In survival analysis, accelerated failure time models are useful in modeling the relationship between failure times and the associated covariates, where covariate effects are assumed to appear in a linear form in the model. Such an assumption of covariate effects is, however, quite restrictive for many practical problems. To incorporate flexible nonlinear relationship between covariates and transformed failure times, we propose partially linear single index models to facilitate complex relationship between transformed failure times and covariates. We develop two inference methods which handle the unknown nonlinear function in the model from different perspectives. The first approach is weakly parametric which approximates the nonlinear function globally, whereas the second method is a semiparametric quasi-likelihood approach which focuses on picking up local features. We establish the asymptotic properties for the proposed methods. A real example is used to illustrate the usage of the proposed methods, and simulation studies are conducted to assess the performance of the proposed methods for a broad variety of situations.

中文翻译：

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灵活的模型类别下生存数据的参数和半参数估计方法。

在生存分析中，加速失效时间模型可用于建模失效时间与相关协变量之间的关系，其中协变量效应被假定为以线性形式出现在模型中。然而，这种协变量效应的假设对于许多实际问题来说是非常严格的。为了合并协变量和转换失败时间之间的灵活非线性关系，我们提出了部分线性单指数模型，以促进转换失败时间和协变量之间的复杂关系。我们开发了两种从不同角度处理模型中未知非线性函数的推理方法。第一种方法是弱参数化，可以全局近似非线性函数，而第二种方法是半参数拟似然方法，其重点是拾取局部特征。我们建立了所提出方法的渐近性质。一个真实的例子用来说明所提出的方法的用法，并进行了仿真研究以评估所提出方法在各种情况下的性能。