Randomized Controlled Trials (RCTs) may suffer from limited scope. In particular, samples may be unrepresentative: some RCTs over- or under- sample individuals with certain characteristics compared to the target population, for which one wants conclusions on treatment effectiveness. Re-weighting trial individuals to match the target population can improve the treatment effect estimation. In this work, we establish the exact expressions of the bias and variance of such reweighting procedures -- also called Inverse Propensity of Sampling Weighting (IPSW) -- in presence of categorical covariates for any sample size. Such results allow us to compare the theoretical performance of different versions of IPSW estimates. Besides, our results show how the performance (bias, variance, and quadratic risk) of IPSW estimates depends on the two sample sizes (RCT and target population). A by-product of our work is the proof of consistency of IPSW estimates. Results also reveal that IPSW performances are improved when the trial probability to be treated is estimated (rather than using its oracle counterpart). In addition, we study choice of variables: how including covariates that are not necessary for identifiability of the causal effect may impact the asymptotic variance. Including covariates that are shifted between the two samples but not treatment effect modifiers increases the variance while non-shifted but treatment effect modifiers do not. We illustrate all the takeaways in a didactic example, and on a semi-synthetic simulation inspired from critical care medicine.

翻译：随机对照试验（RCT）可能存在适用范围的局限性。具体而言，样本可能缺乏代表性：某些RCT中，相较于目标人群（即我们希望得出治疗效果结论的群体），特定特征的个体被过度或不足抽样。对试验个体进行重加权以匹配目标人群分布，可改善治疗效果估计。本研究针对存在分类协变量的场景，建立了任意样本量下此类重加权方法（亦称逆抽样倾向加权，IPSW）的偏差与方差精确表达式。这些结果使我们能够比较不同版本IPSW估计量的理论性能。此外，我们的研究表明IPSW估计量的性能（偏差、方差和二次风险）如何依赖于两个样本量（RCT与目标人群）。本研究的副产品之一是证明了IPSW估计量的一致性。结果还揭示，当采用处理概率的估计值（而非其理想化真实值）时，IPSW性能更优。进一步地，我们研究了变量选择问题：纳入对因果效应可识别性不必要的协变量如何影响渐近方差。纳入在两样本间分布存在差异但非处理效应修饰因子的协变量会增大方差，而分布无差异的处理效应修饰因子则不会。我们通过一个教学案例及基于重症医学的半合成模拟研究，对上述结论进行了全面阐释。