导出一个分析解决方案的反转的罗伊斯顿/帕马尔限制立方支线参数生存模型对离散事件模拟
George Bungey1, Jorgen Moller2, James Saunders3
1Evidera, part of Thermo Fisher Scientific, Second Floor, The Ark, 201 Talgarth Road, London, W6 8BJ, UK. george.bungey@thermofisher.com.
PharmacoEconomics
|December 4, 2025
概括
研究人员为罗伊斯顿/帕马尔限制立方线模型获得了分析解决方案,通过能够精确地估计事件时间,显著加快离散事件模拟 (DES). 微软Excel中的这种分析反转方法比数值近似方法快得多.
科学领域:
- 生物统计学 生物统计学
- 计算统计学 计算统计学
- 生存分析的分析.
背景情况:
- 离散事件模拟 (DES) 模型需要事件时间,通常来自生存函数.
- 参数生存模型通常提供累积的生存概率,需要对事件时间进行生存函数反转.
- 对反转的数值方法在计算上可能很昂贵,特别是在大规模的模拟中.
研究的目的:
- 为了推导一个用于逆转罗伊斯顿/帕马尔限制立方线生存模型的分析解决方案.
- 将这个分析解决方案的计算速度与微软Excel中的数值方法 (目标搜索,布伦特算法) 进行比较.
- 评估对事件时间生成的离散事件模拟速度的影响.
主要方法:
- 开发了Royston/Parmar限制立方线反函数的分析解决方案,根据生存估计与模型节点相对的定位处理不同的情况.
- 在微软Excel中实现了分析解决方案作为应用程序视觉基础 (VBA) 用户定义的函数.
- 与Goal Seek (默认和高精度) 和使用结肠癌数据进行100多次复制的混合布伦特方法进行执行速度比较.
主要成果:
- 分析解决方案VBA函数实现了0.612秒的平均执行时间.
- 这比Goal Seek (10.567s和12.230s) 和混合布伦特方法 (1.140s) 快得多.
- 分析解决方案显示,平均执行时间减少了94.2% (与默认目标搜索相比),95.0% (与高精度目标搜索相比) 和46.3% (与布伦特方法相比).
结论:
- 罗伊斯顿/帕马尔限制立方线模型的分析反转提供了精确的事件时间估计,并显著加快了Excel中的离散事件模拟.
- 衍生出来的分析溶液也可以帮助创建一个量子函数.
- 建议进行进一步的研究,以评估其他软件 (如R) 的性能,并扩展到时间变化的共变量.
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