Performance guarantees for individualized treatment rules

Qian, Min; Murphy, Susan A.

doi:10.1214/10-aos864

Cited by 470 publications

(661 citation statements)

References 35 publications

Supporting

Mentioning

657

Contrasting

Order By: Relevance

“…The reason why we compare our sHinge method with the ROWSi is that Xu et al (2015) showed by simulation that the ROWSi was superior over the method solving (9) with h k replaced by the hinge loss, which was proposed in Zhao et al (2012) except that LASSO penalty instead of L 2 penalty was used for variable selection. Xu et al (2015) also showed by simulation that ROWSi was superior over other four recently proposed methods, the interaction tree by Su, Tsai, Wang, Nickerson, and Li (2009), the virtual twins by Foster, Taylor, and Ruberg (2011), the logistic regression with LASSO penalty by Qian and Murphy (2011), and the FindIt by Imai and Ratkovic (2013).…”

Section: Simulation Resultsmentioning

confidence: 89%

See 1 more Smart Citation

Personalised treatment assignment maximising expected benefit with smooth hinge loss

Liu

Shao

2017

Statistical Theory and Related Fields

View full text Add to dashboard Cite

In personalised medicine, the goal is to make a treatment recommendation for each patient with a given set of covariates to maximise the treatment benefit measured by patient's response to the treatment. In application, such a treatment assignment rule is constructed using a sample training data consisting of patients' responses and covariates. Instead of modelling responses using treatments and covariates, an alternative approach is maximising a response-weighted target function whose value directly reflects the effectiveness of treatment assignments. Since the target function involves a loss function, efforts have been made recently on the choice of the loss function to ensure a computationally feasible and theoretically sound solution. We propose to use a smooth hinge loss function so that the target function is convex and differentiable, which possesses good asymptotic properties and numerical advantages. To further simplify the computation and interpretability, we focus on the rules that are linear functions of covariates and discuss their asymptotic properties. We also examine the performances of our method with simulation studies and real data analysis.

show abstract

Section: Simulation Resultsmentioning

confidence: 89%

“…Let D(X) be a treatment assignment rule as a function of X, P be the joint distribution of (Y, T, X), and P D be the conditional distribution of (Y, T, X) given T = D(X). Then, the expected outcome under rule D is given by (Qian & Murphy, 2011) …”

Section: Target Function Hinge Loss and Linear Rulesmentioning

confidence: 99%

Personalised treatment assignment maximising expected benefit with smooth hinge loss

Liu

Shao

2017

Statistical Theory and Related Fields

View full text Add to dashboard Cite

show abstract

“…Qian and Murphy (2011) propose a plug-in approach using E(Y d |X) estimated by penalized least squares. They derive welfare convergence rate of n −1/2 or better (with a margin condition), assuming that E(Y d |X) is well approximated by a sparse representation.…”

Section: Related Literaturementioning

confidence: 99%

Who should be treated? Empirical welfare maximization methods for treatment choice

Kitagawa

Tetenov²

2017

View full text Add to dashboard Cite

One of the main objectives of empirical analysis of experiments and quasi-experiments is to inform policy decisions that determine the allocation of treatments to individuals with different observable covariates. We study the properties and implementation of the Empirical Welfare Maximization (EWM) method, which estimates a treatment assignment policy by maximizing the sample analog of average social welfare over a class of candidate treatment policies. The EWM approach is attractive in terms of both statistical performance and practical implementation in realistic settings of policy design. Common features of these settings include: (i) feasible treatment assignment rules are constrained exogenously for ethical, legislative, or political reasons, (ii) a policy maker wants a simple treatment assignment rule based on one or more eligibility scores in order to reduce the dimensionality of individual observable characteristics, and/or (iii) the proportion of individuals who can receive the treatment is a priori limited due to a budget or a capacity constraint. We show that when the propensity score is known, the average social welfare attained by EWM rules converges at least at n −1/2 rate to the maximum obtainable welfare uniformly over a minimally constrained class of data distributions, and this uniform convergence rate is minimax optimal. We examine how the uniform convergence rate depends on the richness of the class of candidate decision rules, the distribution of conditional treatment effects, and the lack of knowledge of the propensity score. We offer easily implementable algorithms for computing the EWM rule and an application using experimental data from the National JTPA Study.

show abstract

“…In this respect, it is related to other approaches that aim at computing performance guarantees on the returns of inferred policies [24], [25], [26].…”

Section: Related Workmentioning

confidence: 99%

Lipschitz robust control from off-policy trajectories

Fonteneau

Ernst

Boigelot

et al. 2014

53rd IEEE Conference on Decision and Control

View full text Add to dashboard Cite

Abstract-We study the min max optimization problem introduced in [Fonteneau et al. (2011), "Towards min max reinforcement learning", Springer CCIS, vol. 129, for computing control policies for batch mode reinforcement learning in a deterministic setting with fixed, finite optimization horizon. First, we state that the min part of this problem is NP-hard. We then provide two relaxation schemes. The first relaxation scheme works by dropping some constraints in order to obtain a problem that is solvable in polynomial time. The second relaxation scheme, based on a Lagrangian relaxation where all constraints are dualized, can also be solved in polynomial time. We theoretically show that both relaxation schemes provide better results than those given in [Fonteneau et al. (2011)].

show abstract

Performance guarantees for individualized treatment rules

Cited by 470 publications

References 35 publications

Personalised treatment assignment maximising expected benefit with smooth hinge loss

Personalised treatment assignment maximising expected benefit with smooth hinge loss

Who should be treated? Empirical welfare maximization methods for treatment choice

Lipschitz robust control from off-policy trajectories

Contact Info

Product

Resources

About