Shuxiao Chen, Bo Zhang
arXiv 15 Apr 2021 · Statistics — Methodology
arXiv:2104.07822 · PDF · Extracted main text
Estimating dynamic treatment regimes (DTRs) from retrospective observational data is challenging as some degree of unmeasured confounding is often expected. In this work, we develop a framework of estimating properly defined "optimal" DTRs with a time-varying instrumental variable (IV) when unmeasured covariates confound the treatment and outcome, rendering the potential outcome distributions only partially identified. We derive a novel Bellman equation under partial identification, use it to define a generic class of estimands (termed IV-optimal DTRs), and study the associated estimation problem. We then extend the IV-optimality framework to tackle the policy improvement problem, delivering IV-improved DTRs that are guaranteed to perform no worse and potentially better than a pre-specified baseline DTR. Importantly, our IV-improvement framework opens up the possibility of strictly improving upon DTRs that are optimal under the no unmeasured confounding assumption (NUCA). We demonstrate via extensive simulations the superior performance of IV-optimal and IV-improved DTRs over the DTRs that are optimal only under the NUCA. In a real data example, we embed retrospective observational registry data into a natural, two-stage experiment with noncompliance using a time-varying IV and estimate useful IV-optimal DTRs that assign mothers to high-level or low-level neonatal intensive care units based on their prognostic variables.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Cui, Y. and Tchetgen Tchetgen, E (2021) Machine intelligence for individualized decision making under a counterfactual world: A rejoinder | 1.000 | 6 | 3 | 100% |
| 2 | Murphy, S. A (2003) Optimal dynamic treatment regimes | 1.000 | 6 | 3 | 100% |
| 3 | Pu, H. and Zhang, B (2020) Estimating optimal treatment rules with an instrumental variable: A partial identification learning approach self | 0.874 | 6 | 2 | 100% |
| 4 | Cui, Y. and Tchetgen Tchetgen, E (2020) A semiparametric instrumental variable approach to optimal treatment regimes under endogeneity | 0.874 | 5 | 2 | 100% |
| 5 | Manski, C. F (2003) Partial identification of probability distributions | 0.843 | 3 | 3 | 100% |
| 6 | Michael, H., Cui, Y., Lorch, S., and Tchetgen, E. T (2020) Instrumental variable estimation of marginal structural mean models for time-varying treatment | 0.843 | 3 | 3 | 100% |
| 7 | Schulte, P. J., Tsiatis, A. A., Laber, E. B., and Davidian, M (2014) Q-and a-learning methods for estimating optimal dynamic treatment regimes | 0.811 | 4 | 2 | 100% |
| 8 | Kallus, N., Mao, X., and Zhou, A (2019) Interval estimation of individual-level causal effects under unobserved confounding | 0.737 | 3 | 2 | 100% |
| 9 | Kallus, N. and Zhou, A (2020) Minimax-optimal policy learning under unobserved confounding | 0.737 | 3 | 2 | 100% |
| 10 | Lorch, S. A., Baiocchi, M., Ahlberg, C. E., and Small, D. S (2012) The differential impact of delivery hospital on the outcomes of premature infants | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 71 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Dynamic Local Average Treatment Effects | 0.874 | 5 | 2 |