LASSO-type instrumental variable selection methods with an application to Mendelian randomization.

Area of Science:

• Econometrics
• Biostatistics
• Genetics

Background:

• Instrumental variables (IVs) are crucial for causal inference but often suffer from invalidity and weakness.
• Existing methods struggle with bias and precision when many weak and invalid instruments are present.

Purpose of the Study:

• To develop robust statistical methods for estimating causal effects in the presence of numerous weak and invalid instrumental variables.
• To address limitations of current IV estimation techniques in linear models and heteroscedastic data.

Main Methods:

• Derivation of a LASSO procedure for k-class IV estimation in linear models.
• Proposal of a jackknife IV method utilizing LASSO to handle many weak invalid instruments with heteroscedasticity.
• Development of two-step numerical algorithms for causal effect estimation.

Main Results:

• The proposed LASSO and jackknife IV methods demonstrate robustness in estimating causal effects with mixed valid and invalid instruments.
• Theoretical assurances support the reliable execution of the developed methods.
• Monte Carlo simulations and an empirical application confirm the performance of the proposed estimators.

Conclusions:

• The novel LASSO-based IV methods offer a significant improvement for causal inference when dealing with prevalent weak and invalid instruments.
• These methods provide reliable estimation of causal effects, as validated by simulations and real-world data.
• The study successfully applies these techniques to Mendelian randomization, estimating the impact of body mass index on quality of life.