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Identification of causal effects with latent confounding and classical additive errors in treatment
Author(s) -
Li Wei,
Jiang Zhichao,
Geng Zhi,
Zhou XiaoHua
Publication year - 2018
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.201700048
Subject(s) - identifiability , confounding , causal inference , categorical variable , latent variable , instrumental variable , statistics , framingham heart study , econometrics , latent variable model , mathematics , computer science , medicine , disease , framingham risk score
In this paper, we discuss the identifiability and estimation of causal effects of a continuous treatment on a binary response when the treatment is measured with errors and there exists a latent categorical confounder associated with both treatment and response. Under some widely used parametric models, we first discuss the identifiability of the causal effects and then propose an approach for estimation and inference. Our approach can eliminate the biases induced by latent confounding and measurement errors by using only a single instrumental variable. Based on the identification results, we give guidelines for determining the existence of a latent categorical confounder and for selecting the number of levels of the latent confounder. We apply the proposed approach to a data set from the Framingham Heart Study to evaluate the effect of the systolic blood pressure on the coronary heart disease.