This paper develops power and sample size formulas for causal inference with time-to-event outcomes. The target estimand is the marginal hazard ratio: the coefficient of a marginal structural Cox proportional hazard model with treatment as the only predictor. We extend the robust sandwich variance theory and derive the analytical form of the asymptotic variance for the inverse probability weighted partial likelihood estimator. Building on this, we derive a new sample size formula valid at any prespecified effect size, applicable to both randomized trials and observational studies. For randomized trials, the formula requires only the canonical inputs of treatment proportion, effect size, and event rate. The new formula corrects the mischaracterization of classic log-rank-based formulas. For observational studies, one additional input suffices: an overlap coefficient summarizing covariate similarity between comparison groups. We further develop a variance inflation approach applicable to any propensity score balancing weights, anchored to the corrected baseline variance.

翻译：本文提出针对时间至事件结局因果推断的统计功效与样本量公式。目标估计量为边际风险比——以处理变量为唯一预测因子的边际结构Cox比例风险模型系数。我们拓展了稳健三明治方差理论，推导出逆概率加权部分似然估计量渐近方差的解析形式。在此基础上，建立适用于任意预设效应量的新型样本量公式，可同时应用于随机对照试验与观察性研究。对于随机对照试验，该公式仅需提供处理比例、效应量与事件率三项基础参数。新公式修正了经典对数秩检验类公式的误判特征。在观察性研究中，仅需额外引入一个群组间协变量相似度的重叠系数。我们进一步开发了基于校正基准方差、适用于任意倾向性评分平衡权重的方差膨胀方法。