Relative contrast estimation and inference for treatment recommendation

When there are resource constraints, it may be necessary to rank individualized treatment benefits to facilitate the prioritization of assigning different treatments. Most existing literature on individualized treatment rules targets absolute conditional treatment effect differences as a metric for the benefit. However, there can be settings where relative differences may better represent such benefit. In this paper, we consider modeling such relative differences formed as scale-invariant contrasts between the conditional treatment effects. By showing that all scale-invariant contrasts are monotonic transformations of each other, we posit a single index model for a particular relative contrast. We then characterize semiparametric estimating equations, including the efficient score, to estimate index parameters. To achieve semiparametric efficiency, we propose a two-step approach that minimizes a doubly robust loss function for initial estimation and then performs a one-step efficiency augmentation procedure. Careful theoretical and numerical studies are provided to show the superiority of our proposed approach.

Automated summary

When resources are limited, it may be necessary to prioritize assigning different treatments by ranking individualized treatment benefits. Existing literature mainly focuses on using absolute conditional treatment effect differences as a metric for benefit evaluation. However, in some cases, relative differences may better represent such benefits. In this paper, we propose a single index model for a specific relative contrast and develop semiparametric estimating equations to estimate index parameters efficiently. Our proposed approach shows superiority in both theoretical and numerical studies.