Stable Weights that Balance Covariates for Estimation With Incomplete Outcome Data

Zubizarreta, José R.

doi:10.1080/01621459.2015.1023805

Cited by 296 publications

(348 citation statements)

References 40 publications

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“…When

p ≫ n_{normalc}

, there will in general be no weights γ i for which

{\overset{X}{true}}_{normalt} - {normalΣ}_{{i : W_{i} = 0}} γ_{i} X_{i} = 0

, and even in settings where

p < n_{normalc}

but p is large such estimators would not have good properties. Zubizarreta () extended the balancing weights approach to allow for weights that achieve approximate balance instead of exact balance; however, directly using his approach does not allow for √ n ‐consistent estimation in a regime where p is much larger than n .…”

Section: Estimating Average Treatment Effects In High Dimensionsmentioning

confidence: 99%

“…Approximate balancing on all pretreatment variables (rather than exact balance on a subset of features, as in a regularized regression, or weighting using a regularized propensity model that may not be able to capture all relevant dimensions) enables us to guarantee that the bias arising from a potential failure to adjust for a large number of weak confounders can be bounded. Formally, this second step of reweighting residuals by using the weights that were proposed by Zubizarreta () is closely related to debiasing corrections studied in the high dimensional regression literature (Javanmard and Montanari, ; Van de Geer et al ., ; Zhang and Zhang, ); we comment further on this connection in Section .…”

Section: Introductionmentioning

confidence: 99%

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Approximate Residual Balancing: Debiased Inference of Average Treatment Effects in High Dimensions

Athey

Imbens

Wager

2018

Journal of the Royal Statistical Society Series B: Statistical Methodology

281

295

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Summary There are many settings where researchers are interested in estimating average treatment effects and are willing to rely on the unconfoundedness assumption, which requires that the treatment assignment be as good as random conditional on pretreatment variables. The unconfoundedness assumption is often more plausible if a large number of pretreatment variables are included in the analysis, but this can worsen the performance of standard approaches to treatment effect estimation. We develop a method for debiasing penalized regression adjustments to allow sparse regression methods like the lasso to be used for √n‐consistent inference of average treatment effects in high dimensional linear models. Given linearity, we do not need to assume that the treatment propensities are estimable, or that the average treatment effect is a sparse contrast of the outcome model parameters. Rather, in addition to standard assumptions used to make lasso regression on the outcome model consistent under 1‐norm error, we require only overlap, i.e. that the propensity score be uniformly bounded away from 0 and 1. Procedurally, our method combines balancing weights with a regularized regression adjustment.

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“…When

p ≫ n_{normalc}

, there will in general be no weights γ i for which

{\overset{X}{true}}_{normalt} - {normalΣ}_{{i : W_{i} = 0}} γ_{i} X_{i} = 0

, and even in settings where

p < n_{normalc}

Section: Estimating Average Treatment Effects In High Dimensionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Approximate Residual Balancing: Debiased Inference of Average Treatment Effects in High Dimensions

Athey

Imbens

Wager

2018

Journal of the Royal Statistical Society Series B: Statistical Methodology

281

295

View full text Add to dashboard Cite

show abstract

“…Several other techniques similar to the covariate balancing propensity method that estimate propensity score weights with methods beyond logistic regression have been proposed 22;23;24 . Many of them design weights that are not equal to the inverse of the propensity score but are chosen explicitly to optimize balance between the covariate distributions in the exposed and control groups.…”

Section: Other Design-based Alternatives To Covariate Balancing Propementioning

confidence: 99%

The Right Tool for the Job

et al. 2017

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Estimating the causal effect of an exposure (versus some control) on an outcome using observational data often requires addressing the fact that exposed and control groups differ on pre-exposure characteristics that may be related to the outcome (confounders). Propensity score methods have long been used as a tool for adjusting for observed confounders in order to produce more valid causal effect estimates under the strong ignorability assumption. In this article, we compare two promising propensity score estimation methods (for time invariant binary exposures) when assessing the average treatment effect on the treated: the generalized boosted models and covariate-balancing propensity scores, with the main objective to provide analysts with some rules-of-thumb when choosing between these two methods. We compare the methods across different dimensions including the presence of extraneous variables, the complexity of the relationship between exposure or outcome and covariates, and the residual variance in outcome and exposure. We found that when non-complex relationships exist between outcome or exposure and covariates, the covariate-balancing method outperformed the boosted method, but under complex relationships, the boosted method performed better. We lay out criteria for when one method should be expected to outperform the other with no blanket statement on whether one method is always better than the other.

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“…In particular, note that the score equations

P_{n} D_{A, \overset{g}{true}, \overset{λ}{true}} = 0

and

P_{n} D_{M, \overset{g}{true}, \overset{λ}{true}} = 0

are balancing equations that ensure that the empirical mean of

italicê false(W false)

is equal to its reweighted mean when using weights

A_{i} false/ {\overset{g}{true}}_{A} false(W_{i} false)

and

A_{i} M_{i} false/ \overset{g}{true} false(W_{i} false)

. Covariate‐balanced estimators have been traditionally used to reduce bias in observational studies and missing data models, but covariate selection for balancing remains an open problem. We conjecture that our theory may help to solve this problem by shedding light on key transformations of the covariates that require balance, such as

italicê false(W false)

.…”

Section: Discussionmentioning

confidence: 99%

Doubly robust inference for targeted minimum loss–based estimation in randomized trials with missing outcome data

Díaz

Laan

2017

Statistics in Medicine

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Missing outcome data is one of the principal threats to the validity of treatment effect estimates from randomized trials. The outcome distributions of participants with missing and observed data are often different, which increases the risk of bias. Causal inference methods may aid in reducing the bias and improving efficiency by incorporating baseline variables into the analysis. In particular, doubly robust estimators incorporate estimates of two nuisance parameters: the outcome regression and the missingness mechanism (i.e., the probability of missingness conditional on treatment assignment and baseline variables), to adjust for differences in the observed and unobserved groups that can be explained by observed covariates.To obtain consistent estimators of the treatment effect, one of these two nuisance parameters mechanism must be consistently estimated. Such nuisance parameters are traditionally estimated using parametric models, which generally preclude consistent estimation, particularly in moderate to high dimensions. Recent research on missing data has focused on data-adaptive * corresponding author: ild2005@med.cornell.edu 1 arXiv:1704.01538v1 [stat.ME] 5 Apr 2017 estimation of the nuisance parameters in order to achieve consistency, but the large sample properties of such estimators are poorly understood. In this article we discuss a doubly robust estimator that is consistent and asymptotically normal (CAN) under data-adaptive consistent estimation of the outcome regression or the missingness mechanism. We provide a formula for an asymptotically valid confidence interval under minimal assumptions. We show that our proposed estimator has smaller finite-sample bias compared to standard doubly robust estimators. We present a simulation study demonstrating the enhanced performance of our estimators in terms of bias, efficiency, and coverage of the confidence intervals. We present the results of an illustrative example: a randomized, double-blind phase II/III trial of antiretroviral therapy in HIV-infected persons, and provide R code implementing our proposed estimators.

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Stable Weights that Balance Covariates for Estimation With Incomplete Outcome Data

Cited by 296 publications

References 40 publications

Approximate Residual Balancing: Debiased Inference of Average Treatment Effects in High Dimensions

Approximate Residual Balancing: Debiased Inference of Average Treatment Effects in High Dimensions

The Right Tool for the Job

Doubly robust inference for targeted minimum loss–based estimation in randomized trials with missing outcome data

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