Orbe Jesus, Virto Jorge
Department of Econometrics and Statistics, University of the Basque Country UPV/EHU, Bilbao, Spain.
Biom J. 2018 Sep;60(5):947-961. doi: 10.1002/bimj.201700213. Epub 2018 Jun 25.
In this paper, we consider the problem of nonparametric curve fitting in the specific context of censored data. We propose an extension of the penalized splines approach using Kaplan-Meier weights to take into account the effect of censorship and generalized cross-validation techniques to choose the smoothing parameter adapted to the case of censored samples. Using various simulation studies, we analyze the effectiveness of the censored penalized splines method proposed and show that the performance is quite satisfactory. We have extended this proposal to a generalized additive models (GAM) framework introducing a correction of the censorship effect, thus enabling more complex models to be estimated immediately. A real dataset from Stanford Heart Transplant data is also used to illustrate the methodology proposed, which is shown to be a good alternative when the probability distribution for the response variable and the functional form are not known in censored regression models.
在本文中，我们考虑在删失数据的特定背景下的非参数曲线拟合问题。我们提出了一种惩罚样条方法的扩展，使用Kaplan-Meier权重来考虑删失的影响，并采用广义交叉验证技术来选择适用于删失样本情况的平滑参数。通过各种模拟研究，我们分析了所提出的删失惩罚样条方法的有效性，并表明其性能相当令人满意。我们已将此提议扩展到广义相加模型（GAM）框架，引入了对删失效应的校正，从而能够立即估计更复杂的模型。还使用了来自斯坦福心脏移植数据的真实数据集来说明所提出的方法，结果表明，在删失回归模型中响应变量的概率分布和函数形式未知时，该方法是一个很好的选择。
