidney injury (AKI)
  arXiv  Detail & Related papers  (2023-08-24T22:36:22Z)
• Inducing Causal Structure for Abstractive Text Summarization [76.1000380429553]
  We introduce a Structural Causal Model (SCM) to induce the underlying causal structure of the summarization data. We propose a Causality Inspired Sequence-to-Sequence model (CI-Seq2Seq) to learn the causal representations that can mimic the causal factors. Experimental results on two widely used text summarization datasets demonstrate the advantages of our approach.
  arXiv  Detail & Related papers  (2023-08-24T16:06:36Z)
• Temporal Relevance Analysis for Video Action Models [70.39411261685963]
  We first propose a new approach to quantify the temporal relationships between frames captured by CNN-based action models. We then conduct comprehensive experiments and in-depth analysis to provide a better understanding of how temporal modeling is affected.
  arXiv  Detail & Related papers  (2022-04-25T19:06:48Z)
• Adversarially Robust Estimate and Risk Analysis in Linear Regression [17.931533943788335]
  Adversarially robust learning aims to design algorithms that are robust to small adversarial perturbations on input variables. By discovering the statistical minimax rate of convergence of adversarially robust estimators, we emphasize the importance of incorporating model information. We propose a straightforward two-stage adversarial learning framework, which facilitates to utilize model structure information to improve adversarial robustness.
  arXiv  Detail & Related papers  (2020-12-18T14:55:55Z)
• Targeting Learning: Robust Statistics for Reproducible Research [1.1455937444848387]
  Targeted Learning is a subfield of statistics that unifies advances in causal inference, machine learning and statistical theory to help answer scientifically impactful questions with statistical confidence. The roadmap of Targeted Learning emphasizes tailoring statistical procedures so as to minimize their assumptions, carefully grounding them only in the scientific knowledge available.
  arXiv  Detail & Related papers  (2020-06-12T17:17:01Z)
• A General Framework for Survival Analysis and Multi-State Modelling [70.31153478610229]
  We use neural ordinary differential equations as a flexible and general method for estimating multi-state survival models. We show that our model exhibits state-of-the-art performance on popular survival data sets and demonstrate its efficacy in a multi-state setting.
  arXiv  Detail & Related papers  (2020-06-08T19:24:54Z)
• Survival Cluster Analysis [93.50540270973927]
  There is an unmet need in survival analysis for identifying subpopulations with distinct risk profiles. An approach that addresses this need is likely to improve characterization of individual outcomes.
  arXiv  Detail & Related papers  (2020-02-29T22:41:21Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.