A Bayesian Nonparametric Approach to Causal Inference on Quantiles

Xu, Dandan; Daniels, Michael J.; Winterstein, Almut G.

doi:10.1111/biom.12863

Cited by 28 publications

(37 citation statements)

References 38 publications

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“…For simplicity, we will focus here on the situation where

q = 2

. Some examples include:

E false(Y^{1} - Y^{0}

): average causal effect (continuous outcome) or average causal risk difference (binary outcome)

E false(Y^{1} false) / E false(Y^{0} false)

: average causal relative risk (binary outcome)

E false(Y^{1} - Y^{0} false| V false)

: conditional average causal effect (where

V \subset L

)

E false(Y^{1} - Y^{0} false| A = 1 false)

: average effect of treatment on treated

F_{1}^{- 1} false(p false) - F_{0}^{- 1} false(p false)

, where

F_{a}^{- 1} false(p false)

is the p th quantile of the cumulative distribution function

P false(Y^{a} \leq y false)

: a quantile causal effect (Xu, et al, ().…”

Section: Causal Effectsmentioning

confidence: 99%

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Bayesian Nonparametric Generative Models for Causal Inference with Missing at Random Covariates

et al. 2018

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We propose a general Bayesian nonparametric (BNP) approach to causal inference in the point treatment setting. The joint distribution of the observed data (outcome, treatment, and confounders) is modeled using an enriched Dirichlet process. The combination of the observed data model and causal assumptions allows us to identify any type of causal effect-differences, ratios, or quantile effects, either marginally or for subpopulations of interest. The proposed BNP model is well-suited for causal inference problems, as it does not require parametric assumptions about the distribution of confounders and naturally leads to a computationally efficient Gibbs sampling algorithm. By flexibly modeling the joint distribution, we are also able to impute (via data augmentation) values for missing covariates within the algorithm under an assumption of ignorable missingness, obviating the need to create separate imputed data sets. This approach for imputing the missing covariates has the additional advantage of guaranteeing congeniality between the imputation model and the analysis model, and because we use a BNP approach, parametric models are avoided for imputation. The performance of the method is assessed using simulation studies. The method is applied to data from a cohort study of human immunodeficiency virus/hepatitis C virus co-infected patients.

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“…For simplicity, we will focus here on the situation where

q = 2

. Some examples include:

E false(Y^{1} - Y^{0}

): average causal effect (continuous outcome) or average causal risk difference (binary outcome)

E false(Y^{1} false) / E false(Y^{0} false)

: average causal relative risk (binary outcome)

E false(Y^{1} - Y^{0} false| V false)

: conditional average causal effect (where

V \subset L

)

E false(Y^{1} - Y^{0} false| A = 1 false)

: average effect of treatment on treated

F_{1}^{- 1} false(p false) - F_{0}^{- 1} false(p false)

, where

F_{a}^{- 1} false(p false)

is the p th quantile of the cumulative distribution function

P false(Y^{a} \leq y false)

: a quantile causal effect (Xu, et al, ().…”

Section: Causal Effectsmentioning

confidence: 99%

“…is the pth quantile of the cumulative distribution function P(Y a ≤ y): a quantile causal effect (Xu, et al, 2018).…”

Section: Causal Effectsmentioning

confidence: 99%

Bayesian Nonparametric Generative Models for Causal Inference with Missing at Random Covariates

et al. 2018

Self Cite

View full text Add to dashboard Cite

show abstract

“…In these workflows, the analyst first focuses on optimizing a fit to the observed data distribution, often employing heuristics such as cross validation to select or combine models. The analyst then plugs predictions from this model into an estimation step tailored to the estimand of interest (Van der Laan and Rose, 2011; Chernozhukov et al, 2016;Xu et al, 2018). A sensitivity analysis based on Tukey's factorization would allow investigators to assess sensitivity in this workflow without putting constraints on the flexible model used in the first stage.…”

Section: Discussionmentioning

confidence: 99%

Flexible Sensitivity Analysis for Observational Studies Without Observable Implications

Franks

D’Amour

Feller

2019

Journal of the American Statistical Association

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A fundamental challenge in observational causal inference is that assumptions about unconfoundedness are not testable from data. Assessing sensitivity to such assumptions is therefore important in practice. Unfortunately, some existing sensitivity analysis approaches inadvertently impose restrictions that are at odds with modern causal inference methods, which emphasize flexible models for observed data. To address this issue, we propose a framework that allows (1) flexible models for the observed data and (2) clean separation of the identified and unidentified parts of the sensitivity model. Our framework extends an approach from the missing data literature, known as Tukey's factorization, to the causal inference setting. Under this factorization, we can represent the distributions of unobserved potential outcomes in terms of unidentified selection functions that posit an unidentified relationship between the treatment assignment indicator and unobserved potential outcomes. The sensitivity parameters in this framework are easily interpreted, and we provide heuristics for calibrating these parameters against observable quantities. We demonstrate the flexibility of this approach in two examples, where we estimate both average treatment effects and quantile treatment effects using Bayesian nonparametric models for the observed data.

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“…In addition to the propensity score methods described in the Introduction, alternative Bayesian methods for causal inference have been proposed, and yet the ATT is a useful estimand that has been largely overlooked in the Bayesian literature. For example, Xu et al used Bayesian nonparametric generative models to induce the conditional distribution of the outcome given covariates for causal inference using the propensity score. They used a sequential Bayesian additive regression tree approach to impute the missing covariates and estimate the quantile causal effects.…”

Section: Discussionmentioning

confidence: 99%

Bayesian estimation of the average treatment effect on the treated using inverse weighting

Capistrano

Moodie

Schmidt

2019

Statistics in Medicine

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We develop a Bayesian approach to estimate the average treatment effect on the treated in the presence of confounding. The approach builds on developments proposed by Saarela et al in the context of marginal structural models, using importance sampling weights to adjust for confounding and estimate a causal effect. The Bayesian bootstrap is adopted to approximate posterior distributions of interest and avoid the issue of feedback that arises in Bayesian causal estimation relying on a joint likelihood. We present results from simulation studies to estimate the average treatment effect on the treated, evaluating the impact of sample size and the strength of confounding on estimation. We illustrate our approach using the classic Right Heart Catheterization data set and find a negative causal effect of the exposure on 30-day survival, in accordance with previous analyses of these data. We also apply our approach to the data set of the National Center for Health Statistics Birth Data and obtain a negative effect of maternal smoking during pregnancy on birth weight.

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A Bayesian Nonparametric Approach to Causal Inference on Quantiles

Cited by 28 publications

References 38 publications

Bayesian Nonparametric Generative Models for Causal Inference with Missing at Random Covariates

Bayesian Nonparametric Generative Models for Causal Inference with Missing at Random Covariates

Flexible Sensitivity Analysis for Observational Studies Without Observable Implications

Bayesian estimation of the average treatment effect on the treated using inverse weighting

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