概率减压模型中的风险函数优化和验证方法

Optimization and Validation Methods for Risk Functions in Probabilistic Decompression Models

摘要: 背景：概率减压模型可量化评估潜水后发生减压病的概率。风险函数是概率减压模型的核心组成部分，其数学形式显著影响模型预测质量。方法：文章设计构建了多种不同形式的风险函数，随后选取猪的饱和潜水实验数据作为验证样本，采用指数–指数动力学模型计算组织张力，结合平行理论组织模型模拟不同组织的风险积累差异；采用生存分析方法，通过对瞬时风险函数积分量化整个潜水过程的风险，进而计算发生减压病的概率；通过构建对数似然函数，最大化对数似然值以优化参数。利用AICc校验权衡模型的复杂度和拟合数据的优良性最终筛选出该实验场景下表现最优的几类风险函数。结果：引入非线性指数项与生理阈值项的风险函数在区分能力与校准性方面均表现出较为理想的效果。结论：本研究采用的风险函数优化与验证方法表现优异，具备拓展应用于构建其他潜水减压概率模型的潜力。

Abstract: Background: Probabilistic decompression models enable quantitative assessment of the probability of decompression sickness (DCS) following diving exposure. As the core component of a probabilistic decompression model, the mathematical formulation of the risk function exerts a significant impact on the model’s predictive performance. Methods: In this paper, multiple risk functions with distinct mathematical forms were designed and constructed. Experimental data from porcine saturation diving trials were selected as the validation dataset. Tissue tension was calculated using an exponential-exponential kinetic model, and a parallel theoretical tissue model was adopted to simulate the heterogeneity of risk accumulation across different tissues. Based on survival analysis principles, the total risk over the entire diving profile was quantified via integration of the instantaneous hazard function, from which the probability of DCS occurrence was derived. A log-likelihood function was established, and parameter optimization was performed by maximizing the log-likelihood value. The corrected Akaike Information Criterion (AICc) was applied to balance model complexity and goodness-of-fit, to ultimately screen out the risk functions with optimal performance under this experimental scenario. Results: The risk function incorporating a nonlinear exponential term and a physiological threshold term achieved favorable and robust performance in both discrimination and calibration. Conclusion: The optimization and validation methodology for risk functions adopted in this paper exhibits excellent performance and holds broad potential for extended application in the development of other probabilistic diving decompression models.