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.

The dependence of correlations of neutron multiplicity ν and γ-ray multiplicity Mγ in spontaneous fission of Cf252 on fragment mass A∗ and total kinetic energy (TKE) have been investigated by employing the ratio of Mγ/ν and the form of Mγ(ν). We show for the first time that Mγ and ν have a complex correlation for heavy fragment masses, while there is a positive dependence of Mγ for light fragment masses and for near-symmetric mass splits. The ratio Mγ/ν exhibits strong shell effects for neutron magic number N=50 and near doubly magic number shell closure at Z=50 and N=82. The γ-ray multiplicity Mγ has a maximum for TKE=165-170 MeV. Above 170 MeV Mγ(TKE) is approximately linear, while it deviates significantly from a linear dependence at lower TKE. The correlation between the average neutron and γ-ray multiplicities can be partly reproduced by model calculations.