Double Negative Control Inference With Some Invalid Negative Control Exposures for Continuous Outcome.

Area of Science:

• Epidemiology
• Biostatistics
• Causal Inference

Background:

• Negative controls are crucial for causal inference, especially with unmeasured confounding.
• Valid negative control exposures (NCEs) do not affect the outcome, and valid negative control outcomes (NCOs) are not affected by exposure.
• Identifying valid NCEs is challenging, and invalid NCEs can bias causal effect estimates.

Purpose of the Study:

• To develop a double negative control framework for continuous outcomes addressing the challenge of invalid NCEs.
• To establish conditions under which causal effects can be identified and estimated despite the presence of invalid NCEs.
• To introduce a robust methodology for selecting valid NCEs and estimating causal effects in observational studies.

Main Methods:

• Proving identifiability of causal effects using a known valid NCO and a set of NCEs without prior knowledge of their validity.
• Demonstrating consistent estimation of average causal effects when over 50% of NCEs are valid.
• Designing an L1 procedure for selecting valid NCEs and developing two double negative control estimators (sisvNCE and naiveNCE-Median).

Main Results:

• The proposed framework enables causal effect identification with a valid NCO and a set of NCEs, even with some invalid ones.
• Consistent estimation of average causal effects is achievable if more than 50% of NCEs are valid.
• Simulation results confirm the robustness of the proposed methods when the proportion of invalid NCEs is below a threshold.

Conclusions:

• The double negative control framework offers a viable approach for causal inference in the presence of invalid negative control exposures.
• The developed L1 selection procedure and estimators provide theoretical guarantees for performance.
• The method shows promise for application in public health research, particularly in improving the reliability of observational studies.