Department of Haematology, Aalborg University Hospital, Aalborg, Denmark.
Department of Clinical Medicine, Aalborg University, Aalborg, Denmark.
Stat Methods Med Res. 2020 Sep;29(9):2683-2696. doi: 10.1177/0962280220910193. Epub 2020 Mar 17.
In time to event studies, censoring often occurs and models that take this into account are wide-spread. In the presence of outliers, standard estimators of model parameters may be affected such that results and conclusions are not reliable anymore. This in turn also hampers the detection of these outliers due to masking effects. To cope with outliers when using proportional hazard models, we propose to use the Brier score as a loss function. Since the coefficients often vary over time, we focus on the piecewise constant hazard model, which can flexibly model time-varying coefficients if a large number of cut-points is used. To prevent overfitting, we add a penalty term that potentially shrinks time-varying effects to constant effects. By fitting the coefficients of the piecewise constant hazard model using a penalized Brier score loss, we obtain a robust model that can handle time-varying coefficients. Its good performance is illustrated in a simulation study and using two datasets from practice.
在生存时间研究中，通常会发生删失，并且广泛使用考虑这种情况的模型。在存在异常值的情况下，模型参数的标准估计量可能会受到影响，从而导致结果和结论不再可靠。这反过来也会由于掩蔽效应而阻碍异常值的检测。为了在使用比例风险模型时处理异常值，我们建议使用 Brier 得分作为损失函数。由于系数经常随时间变化，我们专注于分段常数风险模型，如果使用大量的分割点，它可以灵活地对时变系数进行建模。为了防止过拟合，我们添加一个惩罚项，将时变效应潜在地收缩为常数效应。通过使用惩罚 Brier 得分损失拟合分段常数风险模型的系数，我们得到了一个稳健的模型，可以处理时变系数。它的良好性能在一项模拟研究和两个实际数据集上得到了说明。
