Kernel-based covariate functional balancing for observational studies

Wong, Raymond K. W.; Chan, Kwun Chuen Gary

doi:10.1093/biomet/asx069

Cited by 56 publications

(97 citation statements)

References 32 publications

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“…Some of these methods also minimize a measure of dispersion of the weights. Examples include Hainmueller (2012), Zubizarreta (2015), Chan et al (2016), Zhao and Percival (2017), Wong and Chan (2018), and Zhao (2018). Earlier and related methods include Deville and Särndal (1992), Hellerstein and Imbens (1999), Imai and Ratkovic (2014), and Li et al (2018).…”

Section: Weighting Methods For Covariate Adjustmentmentioning

confidence: 99%

Minimal dispersion approximately balancing weights: asymptotic properties and practical considerations

2019

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Weighting methods are widely used to adjust for covariates in observational studies, sample surveys, and regression settings. In this paper, we study a class of recently proposed weighting methods which find the weights of minimum dispersion that approximately balance the covariates. We call these weights minimal weights and study them under a common optimization framework. The key observation is the connection between approximate covariate balance and shrinkage estimation of the propensity score. This connection leads to both theoretical and practical developments. From a theoretical standpoint, we characterize the asymptotic properties of minimal weights and show that, under standard smoothness conditions on the propensity score function, minimal weights are consistent estimates of the true inverse probability weights. Also, we show that the resulting weighting estimator is consistent, asymptotically normal, and semiparametrically efficient. From a practical standpoint, we present a finite sample oracle inequality that bounds the loss incurred by balancing more functions of the covariates than strictly needed. This inequality shows that minimal weights implicitly bound the number of active covariate balance constraints. We finally provide a tuning algorithm for choosing the degree of approximate balance in minimal weights. We conclude the paper with 1 arXiv:1705.00998v3 [stat.ME] 25 Apr 2019 four empirical studies that suggest approximate balance is preferable to exact balance, especially when there is limited overlap in covariate distributions. In these studies, we show that the root mean squared error of the weighting estimator can be reduced by as much as a half with approximate balance.

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Section: Weighting Methods For Covariate Adjustmentmentioning

confidence: 99%

Minimal dispersion approximately balancing weights: asymptotic properties and practical considerations

2019

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“…In more generality, B(X) = (B 1 (X), … , B K (X)) ⊤ can be modified to assess balance of higher order univariate and multivariate moments of X, 31 basis functions for general function-spaces including sieves, 21 and representers of Reproducing Kernel Hilbert Spaces. 32 In Section 4.2, we will describe the balancing approach to weighting and see that this approach directly constrains or minimizes the TASMD in Equation (6). Following much of the applied causal inference literature, after weighting, we recommend plotting the TASMDs for each treatment group in order to visualize targeted balance and assess the comparability of each of the treatment groups relative to the target.…”

Section: Weighting For Balancementioning

confidence: 99%

“…In particular, if K = p and B k ( X ) retrieves the k th coordinate of X , then () reduces to () in order to assess balance of the k th original covariate. In more generality,

B (X) = {(B_{1} (X), \dots, B_{K} (X))}^{⊤}

can be modified to assess balance of higher order univariate and multivariate moments of X , 31 basis functions for general function‐spaces including sieves, 21 and representers of Reproducing Kernel Hilbert Spaces 32 …”

Section: Weighting Wish List: What Are We Weighting For?mentioning

confidence: 99%

“…Examples of this approach include the methods by Hainmueller (2012), 17 Zubizarreta (2015), 10 and Chan et al (2016) 18 . Related approaches are Imai and Ratkovic (2014), 14 Fan et al (2016), 16 Tan (2020), 47 Zhao and Percival (2017), 48 Li et al (2018), 39 Wong and Chan (2018), 32 Yiu and Su (2018), 49 Zhao (2019), 50 and Ning et al (2018) 51 . Unless stated otherwise, in the rest of the article, we will use the terms minimal weights and the balancing approach to weighting interchangeably, although the latter class is more general.…”

Section: Two Approaches To Weightingmentioning

confidence: 99%

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Balancing vs modeling approaches to weighting in practice

Chattopadhyay

Hase

Zubizarreta

2020

Statistics in Medicine

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There are two seemingly unrelated approaches to weighting in observational studies. One of them maximizes the fit of a model for treatment assignment to then derive weights-we call this the modeling approach. The other directly optimizes certain features of the weights-we call this the balancing approach. The implementations of these two approaches are related: the balancing approach implicitly models the propensity score, while instances of the modeling approach impose balance conditions on the covariates used to estimate the propensity score. In this article, we review and compare these two approaches to weighting. Previous review papers have focused on the modeling approach, emphasizing the importance of checking covariate balance. However, as we discuss, the dispersion of the weights is another important aspect of the weights to consider, in addition to the representativeness of the weighted sample and the sample boundedness of the weighted estimator. In particular, the dispersion of the weights is important because it translates into a measure of effective sample size, which can be used to select between alternative weighting schemes. In this article, we examine the balancing approach to weighting, discuss recent methodological developments, and compare instances of the balancing and modeling approaches in a simulation study and an empirical study. In practice, unless the treatment assignment model is known, we recommend using the balancing approach to weighting, as it systematically results in better covariate balance with weights that are minimally dispersed. As a result, effect estimates tend to be more accurate and stable.

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“…Recently, several weighting based covariate balancing methods are proposed to estimate the treatment effects. [20][21][22][23][24][25] Covariate balance means that the distributions of measured covariates of observations between the treatment and control groups are similar to each other. The covariate balancing propensity score method (CBPS) is introduced to model the treatment assignment using a logistic model while simultaneously optimizing the covariate balance.…”

Section: Introductionmentioning

confidence: 99%

Multiply robust estimation of causal quantile treatment effects

Xie

Cotton

Zhu

2020

Statistics in Medicine

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In causal inference, often the interest lies in the estimation of the average causal effect. Other quantities such as the quantile treatment effect may be of interest as well. In this article, we propose a multiply robust method for estimating the marginal quantiles of potential outcomes by achieving mean balance in (a) the propensity score, and (b) the conditional distributions of potential outcomes. An empirical likelihood or entropy measure approach can be utilized for estimation instead of inverse probability weighting, which is known to be sensitive to the misspecification of the propensity score model. Simulation studies are conducted across different scenarios of correctness in both the propensity score models and the outcome models. Both simulation results and theoretical development indicate that our proposed estimator is consistent if any of the models are correctly specified. In the data analysis, we investigate the quantile treatment effect of mothers' smoking status on infants' birthweight.

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Kernel-based covariate functional balancing for observational studies

Cited by 56 publications

References 32 publications

Minimal dispersion approximately balancing weights: asymptotic properties and practical considerations

Minimal dispersion approximately balancing weights: asymptotic properties and practical considerations

Balancing vs modeling approaches to weighting in practice

Multiply robust estimation of causal quantile treatment effects

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