The Biostatistics Center, Departments of Epidemiology and Biostatistics, and Statistics, The George Washington University, 6110 Executive Boulevard, Suite 750, Rockville, MD 20852, USA.
Stat Med. 2013 Jan 30;32(2):220-9. doi: 10.1002/sim.5480. Epub 2012 Jul 16.
Power for time-to-event analyses is usually assessed under continuous-time models. Often, however, times are discrete or grouped, as when the event is only observed when a procedure is performed. Wallenstein and Wittes (Biometrics, 1993) describe the power of the Mantel-Haenszel test for discrete lifetables under their chained binomial model for specified vectors of event probabilities over intervals of time. Herein, the expressions for these probabilities are derived under a piecewise exponential model allowing for staggered entry and losses to follow-up. Radhakrishna (Biometrics, 1965) showed that the Mantel-Haenszel test is maximally efficient under the alternative of a constant odds ratio and derived the optimal weighted test under other alternatives. Lachin (Biostatistical Methods: The Assessment of Relative Risks, 2011) described the power function of this family of weighted Mantel-Haenszel tests. Prentice and Gloeckler (Biometrics, 1978) described a generalization of the proportional hazards model for grouped time data and the corresponding maximally efficient score test. Their test is also shown to be a weighted Mantel-Haenszel test, and its power function is likewise obtained. There is trivial loss in power under the discrete chained binomial model relative to the continuous-time case provided that there is a modest number of periodic evaluations. Relative to the case of homogeneity of odds ratios, there can be substantial loss in power when there is substantial heterogeneity of odds ratios, especially when heterogeneity occurs early in a study when most subjects are at risk, but little loss in power when there is heterogeneity late in a study.
用于事件时间分析的功效通常在连续时间模型下进行评估。然而，时间通常是离散的或分组的，例如，当事件仅在进行程序时才被观察到时。Wallenstein 和 Wittes（Biometrics，1993）在他们的连锁二项式模型下描述了离散生命表的 Mantel-Haenszel 检验在指定的时间间隔内的事件概率向量下的功效。在此，在允许交错进入和随访损失的分段指数模型下推导出这些概率的表达式。Radhakrishna（Biometrics，1965）表明，Mantel-Haenszel 检验在替代恒定优势比的情况下具有最大功效，并在其他替代情况下推导出最优加权检验。Lachin（Biostatistical Methods: The Assessment of Relative Risks，2011）描述了这种加权 Mantel-Haenszel 检验的功效函数。Prentice 和 Gloeckler（Biometrics，1978）描述了分组时间数据的比例风险模型的广义形式和相应的最大功效评分检验。还表明，他们的检验也是加权 Mantel-Haenszel 检验，并且同样获得了其功效函数。在离散连锁二项式模型下，相对于连续时间情况，只要有适度数量的定期评估，功效就会略有损失。与优势比均匀性的情况相比，当优势比存在实质性异质性时，功效可能会有实质性损失，特别是当异质性发生在大多数受试者处于风险中时的研究早期，但当研究后期存在异质性时，功效损失很小。
