Saddlepoint Approximations for Survival Analysis

回复：NSF DMS-9704570生存分析的鞍点近似值 怀俄明州大学 本研究的主要目的是开发鞍点 生存和危险函数的近似值 生物医学数据或替代地，用于工程数据的可靠性函数的近似。生存数据的建模导致复杂的等待时间，其精确分布 是难以处理的，但它们可以使用鞍点方法近似。后者是基于“高阶”渐近方法，并产生非常准确的近似密度和分布函数，然后可以结合起来，给近似的生存和危险函数。 由于计算的性质，这一方法需要大量的计算机。 生存分析主要是关于各种情况下的等待时间分布的模型。 研究者研究疾病的线性和非循环进展模型，竞争风险模型，循环行为反馈模型以及异质人群的脆弱模型。由于复杂的 在这些情况下，描述等待时间行为的分布，常规方法限于主要使用指数分布的模型。鞍点法的使用消除了这一限制，在建模中产生了更大的灵活性。 上述模型在研究各种疾病的进展方面非常有用。 例如，艾滋病毒的进展主要是从一个阶段到下一个阶段;但在某些情况下，患者可以跳过阶段，在恶化之前也会好转。 疾病的进展也使用脆弱模型进行研究，即整个人口没有相同的疾病风险的情况。例如，某些亚组比其他亚组更容易患糖尿病，或者亚组人群可能由于暴露于不同的环境因素而具有不同的风险。 同样，在不同的亚组中对疾病的进展进行建模可能会导致相当复杂的模型，这些模型会对目前使用的方法造成负担，但可以使用鞍点方法进行处理。 最后，从本研究中获得的方法很容易转换成可靠性模型，用于工程和制造。

Re: NSF DMS-9704570 Saddlepoint Approximations for Survival Analysis Snehalata V. Huzurbazar University of Wyoming The primary goal of this research is to develop saddlepoint approximations to survival and hazard functions used for bio-medical data or alternatively, approximations to reliability functions used for engineering data. Modelling of survival data results in complicated waiting times whose exact distributions are intractable but they can be approximated using saddlepoint methods. The latter are based on `higher-order' asymptotic methods and yield extremely accurate approximations for density and distribution functions which can then be combined to give approximate survival and hazard functions. The methodology is extremely computer-intensive due to the nature of the calculations. Survival analysis is primarily concerned with the modelling of waiting time distributions arising from various scenarios. The investigator studies models for linear as well as acyclic progression of diseases, models for competing risks, models with feedback for cyclic behaviour as well as frailty models for populations which are heterogeneous. Due to the complexity of the distributions that describe waiting time behaviour in these situations, conventional methods are restricted to models which mainly use the exponential distribution. Use of saddlepoint methods removes this restriction, yielding much more flexibility in modelling. The above models are tremendously useful in studying the progression of various diseases. For example, progression of the HIV virus is mainly from one stage to the next; but in some cases, patients can skip stages and also get better before getting worse. Progression of diseases is also studied using frailty models, that is, situations in which the whole population does not have the same risk for a disease. For example, certain subgroups are more susceptible to diabetes than other subgroups, or subpopulations may have different ri sks due to exposure to different environmental factors. Again, modelling the progression of a disease in the different subgroups can lead to fairly complicated models which tax currently used methodology but can be handled using saddlepoint methods. Finally, the methods obtained from this research are easily transferred into reliability models used in engineering and manufacturing.