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Register a new user$Q$- and $A$-Learning Methods for Estimating Optimal Dynamic Treatment Regimes
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In clinical practice, physicians make a series of treatment decisions over the course of a patients disease based on his/her baseline and evolving characteristics. A dynamic treatment regime is a set of sequential decision rules that operationalizes this process. Each rule corresponds to a decision point and dictates the next treatment action based on the accrued information. Using existing data, a key goal is estimating the optimal regime, that, if followed by the patient population, would yield the most favorable outcome on average. Q- and A-learning are two main approaches for this purpose. We provide a detailed account of these methods, study their performance, and illustrate them using data from a depression study.
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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.
Causal inference of treatment effects is a challenging undertaking in it of itself; inference for sequential treatments leads to even more hurdles. In precision medicine, one additional ambitious goal may be to infer about effects of dynamic treatment regimes (DTRs) and to identify optimal DTRs. Conventional methods for inferring about DTRs involve powerful semi-parametric estimators. However, these are not without their strong assumptions. Dynamic Marginal Structural Models (MSMs) are one semi-parametric approach used to infer about optimal DTRs in a family of regimes. To achieve this, investigators are forced to model the expected outcome under adherence to a DTR in the family; relatively straightforward models may lead to bias in the optimum. One way to obviate this difficulty is to perform a grid search for the optimal DTR. Unfortunately, this approach becomes prohibitive as the complexity of regimes considered increases. In recently developed Bayesian methods for dynamic MSMs, computational challenges may be compounded by the fact that at each grid point, a posterior mean must be calculated. We propose a manner by which to alleviate modelling difficulties for DTRs by using Gaussian process optimization. More precisely, we show how to pair this optimization approach with robust estimators for the causal effect of adherence to a DTR to identify optimal DTRs. We examine how to find the optimum in complex, multi-modal settings which are not generally addressed in the DTR literature. We further evaluate the sensitivity of the approach to a variety of modeling assumptions in the Gaussian process.
There is a fast-growing literature on estimating optimal treatment regimes based on randomized trials or observational studies under a key identifying condition of no unmeasured confounding. Because confounding by unmeasured factors cannot generally be ruled out with certainty in observational studies or randomized trials subject to noncompliance, we propose a general instrumental variable approach to learning optimal treatment regimes under endogeneity. Specifically, we establish identification of both value function $E[Y_{mathcal{D}(L)}]$ for a given regime $mathcal{D}$ and optimal regimes $text{argmax}_{mathcal{D}} E[Y_{mathcal{D}(L)}]$ with the aid of a binary instrumental variable, when no unmeasured confounding fails to hold. We also construct novel multiply robust classification-based estimators. Furthermore, we propose to identify and estimate optimal treatment regimes among those who would comply to the assigned treatment under a standard monotonicity assumption. In this latter case, we establish the somewhat surprising result that complier optimal regimes can be consistently estimated without directly collecting compliance information and therefore without the complier average treatment effect itself being identified. Our approach is illustrated via extensive simulation studies and a data application on the effect of child rearing on labor participation.
Data-driven individualized decision making has recently received increasing research interests. Most existing methods rely on the assumption of no unmeasured confounding, which unfortunately cannot be ensured in practice especially in observational studies. Motivated by the recent proposed proximal causal inference, we develop several proximal learning approaches to estimating optimal individualized treatment regimes (ITRs) in the presence of unmeasured confounding. In particular, we establish several identification results for different classes of ITRs, exhibiting the trade-off between the risk of making untestable assumptions and the value function improvement in decision making. Based on these results, we propose several classification-based approaches to finding a variety of restricted in-class optimal ITRs and develop their theoretical properties. The appealing numerical performance of our proposed methods is demonstrated via an extensive simulation study and one real data application.
This paper develops new tools to quantify uncertainty in optimal decision making and to gain insight into which variables one should collect information about given the potential cost of measuring a large number of variables. We investigate simultaneous inference to determine if a group of variables is relevant for estimating an optimal decision rule in a high-dimensional semiparametric framework. The unknown link function permits flexible modeling of the interactions between the treatment and the covariates, but leads to nonconvex estimation in high dimension and imposes significant challenges for inference. We first establish that a local restricted strong convexity condition holds with high probability and that any feasible local sparse solution of the estimation problem can achieve the near-oracle estimation error bound. We further rigorously verify that a wild bootstrap procedure based on a debiased version of the local solution can provide asymptotically honest uniform inference for the effect of a group of variables on optimal decision making. The advantage of honest inference is that it does not require the initial estimator to achieve perfect model selection and does not require the zero and nonzero effects to be well-separated. We also propose an efficient algorithm for estimation. Our simulations suggest satisfactory performance. An example from a diabetes study illustrates the real application.
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