A Finite Sample Theorem for Longitudinal Causal Inference with Machine Learning: Long Term, Dynamic, and Mediated Effects

Singh, Krishna Nand

doi:10.48550/arxiv.2112.14249

Cited by 5 publications

(10 citation statements)

References 64 publications

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“…I quote a Gaussian approximation and variance estimation lemma with abstract conditions that I will verify for the new subroutines proposed in Algorithm 6.1. Lemma E.3 (Confidence interval; Corollary 6.1 of [33]). Suppose that the moment function is Neyman orthogonal and 4. σ2 {R(η ℓ )} 1/2 p → 0;…”

Section: E21 Abstract Conditionsmentioning

confidence: 99%

“…It appears that no procedures of any kind exist for long term dose responses and counterfactual distributions. To justify semiparametric inference, I appeal to the multiply robust moment function of [10] and the abstract rate conditions of [33]. See the latter for references on semiparametric theory, double robustness, sample splitting, and targeted and debiased machine learning.…”

Section: Related Workmentioning

confidence: 99%

“…6 Semiparametric treatment effects Towards this end, I quote the multiply robust moment function for the long term causal model parametrized to avoid density estimation. Lemma 6.1 (Multiply robust moment for long term effect [10,33]). If Assumption 3.1 holds then…”

Section: If In Addition Assumption 32 Holds Thenmentioning

confidence: 99%

“…The meta algorithm that combines the multiply robust moment function from Lemma 6.1 with sample splitting is called debiased machine learning (DML) for long term treatment effects [12,33]. I instantiate DML for long term treatment effects using a new nonparametric estimator ν, which involves the sequential mean embedding.…”

Section: If In Addition Assumption 32 Holds Thenmentioning

confidence: 99%

“…See [33,Theorem 6.1] for finite sample Gaussian approximation and [33,Theorem 6.2] for finite sample variance estimation guarantees that give rise to Lemma E.3.…”

Section: E22 Treatment Effectsmentioning

confidence: 99%

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Generalized Kernel Ridge Regression for Long Term Causal Inference: Treatment Effects, Dose Responses, and Counterfactual Distributions

Singh¹

2022

Preprint

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I propose kernel ridge regression estimators for long term causal inference, where a short term experimental data set containing randomized treatment and short term surrogates is fused with a long term observational data set containing short term surrogates and long term outcomes. I propose estimators of treatment effects, dose responses, and counterfactual distributions with closed form solutions in terms of kernel matrix operations. I allow covariates, treatment, and surrogates to be discrete or continuous, and low, high, or infinite dimensional. For long term treatment effects, I prove √ n consistency, Gaussian approximation, and semiparametric efficiency. For long term dose responses, I prove uniform consistency with finite sample rates. For long term counterfactual distributions, I prove convergence in distribution.Preprint. Under review.

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Section: E21 Abstract Conditionsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: If In Addition Assumption 32 Holds Thenmentioning

confidence: 99%

Section: If In Addition Assumption 32 Holds Thenmentioning

confidence: 99%

“…See [33,Theorem 6.1] for finite sample Gaussian approximation and [33,Theorem 6.2] for finite sample variance estimation guarantees that give rise to Lemma E.3.…”

Section: E22 Treatment Effectsmentioning

confidence: 99%

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Generalized Kernel Ridge Regression for Long Term Causal Inference: Treatment Effects, Dose Responses, and Counterfactual Distributions

Singh¹

2022

Preprint

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Long-term causal inference under persistent confounding via data combination

Imbens,

Kallus,

Mao

et al. 2024

Journal of the Royal Statistical Society Series B: Statistical Methodology

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We study the identification and estimation of long-term treatment effects by combining short-term experimental data and long-term observational data subject to unobserved confounding. This problem arises often when concerned with long-term treatment effects since experiments are often short-term due to operational necessity while observational data can be more easily collected over longer time frames but may be subject to confounding. In this paper, we tackle the challenge of persistent confounding: unobserved confounders that can simultaneously affect the treatment, short-term outcomes, and long-term outcome. In particular, persistent confounding invalidates identification strategies in previous approaches to this problem. To address this challenge, we exploit the sequential structure of multiple short-term outcomes and develop several novel identification strategies for the average long-term treatment effect. Based on these, we develop estimation and inference methods with asymptotic guarantees. To demonstrate the importance of handling persistent confounders, we apply our methods to estimate the effect of a job training program on long-term employment using semi-synthetic data.

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Long-term Causal Inference Under Persistent Confounding via Data Combination

Imbens¹,

Kallus²,

Mao³

et al. 2022

Preprint

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We study the identification and estimation of long-term treatment effects when both experimental and observational data are available. Since long-term outcome is observed only after a long delay, it is not measured in the experimental data, but only recorded in the observational data. However, both types of data include observations of some short-term outcomes. In this paper, we uniquely tackle the challenge of persistent unmeasured confounders, i.e., some unmeasured confounders that can simultaneously affect the treatment, short-term outcomes and the long-term outcome, noting that they invalidate identification strategies in previous literature. To address this challenge, we exploit the sequential structure of multiple short-term outcomes, and develop three novel identification strategies for the average long-term treatment effect. We further propose three corresponding estimators and prove their asymptotic consistency and asymptotic normality. We finally apply our methods to estimate the effect of a job training program on long-term employment using semi-synthetic data. We numerically show that our proposals outperform existing methods that fail to handle persistent confounders.

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A Finite Sample Theorem for Longitudinal Causal Inference with Machine Learning: Long Term, Dynamic, and Mediated Effects

Cited by 5 publications

References 64 publications

Generalized Kernel Ridge Regression for Long Term Causal Inference: Treatment Effects, Dose Responses, and Counterfactual Distributions

Generalized Kernel Ridge Regression for Long Term Causal Inference: Treatment Effects, Dose Responses, and Counterfactual Distributions

Long-term causal inference under persistent confounding via data combination

Long-term Causal Inference Under Persistent Confounding via Data Combination

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