Counterfactual Uncertainty Quantification of Factual Estimand of Efficacy from Before-and-After Treatment Repeated Measures Randomized Controlled Trials

The ideal estimand for comparing treatment $Rx$ with a control $C$ is the $\textit{counterfactual}$ efficacy $Rx:C$, the expected differential outcome between $Rx$ and $C$ if each patient were given $\textit{both}$. One hundred years ago, Neyman (1923a) proved unbiased $\textit{point estimation}$ of counterfactual efficacy from designed $\textit{factual}$ experiments is achievable. But he left the determination of how much might the counterfactual variance of this estimate be smaller than the factual variance as an open challenge. This article shows $\textit{counterfactual}$ uncertainty quantification (CUQ), quantifying uncertainty for factual point estimates but in a counterfactual setting, is achievable for Randomized Controlled Trials (RCTs) with Before-and-After treatment Repeated Measures which are common in many therapeutic areas. We achieve CUQ whose variability is typically smaller than factual UQ by creating a new statistical modeling principle called ETZ. We urge caution in using predictors with measurement error which violates standard regression assumption and can cause $\textit{attenuation}$ in estimating treatment effects. Fortunately, we prove that, for traditional medicine in general, and for targeted therapy with efficacy defined as averaged over the population, counterfactual point estimation is unbiased. However, for both Real Human and Digital Twins approaches, predicting treatment effect in $\textit{subgroups}$ may have attenuation bias.