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 nonparametric 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 introduce a general single index semiparametric measurement error model for the case that the main covariate of interest is measured with error and modeled parametrically, and where there are many other variables also important to the modeling. We propose a semiparametric bias-correction approach to estimate the effect of the covariate of interest. The resultant estimators are shown to be root-n consistent, asymptotically normal and locally efficient. Comprehensive simulations and an analysis of an empirical data set are performed to demonstrate the finite sample performance and the bias reduction of the locally efficient estimators.

The presence of measurement error may cause bias in parameter estimation and can lead to incorrect conclusions in data analyses. Despite a large body of literature on general measurement error problems, relatively few works exist to handle Poisson models. In this article we thoroughly study Poisson models with errors in covariates and propose consistent and locally efficient semiparametric estimators. We assess the finite sample performance of the estimators through extensive simulation studies and illustrate the proposed methodologies by analyzing data from the Stroke Recovery in Underserved Populations Study. The Canadian Journal of Statistics 47: 157–181; 2019 © 2019 Statistical Society of Canada

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The goal of most empirical studies in social sciences and medical research is to determine whether an alteration in an intervention or a treatment will cause a change in the desired outcome response. Unlike randomized designs, establishing the causal relationship based on observational studies is a challenging problem because the ceteris paribus condition is violated. When the covariates of interest are measured with errors, evaluating the causal effects becomes a thorny issue. We propose a semiparametric method to establish the causal relationship, which yields a consistent estimator of the average causal effect. The method we proposed results in locally efficient estimators of the covariate effects. We study their theoretical properties and demonstrate their finite sample performance on simulated data. We further apply the proposed method to the Stroke Recovery in Underserved Populations (SRUP) study by the National Institute on Aging.