Relative contrast estimation and inference for treatment recommendation

• Published in: Biometrics Vol. 79; no. 4; pp. 2920 - 2932
• Main Authors: Liang, Muxuan, Yu, Menggang
• Format: Journal Article
• Language: English
• Published: United States Blackwell Publishing Ltd 01.12.2023
• Subjects: biometry; equations; Estimation; individualized treatment rule; Invariants; Models, Statistical; Observational studies; observational study; Parametric statistics; Precision medicine; Precision Medicine - methods; prioritization; Robustness (mathematics); semiparametric efficiency; single index model; precision medicine; single index model; individualized treatment rule; semiparametric efficiency; observational study
• ISSN: 0006-341X; 1541-0420; 1541-0420
• DOI: 10.1111/biom.13826

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.