When there are resource constraints, it is important to rank or estimate treatment benefits according to patient characteristics. This facilitates prioritization of assigning different treatments. Most existing literature on individualized treatment rules targets absolute conditional treatment effect differences as the metric for benefits. However, there can be settings where relative differences may better represent such benefits. In this paper, we consider modeling such relative differences that form scale-invariant contrasts between conditional treatment effects. We show that all scale-invariant contrasts are monotonic transformations of each other. Therefore we posit a single index model for a particular relative contrast. We then derive estimating equations and efficient scores via semiparametric efficiency theory. Theoretical properties of the estimation and inference procedures are provided. Simulations and real data analysis are conducted to demonstrate the proposed approach.
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