Tsodikov A
Huntsman Cancer Institute, University of Utah, Salt Lake City 84108, USA.
Biometrics. 1998 Dec;54(4):1508-16.
A proportional hazards (PH) model is modified to take account of long-term survivors by assuming the cumulative hazard to be bounded but otherwise unspecified to yield an improper survival function. A marginal likelihood is derived under the restriction for type I censoring patterns. For a PH model with cure, the marginal and the partial likelihood are not the same. In the absence of covariate information, the estimate of the cure rate based on the marginal likelihood reduces to the value of the Kaplan-Meier estimate at the end of the study. An example of low asymptotic efficiency of the partial likelihood as compared to the marginal, profile, and parametric likelihoods is given. An algorithm is suggested to fit the full PH model with cure.
通过假设累积风险有界但其他方面未指定以产生一个不恰当的生存函数，对比例风险（PH）模型进行修改，以考虑长期存活者。在对I型删失模式的限制下推导出边际似然。对于具有治愈情况的PH模型，边际似然和偏似然并不相同。在没有协变量信息的情况下，基于边际似然的治愈率估计在研究结束时简化为Kaplan-Meier估计的值。给出了一个与边际、轮廓和参数似然相比偏似然渐近效率较低的例子。建议使用一种算法来拟合具有治愈情况的完整PH模型。
