Moodie Patricia F, Nelson Norma A, Koch Gary G
Department of Mathematics and Statistics, University of Winnipeg, 515 Portage Avenue Winnipeg, MB, Canada R3B 2E9.
Stat Med. 2004 Apr 15;23(7):1075-93. doi: 10.1002/sim.1696.
This paper addresses the problem of combining information from independent clinical trials which compare survival distributions of two treatment groups. Current meta-analytic methods which take censoring into account are often not feasible for meta-analyses which synthesize summarized results in published (or unpublished) references, as these methods require information usually not reported. The paper presents methodology which uses the log(-log) survival function difference, (i.e. log(-logS2(t))-log(-logS1(t)), as the contrast index to represent the multiplicative treatment effect on survival in independent trials. This article shows by the second mean value theorem for integrals that this contrast index, denoted as theta, is interpretable as a weighted average on a natural logarithmic scale of hazard ratios within the interval [0,t] in a trial. When the within-trial proportional hazards assumption is true, theta is the logarithm of the proportionality constant for the common hazard ratio for the interval considered within the trial. In this situation, an important advantage of using theta as a contrast index in the proposed methodology is that the estimation of theta is not affected by length of follow-up time. Other commonly used indices such as the odds ratio, risk ratio and risk differences do not have this invariance property under the proportional hazard model, since their estimation may be affected by length of follow-up time as a technical artefact. Thus, the proposed methodology obviates problems which often occur in survival meta-analysis because trials do not report survival at the same length of follow-up time. Even when the within-trial proportional hazards assumption is not realistic, the proposed methodology has the capability of testing a global null hypothesis of no multiplicative treatment effect on the survival distributions of two groups for all studies. A discussion of weighting schemes for meta-analysis is provided, in particular, a weighting scheme based on effective sample sizes is suggested for the meta-analysis of time-to-event data which involves censoring. A medical example illustrating the methodology is given. A simulation investigation suggested that the methodology performs well in the presence of moderate censoring.
本文探讨了整合来自独立临床试验信息的问题，这些试验比较了两个治疗组的生存分布。当前考虑删失情况的荟萃分析方法，对于综合已发表（或未发表）参考文献中的汇总结果进行荟萃分析而言，往往不可行，因为这些方法需要通常未报告的信息。本文提出了一种方法，该方法使用对数（-对数）生存函数差异（即log(-logS2(t)) - log(-logS1(t))）作为对比指标，以表示独立试验中治疗对生存的乘法效应。本文通过积分的第二中值定理表明，这个对比指标（记为θ）可解释为试验中在区间[0,t]内风险比自然对数尺度上的加权平均值。当试验内比例风险假设成立时，θ是试验所考虑区间内共同风险比的比例常数的对数。在这种情况下，在所提出的方法中使用θ作为对比指标的一个重要优势是，θ的估计不受随访时间长度的影响。其他常用指标，如比值比、风险比和风险差异，在比例风险模型下不具有这种不变性，因为它们的估计可能会受到随访时间长度这种技术因素的影响。因此，所提出的方法避免了生存荟萃分析中经常出现的问题，因为试验没有报告相同随访时间长度下的生存情况。即使试验内比例风险假设不现实，所提出的方法也能够对所有研究中两组生存分布不存在乘法治疗效应的全局零假设进行检验。本文提供了关于荟萃分析加权方案的讨论，特别是针对涉及删失的事件发生时间数据的荟萃分析，建议了一种基于有效样本量的加权方案。给出了一个说明该方法的医学实例。一项模拟研究表明，该方法在存在中度删失的情况下表现良好。
