Webb Annabel, Ma Jun
Department of Mathematics and Statistics, Macquarie University, Macquarie Park, New South Wales, Australia.
Stat Med. 2023 Mar 15;42(6):815-833. doi: 10.1002/sim.9645. Epub 2022 Dec 30.
Time-varying covariates can be important predictors when model based predictions are considered. A Cox model that includes time-varying covariates is usually referred to as an extended Cox model. When only right censoring is presented in the observed survival times, the conventional partial likelihood method is still applicable to estimate the regression coefficients of an extended Cox model. However, if there are interval-censored survival times, then the partial likelihood method is not directly available unless an imputation, such as the middle point imputation, is used to replaced the left- and interval-censored data. However, such imputation methods are well known for causing biases. This paper considers fitting of the extended Cox models using the maximum penalised likelihood method allowing observed survival times to be partly interval censored, where a penalty function is used to regularise the baseline hazard estimate. We present simulation studies to demonstrate the performance of our proposed method, and illustrate our method with applications to two real datasets from medical research.
在考虑基于模型的预测时，时变协变量可能是重要的预测因子。包含时变协变量的Cox模型通常被称为扩展Cox模型。当观察到的生存时间中仅存在右删失时，传统的偏似然方法仍可用于估计扩展Cox模型的回归系数。然而，如果存在区间删失的生存时间，那么除非使用诸如中点插补等插补方法来替换左删失和区间删失的数据，否则偏似然方法无法直接使用。然而，这种插补方法因会导致偏差而广为人知。本文考虑使用最大惩罚似然方法来拟合扩展Cox模型，该方法允许观察到的生存时间部分为区间删失，其中使用惩罚函数来正则化基线风险估计。我们进行了模拟研究以证明我们提出的方法的性能，并用医学研究中的两个真实数据集的应用来说明我们的方法。
