Interactive
            <i>Q</i>
            -Learning for Quantiles

Linn, Kristin A.; Laber, Eric B.; Stefanski, Leonard A.

doi:10.1080/01621459.2016.1155993

Cited by 43 publications

(34 citation statements)

References 50 publications

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“…Then, the conditional quantile‐based optimal individualized treatment rule is defined as

g_{τ}^{opt} (x) = {argmax}_{a \in A} Q_{τ} (x, a), τ \in (0, 1) .

For a conditional quantile‐based treatment rule g , the value function is defined as V τ ( g ) = E X [ Q τ { X , g ( X )}] and

g_{τ}^{opt} = {argmax}_{g} V_{τ} false(g false)

. It is noted that our defined value function is different from those recently studied in the literature . Specifically, they considered the marginal cumulative distribution function of the potential outcome,

F_{Y_{i}^{*} false(a false)} false(y false) = pr false{Y_{i}^{*} false(a false) \leq y false}

.…”

Section: New Optimal Treatment Estimation Framework: Robust Regressionmentioning

confidence: 99%

Robust regression for optimal individualized treatment rules

Wei

Zhang

2019

Statistics in Medicine

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Because different patients may respond quite differently to the same drug or treatment, there is increasing interest in discovering individualized treatment rules. In particular, there is an emerging need to find optimal individualized treatment rules which would lead to the “best” clinical outcome. In this paper, we propose a new class of loss functions and estimators based on robust regression to estimate the optimal individualized treatment rules. Compared to existing estimation methods in the literature, the new estimators are novel and advantageous in the following aspects: first, they are robust against skewed, heterogeneous, heavy-tailed errors or outliers in data; second, they are robust against a misspecification of the baseline function; third, under some general situations, the new estimator coupled with the pinball loss approximately maximizes the outcome’s conditional quantile instead of the conditional mean, which leads to a more robust optimal individualized treatment rule than traditional mean-based estimators. Consistency and asymptotic normality of the proposed estimators are established. Their empirical performance is demonstrated via extensive simulation studies and an analysis of an AIDS data set.

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“…Then, the conditional quantile‐based optimal individualized treatment rule is defined as

g_{τ}^{opt} (x) = {argmax}_{a \in A} Q_{τ} (x, a), τ \in (0, 1) .

For a conditional quantile‐based treatment rule g , the value function is defined as V τ ( g ) = E X [ Q τ { X , g ( X )}] and

g_{τ}^{opt} = {argmax}_{g} V_{τ} false(g false)

F_{Y_{i}^{*} false(a false)} false(y false) = pr false{Y_{i}^{*} false(a false) \leq y false}

.…”

Section: New Optimal Treatment Estimation Framework: Robust Regressionmentioning

confidence: 99%

Robust regression for optimal individualized treatment rules

Wei

Zhang

2019

Statistics in Medicine

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“…() and Linn et al . () (see also chapter 7 of Chakraborty and Moodie, ). Such examples are rare, however, and typically grounded in methods that do not offer a great deal of flexibility or robustness in modeling.…”

Section: Introductionmentioning

confidence: 99%

Model Selection for G-Estimation of Dynamic Treatment Regimes

2019

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Dynamic treatment regimes (DTRs) aim to formalize personalized medicine by tailoring treatment decisions to individual patient characteristics. G-estimation for DTR identification targets the parameters of a structural nested mean model, known as the blip function, from which the optimal DTR is derived. Despite its potential, G-estimation has not seen widespread use in the literature, owing in part to its often complex presentation and implementation, but also due to the necessity for correct specification of the blip. Using a quadratic approximation approach inspired by iteratively reweighted least squares, we derive a quasilikelihood function for G-estimation within the DTR framework, and show how it can be used to form an information criterion for blip model selection. We outline the theoretical properties of this model selection criterion and demonstrate its application in a variety of simulation studies as well as in data from the Sequenced Treatment Alternatives to Relieve Depression study. K E Y W O R D S adaptive treatment strategies, dynamic treatment regimes, iteratively reweighted least squares, quasi-likelihood information criterion, structural nested models E Y log( [ ( ) ]) = log( [ ]) − J J j J opt = 1

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“…Examples include Murphy (2003); Robins (2004); Henderson et al (2010), and Henderson et al (2011). In Q-learning, where Q is taken from quality, the response itself is modelled at each decision time as a function of history to date, and optimal actions are determined sequentially Laber et al, 2014;Moodie et al, 2014;Wallace and Moodie, 2015;Song et al, 2015;Linn et al, 2017). A-and Q-learning are reviewed by Chakraborty and Moodie (2013) and Schulte et al (2014).…”

Section: Introductionmentioning

confidence: 99%

Adaptive treatment and robust control

et al. 2020

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A control theory perspective on determination of optimal dynamic treatment regimes is considered. The aim is to adapt statistical methodology that has been developed for medical or other biostatistical applications so as to incorporate powerful control techniques that have been designed for engineering or other technological problems. Data tend to be sparse and noisy in the biostatistical area and interest has tended to be in statistical inference for treatment effects. In engineering fields, experimental data can be more easily obtained and reproduced and interest is more often in performance and stability of proposed controllers rather than modelling and inference per se. We propose that modelling and estimation be based on standard statistical techniques but subsequent treatment policy be obtained from robust control. To bring focus, we concentrate on A-learning methodology as developed in the biostatistical literature and H ∞-synthesis from control theory. Simulations and two applications demonstrate robustness of the H ∞ strategy compared to standard A-learning in the presence of model misspecification or measurement error.

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Interactive Q -Learning for Quantiles

Cited by 43 publications

References 50 publications

Robust regression for optimal individualized treatment rules

Robust regression for optimal individualized treatment rules

Model Selection for G-Estimation of Dynamic Treatment Regimes

Adaptive treatment and robust control

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