Resampling‐based confidence intervals for model‐free robust inference on optimal treatment regimes

Wu, Yunan; Wang, Lan

doi:10.1111/biom.13337

Cited by 11 publications

(6 citation statements)

References 55 publications

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“…In order to handle these two challenges, we consider the smoothing methods. [35][36][37] Let (⋅) be a differentiable bounded continuous function satisfying  s→−∞ (s) = 0,  s→+∞ (s) = 1 and some regularity conditions. 35 We use the kernel smooth function  (…”

Section: Penalized Smoothed Inverse Probability Weighted Estimationmentioning

confidence: 99%

“…Second, existing work on threshold regression showed that the asymptotic distribution of the direct estimators for threshold coefficients are often nonstandard, 16,17,19 which is too complicated for statistical inference. In order to handle these two challenges, we consider the smoothing methods 35‐37 . Let

𝒦 false(\cdot false)

be a differentiable bounded continuous function satisfying

\underset{s \to - \infty}{𝒦} (s) = 0

\underset{s \to + \infty}{𝒦} (s) = 1

and some regularity conditions 35 .…”

Section: Models and Estimatesmentioning

confidence: 99%

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Multiply robust subgroup analysis based on a single‐index threshold linear marginal model for longitudinal data with dropouts

Wei

Zhu

Qin

et al. 2022

Statistics in Medicine

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Identifying subpopulations that may be sensitive to the specific treatment is an important step toward precision medicine. On the other hand, longitudinal data with dropouts is common in medical research, and subgroup analysis for this data type is still limited. In this paper, we consider a single‐index threshold linear marginal model, which can be used simultaneously to identify subgroups with differential treatment effects based on linear combination of the selected biomarkers, estimate the treatment effects in different subgroups based on regression coefficients, and test the significance of the difference in treatment effects based on treatment‐subgroup interaction. The regression parameters are estimated by solving a penalized smoothed generalized estimating equation and the selection bias caused by missingness is corrected by a multiply robust weighting matrix, which allows multiple missingness models to be taken account into estimation. The proposed estimator remains consistent when any model for missingness is correctly specified. Under regularity conditions, the asymptotic normality of the estimator is established. Simulation studies confirm the desirable finite‐sample performance of the proposed method. As an application, we analyze the data from a clinical trial on pancreatic cancer.

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Section: Penalized Smoothed Inverse Probability Weighted Estimationmentioning

confidence: 99%

𝒦 false(\cdot false)

be a differentiable bounded continuous function satisfying

\underset{s \to - \infty}{𝒦} (s) = 0

\underset{s \to + \infty}{𝒦} (s) = 1

and some regularity conditions 35 .…”

Section: Models and Estimatesmentioning

confidence: 99%

Multiply robust subgroup analysis based on a single‐index threshold linear marginal model for longitudinal data with dropouts

Wei

Zhu

Qin

et al. 2022

Statistics in Medicine

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show abstract

“…Motivated by Wu and Wang (2021) for mean-optimal treatment regime with complete data, we consider the following smoothed estimator…”

Section: Smoothed Resampling Inferencementioning

confidence: 99%

“…Replacing the indicator function in the treatment regime by the kernel function helps alleviates the sharp edge effect. Write Wu and Wang (2021), it is expected that √ nh β − β 0 is asymptotically normal. Note that β n minimizes the loss function…”

Section: Smoothed Resampling Inferencementioning

confidence: 99%

Transformation-Invariant Learning of Optimal Individualized Decision Rules with Time-to-Event Outcomes

Zhou¹,

Wang²,

Song³

et al. 2022

Preprint

Self Cite

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In many important applications of precision medicine, the outcome of interest is time to an event (e.g., death, relapse of disease) and the primary goal is to identify the optimal individualized decision rule (IDR) to prolong survival time. Existing work in this area have been mostly focused on estimating the optimal IDR to maximize the restricted mean survival time in the population. We propose a new robust framework for estimating an optimal static or dynamic IDR with time-to-event outcomes based on an easy-to-interpret quantile criterion. The new method does not need to specify an outcome regression model and is robust for heavy-tailed distribution. The estimation problem corresponds to a nonregular M-estimation problem with both finite and infinite-dimensional nuisance parameters. Employing advanced empirical process techniques, we establish the statistical theory of the estimated parameter indexing the optimal IDR. Furthermore, we prove a novel result that the proposed approach can consistently estimate the optimal value function under mild conditions even when the optimal IDR is non-unique, which happens in the challenging setting of exceptional laws. We also propose a smoothed resampling procedure for inference. The proposed methods are implemented in the R-package QTOCen. We demonstrate the performance of the proposed new methods via extensive Monte Carlo studies and a real data application.

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“…OPE is an important problem in settings where it is expensive or unethical to directly run an experiment that implements the target policy. This includes applications in precision medicine (Murphy;2003;Chakraborty and Murphy;2014;Matsouaka et al;2014;Gottesman et al;Wu and Wang;2020), autonomous driving 2020),robotics (Kober et al;, natural language processing , education (Mandel et al;2014), among many others. This paper is concerned with OPE under infinite horizon settings where the number of decision points is not necessarily fixed and is allowed to diverge to infinity.…”

Section: Introductionmentioning

confidence: 99%

Off-Policy Confidence Interval Estimation with Confounded Markov Decision Process

Shi¹,

Zhu²,

Ye³

et al. 2022

Preprint

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This paper is concerned with constructing a confidence interval for a target policy's value offline based on a pre-collected observational data in infinite horizon settings. Most of the existing works assume no unmeasured variables exist that confound the observed actions. This assumption, however, is likely to be violated in real applications such as healthcare and technological industries. In this paper, we show that with some auxiliary variables that mediate the effect of actions on the system dynamics, the target policy's value is identifiable in a confounded Markov decision process. Based on this result, we develop an efficient off-policy value estimator that is robust to potential model misspecification and provide rigorous uncertainty quantification. Our method is justified by theoretical results, simulated and real datasets obtained from ridesharing companies.

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Resampling‐based confidence intervals for model‐free robust inference on optimal treatment regimes

Cited by 11 publications

References 55 publications

Multiply robust subgroup analysis based on a single‐index threshold linear marginal model for longitudinal data with dropouts

Multiply robust subgroup analysis based on a single‐index threshold linear marginal model for longitudinal data with dropouts

Transformation-Invariant Learning of Optimal Individualized Decision Rules with Time-to-Event Outcomes

Off-Policy Confidence Interval Estimation with Confounded Markov Decision Process

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