# Instrumental-Variables

## IV & MR

Project page for the statistical methods for instrumental variables and Mendelian randomization.

## The statistics of summary-data Mendelian randomization

Invited talk giving an overview of my research on summary-data Mendelian randomization.

## Mendelian randomization: A tutorial

Tutorial talk for the theory, methods, and practice of Mendelian randomization.

## A Mendelian randomization study of the role of lipoprotein subfractions in coronary artery disease

We apply the MR-RAPS method we developed in previous articles to infer the potential causal role of lipoprotein subfractions in CAD. This is motivated by the finding in our earlier IJE paper that the association between genetically-determined HDL-C and CAD is heterogeneous according to instrument strength. In this study, We find that HDL subfraction traits, unlike LDL and VLDL subfractions, appear to have heterogeneous effects on coronary artery disease according to particle size. The concentration of medium HDL particles may have a protective effect on CAD that is independent of traditional lipid factors.

## Falsification tests for instrumental variable designs with an application to tendency to operate

We propose a falsification test for the IV assumptions using sub-populations of the data with overwhelming proportion of treated or untreated units. If the IV assumptions hold, we should find the intention-to-treat effect is zero within these …

## Graphical diagnosis of confounding bias in instrumental variables analysis

This research letter proposes a new diagnostic plot for IV analysis, so large bias ratios (compared to OLS estimator) are not over-interpreted when the covariate is unrelated to the outcome.

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

We extend the MR-RAPS method in our previous paper using the empirical partially Bayes framework described by Lindsay, allowing a true genome-wide design for Mendelian randomization.

## Improving the accuracy of two-sample summary data Mendelian randomization: moving beyond the NOME assumption

This paper proposes a modified Cochran's $Q$ statistic to detect horizontal pleiotropy in Mendelian randomization. This extension is quite important when there are many weak genetic instruments.

## Statistical inference in two-sample summary-data Mendelian randomization using robust adjusted profile score

We provide a comprehensive theoretical basis for two-sample summary-data Mendelian randomization. We find that horizontal pleiotropy is pervasive in MR studies. We propose a new method---robust adjusted profile score---that can consistently estimate …

## Two-sample instrumental variable analyses using heterogeneous samples

Many modern IV studies (especially Mendelian Randomization) are carried out with the two-sample design, where the samples may come from different populations. We derive a new class of linear IV estimates that are robust to sample heterogeneity. We …