Sufficient Dimension Reduction for Feasible and Robust Estimation of Average Causal Effect.
Ontology highlight
ABSTRACT:
SUBMITTER: Ghosh T
PROVIDER: S-EPMC8439424 | biostudies-literature |
REPOSITORIES: biostudies-literature
Similar Datasets
Project description:The estimation of treatment effects based on observational data usually involves multiple confounders, and dimension reduction is often desirable and sometimes inevitable. We first clarify the definition of a central subspace that is relevant for the efficient estimation of average treatment effects. A criterion is then proposed to simultaneously estimate the structural dimension, the basis matrix of the joint central subspace, and the optimal bandwidth for estimating the conditional treatment effects. The method can easily be implemented by forward selection. Semiparametric efficient estimation of average treatment effects can be achieved by averaging the conditional treatment effects with a different data-adaptive bandwidth to ensure optimal undersmoothing. Asymptotic properties of the estimated joint central subspace and the corresponding estimator of average treatment effects are studied. The proposed methods are applied to a nutritional study, where the covariate dimension is reduced from 11 to an effective dimension of one.
| S-EPMC5793490 | biostudies-literature
Project description:We develop an efficient estimation procedure for identifying and estimating the central subspace. Using a new way of parameterization, we convert the problem of identifying the central subspace to the problem of estimating a finite dimensional parameter in a semiparametric model. This conversion allows us to derive an efficient estimator which reaches the optimal semiparametric efficiency bound. The resulting efficient estimator can exhaustively estimate the central subspace without imposing any distributional assumptions. Our proposed efficient estimation also provides a possibility for making inference of parameters that uniquely identify the central subspace. We conduct simulation studies and a real data analysis to demonstrate the finite sample performance in comparison with several existing methods.
| S-EPMC3777433 | biostudies-literature
Project description:A fundamental assumption used in causal inference with observational data is that treatment assignment is ignorable given measured confounding variables. This assumption of no missing confounders is plausible if a large number of baseline covariates are included in the analysis, as we often have no prior knowledge of which variables can be important confounders. Thus, estimation of treatment effects with a large number of covariates has received considerable attention in recent years. Most existing methods require specifying certain parametric models involving the outcome, treatment and confounding variables, and employ a variable selection procedure to identify confounders. However, selection of a proper set of confounders depends on correct specification of the working models. The bias due to model misspecification and incorrect selection of confounding variables can yield misleading results. We propose a robust and efficient approach for inference about the average treatment effect via a flexible modeling strategy incorporating penalized variable selection. Specifically, we consider an estimator constructed based on an efficient influence function that involves a propensity score and an outcome regression. We then propose a new sparse sufficient dimension reduction method to estimate these two functions without making restrictive parametric modeling assumptions. The proposed estimator of the average treatment effect is asymptotically normal and semiparametrically efficient without the need for variable selection consistency. The proposed methods are illustrated via simulation studies and a biomedical application.
| S-EPMC6588012 | biostudies-literature
Project description:Methodology of sufficient dimension reduction (SDR) has offered an effective means to facilitate regression analysis of high-dimensional data. When the response is censored, however, most existing SDR estimators cannot be applied, or require some restrictive conditions. In this article, we propose a new class of inverse censoring probability weighted SDR estimators for censored regressions. Moreover, regularization is introduced to achieve simultaneous variable selection and dimension reduction. Asymptotic properties and empirical performance of the proposed methods are examined.
| S-EPMC3018713 | biostudies-literature
Project description:Recent efforts to characterize the human microbiome and its relation to chronic diseases have led to a surge in statistical development for compositional data. We develop likelihood-based sufficient dimension reduction methods (SDR) to find linear combinations that contain all the information in the compositional data on an outcome variable, i.e., are sufficient for modeling and prediction of the outcome. We consider several models for the inverse regression of the compositional vector or transformations of it, as a function of outcome. They include normal, multinomial, and Poisson graphical models that allow for complex dependencies among observed counts. These methods yield efficient estimators of the reduction and can be applied to continuous or categorical outcomes. We incorporate variable selection into the estimation via penalties and address important invariance issues arising from the compositional nature of the data. We illustrate and compare our methods and some established methods for analyzing microbiome data in simulations and using data from the Human Microbiome Project. Displaying the data in the coordinate system of the SDR linear combinations allows visual inspection and facilitates comparisons across studies.
| S-EPMC8677486 | biostudies-literature
Project description:Motivated by a study conducted to evaluate the associations of 51 inflammatory markers and lung cancer risk, we propose several approaches of varying computational complexity for analyzing multiple correlated markers that are also censored due to lower and/or upper limits of detection, using likelihood-based sufficient dimension reduction (SDR) methods. We extend the theory and the likelihood-based SDR framework in two ways: (i) we accommodate censored predictors directly in the likelihood, and (ii) we incorporate variable selection. We find linear combinations that contain all the information that the correlated markers have on an outcome variable (i.e., are sufficient for modeling and prediction of the outcome) while accounting for censoring of the markers. These methods yield efficient estimators and can be applied to any type of outcome, including continuous and categorical. We illustrate and compare all methods using data from the motivating study and in simulations. We find that explicitly accounting for the censoring in the likelihood of the SDR methods can lead to appreciable gains in efficiency and prediction accuracy, and also outperformed multiple imputations combined with standard SDR.
| S-EPMC6543825 | biostudies-literature
Project description:We consider estimation of the causal effect of a binary treatment on an outcome, conditionally on covariates, from observational studies or natural experiments in which there is a binary instrument for treatment. We describe a doubly robust, locally efficient estimator of the parameters indexing a model for the local average treatment effect conditionally on covariates V when randomization of the instrument is only true conditionally on a high dimensional vector of covariates X, possibly bigger than V. We discuss the surprising result that inference is identical to inference for the parameters of a model for an additive treatment effect on the treated conditionally on V that assumes no treatment-instrument interaction. We illustrate our methods with the estimation of the local average effect of participating in 401(k) retirement programs on savings by using data from the US Census Bureau's 1991 Survey of Income and Program Participation.
| S-EPMC4315264 | biostudies-literature
Project description:The problem of estimating the average treatment effects is important when evaluating the effectiveness of medical treatments or social intervention policies. Most of the existing methods for estimating the average treatment effect rely on some parametric assumptions about the propensity score model or the outcome regression model one way or the other. In reality, both models are prone to misspecification, which can have undue influence on the estimated average treatment effect. We propose an alternative robust approach to estimating the average treatment effect based on observational data in the challenging situation when neither a plausible parametric outcome model nor a reliable parametric propensity score model is available. Our estimator can be considered as a robust extension of the popular class of propensity score weighted estimators. This approach has the advantage of being robust, flexible, data adaptive, and it can handle many covariates simultaneously. Adopting a dimension reduction approach, we estimate the propensity score weights semiparametrically by using a non-parametric link function to relate the treatment assignment indicator to a low-dimensional structure of the covariates which are formed typically by several linear combinations of the covariates. We develop a class of consistent estimators for the average treatment effect and study their theoretical properties. We demonstrate the robust performance of the estimators on simulated data and a real data example of investigating the effect of maternal smoking on babies' birth weight.
| S-EPMC6089681 | biostudies-literature
Project description:Gene set analysis (GSA) aims to evaluate the association between the expression of biological pathways, or a priori defined gene sets, and a particular phenotype. Numerous GSA methods have been proposed to assess the enrichment of sets of genes. However, most methods are developed with respect to a specific alternative scenario, such as a differential mean pattern or a differential coexpression. Moreover, a very limited number of methods can handle either binary, categorical, or continuous phenotypes. In this paper, we develop two novel GSA tests, called SDRs, based on the sufficient dimension reduction technique, which aims to capture sufficient information about the relationship between genes and the phenotype. The advantages of our proposed methods are that they allow for categorical and continuous phenotypes, and they are also able to identify a variety of enriched gene sets.Through simulation studies, we compared the type I error and power of SDRs with existing GSA methods for binary, triple, and continuous phenotypes. We found that SDR methods adequately control the type I error rate at the pre-specified nominal level, and they have a satisfactory power to detect gene sets with differential coexpression and to test non-linear associations between gene sets and a continuous phenotype. In addition, the SDR methods were compared with seven widely-used GSA methods using two real microarray datasets for illustration.We concluded that the SDR methods outperform the others because of their flexibility with regard to handling different kinds of phenotypes and their power to detect a wide range of alternative scenarios. Our real data analysis highlights the differences between GSA methods for detecting enriched gene sets.
| S-EPMC4744442 | biostudies-literature
Project description:In high-dimensional data analysis, it is of primary interest to reduce the data dimensionality without loss of information. Sufficient dimension reduction (SDR) arises in this context, and many successful SDR methods have been developed since the introduction of sliced inverse regression (SIR) [Li (1991) Journal of the American Statistical Association 86, 316-327]. Despite their fast progress, though, most existing methods target on regression problems with a continuous response. For binary classification problems, SIR suffers the limitation of estimating at most one direction since only two slices are available. In this article, we develop a new and flexible probability-enhanced SDR method for binary classification problems by using the weighted support vector machine (WSVM). The key idea is to slice the data based on conditional class probabilities of observations rather than their binary responses. We first show that the central subspace based on the conditional class probability is the same as that based on the binary response. This important result justifies the proposed slicing scheme from a theoretical perspective and assures no information loss. In practice, the true conditional class probability is generally not available, and the problem of probability estimation can be challenging for data with large-dimensional inputs. We observe that, in order to implement the new slicing scheme, one does not need exact probability values and the only required information is the relative order of probability values. Motivated by this fact, our new SDR procedure bypasses the probability estimation step and employs the WSVM to directly estimate the order of probability values, based on which the slicing is performed. The performance of the proposed probability-enhanced SDR scheme is evaluated by both simulated and real data examples.
| S-EPMC4670268 | biostudies-literature