Loughin T M
Department of Statistics and Statistical Laboratory, Kansas State University, Manhattan 66506, USA.
Lifetime Data Anal. 1998;4(4):393-403. doi: 10.1023/a:1009686119993.
Recent literature has provided encouragement for using the bootstrap for inference on regression parameters in the Cox proportional hazards (PH) model. However, generating and performing the necessary partial likelihood computations on multitudinous bootstrap samples greatly increases the chances of incurring problems with monotone likelihood at some point in the analysis. The only symptom of monotone likelihood may be a failure to converge in the numerical maximization procedure, and so the problem might naïvely be dismissed by deleting the offending data set and replacing it with a new one. This strategy is shown to lead to potentially high selection biases in the subsequent summary statistics. This note discusses the importance of keeping track of these monotone likelihood cases and provides recommendations for their use in interpreting bootstrap findings, and for avoiding unwanted biases that may result from high rates of occurrence. In many cases, high monotone likelihood rates indicate that a more highly-specified model may be preferred. Special consideration is given to the problem of high monotone likelihood incidence in Monte Carlo studies of the bootstrap.
近期文献鼓励在Cox比例风险（PH）模型中使用自助法对回归参数进行推断。然而，在大量自助样本上生成并执行必要的偏似然计算，会大大增加在分析过程中的某个时刻出现单调似然问题的几率。单调似然的唯一症状可能是数值最大化过程中无法收敛，因此，这个问题可能会被简单地通过删除有问题的数据集并替换为新数据集而忽略。结果表明，这种策略会导致后续汇总统计中潜在的高选择偏差。本说明讨论了跟踪这些单调似然情况的重要性，并为在解释自助法结果时使用它们以及避免可能因高发生率而产生的不必要偏差提供了建议。在许多情况下，高单调似然率表明可能更倾向于使用一个更具特定性的模型。本文特别关注了自助法蒙特卡罗研究中高单调似然发生率的问题。
