Semiparametric single-index model for estimating optimal individualized treatment strategy

Song, Rui; Luo, Shuyi; Zeng, Donglin; Zhang, Hao Helen; Li, Zhiguo

doi:10.1214/17-ejs1226

Cited by 26 publications

(55 citation statements)

References 25 publications

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“…As an extension of the VC model, the varying-index coefficient model considered in Ma and Song (2015) can be applied to the cases with several covariates and continuous responses. Moreover, an important and related work, Song et al (2017), proposed a semiparametric model in which g 1 has a single-index structure and g 2 is a pure nonparametric function of X. This model suffers from the curse of dimensionality when the number of covariates is large.…”

Section: Methodsmentioning

confidence: 99%

Estimation of Optimal Individualized Treatment Rules Using a Covariate-Specific Treatment Effect Curve With High-Dimensional Covariates

Zhou

2021

Journal of the American Statistical Association

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With a large number of baseline covariates, we propose a new semiparametric modeling strategy for heterogeneous treatment effect estimation and individualized treatment selection, which are two major goals in personalized medicine. We achieve the first goal through estimating a covariate-specific treatment effect (CSTE) curve modeled as an unknown function of a weighted linear combination of all baseline covariates. The weight or the coefficient for each covariate is estimated by fitting a sparse semiparametric logistic single-index coefficient model. The CSTE curve is estimated by a spline-backfitted kernel procedure, which enables us to further construct a simultaneous confidence band (SCB) for the CSTE curve under a desired confidence level. Based on the SCB, we find the subgroups of patients that benefit from each treatment, so that we can make individualized treatment selection. The innovations of the proposed method are 3-fold. First, the proposed method can quantify variability associated with the estimated optimal individualized treatment rule with high-dimensional covariates. Second, the proposed method is very flexible to depict both local and global associations between the treatment and baseline covariates in the presence of high-dimensional covariates, and thus it enjoys flexibility while achieving dimensionality reduction. Third, the SCB achieves the nominal confidence level asymptotically, and it provides a uniform inferential tool in making individualized treatment decisions. Supplementary materials for this article are available online.

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Section: Methodsmentioning

confidence: 99%

Estimation of Optimal Individualized Treatment Rules Using a Covariate-Specific Treatment Effect Curve With High-Dimensional Covariates

Zhou

2021

Journal of the American Statistical Association

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“…Toward that end, an important step is to understand how treatment effect varies across patient characteristics, known as the conditional average treatment effect (CATE) (Rothwell, 2005). A large body of literature focuses on modeling the treatment-specific prognostic score (e.g., Chakraborty et al, 2010;Zhao et al, 2011;Song et al, 2017), since the CATE is simply the difference between the treated and control prognostic scores. However, modeling prognostic scores may lead to an overfitting problem for the CATE, and direct modeling of the CATE may provide a more accurate characterization of treatment effects, avoiding redundancy of non-useful features; see Section 2.2.…”

Section: Introductionmentioning

confidence: 99%

Robust Inference of Conditional Average Treatment Effects Using Dimension Reduction

Huang¹,

Yang²

2023

STAT SINICA

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Personalized treatment aims at tailoring treatments to individual characteristics. An important step is to understand how treatment effect varies across individual characteristics, known as the conditional average treatment effect (CATE). This article concerns making robust inferences of the CATE from observational data, which becomes challenging with multivariate confounder. To reduce the curse of dimensionality while keeping the nonparametric merit, we propose double dimension reductions that achieve different goals: first, we target at identifying the central mean subspace of the CATE directly using dimension reduction in order to detect the most accurate and parsimonious structure of the CATE; second, a nonparametric regression with prior dimension reduction is used to impute counterfactual outcomes, which helps to improve the stability of the imputation. We establish the asymptotic properties of the proposed estimator taking into account the two-step double dimension reduction, and propose an effective bootstrapping procedure without bootstrapping the estimated central mean subspace to make valid inferences. Simulation and applications show that the proposed estimator outperforms existing competitors.

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“…The rules based on machine learning techniques to determine the relationship between clinical outcomes and treatment plus covariates, such as in Zhao et al (2009Zhao et al ( , 2011, are nonparametric and flexible but are often complex and may have large variability. Existing semiparametric methodologies, such as Murphy (2003) and Song et al (2017), flexibly incorporate the relationship between the covariates and the response variables, but are not efficient due to the challenges in estimating the decision rules. Moreover, to the best of our knowledge, these existing semiparametric models do not allow covariate adjusted randomization, where a patient is randomized to one of the treatment arms based on the patient's covariate and a predetermined randomization scheme.…”

Section: Introductionmentioning

confidence: 99%

“…f (X) in (1), is unspecified and inestimable due to the curse of dimensionality caused by the multi-dimension of X. Fourth, different from Song et al (2017) where B-spline expansion were used, we employ kernel smoothing techniques into the estimation and inference for optimal treatment regimes. Fifth, our method is more flexible in terms of model assumptions compared to Zhu et al (2020).…”

Section: Introductionmentioning

confidence: 99%

Flexible Inference of Optimal Individualized Treatment Strategy in Covariate Adjusted Randomization with Multiple Covariates

Ghosh¹,

Song²,

Zhong³

2021

Preprint

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To maximize clinical benefit, clinicians routinely tailor treatment to the individual characteristics of each patient, where individualized treatment rules are needed and are of significant research interest to statisticians. In the covariate-adjusted randomization clinical trial with many covariates, we model the treatment effect with an unspecified function of a single index of the covariates and leave the baseline response completely arbitrary. We devise a class of estimators to consistently estimate the treatment effect function and its associated index while bypassing the estimation of the baseline response, which is subject to the curse of dimensionality. We further develop inference tools to identify predictive covariates and isolate effective treatment region. The usefulness of the methods is demonstrated in both simulations and a clinical data example.

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Semiparametric single-index model for estimating optimal individualized treatment strategy

Cited by 26 publications

References 25 publications

Estimation of Optimal Individualized Treatment Rules Using a Covariate-Specific Treatment Effect Curve With High-Dimensional Covariates

Estimation of Optimal Individualized Treatment Rules Using a Covariate-Specific Treatment Effect Curve With High-Dimensional Covariates

Robust Inference of Conditional Average Treatment Effects Using Dimension Reduction

Flexible Inference of Optimal Individualized Treatment Strategy in Covariate Adjusted Randomization with Multiple Covariates

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