Electronic Journal of Statistics

Identifying and estimating net effects of treatments in sequential causal inference

Xiaoqin Wang and Li Yin

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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.

Article information

Electron. J. Statist., Volume 9, Number 1 (2015), 1608-1643.

Received: August 2014
First available in Project Euclid: 6 August 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62H12: Estimation
Secondary: 62H15: Hypothesis testing 62F03: Hypothesis testing 62F30: Inference under constraints

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


Wang, Xiaoqin; Yin, Li. Identifying and estimating net effects of treatments in sequential causal inference. Electron. J. Statist. 9 (2015), no. 1, 1608--1643. doi:10.1214/15-EJS1046. https://projecteuclid.org/euclid.ejs/1438883470

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Supplemental materials

  • SAS codes and SAS data sets. The supplementary material contains (1) SAS codes and SAS data sets for the simulation study in Section 6.2 and (2) SAS code and SAS data set for the illustrative study in Section 6.3. (Zip file).