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For ordinal outcomes, the average treatment effect is often ill-defined andhard to interpret. Echoing Agresti and Kateri (2017), we argue that therelative treatment effect can be a useful measure especially for ordinaloutcomes, which is defined as $\gamma = \mathrm{pr}\{ Y_i(1) > Y_i(0) \} -\mathrm{pr}\{ Y_i(1) < Y_i(0) \}$, with $Y_i(1)$ and $Y_i(0)$ being thepotential outcomes of unit $i$ under treatment and control, respectively. Giventhe marginal distributions of the potential outcomes, we derive the sharpbounds on $\gamma,$ which are identifiable parameters based on the observeddata. Agresti and Kateri (2017) focused on modeling strategies under theassumption of independent potential outcomes, but we allow for arbitrarydependence.

Sharp bounds on the relative treatment effect for ordinal outcomes