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February 2020 New $G$-formula for the sequential causal effect and blip effect of treatment in sequential causal inference
Xiaoqin Wang, Li Yin
Ann. Statist. 48(1): 138-160 (February 2020). DOI: 10.1214/18-AOS1795

Abstract

In sequential causal inference, two types of causal effects are of practical interest, namely, the causal effect of the treatment regime (called the sequential causal effect) and the blip effect of treatment on the potential outcome after the last treatment. The well-known $G$-formula expresses these causal effects in terms of the standard parameters. In this article, we obtain a new $G$-formula that expresses these causal effects in terms of the point observable effects of treatments similar to treatment in the framework of single-point causal inference. Based on the new $G$-formula, we estimate these causal effects by maximum likelihood via point observable effects with methods extended from single-point causal inference. We are able to increase precision of the estimation without introducing biases by an unsaturated model imposing constraints on the point observable effects. We are also able to reduce the number of point observable effects in the estimation by treatment assignment conditions.

Citation

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Xiaoqin Wang. Li Yin. "New $G$-formula for the sequential causal effect and blip effect of treatment in sequential causal inference." Ann. Statist. 48 (1) 138 - 160, February 2020. https://doi.org/10.1214/18-AOS1795

Information

Received: 1 January 2018; Revised: 1 December 2018; Published: February 2020
First available in Project Euclid: 17 February 2020

zbMATH: 07196533
MathSciNet: MR4065156
Digital Object Identifier: 10.1214/18-AOS1795

Subjects:
Primary: 62H12
Secondary: 62F03, 62F30, 62H15

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.48 • No. 1 • February 2020
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