skip to main content

Attention:

The NSF Public Access Repository (NSF-PAR) system and access will be unavailable from 5:00 PM ET until 11:00 PM ET on Friday, June 21 due to maintenance. We apologize for the inconvenience.


Title: Estimating average treatment effects with a double‐index propensity score
Abstract

We consider estimating average treatment effects (ATE) of a binary treatment in observational data when data‐driven variable selection is needed to select relevant covariates from a moderately large number of available covariates . To leverage covariates among predictive of the outcome for efficiency gain while using regularization to fit a parametric propensity score (PS) model, we consider a dimension reduction of based on fitting both working PS and outcome models using adaptive LASSO. A novel PS estimator, the Double‐index Propensity Score (DiPS), is proposed, in which the treatment status is smoothed over the linear predictors for from both the initial working models. The ATE is estimated by using the DiPS in a normalized inverse probability weighting estimator, which is found to maintain double robustness and also local semiparametric efficiency with a fixed number of covariatesp. Under misspecification of working models, the smoothing step leads to gains in efficiency and robustness over traditional doubly robust estimators. These results are extended to the case wherepdiverges with sample size and working models are sparse. Simulations show the benefits of the approach in finite samples. We illustrate the method by estimating the ATE of statins on colorectal cancer risk in an electronic medical record study and the effect of smoking on C‐reactive protein in the Framingham Offspring Study.

 
more » « less
NSF-PAR ID:
10456582
Author(s) / Creator(s):
 ;  ;  ;  
Publisher / Repository:
Oxford University Press
Date Published:
Journal Name:
Biometrics
Volume:
76
Issue:
3
ISSN:
0006-341X
Format(s):
Medium: X Size: p. 767-777
Size(s):
["p. 767-777"]
Sponsoring Org:
National Science Foundation
More Like this
  1. Summary

    Comparative effectiveness research often involves evaluating the differences in the risks of an event of interest between two or more treatments using observational data. Often, the post‐treatment outcome of interest is whether the event happens within a pre‐specified time window, which leads to a binary outcome. One source of bias for estimating the causal treatment effect is the presence of confounders, which are usually controlled using propensity score‐based methods. An additional source of bias is right‐censoring, which occurs when the information on the outcome of interest is not completely available due to dropout, study termination, or treatment switch before the event of interest. We propose an inverse probability weighted regression‐based estimator that can simultaneously handle both confounding and right‐censoring, calling the method CIPWR, with the letter C highlighting the censoring component. CIPWR estimates the average treatment effects by averaging the predicted outcomes obtained from a logistic regression model that is fitted using a weighted score function. The CIPWR estimator has a double robustness property such that estimation consistency can be achieved when either the model for the outcome or the models for both treatment and censoring are correctly specified. We establish the asymptotic properties of the CIPWR estimator for conducting inference, and compare its finite sample performance with that of several alternatives through simulation studies. The methods under comparison are applied to a cohort of prostate cancer patients from an insurance claims database for comparing the adverse effects of four candidate drugs for advanced stage prostate cancer.

     
    more » « less
  2. 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 non-parametric 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.

     
    more » « less
  3. Summary

    Methodological advancements, including propensity score methods, have resulted in improved unbiased estimation of treatment effects from observational data. Traditionally, a “throw in the kitchen sink” approach has been used to select covariates for inclusion into the propensity score, but recent work shows including unnecessary covariates can impact both the bias and statistical efficiency of propensity score estimators. In particular, the inclusion of covariates that impact exposure but not the outcome, can inflate standard errors without improving bias, while the inclusion of covariates associated with the outcome but unrelated to exposure can improve precision. We propose the outcome-adaptive lasso for selecting appropriate covariates for inclusion in propensity score models to account for confounding bias and maintaining statistical efficiency. This proposed approach can perform variable selection in the presence of a large number of spurious covariates, that is, covariates unrelated to outcome or exposure. We present theoretical and simulation results indicating that the outcome-adaptive lasso selects the propensity score model that includes all true confounders and predictors of outcome, while excluding other covariates. We illustrate covariate selection using the outcome-adaptive lasso, including comparison to alternative approaches, using simulated data and in a survey of patients using opioid therapy to manage chronic pain.

     
    more » « less
  4. Abstract

    Semi-supervised (SS) inference has received much attention in recent years. Apart from a moderate-sized labeled data, $\mathcal L$, the SS setting is characterized by an additional, much larger sized, unlabeled data, $\mathcal U$. The setting of $|\mathcal U\ |\gg |\mathcal L\ |$, makes SS inference unique and different from the standard missing data problems, owing to natural violation of the so-called ‘positivity’ or ‘overlap’ assumption. However, most of the SS literature implicitly assumes $\mathcal L$ and $\mathcal U$ to be equally distributed, i.e., no selection bias in the labeling. Inferential challenges in missing at random type labeling allowing for selection bias, are inevitably exacerbated by the decaying nature of the propensity score (PS). We address this gap for a prototype problem, the estimation of the response’s mean. We propose a double robust SS mean estimator and give a complete characterization of its asymptotic properties. The proposed estimator is consistent as long as either the outcome or the PS model is correctly specified. When both models are correctly specified, we provide inference results with a non-standard consistency rate that depends on the smaller size $|\mathcal L\ |$. The results are also extended to causal inference with imbalanced treatment groups. Further, we provide several novel choices of models and estimators of the decaying PS, including a novel offset logistic model and a stratified labeling model. We present their properties under both high- and low-dimensional settings. These may be of independent interest. Lastly, we present extensive simulations and also a real data application.

     
    more » « less
  5. Machine learning (ML) methods for causal inference have gained popularity due to their flexibility to predict the outcome model and the propensity score. In this article, we provide a within-group approach for ML-based causal inference methods in order to robustly estimate average treatment effects in multilevel studies when there is cluster-level unmeasured confounding. We focus on one particular ML-based causal inference method based on the targeted maximum likelihood estimation (TMLE) with an ensemble learner called SuperLearner. Through our simulation studies, we observe that training TMLE within groups of similar clusters helps remove bias from cluster-level unmeasured confounders. Also, using within-group propensity scores estimated from fixed effects logistic regression increases the robustness of the proposed within-group TMLE method. Even if the propensity scores are partially misspecified, the within-group TMLE still produces robust ATE estimates due to double robustness with flexible modeling, unlike parametric-based inverse propensity weighting methods. We demonstrate our proposed methods and conduct sensitivity analyses against the number of groups and individual-level unmeasured confounding to evaluate the effect of taking an eighth-grade algebra course on math achievement in the Early Childhood Longitudinal Study.

     
    more » « less