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2015 Identifying and estimating net effects of treatments in sequential causal inference
Xiaoqin Wang, Li Yin
Electron. J. Statist. 9(1): 1608-1643 (2015). DOI: 10.1214/15-EJS1046

Abstract

Suppose that a sequence of treatments are assigned to influence an outcome of interest that occurs after the last treatment. Between treatments, there are time-dependent covariates that may be post-treatment variables of the earlier treatments and confounders of the subsequent treatments. In this article, we study identification and estimation of the net effect of each treatment in the treatment sequence. We construct a point parametrization for the joint distribution of treatments, time-dependent covariates and the outcome, in which the point parameters of interest are the point effects of treatments considered as single-point treatments. We identify net effects of treatments by their expressions in terms of point effects of treatments and express patterns of net effects of treatments by constraints on point effects of treatments. We estimate net effects of treatments through their point effects under the constraint by maximum likelihood and reduce the number of point parameters in the estimation by the treatment assignment condition. As a result, we obtain an unbiased consistent maximum-likelihood estimate for the net effect of treatment even in a long treatment sequence. We also show by simulation that the interval estimation of the net effect of treatment achieves the nominal coverage probability.

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Xiaoqin Wang. Li Yin. "Identifying and estimating net effects of treatments in sequential causal inference." Electron. J. Statist. 9 (1) 1608 - 1643, 2015. https://doi.org/10.1214/15-EJS1046

Information

Received: 1 August 2014; Published: 2015
First available in Project Euclid: 6 August 2015

zbMATH: 1327.62350
MathSciNet: MR3379004
Digital Object Identifier: 10.1214/15-EJS1046

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

Keywords: constraint on point effects of treatments , Net effect of treatment , pattern of net effects of treatments , point effect of treatment , sequential causal inference , treatment assignment condition

Rights: Copyright © 2015 The Institute of Mathematical Statistics and the Bernoulli Society

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Vol.9 • No. 1 • 2015
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