Statistical Inferences, Computing, and Applications of Semiparametric Accelerated Failure Time Models

加速失效时间（AFT）模型在实践中的应用要比相对风险模型少得多，因为推理困难和标准软件的可用性有限。 研究人员开发了1）适用于青少年抑郁症的多变量AFT模型的广义估计方程（GEE），2）用于设计缺失协变量的AFT模型的诱导平滑秩基方法和最小二乘法，3）用于高维协变量的AFT模型的正则化估计，以及4）用于AFT模型推断的开源，高质量和用户友好的软件实现。 GEE方法被纳入到一个迭代过程中，以估计多元AFT模型中的回归系数，初始化从一个一致的和渐近正态的估计与诱导平滑。 设计缺失协变量的推断使用适当构造的估计函数的选择权重进行。 正则化估计是通过最小化目标函数来完成的，其中三个新的风险函数的选择与各种惩罚函数相结合，包括非凸的，如极大极小凹惩罚。 由于计算和推理方面的挑战，AFT模型的方法学发展远远落后于相对风险模型。研究人员缩短了差距与全面收集的方法和软件实现的AFT模型在实际环境中，经常遇到的生物医学，流行病学和社会科学研究。预计这些方法和软件实现将对故障时间建模的实践产生重大影响。 开源实现为删失数据回归的相对风险模型提供了一个现实的替代方案。 将这些方法应用于激发拟议研究的正在进行的合作项目具有跨界影响。 抑郁持续时间和主要压力源持续时间的双变量AFT模型为深入了解抑郁发作的发生和维持提供了一个新的视角。该项目通过本科生/研究生论文咨询，研究生课程以及统计界和心理学界会议的短期课程与教育自然融合。公开可用的软件使那些在科学发现中需要它们的人可以使用尖端的统计方法。

Accelerated failure time (AFT) models are much less utilized in practice than relative risk models because of difficulty in inference and limited availability in standard software. The investigators develop 1) generalized estimating equations (GEE) for multivariate AFT models with application to adolescent depression, 2) induced smoothing rank-based approach and least squares approach for AFT models with covariates missing by design, 3) regularized estimation for AFT models with high dimensional covariates, and 4) an open source, high-quality, and user-friendly software implementation for inferences with AFT models. The GEE approach is incorporated into an iterative procedure to estimate the regression coefficients in multivariate AFT models, initializing from a consistent and asymptotically normal estimator obtained with induced smoothing. Inferences with covariates missing by design proceed with appropriately constructed selection weights for estimating functions. Regularized estimation is done by minimizing an objective function, where three novel choices of risk functions are combined with a variety of penalty functions, including nonconvex ones such as minimax concave penalty. Software implementation will be made available as R packages.Methodological development on AFT models is far behind that on relative risk models due to computational and inferential challenges. The investigators shorten the gap with a comprehensive collection of methodologies and software implementation for AFT models in practical settings that are frequently encountered in biomedical, epidemiological, and social science studies. The methodologies and software implementation are expected to have an influential impact on the practice of failure time modeling. The open source implementation provides a realistic alternative to the relative risk model for censored data regression. Applications of the methods to ongoing collaborative projects that motivated the proposed research have cross-boundary effects. A bivariate AFT model for the duration of depression and the duration of major stressors offers a novel perspective to gain insight into onset and maintenance of depressive episodes. The project is naturally integrated with education through undergraduate/graduate student thesis advising, graduate level courses, and short courses at conferences in both the statistics community and the psychology community. The publicly available software makes the cutting-edge statistical methodology accessible to those who need them in scientific discoveries.