Identifiability and Estimation for Potential-Outcome Means with Misclassified Outcomes

Shaojie Wei, Chao Zhang, Zhi Geng and Shanshan Luo ()
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Shaojie Wei: School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 100048, China
Chao Zhang: School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 100048, China
Zhi Geng: School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 100048, China
Shanshan Luo: School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 100048, China

Mathematics, 2024, vol. 12, issue 18, 1-19

Abstract: Potential outcomes play a fundamental and important role in many causal inference problems. If the potential-outcome means are identifiable, a series of causal effect measures, including the risk difference, the risk ratio, and the treatment benefit rate, among others, can also be identified. However, current identification and estimation methods for these means often implicitly assume that the collected data for analysis are measured precisely. In many fields such as medicine and economics, the collected variables may be subject to measurement errors, such as medical diagnostic results and individual wage data. Misclassification, as a non-classic measurement error, can lead to severely biased estimates in causal inference. In this paper, we leverage a combined sample to study the identifiability of potential-outcome means corresponding to different treatment levers under a plausible misclassification assumption for the outcome, allowing the misclassification probability to depend on not only the true outcome but also the covariates. Furthermore, we propose the multiply-robust and semiparametric efficient estimators for the means, consistent even under partial misspecification of the observed data law, based on the semiparametric theory framework. The simulation studies and real data analysis demonstrate the satisfactory performance of the proposed method.

Keywords: causal inference; misclassification; multiply robustness; potential outcomes; semiparametric theory (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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