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Abstract Instrumental variables have been widely used to estimate the causal effect of a treatment on an outcome. Existing confidence intervals for causal effects based on instrumental variables assume that all of the putative instrumental variables are valid; a valid instrumental variable is a variable that affects the outcome only by affecting the treatment and is not related to unmeasured confounders. However, in practice, some of the putative instrumental variables are likely to be invalid. This paper presents two tools to conduct valid inference and tests in the presence of invalid instruments. First, we propose a simple and general approach to construct confidence intervals based on taking unions of well‐known confidence intervals. Second, we propose a novel test for the null causal effect based on a collider bias. Our two proposals outperform traditional instrumental variable confidence intervals when invalid instruments are present and can also be used as a sensitivity analysis when there is concern that instrumental variables assumptions are violated. The new approach is applied to a Mendelian randomization study on the causal effect of low‐density lipoprotein on globulin levels.
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This content will become publicly available on February 6, 2026
A Calibrated Sensitivity Analysis for Weighted Causal Decompositions
ABSTRACT Disparities in health or well‐being experienced by minority groups can be difficult to study using the traditional exposure‐outcome paradigm in causal inference, since potential outcomes in variables such as race or sexual minority status are challenging to interpret. Causal decomposition analysis addresses this gap by positing causal effects on disparities under interventions to other intervenable exposures that may play a mediating role in the disparity. While invoking weaker assumptions than causal mediation approaches, decomposition analyses are often conducted in observational settings and require uncheckable assumptions that eliminate unmeasured confounders. Leveraging the marginal sensitivity model, we develop a sensitivity analysis for weighted causal decomposition estimators and use the percentile bootstrap to construct valid confidence intervals for causal effects on disparities. We also propose a two‐parameter reformulation that enhances interpretability and facilitates an intuitive understanding of the plausibility of unmeasured confounders and their effects. We illustrate our framework on a study examining the effect of parental support on disparities in suicidal ideation among sexual minority youth. We find that the effect is small and sensitive to unmeasured confounding, suggesting that further screening studies are needed to identify mitigating interventions in this vulnerable population.
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- Award ID(s):
- 2142146
- PAR ID:
- 10574661
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Statistics in Medicine
- Volume:
- 44
- Issue:
- 5
- ISSN:
- 0277-6715
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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