[Paper Review] Multiply robust dose-response estimation for multivalued causal inference problems

Cian Naik, Emma J. McCoy+1 more|arXiv (Cornell University)|Nov 8, 2016

Advanced Causal Inference Techniques17 references4 citations

TL;DR

This paper introduces a multiply robust dose-response estimator for multivalued treatments by combining generalized propensity score (GPS) and outcome regression (OR) models, ensuring consistent estimation of average potential outcomes if at least one model in either family is correctly specified. The method extends doubly robust estimation to multivalued settings and demonstrates robustness to confounding and model misspecification through theoretical proofs and simulations.

ABSTRACT

This paper develops a multiply robust (MR) dose-response estimator for causal inference problems involving multivalued treatments. We combine a family of generalised propensity score (GPS) models and a family of outcome regression (OR) models to achieve an average potential outcomes estimator that is consistent if just one of the GPS or OR models in each family is correctly specified. We provide proofs and simulations that demonstrate multiple robustness in the context of multivalued causal inference problems.

Motivation & Objective

• To address the lack of robust methods for dose-response estimation in multivalued treatment settings.
• To extend multiply robust estimation—previously used in missing data—to causal inference with multivalued treatments.
• To provide a method that remains consistent even if most models in the GPS or OR families are misspecified.
• To demonstrate theoretical and empirical robustness to confounding and functional form misspecification in multivalued causal inference.

Proposed method

• The method combines a family of generalized propensity score (GPS) models and a family of outcome regression (OR) models to construct an average potential outcome (APO) estimator.
• It uses a doubly robust estimating equation that leverages inverse probability weighting and outcome regression, adapted for multivalued treatments.
• The estimator is consistent if either the GPS model family contains a correctly specified model or the OR model family contains a correctly specified model.
• The approach is grounded in the theory of multiply robust estimation from missing data, adapted to causal inference via potential outcomes.
• An algorithm for numerical implementation is proposed, based on iterative estimation and model averaging across multiple GPS and OR models.
• Theoretical consistency is proven using the law of iterated expectations and the no unmeasured confounders assumption.

Experimental results

Research questions

• RQ1 Can multiply robust estimation be extended from missing data to multivalued causal inference problems?
• RQ2 Does combining multiple GPS and OR models yield an estimator that remains consistent when only one model in either family is correctly specified?
• RQ3 How does the proposed method perform under confounding and functional form misspecification in dose-response estimation?
• RQ4 Can the method provide accurate estimates of average potential outcomes across different treatment levels in multivalued treatment settings?

Key findings

• The proposed estimator is multiply robust: it consistently estimates average potential outcomes if any single GPS or OR model in their respective families is correctly specified.
• Simulations show the estimator maintains low bias (ranging from -0.007 to -0.003) and good coverage under both confounding and model misspecification.
• The method effectively approximates both linear and nonlinear dose-response functions, even when the true functional form is unknown.
• Theoretical proof confirms that the second-order term in the estimating equation vanishes under correct specification of either the GPS or OR model, ensuring consistency.
• The estimator achieves asymptotic normality and maintains robust performance across diverse simulation scenarios, including high-dimensional and misspecified models.