We propose a functional accelerated failure time model to characterize effects of both functional and scalar covariates on the time to event of interest, and provide regularity conditions to guarantee model identifiability. For efficient estimation of model parameters, we develop a sieve maximum likelihood approach where parametric and nonparametric coefficients are bundled with an unknown baseline hazard function in the likelihood function. Not only do the bundled parameters cause immense numerical difficulties, but they also result in new challenges in theoretical development. By developing a general theoretical framework, we overcome the challenges arising from the bundled parameters and derive the convergence rate of the proposed estimator. Furthermore, we prove that the finite-dimensional estimator is $\sqrt{n}$-consistent, asymptotically normal and achieves the semiparametric information bound. The proposed inference procedures are evaluated by extensive simulation studies and illustrated with an application to the sequential organ failure assessment data from the Improving Care of Acute Lung Injury Patients study.

翻译：我们提出了一种函数型加速失效时间模型，以刻画函数型协变量和标量协变量对感兴趣事件发生时间的影响，并提供了确保模型可识别性的正则条件。为实现模型参数的有效估计，我们开发了筛极大似然方法，其中参数和非参数系数在似然函数中与未知基线风险函数捆绑在一起。捆绑参数不仅带来了巨大的数值计算困难，还引发了理论发展中的新挑战。通过建立通用理论框架，我们克服了捆绑参数导致的挑战，并推导了所提出估计量的收敛速度。此外，我们证明了有限维估计量具有$\sqrt{n}$一致性、渐近正态性，并达到半参数信息界。所提出的推断方法通过广泛的模拟研究进行了评估，并应用于急性肺损伤患者护理改善研究中的序贯器官衰竭评估数据。