Search for: All records

Summary 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. 

We develop a new method to fit the multivariate response linear regression model that exploits a parametric link between the regression coefficient matrix and the error covariance matrix. Specifically, we assume that the correlations between entries in the multivariate error random vector are proportional to the cosines of the angles between their corresponding re- gression coefficient matrix columns, so as the angle between two regression coefficient matrix columns decreases, the correlation between the corresponding errors increases. We highlight two models under which this parameterization arises: a latent variable reduced-rank regression model and the errors-in-variables regression model. We propose a novel non-convex weighted residual sum of squares criterion which exploits this parameterization and admits a new class of penalized estimators. The optimization is solved with an accelerated proximal gradient de- scent algorithm. Our method is used to study the association between microRNA expression and cancer drug activity measured on the NCI-60 cell lines. An R package implementing our method, MCMVR, is available online. 

To find optimal decision rule, Fan et al. (2016) proposed an innovative concordance-assisted learning algorithm which is based on maximum rank correlation estimator. It makes better use of the available information through pairwise comparison. However the objective function is discontinuous and computationally hard to optimize. In this paper, we consider a convex surrogate loss function to solve this problem. In addition, our algorithm ensures sparsity of decision rule and renders easy interpretation. We derive the L2 error bound of the estimated coefficients under ultra-high dimension. Simulation results of various settings and application to STAR*D both illustrate that the proposed method can still estimate optimal treatment regime successfully when the number of covariates is large.