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Register a new userSelective Inference in Propensity Score Analysis
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Added by
Yoshiyuki Ninomiya
Publication date
2021
fields
Mathematical Statistics
and research's language is
English
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Selective inference (post-selection inference) is a methodology that has attracted much attention in recent years in the fields of statistics and machine learning. Naive inference based on data that are also used for model selection tends to show an overestimation, and so the selective inference conditions the event that the model was selected. In this paper, we develop selective inference in propensity score analysis with a semiparametric approach, which has become a standard tool in causal inference. Specifically, for the most basic causal inference model in which the causal effect can be written as a linear sum of confounding variables, we conduct Lasso-type variable selection by adding an $ell_1$ penalty term to the loss function that gives a semiparametric estimator. Confidence intervals are then given for the coefficients of the selected confounding variables, conditional on the event of variable selection, with asymptotic guarantees. An important property of this method is that it does not require modeling of nonparametric regression functions for the outcome variables, as is usually the case with semiparametric propensity score analysis.
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In this paper, we propose a propensity score adapted variable selection procedure to select covariates for inclusion in propensity score models, in order to eliminate confounding bias and improve statistical efficiency in observational studies. Our variable selection approach is specially designed for causal inference, it only requires the propensity scores to be $sqrt{n}$-consistently estimated through a parametric model and need not correct specification of potential outcome models. By using estimated propensity scores as inverse probability treatment weights in performing an adaptive lasso on the outcome, it successfully excludes instrumental variables, and includes confounders and outcome predictors. We show its oracle properties under the linear association conditions. We also perform some numerical simulations to illustrate our propensity score adapted covariate selection procedure and evaluate its performance under model misspecification. Comparison to other covariate selection methods is made using artificial data as well, through which we find that it is more powerful in excluding instrumental variables and spurious covariates.
Understanding how treatment effects vary on individual characteristics is critical in the contexts of personalized medicine, personalized advertising and policy design. When the characteristics are of practical interest are only a subset of full covariate, non-parametric estimation is often desirable; but few methods are available due to the computational difficult. Existing non-parametric methods such as the inverse probability weighting methods have limitations that hinder their use in many practical settings where the values of propensity scores are close to 0 or 1. We propose the propensity score regression (PSR) that allows the non-parametric estimation of the heterogeneous treatment effects in a wide context. PSR includes two non-parametric regressions in turn, where it first regresses on the propensity scores together with the characteristics of interest, to obtain an intermediate estimate; and then, regress the intermediate estimates on the characteristics of interest only. By including propensity scores as regressors in the non-parametric manner, PSR is capable of substantially easing the computational difficulty while remain (locally) insensitive to any value of propensity scores. We present several appealing properties of PSR, including the consistency and asymptotical normality, and in particular the existence of an explicit variance estimator, from which the analytical behaviour of PSR and its precision can be assessed. Simulation studies indicate that PSR outperform existing methods in varying settings with extreme values of propensity scores. We apply our method to the national 2009 flu survey (NHFS) data to investigate the effects of seasonal influenza vaccination and having paid sick leave across different age groups.
The two-stage process of propensity score analysis (PSA) includes a design stage where propensity scores are estimated and implemented to approximate a randomized experiment and an analysis stage where treatment effects are estimated conditional upon the design. This paper considers how uncertainty associated with the design stage impacts estimation of causal effects in the analysis stage. Such design uncertainty can derive from the fact that the propensity score itself is an estimated quantity, but also from other features of the design stage tied to choice of propensity score implementation. This paper offers a procedure for obtaining the posterior distribution of causal effects after marginalizing over a distribution of design-stage outputs, lending a degree of formality to Bayesian methods for PSA (BPSA) that have gained attention in recent literature. Formulation of a probability distribution for the design-stage output depends on how the propensity score is implemented in the design stage, and propagation of uncertainty into causal estimates depends on how the treatment effect is estimated in the analysis stage. We explore these differences within a sample of commonly-used propensity score implementations (quantile stratification, nearest-neighbor matching, caliper matching, inverse probability of treatment weighting, and doubly robust estimation) and investigate in a simulation study the impact of statistician choice in PS model and implementation on the degree of between- and within-design variability in the estimated treatment effect. The methods are then deployed in an investigation of the association between levels of fine particulate air pollution and elevated exposure to emissions from coal-fired power plants.
Most epidemiologic cohorts are composed of volunteers who do not represent the general population. To enable population inference from cohorts, we and others have proposed utilizing probability survey samples as external references to develop a propensity score (PS) for membership in the cohort versus survey. Herein we develop a unified framework for PS-based weighting (such as inverse PS weighting (IPSW)) and matching methods (such as kernel-weighting (KW) method). We identify a fundamental Strong Exchangeability Assumption (SEA) underlying existing PS-based matching methods whose failure invalidates inference even if the PS-model is correctly specified. We relax the SEA to a Weak Exchangeability Assumption (WEA) for the matching method. Also, we propose IPSW.S and KW.S methods that reduce the variance of PS-based estimators by scaling the survey weights used in the PS estimation. We prove consistency of the IPSW.S and KW.S estimators of population means and prevalences under WEA, and provide asymptotic variances and consistent variance estimators. In simulations, the KW.S and IPSW.S estimators had smallest MSE. In our data example, the original KW estimates had large bias, whereas the KW.S estimates had the smallest MSE.
Inverse probability of treatment weighting (IPTW) is a popular method for estimating the average treatment effect (ATE). However, empirical studies show that the IPTW estimators can be sensitive to the misspecification of the propensity score model. To address this problem, researchers have proposed to estimate propensity score by directly optimizing the balance of pre-treatment covariates. While these methods appear to empirically perform well, little is known about how the choice of balancing conditions affects their theoretical properties. To fill this gap, we first characterize the asymptotic bias and efficiency of the IPTW estimator based on the Covariate Balancing Propensity Score (CBPS) methodology under local model misspecification. Based on this analysis, we show how to optimally choose the covariate balancing functions and propose an optimal CBPS-based IPTW estimator. This estimator is doubly robust; it is consistent for the ATE if either the propensity score model or the outcome model is correct. In addition, the proposed estimator is locally semiparametric efficient when both models are correctly specified. To further relax the parametric assumptions, we extend our method by using a sieve estimation approach. We show that the resulting estimator is globally efficient under a set of much weaker assumptions and has a smaller asymptotic bias than the existing estimators. Finally, we evaluate the finite sample performance of the proposed estimators via simulation and empirical studies. An open-source software package is available for implementing the proposed methods.
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