Quantile-Optimal Treatment Regimes

Wang, Lan; Zhou, Yu; Song, Rui; Sherwood, Ben

doi:10.1080/01621459.2017.1330204

Cited by 61 publications

(52 citation statements)

References 70 publications

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“…Such questions, especially in the medical arena, require answers to thorny risk assessment questions where a distributional perspective on heterogeneous treatment effects can be crucial. A novel perspective on these issues is offered in recent work of Wang, Zhou, Song, and Sherwood (2016) based partially on Manski (2004).…”

Section: Multiple Treatments Concomitant Covariates and Interactionsmentioning

confidence: 99%

Quantile Regression: 40 Years On

2017

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Since Quetelet's work in the 19th century social science has iconified "the average man," that hypothetical man without qualities who is comfortable with his head in the oven, and his feet in a bucket of ice. Conventional statistical methods, since Quetelet, have sought to estimate the effects of policy treatments for this average man. But such effects are often quite heterogenous: medical treatments may improve life expectancy, but also impose serious short term risks; reducing class sizes may improve performance of good students, but not help weaker ones or vice versa. Quantile regression methods can help to explore these heterogeneous effects. Some recent developments in quantile regression methods are surveyed below.

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Section: Multiple Treatments Concomitant Covariates and Interactionsmentioning

confidence: 99%

Quantile Regression: 40 Years On

2017

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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%

“…However, the ITR that maximizes the marginal quantile has its own merits. First, the ITR maximizing the marginal quantile can be estimated in a model‐free way, for example, as studied in the work of Wang et al, but the ITR maximizing the conditional quantile usually cannot because it requires a model for the conditional quantile function Q τ ( x , a ). In this sense, the ITR maximizing the marginal quantile is more robust to model misspecification.…”

Section: New Optimal Treatment Estimation Framework: Robust Regressionmentioning

confidence: 99%

“…Optimal individualized treatment rules based on quantiles have been previously studied in Zhang et al, 9 Linn et al, 10 and Wang et al 11 These papers focus on estimating optimal individualized treatment rules that maximize the marginal quantile of the potential outcome. However, our method is fundamentally different from these works by modeling the conditional quantiles of the response and maximizing the conditional quantile of the potential outcome.…”

Section: Introductionmentioning

confidence: 99%

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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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“…1,2 An optimal treatment regime maximizes the mean utility if applied to select interventions in the patient population of interest. [3][4][5] Optimal treatment regimes have been estimated across a wide range of application areas including anticoagulation, [6][7][8] cancer, 9,10 mental disorders, [11][12][13] and HIV. [14][15][16] In these and nearly all other biomedical application areas, the observed data are subject to missingness, which can include missing measurements, treatments, and outcomes.…”

Section: Introductionmentioning

confidence: 99%

Ascertaining properties of weighting in the estimation of optimal treatment regimes under monotone missingness

Dong

Laber

Goldberg

et al. 2020

Statistics in Medicine

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Dynamic treatment regimes operationalize precision medicine as a sequence of decision rules, one per stage of clinical intervention, that map up-to-date patient information to a recommended intervention. An optimal treatment regime maximizes the mean utility when applied to the population of interest. Methods for estimating an optimal treatment regime assume the data to be fully observed, which rarely occurs in practice. A common approach is to first use multiple imputation and then pool the estimators across imputed datasets. However, this approach requires estimating the joint distribution of patient trajectories, which can be high-dimensional, especially when there are multiple stages of intervention. We examine the application of inverse probability weighted estimating equations as an alternative to multiple imputation in the context of monotonic missingness. This approach applies to a broad class of estimators of an optimal treatment regime including both Q-learning and a generalization of outcome weighted learning. We establish consistency under mild regularity conditions and demonstrate its advantages in finite samples using a series of simulation experiments and an application to a schizophrenia study.

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Quantile-Optimal Treatment Regimes

Cited by 61 publications

References 70 publications

Quantile Regression: 40 Years On

Quantile Regression: 40 Years On

Robust regression for optimal individualized treatment rules

Ascertaining properties of weighting in the estimation of optimal treatment regimes under monotone missingness

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