The best known methods for estimating hazard rate functions in survival analysis models are either purely parametric or purely nonparametric. The parametric ones are sometimes too biased while the nonparametric ones are sometimes too variable. In the present paper a certain semiparametric approach to hazard rate estimation, proposed in Hjort (1991), is developed further, aiming to combine parametric and nonparametric features. It uses a dynamic local likelihood approach to fit the locally most suitable member in a given parametric class of hazard rates, and amounts to a version of nonparametric parameter smoothing within the parametric class. Thus the parametric hazard rate estimate at time $s$ inserts a parameter estimate that also depends on $s$. We study bias and variance properties of the resulting estimator and methods for choosing the local smoothing parameter. It is shown that dynamic likelihood estimation often leads to better performance than the purely nonparametric methods, while also having capacity for not losing much to the parametric methods in cases where the model being smoothed is adequate.

翻译：生存分析模型中估计风险率函数的最著名方法要么是完全参数化的，要么是完全非参数化的。参数化方法有时偏差过大，而非参数化方法有时变异性过高。本文进一步发展了Hjort（1991）提出的某种半参数化风险率估计方法，旨在结合参数化和非参数化特征。该方法采用动态局部似然方法，在给定的参数化风险率类别中拟合局部最合适的成员，本质上相当于在参数化类别内进行非参数化参数平滑的一种形式。因此，时间$s$处的参数化风险率估计会插入一个同样依赖于$s$的参数估计量。我们研究了所得估计量的偏差与方差特性，以及选择局部平滑参数的方法。研究表明，动态似然估计通常比纯粹的非参数化方法具有更好的性能，同时在所平滑模型适用的情况下，其表现也不会显著逊色于参数化方法。