Quantifying Treatment Effects: Estimating Risk Ratios in Causal Inference

Abstract: Randomized Controlled Trials (RCT) are the current gold standards to empirically measure the effect of a new drug. However, they may be of limited size and resorting to complementary non-randomized data, referred to as observational, is promising, as additional sources of evidence. In both RCT and observational data, the Risk Difference (RD) is often used to characterize the effect of a drug. Additionally, medical guidelines recommend to also report the Risk Ratio (RR), which may provide a different comprehension of the effect of the same drug. While different methods have been proposed and studied to estimate the RD, few methods exist to estimate the RR. In this paper, we propose estimators of the RR both in RCT and observational data and provide both asymptotical and finite-sample analyses. We show that, even in an RCT, estimating treatment allocation probability or adjusting for covariates leads to lower asymptotic variance. In observational studies, we propose weighting and outcome modeling estimators and derive their asymptotic bias and variance for well-specified models. Using semi-parametric theory, we define two doubly robusts estimators with minimal variances among unbiased estimators. We support our theoretical analysis with empirical evaluations and illustrate our findings through experiments.