159 S/F94 as a proxy for COVID-19 severity 7 where denotes convergence in probability. If in addition we assume is mean ergodic, then using Equation 13 gives Now consider an individual-specific treatment effect given by for some function f taking values in [0,1] that may in principle depend on all covariates. Let be the change in associated with this treatment effect in Equation 17 and Equation 19 respectively. That is, Our estimator for the average change in protocolised S/F94 associated with the treatment effect f is obtained by subtracting Equation 19 from Equation 25, dividing by and averaging over the sample, We now show this is a consistent estimator for at first order in . Consider We assume f is analytic, and Taylor expand the third term in Equation 27 to first order around =0. Let , where pi is understood to be a function of via Equation 17. Then
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