Nonparametric interaction test with censored data

两个变量之间交互作用的检验在许多实际领域都很有意义。例如，在临床试验中，经常需要进行亚组分析，以评估治疗效果在所有患者亚组中是否一致，或者确定从治疗中特别受益的一组患者。在这项建议中，我们将考虑基于经审查的生存数据的交互作用的检验。在当前的医学应用中，这几乎完全基于Cox比例风险模型，该模型要求假设比例风险，而临床数据可能不满足该假设。因此，需要一种替代方法，特别是在统计检验或实际背景表明可能违反这一假设的情况下。我们首先建议在两个二元自变量的背景下简化一些用于因子生存研究的一般非参数方法，并构造检验统计量的刀刀方差估计，这将使应用统计学家更容易使用这些方法。此外，我们还将基于我们最近导出的交互作用的非参数度量的平滑估计或风险比的核估计来开发新的非参数检验程序。我们将讨论诸如带宽选择等实际问题，并将使用Bootstrap等重抽样方法来逼近所得到的新检验统计量的分布。将进行广泛的模拟，以评估和比较所有这些方法的实际显著性水平(I类错误)和威力(1-II类错误)。将开发执行这些程序的软件。希望这项研究将为参与实际研究的应用统计学家提供新的工具，并为这些统计方法在实际领域的应用奠定坚实的理论基础，以确保这些方法得出的结论准确可靠。

The test of interaction between two variables is of interest in many practical fields.  For example, in clinical trials, it is often of interest to perform subgroup analyses to assess whether treatment effect is uniform in all patient subgroups or to identify a subgroup of patients who particularly benefit from the treatment.  In this proposal, we will consider the test of interaction based on censored survival data.  In current medical applications, this is done almost exclusively based on the Cox proportional hazard models that require an assumption of proportional hazards that may not be satisfied by the clinical data.  An alternative method is needed, especially if the statistical test or practical background indicates possible violation of this assumption. We propose first to simplify some general nonparametric methods proposed for the factorial survival studies in the context of two binary independent variables and to construct the jackknife variance estimate for the test statistics, which would make these methods more accessible to applied statisticians.  New nonparametric test procedures will also be developed based on the smoothed estimate for a nonparametric measure of the interaction or the kernel estimate of the hazard ratio we derived recently.  Practical issues such as bandwidth selection will be discussed and the resampling method such as bootstrap will be used to approximate the distribution of the new test statistics derived. Extensive simulations will be performed to evaluate and compare all of these procedures in terms of actual significance level (type I error) and power (1-type II error).  The software implementing these procedures will be developed.  It is expected this research will provide new tools to the applied statisticians involved in the practical research and also build a solid theoretical foundation for the applications of these statistical methods in the practical fields to ensure that conclusions drawn with these methods are accurate and reliable.