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Propensity score methods are widely used for estimating treatment effectsfrom observational studies. A popular approach is to estimate propensity scoresby maximum likelihood based on logistic regression, and then apply inverseprobability weighted estimators or extensions to estimate treatment effects.However, a challenging issue is that such inverse probability weighting methodsincluding doubly robust methods can perform poorly even when the logistic modelappears adequate as examined by conventional techniques. In addition, there isincreasing difficulty to appropriately estimate propensity scores when dealingwith a large number of covariates. To address these issues, we study calibratedestimation as an alternative to maximum likelihood estimation for fittinglogistic propensity score models. We show that, with possible modelmisspecification, minimizing the expected calibration loss underlying thecalibrated estimators involves reducing both the expected likelihood loss and ameasure of relative errors which controls the mean squared errors of inverseprobability weighted estimators. Furthermore, we propose a regularizedcalibrated estimator by minimizing the calibration loss with a Lasso penalty.We develop a novel Fisher scoring descent algorithm for computing the proposedestimator, and provide a high-dimensional analysis of the resulting inverseprobability weighted estimators of population means, leveraging the control ofrelative errors for calibrated estimation. We present a simulation study and anempirical application to demonstrate the advantages of the proposed methodscompared with maximum likelihood and regularization.

Regularized calibrated estimation of propensity scores with model misspecification and high-dimensional data