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Summary Instrumental variable methods can identify causal effects even when the treatment and outcome are confounded. We study the problem of imperfect measurements of the binary instrumental variable, treatment and outcome. We first consider nondifferential measurement errors, that is, the mismeasured variable does not depend on other variables given its true value. We show that the measurement error of the instrumental variable does not bias the estimate, that the measurement error of the treatment biases the estimate away from zero, and that the measurement error of the outcome biases the estimate toward zero. Moreover, we derive sharp bounds on the causal effects without additional assumptions. These bounds are informative because they exclude zero. We then consider differential measurement errors, and focus on sensitivity analyses in those settings.
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Partial Identifiability in Discrete Data with Measurement Error
When data contains measurement errors, it is necessary to make modeling assumptions relating the error-prone measurements to the unobserved true values. Work on measurement error has largely focused on models that fully identify the parameter of interest. As a result, many practically useful models that result in bounds on the target parameter -- known as partial identification -- have been neglected. In this work, we present a method for partial identification in a class of measurement error models involving discrete variables. We focus on models that impose linear constraints on the tar- get parameter, allowing us to compute partial identification bounds using off-the-shelf LP solvers. We show how several common measurement error assumptions can be composed with an extended class of instrumental variable-type models to create such linear constraint sets. We further show how this approach can be used to bound causal parameters, such as the average treatment effect, when treatment or outcome variables are measured with error. Using data from the Oregon Health Insurance Experiment, we apply this method to estimate bounds on the effect Medicaid enrollment has on depression when depression is measured with error.
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- Award ID(s):
- 1942239
- PAR ID:
- 10329246
- Editor(s):
- Cassio de Campos; Marloes H. Maathuis
- Date Published:
- Journal Name:
- Proceedings of the Thirty Seventh Conference on Uncertainty in Artificial Intelligence
- Volume:
- 161
- Page Range / eLocation ID:
- 1798-1808
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
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