Inference with many correlated weak instruments and summary statistics

by   Ashish Patel, et al.

This paper concerns inference in instrumental variable models with a high-dimensional set of correlated weak instruments. Our focus is motivated by Mendelian randomization, the use of genetic variants as instrumental variables to identify the unconfounded effect of an exposure on disease. In particular, we consider the scenario where a large number of genetic instruments may be exogenous, but collectively they explain a low proportion of exposure variation. Additionally, we assume that individual-level data are not available, but rather summary statistics on genetic associations with the exposure and outcome, as typically published from meta-analyses of genome-wide association studies. In a two-stage approach, we first use factor analysis to exploit structured correlations of genetic instruments as expected in candidate gene analysis, and estimate an unknown vector of optimal instruments. The second stage conducts inference on the parameter of interest under scenarios of strong and weak identification. Under strong identification, we consider point estimation based on minimization of a limited information maximum likelihood criterion. Under weak instrument asymptotics, we generalize conditional likelihood ratio and other identification-robust statistics to account for estimated instruments and summary data as inputs. Simulation results illustrate favourable finite-sample properties of the factor-based conditional likelihood ratio test, and we demonstrate use of our method by studying the effect of interleukin-6 signaling on glycated hemoglobin levels.


Weak-Instrument Robust Tests in Two-Sample Summary-Data Mendelian Randomization

Mendelian randomization (MR) is a popular method in genetic epidemiology...

Conditional Likelihood Ratio Test with Many Weak Instruments

This paper extends validity of the conditional likelihood ratio (CLR) te...

Powerful genome-wide design and robust statistical inference in two-sample summary-data Mendelian randomization

Mendelian randomization (MR) uses genetic variants as instrumental varia...

Detecting weak signals by combining small P-values in observational studies with multiple testing

Human health is affected by multiple risk factors. Studies may focus on ...

Inference After Selecting Plausibly Valid Instruments with Application to Mendelian Randomization

Mendelian randomization (MR) is a popular method in genetic epidemiology...

Uniform Inference for Conditional Factor Models with Instrumental and Idiosyncratic Betas

It has been well known in financial economics that factor betas depend o...

Non-Asymptotic Inference in Instrumental Variables Estimation

This paper presents a simple method for carrying out inference in a wide...

Please sign up or login with your details

Forgot password? Click here to reset