In observational studies with survival or time-to-event outcomes, a propensity score weighted marginal Cox proportional hazard model with the treatment variable as the only predictor is commonly used to estimate the causal marginal hazard ratio between two treatments. Observational studies often have more than two treatments, but corresponding analysis methods are limited. In this paper, we combine the propensity score weighting method for multiple treatments and a marginal Cox model with indicators for each treatment to estimate the causal hazard ratios between multiple treatments and a common reference treatment. We illustrate two weighting schemes: inverse probability of treatment weighting and overlap weighting. We prove the consistency of the maximum weighted partial likelihood estimator of the causal marginal hazard ratio and derive a robust sandwich variance estimator. As an important special case of multiple treatments, we elaborate the Cox model for two-way factorial treatments. We apply the method to evaluate the real-world comparative effectiveness of three types of anti-obesity medications on heart failure. We develop an associated R package 'PSsurvival'.

翻译：在具有生存或时间至事件结局的观测研究中，倾向性评分加权边际Cox比例风险模型（以处理变量为唯一预测因子）通常用于估计两种处理间的因果边际风险比。观测研究常涉及两种以上处理，但相应的分析方法有限。本文结合多重处理的倾向性评分加权方法与包含各处理指示变量的边际Cox模型，以估计多重处理与共同参照处理间的因果风险比。我们阐释两种加权方案：处理逆概率加权与重叠加权。证明了因果边际风险比的最大加权偏似然估计量的一致性，并推导出稳健的三明治方差估计量。作为多重处理的重要特例，我们详细阐述了双向因子处理的Cox模型。应用该方法评估了三类抗肥胖药物对心力衰竭的真实世界比较效果。开发了配套R软件包'PSsurvival'。