Background: The Cox model and its extensions assuming proportional hazards is widely used to estimate vaccine efficacy (VE). In the typical situation that VE wanes over time, the VE estimates are not only sensitive to study duration and timing of vaccine delivery in relation to disease seasonality but also biased in the presence of sample attrition. Furthermore, estimates of vaccine impact such as number of cases averted (NCA) are sensitive to background disease incidence and timing of vaccine delivery. Comparison of the estimates between trials with different features can be misleading. Methods: We propose estimation of VE as a function of time in the Cox model framework, using the area under the VE curve as a summary measure of VE, and extension of the method to estimate vaccine impact. We use simulations and re-analysis of a RTS,S/AS01 malaria vaccine trial dataset to demonstrate their properties and applications. Results: Simulation under scenarios with different trial duration, magnitude of sample attrition and timing of vaccine delivery, all assuming vaccine protection wanes over time, demonstrated the problems of conventional methods assuming proportional hazard, robustness and unbiasedness of the proposed methods, and comparability of the proposed estimates of vaccine efficacy and impact across trials with different features. Furthermore, the proposed NCA estimators are informative in determining the optimal vaccine delivery strategy in regions with highly seasonal disease transmission. Conclusions: The proposed method based on estimation of vaccine efficacy trajectory provides a robust, unbiased, and flexible approach to evaluate vaccine effects.

翻译：背景：Cox模型及其基于比例风险假设的扩展方法被广泛用于估计疫苗效力（VE）。在典型情况下，当疫苗效力随时间衰减时，VE估计不仅对研究持续时间、疫苗接种时间与疾病季节性关系的敏感性高，而且在样本流失存在时会产生偏倚。此外，疫苗影响估计（如避免病例数NCA）对背景疾病发病率和疫苗接种时间高度敏感。在不同特征的试验间直接比较这些估计值可能产生误导。方法：我们提出在Cox模型框架下将VE估计为时间的函数，使用VE曲线下面积作为VE的概括性度量，并将该方法扩展至疫苗影响估计。通过模拟实验和对RTS,S/AS01疟疾疫苗试验数据的重新分析，我们展示了这些方法的特性和应用价值。结果：在不同试验持续时间、样本流失程度和疫苗接种时间的模拟场景中（均假设疫苗保护效果随时间衰减），研究揭示了传统比例风险假设方法存在的问题，验证了所提方法的稳健性和无偏性，并证明了所提疫苗效力和影响估计在不同特征试验间的可比性。此外，所提出的NCA估计量对于确定疾病传播高度季节性区域的最佳疫苗接种策略具有重要参考价值。结论：基于疫苗效力轨迹估计的所提方法为评估疫苗效果提供了稳健、无偏且灵活的分析框架。