Measuring Explained Variation in Survival Analysis

项目总结 尽管在癌症研究中广泛使用生存分析来构建癌症的预后因素和 确定癌症复发或治疗后存活的风险因素，对于如何衡量还没有达成共识。 由可用因素解释的事件时间的变化。的系数的许多相似度量 确定，也称为R平方，已被提出用于比例风险模型。然而，一些人 度量的上界是一个远小于1的值，即使是在可用因素确定的时间内， 而其他人对错误相关的因素过于敏感。另一方面，对这方面的研究也很有限。 加速故障时间模型的措施，据我们所知，唯一提出的措施 最近的是基于将总的变化参数划分为可解释和未解释的部分，假设 真正的模式是已知的。为了解决这一问题，本项目的目标是制定适当的统计数据，以 测量事件时间的变化，在流行的权利审查机制下，由可用因素解释。 这一建议的前提是可以用一个方差函数来描述变化的相关性 在相关均值上，并量化了沿方差函数的变化可以度量解释 异方差事件时间的变化。在最近关于广义线性模型的工作中，证明了 基于变量函数的R平方恰当地度量了非高斯的解释变化 回应。在这种成功的扩展的基础上，这里提出的为期两年的研究重点是 遵循两个具体目标：目标1。测量加速失效时间模型的解释偏差。而当 每个加速失效时间模型呈现一个二次方差函数，团队将构造变量- 这种生存模型的基于函数的R-平方，通过适当的积分或 调整。将加速失效时间模型视为删失线性回归模型，这些研究将 还扩展了经典的R平方，对审查问题进行了适当的管理。目标2.测量解释 比例风险模型的变异。以偏似然函数作为 条件Logistic模型中，研究人员将基于变量函数的R平方构造为相关变量 条件Logistic模型，以衡量潜在比例风险的解释差异 模特。此外，该团队将通过测量一个变量的变化来构建一个基于方差函数的R平方 潜在的生存过程，在每个特定的时间呈现一个二进制随机变量。严谨的 模拟癌症研究和真实癌症研究的实验将被设计来验证所提出的措施 在癌症研究中跨越不同的模型。拟议的措施将在可供公众查阅的 R包RSQ，为癌症研究人员提供了进行必要的生存分析的有用工具。这个 该项目的成功最终将有助于量化和了解不同癌症的遗传性。

PROJECT SUMMARY Despite the widely used survival analysis in cancer research for constructing prognostic factors for cancers and identifying risk factors for cancer recurrence or survival after treatment, there is no consensus on how to measure variations of event times explained by available factors. Many analogous measures of the coefficient of determination, also known as R-squared, have been proposed for proportional hazard models. However, some measures are up bounded by a value much smaller than one, even for a time determined by available factors, and others are too sensitive for falsely correlated factors. On the other hand, research is limited on such measures for accelerated failure time models, and to the best of our knowledge, the only measure proposed recently is based on parametrically partitioning the total variation into explained and unexplained parts, assuming that the true model is known. To address this issue, the objective of this project is to develop proper statistics to measure the variation of event times, under popular right censoring mechanisms, explained by available factors. The premise of this proposal is that a variance function can be employed to describe the dependence of variation on the pertinent mean, and quantifying the variation change along the variance function can measure explained variation of heteroscedastic event times. In recent work on generalized linear models, it was demonstrated that a variable-function-based R-squared appropriately measures the explained variation of non-Gaussian responses. Riding on such successful extension, the two-year research study proposed here focuses on the following two specific aims: Aim 1. To measure explained variation for accelerated failure time models. While each accelerated failure-time model presents a quadratic variance function, the team will construct the variable- function-based R-squared for such survival models, by addressing censoring issues via proper integration or adjustment. Treating accelerated failure-time models as censored linear regression models, these studies will also extend the classical R-squared with proper management of censoring issues. Aim 2. To measure explained variation for proportional hazards models. With the partial likelihood function as the likelihood function of a conditional logistic model, the investigators will construct the variable-function-based R-squared for the pertinent conditional logistic model in order to measure the explained variation in the underlying proportional hazards model. In addition, the team will construct a variance-function-based R-squared by measuring variation of an underlying survival process, which presents a binary random variable at each specific time. A rigorous experiment with both simulation and real cancer studies, will be designed to validate the proposed measures across different models in cancer research. The proposed measures will be implemented in a publicly available R package rsq, providing cancer researchers a useful tool to conduct the necessary survival analysis. The success of this project will ultimately help quantify and understand the heritability of different cancers.