The limited scope of Randomized Controlled Trials (RCT) is increasingly under scrutiny, in particular when samples are unrepresentative. Indeed, some RCTs over/under-sample individuals with certain characteristics compared to the target population, for which one want to draw conclusions on treatment effectiveness. Re-weighting trial individuals to match the target population helps to improve the treatment effect estimation. Such procedures require an estimation of the ratio of the two densities (trial and target distributions).
In this talk, we focus on finite-sample performances of such reweighting procedures - also called Inverse Propensity of Sampling Weighting (IPSW) - in presence of categorical covariates. We compare oracle versions of these estimates (when the trial/target distribution or the propensity score are known). Our finite-sample analysis enables us to derive precise asymptotic regimes depending on the two sample sizes (RCT and target population). In particular, we show that IPSW estimates do not benefit from using the true trial distribution if available and that IPSW performances are improved when the trial probability to be treated is estimated. In addition, we study how including covariates that are unnecessary for identifiability may impact the asymptotic variance and illustrate the results on a semi-synthetic simulation inspired from critical care medicine.