Habermehl Christina, Benner Axel, Kopp-Schneider Annette
Department of Biostatistics, German Cancer Research Center (DKFZ), Heidelberg, Germany.
Biom J. 2018 Mar;60(2):275-287. doi: 10.1002/bimj.201600226. Epub 2017 Aug 1.
In recent years, numerous approaches for biomarker-based clinical trials have been developed. One of these developments are multiple-biomarker trials, which aim to investigate multiple biomarkers simultaneously in independent subtrials. For low-prevalence biomarkers, small sample sizes within the subtrials have to be expected, as well as many biomarker-negative patients at the screening stage. The small sample sizes may make it unfeasible to analyze the subtrials individually. This imposes the need to develop new approaches for the analysis of such trials. With an expected large group of biomarker-negative patients, it seems reasonable to explore options to benefit from including them in such trials. We consider advantages and disadvantages of the inclusion of biomarker-negative patients in a multiple-biomarker trial with a survival endpoint. We discuss design options that include biomarker-negative patients in the study and address the issue of small sample size bias in such trials. We carry out a simulation study for a design where biomarker-negative patients are kept in the study and are treated with standard of care. We compare three different analysis approaches based on the Cox model to examine if the inclusion of biomarker-negative patients can provide a benefit with respect to bias and variance of the treatment effect estimates. We apply the Firth correction to reduce the small sample size bias. The results of the simulation study suggest that for small sample situations, the Firth correction should be applied to adjust for the small sample size bias. Additional to the Firth penalty, the inclusion of biomarker-negative patients in the analysis can lead to further but small improvements in bias and standard deviation of the estimates.
近年来，已开发出多种基于生物标志物的临床试验方法。其中一项进展是多生物标志物试验，其旨在在独立的子试验中同时研究多种生物标志物。对于低流行率的生物标志物，子试验中的样本量预计会很小，并且在筛查阶段会有许多生物标志物阴性的患者。样本量小可能会使单独分析子试验变得不可行。这就需要开发新的方法来分析此类试验。鉴于预计会有大量生物标志物阴性的患者，探索将他们纳入此类试验以从中获益的选择似乎是合理的。我们考虑了在具有生存终点的多生物标志物试验中纳入生物标志物阴性患者的优缺点。我们讨论了在研究中纳入生物标志物阴性患者的设计选项，并解决了此类试验中样本量小偏差的问题。我们对一种设计进行了模拟研究，在该设计中生物标志物阴性患者留在研究中并接受标准治疗。我们比较了基于Cox模型的三种不同分析方法，以检验纳入生物标志物阴性患者是否能在治疗效果估计的偏差和方差方面带来益处。我们应用Firth校正来减少样本量小的偏差。模拟研究结果表明，对于小样本情况，应应用Firth校正来调整样本量小的偏差。除了Firth惩罚外，在分析中纳入生物标志物阴性患者可导致估计值的偏差和标准差进一步但微小的改善。
