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Optimal regimes for algorithm-assisted human decision-making

Mats J. Stensrud, Julien Laurendeau, Aaron L. Sarvet

TL;DR

This work introduces optimal regimes for algorithm-assisted human decision-making that are decision functions of measured pre-treatment variables and enjoy a "superoptimality"property whereby they are guaranteed to outperform conventional optimal regimes currently considered in the literature.

Abstract

We consider optimal regimes for algorithm-assisted human decision-making. Such regimes are decision functions of measured pre-treatment variables and, by leveraging natural treatment values, enjoy a "superoptimality" property whereby they are guaranteed to outperform conventional optimal regimes. When there is unmeasured confounding, the benefit of using superoptimal regimes can be considerable. When there is no unmeasured confounding, superoptimal regimes are identical to conventional optimal regimes. Furthermore, identification of the expected outcome under superoptimal regimes in non-experimental studies requires the same assumptions as identification of value functions under conventional optimal regimes when the treatment is binary. To illustrate the utility of superoptimal regimes, we derive new identification and estimation results in a common instrumental variable setting. We use these derivations to analyze examples from the optimal regimes literature, including a case study of the effect of prompt intensive care treatment on survival.

Optimal regimes for algorithm-assisted human decision-making

TL;DR

This work introduces optimal regimes for algorithm-assisted human decision-making that are decision functions of measured pre-treatment variables and enjoy a "superoptimality"property whereby they are guaranteed to outperform conventional optimal regimes currently considered in the literature.

Abstract

We consider optimal regimes for algorithm-assisted human decision-making. Such regimes are decision functions of measured pre-treatment variables and, by leveraging natural treatment values, enjoy a "superoptimality" property whereby they are guaranteed to outperform conventional optimal regimes. When there is unmeasured confounding, the benefit of using superoptimal regimes can be considerable. When there is no unmeasured confounding, superoptimal regimes are identical to conventional optimal regimes. Furthermore, identification of the expected outcome under superoptimal regimes in non-experimental studies requires the same assumptions as identification of value functions under conventional optimal regimes when the treatment is binary. To illustrate the utility of superoptimal regimes, we derive new identification and estimation results in a common instrumental variable setting. We use these derivations to analyze examples from the optimal regimes literature, including a case study of the effect of prompt intensive care treatment on survival.
Paper Structure (27 sections, 21 theorems, 86 equations, 1 figure, 1 table)

This paper contains 27 sections, 21 theorems, 86 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Non-experimental data structure
  4. Potential outcomes and the natural values of treatment
  5. Definitions of treatment regimes
  6. Superoptimal regimes and their properties
  7. On Experimental Data
  8. On algorithm-assisted human decision making
  9. On the non-prescriptive use of superoptimal regimes
  10. Case study: Instrumental variables
  11. Point identification of value functions
  12. Augmenting regimes with instruments
  13. Application: Intensive Care Unit Admissions
  14. Future directions
  15. Instrumental variables (IVs)
  16. ...and 12 more sections

Key Result

Proposition 1

The expected potential outcome under the $L$-superoptimal regime is better than or equal to that under the $L$-optimal regime,

Figures (1)

  • Figure 1: A dynamic SWIG with instrumental variable $Z$ describing a regime that depends on $A$ and $L$, consistent with a superoptimal regime.

Theorems & Definitions (50)

  • Definition 1: Natural value of treatment
  • Definition 2: $L$-optimal regimes
  • Definition 3: $L$-superoptimal regimes
  • Proposition 1: Superoptimality
  • proof
  • Remark 1
  • Lemma 1
  • proof
  • Corollary 1
  • Proposition 2: Identification of superoptimal regimes
  • ...and 40 more