In the analysis of prognosis studies with time-to-event outcomes, dichotomization of patients is often made. As the evaluations of prognostic capacity, the survivals of groups with high/low expression of the biomarker are often estimated by the Kaplan-Meier method, and the difference between groups is summarized via the hazard ratio (HR). The high/low expressions are usually determined by study-specific cutoff values, which brings heterogeneity over multiple prognosis studies and difficulty to synthesizing the results in a simple way. In meta-analysis of diagnostic studies with binary outcomes, the summary receiver operating characteristics (SROC) analysis provides a useful cutoff-free summary over studies. Recently, this methodology has been extended to the time-dependent SROC analysis for time-to-event outcomes in meta-analysis of prognosis studies. In this paper, we propose a sensitivity analysis method for evaluating the impact of publication bias on the time-dependent SROC analysis. Our proposal extends the recently introduced sensitivity analysis method for meta-analysis of diagnostic studies based on the bivariate normal model on sensitivity and specificity pairs. To model the selective publication process specific to prognosis studies, we introduce a trivariate model on the time-dependent sensitivity and specificity and the log-transformed HR. Based on the proved asymptotic property of the trivariate model, we introduce a likelihood based sensitivity analysis method based on the conditional likelihood constrained by the expected proportion of published studies. We illustrate the proposed sensitivity analysis method through the meta-analysis of Ki67 for breast cancer. Simulation studies are conducted to evaluate the performance of the proposed method.

翻译：在具有时间至事件结局的预后研究中，常对患者进行二分类处理。为评估预后能力，通常采用Kaplan-Meier方法估计生物标志物高/低表达组的生存率，并通过风险比（HR）汇总组间差异。高/低表达通常由研究特定的截断值确定，这导致多预后研究间的异质性，并增加了以简单方式综合结果的难度。在基于二分类结局的诊断性研究meta分析中，汇总受试者工作特征（SROC）分析提供了不受截断影响的研究汇总方法。近期，该方法已被扩展至预后研究meta分析中用于时间至事件结局的时间依赖性SROC分析。本文提出一种敏感性分析方法，用于评估发表偏倚对时间依赖性SROC分析的影响。我们的方法扩展了近期基于灵敏度和特异度二元正态模型提出的诊断性研究meta分析敏感性分析方法。为模拟预后研究特有的选择性发表过程，我们引入一个关于时间依赖性灵敏度、特异度及对数转换HR的三元模型。基于该三元模型的渐近性质，我们提出一种基于条件似然的敏感性分析方法，该似然受预期发表研究比例约束。通过Ki67在乳腺癌中作用的meta分析案例，我们阐述了所提出的敏感性分析方法，并通过模拟研究评估了该方法的性能。