Recent years have seen the development of many novel scoring tools for disease prognosis and prediction. To become accepted for use in clinical applications, these tools have to be validated on external data. In practice, validation is often hampered by logistical issues, resulting in multiple small-sized validation studies. It is therefore necessary to synthesize the results of these studies using techniques for meta-analysis. Here we consider strategies for meta-analyzing the concordance probability for time-to-event data ("C-index"), which has become a popular tool to evaluate the discriminatory power of prediction models with a right-censored outcome. We show that standard meta-analysis of the C-index may lead to biased results, as the magnitude of the concordance probability depends on the length of the time interval used for evaluation (defined e.g. by the follow-up time, which might differ considerably between studies). To address this issue, we propose a set of methods for random-effects meta-regression that incorporate time directly as covariate in the model equation. In addition to analyzing nonlinear time trends via fractional polynomial, spline, and exponential decay models, we provide recommendations on suitable transformations of the C-index before meta-regression. Our results suggest that the C-index is best meta-analyzed using fractional polynomial meta-regression with logit-transformed C-index values. Classical random-effects meta-analysis (not considering time as covariate) is demonstrated to be a suitable alternative when follow-up times are small. Our findings have implications for the reporting of C-index values in future studies, which should include information on the length of the time interval underlying the calculations.
翻译:近些年来,已经开发了许多用于疾病预测和预测的新型评分工具。要被接受用于临床应用,这些工具必须被外部数据验证。在实践中,验证往往受到后勤问题的阻碍,导致许多小规模的验证研究。因此有必要使用元分析技术对这些研究结果进行综合分析。这里我们考虑的是利用元分析技术对时间到活动数据的一致概率进行元分析的战略(“C-ind” ),它已成为一种受欢迎的工具,用来评价具有正确检查结果的预测模型的歧视性力量。我们表明,C-index的标准元分析可能导致偏差结果,因为后勤问题往往会阻碍验证,导致多重规模的验证研究。因此,有必要使用元分析技术分析技术来综合这些研究的结果。为了解决这个问题,我们提出了一套随机效应元分析方法,将时间直接包含在模型等式跟踪中。除了分析非线性时间趋势外,C-index-index-alal数值的元分析可能会导致偏差结果,因为C-nex-cal-derial-deal-deal resultraal resultial-deal resultural resultial-deal-deal-deal-deal-deal-deal-deal-deal-deal-deal-demogradudule-deal-deal-deal-deal-deal-deal-deal-deal-deal-deal-deal-deal-deal-deal-deal-deal-deal-deal-demodal-deal-demodal-demodal-deal-al-demodal-deal-deal-deal-deal-deal-deal-deal-deal-deal-deal-deal-deal-deal-deal-deal-deal-deal modal-deal-deal-deal-deal-deal-deal-deal-deal-deal-deal-deal-deal modal-deal-deal-deal-deal-deal-deal-deal-deal-deal-deal-deal-deal-deal-deal-deal-deal-de