Title: Yakovlev Promotion Time Cure Model with Local Polynomial Estimation Show Chinese title

Title: 带有局部多项式估计的雅科夫列夫促进时间治愈模型

Abstract: In modeling survival data with a cure fraction, flexible modeling of covariate effects on the probability of cure has important medical implications, which aids investigators in identifying better treatments to cure. This paper studies a semiparametric form of the Yakovlev promotion time cure model that allows for nonlinear effects of a continuous covariate. We adopt the local polynomial approach and use the local likelihood criterion to derive nonlinear estimates of covariate effects on cure rates, assuming that the baseline distribution function follows a parametric form. This way we adopt a flexible method to estimate the cure rate locally, the important part in cure models, and a convenient way to estimate the baseline function globally. An algorithm is proposed to implement estimation at both the local and global scales. Asymptotic properties of local polynomial estimates, the nonparametric part, are investigated in the presence of both censored and cured data, and the parametric part is shown to be root-n consistent. The proposed methods are illustrated by simulated and real data. Show Chinese abstract

Abstract: 在包含治愈分数的生存数据分析中，灵活地建模协变量对治愈概率的影响具有重要的医学意义，这有助于研究者识别更好的治愈疗法。 本文研究了Yakovlev促进时间治愈模型的一种半参数形式，该形式允许连续协变量的非线性效应。 我们采用局部多项式方法，并利用局部似然准则推导出协变量对治愈率的非线性估计值，假设基线分布函数遵循参数形式。 这样，我们采用了一种灵活的方法来局部估计治愈率（这是治愈模型的重要部分），以及一种方便的方法来全局估计基线函数。 提出了一种算法以在局部和全局尺度上实现估计。 在存在删失数据和治愈数据的情况下，研究了局部多项式估计量（非参数部分）的渐近性质，且证明了参数部分是一致的。 所提出的方法通过模拟数据和真实数据进行了说明。