Dipartimento di Scienze Statistiche e Matematiche S. Vianelli, Università di Palermo, viale delle Scienze, ed. 13, 90128 Palermo, Italy.
Stat Med. 2010 Aug 15;29(18):1947-57. doi: 10.1002/sim.3959.
We propose a simple and flexible framework for the crossing hazards problem. The method is not confined to two-sample problems, but may also work with continuous exposure variables whose effect changes its sign at some time-point of the observed follow-up time. Penalized partial likelihood estimation relies upon the assumption of a smooth hazard ratio via low-rank basis splines with a conventional difference penalty to ensure smoothness, and additional ad hoc penalties to obtain restricted estimates useful in the context of crossing hazards. The framework naturally also leads to a statistical test that has good power for revealing a global effect under several alternatives, including crossing hazards. We provide the results from a real-data analysis and from some simulations to illustrate empirically the performance of the proposed approach as compared with the possible alternatives.
我们提出了一个简单而灵活的框架来处理交叉风险问题。该方法不仅限于两样本问题，也可以用于连续暴露变量，当观察随访时间的某个时间点时，其效应会改变符号。惩罚部分似然估计依赖于通过低秩基样条假设平滑风险比，通过常规差分惩罚来确保平滑性，并额外使用特定的惩罚来获得在交叉风险情况下有用的受限估计。该框架自然也导致了一个统计检验，在几种替代方案（包括交叉风险）下，该检验对揭示全局效应具有良好的功效。我们提供了实际数据分析和一些模拟结果，以经验方式说明与可能的替代方案相比，所提出方法的性能。
