Clinical Research Unit, Academic Medical Centre, Amsterdam, The Netherlands.
Stat Med. 2013 Mar 30;32(7):1223-38. doi: 10.1002/sim.5538. Epub 2012 Jul 25.
The Kaplan-Meier, Nelson-Aalen and Breslow estimators are widely used in the analysis of right-censored time to event data in medical applications. These methods are fully non-parametric and do not put any restriction on the shape of the hazard curve. In some applications, this leads to implausible estimates of the hazard course over time. With non-parametric shape-constrained estimation techniques, one can facilitate an increasing or decreasing hazard and thus generate estimators that better match the biological reasoning, without being as restrictive as parametric methods. We illustrate the advantage of such techniques in the analysis of a large clinical trial in cardiology. Simulation results show that in case the true hazard is monotone, the non-parametric shape-constrained estimators are more accurate than the traditional estimators on the hazard level. On the (cumulative) distribution function level, the shape-constrained estimators show similar performance as the traditional ones.
Kaplan-Meier、Nelson-Aalen 和 Breslow 估计器广泛应用于医学中右删失时间事件数据的分析。这些方法完全是非参数的，不会对危险曲线的形状施加任何限制。在某些应用中，这会导致对随时间变化的危险过程的不合理估计。通过非参数形状约束估计技术，可以促进危险的增加或减少，从而生成更符合生物学推理的估计器，而不会像参数方法那样具有限制性。我们在心脏病学的一项大型临床试验分析中说明了这些技术的优势。模拟结果表明，在真实危险是单调的情况下，非参数形状约束估计器在危险水平上比传统估计器更准确。在（累积）分布函数水平上，形状约束估计器的性能与传统估计器相似。
