Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userCollaborative-controlled LASSO for Constructing Propensity Score-based Estimators in High-Dimensional Data
69
0
0.0
(
0
)
Added by
Cheng Ju
Publication date
2017
fields
Mathematical Statistics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
Propensity score (PS) based estimators are increasingly used for causal inference in observational studies. However, model selection for PS estimation in high-dimensional data has received little attention. In these settings, PS models have traditionally been selected based on the goodness-of-fit for the treatment mechanism itself, without consideration of the causal parameter of interest. Collaborative minimum loss-based estimation (C-TMLE) is a novel methodology for causal inference that takes into account information on the causal parameter of interest when selecting a PS model. This collaborative learning considers variable associations with both treatment and outcome when selecting a PS model in order to minimize a bias-variance trade off in the estimated treatment effect. In this study, we introduce a novel approach for collaborative model selection when using the LASSO estimator for PS estimation in high-dimensional covariate settings. To demonstrate the importance of selecting the PS model collaboratively, we designed quasi-experiments based on a real electronic healthcare database, where only the potential outcomes were manually generated, and the treatment and baseline covariates remained unchanged. Results showed that the C-TMLE algorithm outperformed other competing estimators for both point estimation and confidence interval coverage. In addition, the PS model selected by C-TMLE could be applied to other PS-based estimators, which also resulted in substantive improvement for both point estimation and confidence interval coverage. We illustrate the discussed concepts through an empirical example comparing the effects of non-selective nonsteroidal anti-inflammatory drugs with selective COX-2 inhibitors on gastrointestinal complications in a population of Medicare beneficiaries.
rate research
Read More
Inverse probability weighted estimators are the oldest and potentially most commonly used class of procedures for the estimation of causal effects. By adjusting for selection biases via a weighting mechanism, these procedures estimate an effect of interest by constructing a pseudo-population in which selection biases are eliminated. Despite their ease of use, these estimators require the correct specification of a model for the weighting mechanism, are known to be inefficient, and suffer from the curse of dimensionality. We propose a class of nonparametric inverse probability weighted estimators in which the weighting mechanism is estimated via undersmoothing of the highly adaptive lasso, a nonparametric regression function proven to converge at $n^{-1/3}$-rate to the true weighting mechanism. We demonstrate that our estimators are asymptotically linear with variance converging to the nonparametric efficiency bound. Unlike doubly robust estimators, our procedures require neither derivation of the efficient influence function nor specification of the conditional outcome model. Our theoretical developments have broad implications for the construction of efficient inverse probability weighted estimators in large statistical models and a variety of problem settings. We assess the practical performance of our estimators in simulation studies and demonstrate use of our proposed methodology with data from a large-scale epidemiologic study.
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.
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.
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.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
