Nonparametric interaction test with censored data

两个变量之间相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，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，或者确定特别受益于治疗的患者亚组通常是有意义的。 在这个建议中，我们将考虑基于删失生存数据的交互作用检验。 在当前的医学应用中，这几乎完全是基于考克斯比例风险模型来完成的，该模型需要比例风险的假设，而临床数据可能不满足该假设。 需要一种替代方法，特别是如果统计检验或实际背景表明可能违反这一假设。我们建议首先简化一些一般的非参数方法提出的阶乘生存研究的背景下，两个二进制的独立变量，并构造刀切方差估计的检验统计量，这将使这些方法更容易应用统计学家。 新的非参数检验程序也将开发的基础上平滑估计的非参数测量的相互作用或核估计的风险比，我们最近得到的。 实际问题，如带宽的选择将被讨论，并将使用自举的restaurant方法，如近似的新的测试统计量的分布派生。将进行广泛的模拟，以评价和比较所有这些程序的实际显著性水平（I类错误）和功效（1-II类错误）。 将开发执行这些程序的软件。 期望本研究能为从事实际研究的应用统计学家提供新的工具，也为这些统计方法在实际领域的应用奠定坚实的理论基础，确保用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.