Concordance-Assisted Learning for Estimating Optimal Individualized Treatment Regimes

Journal of the Royal Statistical Society Series B: Statistical Methodology

2018

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Summary A saline feature of data from clinical trials and medical studies is inhomogeneity. Patients not only differ in baseline characteristics, but also the way they respond to treatment. Optimal individualized treatment regimes are developed to select effective treatments based on patient’s heterogeneity. However, the optimal treatment regime might also vary for patients across different subgroups. In this paper, we mainly consider patient’s heterogeneity caused by groupwise individualized treatment effects assuming the same marginal treatment effects for all groups. We propose a new maximin-projection learning for estimating a single treatment decision rule that works reliably for a group of future patients from a possibly new subpopulation. Based on estimated optimal treatment regimes for all subgroups, the proposed maximin treatment regime is obtained by solving a quadratically constrained linear programming (QCLP) problem, which can be efficiently computed by interior-point methods. Consistency and asymptotic normality of the estimator is established. Numerical examples show the reliability of the proposed methodology.

Section: Extensionsmentioning

confidence: 99%

Maximin Projection Learning for Optimal Treatment Decision with Heterogeneous Individualized Treatment Effects

Shi

Journal of the Royal Statistical Society Series B: Statistical Methodology

2018

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“…If the whole problem is offline, many methods have been proposed to solve it (e.g. Murphy, 2003;Zhao et al, 2012;Zhang et al, 2012Zhang et al, , 2013Fan et al, 2017). But when learning decision rules online, we are often faced with the classic dilemma between exploration and exploitation.…”

Section: Introductionmentioning

confidence: 99%

Statistical Inference for Online Decision Making: In a Contextual Bandit Setting

Chen

Journal of the American Statistical Association

2020

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Online decision-making problem requires us to make a sequence of decisions based on incremental information. Common solutions often need to learn a reward model of different actions given the contextual information and then maximize the long-term reward. It is meaningful to know if the posited model is reasonable and how the model performs in the asymptotic sense. We study this problem under the setup of the contextual bandit framework with a linear reward model. The ε-greedy policy is adopted to address the classic exploration-and-exploitation dilemma. Using the martingale central limit theorem, we show that the online ordinary least squares estimator of model parameters is asymptotically normal. When the linear model is misspecified, we propose the online weighted least squares estimator using the inverse propensity score weighting and also establish its asymptotic normality. Based on the properties of the parameter estimators, we further show that the in-sample inverse propensity weighted value estimator is asymptotically normal. We illustrate our results using simulations and an application to a news article recommendation dataset from Yahoo!.

“…Take the AIDS Clinical Trials Group Protocol 175 (ACTG175) study as an example. Many works in the literature have found that the age variable has significant qualitative interaction with the treatment (Lu, Zhang and Zeng, 2013; Fan et al, 2017). It is therefore of great importance to explore the CQTE of a new variable or a set of new variables given the age variable.…”

Section: Introductionmentioning

confidence: 99%

On testing conditional qualitative treatment effects

Shi

2019

Ann. Statist.

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Precision medicine is an emerging medical paradigm that focuses on finding the most effective treatment strategy tailored for individual patients. In the literature, most of the existing works focused on estimating the optimal treatment regime. However, there has been less attention devoted to hypothesis testing regarding the optimal treatment regime. In this paper, we first introduce the notion of conditional qualitative treatment effects (CQTE) of a set of variables given another set of variables and provide a class of equivalent representations for the null hypothesis of no CQTE. The proposed definition of CQTE does not assume any parametric form for the optimal treatment rule and plays an important role for assessing the incremental value of a set of new variables in optimal treatment decision making conditional on an existing set of prescriptive variables. We then propose novel testing procedures for no CQTE based on kernel estimation of the conditional contrast functions. We show that our test statistics have asymptotically correct size and non-negligible power against some nonstandard local alternatives. The empirical performance of the proposed tests are evaluated by simulations and an application to an AIDS data set.