Correction for sample overlap, winner's curse and weak instrument bias in two-sample Mendelian Randomization

Inverse-variance weighted two-sample Mendelian Randomization (IVW-MR) is the most widely used approach that uses genome-wide association studies summary statistics to infer the existence and strength of the causal effect between an exposure and an outcome. Estimates from this approach can be subject to different biases due to: (i) the overlap between the exposure and outcome samples; (ii) the use of weak instruments and winner's curse. We developed a method that aims at tackling all these biases together. Assuming spike-and-slab genomic architecture and leveraging LD-score regression and other techniques, we could analytically derive and reliably estimate the bias of IVW-MR using association summary statistics only. This allowed us to apply a bias correction to IVW-MR estimates, which we tested using simulated data for a wide range of realistic scenarios. In all the explored scenarios, our correction reduced the bias, in some situations by as much as 30 folds. When applied to real data on obesity-related exposures, we observed significant differences between IVW-based and corrected effects, both for non-overlapping and fully overlapping samples. While most studies are extremely careful to avoid any sample overlap when performing two-sample MR analysis, we have demonstrated that the incurred bias is much less substantial than the one due to weak instruments or winner's curse, which are often ignored.

Reexamining the National Savings-Investment Nexus Across Time and Countries

Domestic savings and investment are positively correlated across countries and through time, as Feldstein-Horioka (FH) unveiled 40 years ago. We argue that an interpretation of this correlation based on market failures is more consistent with data patterns than alternative hypotheses. Moreover, resorting to instrumental variables techniques, we conclude that the relationship is causal: an exogenous rise in savings increases investment. This result holds in the full sample of countries and for emerging and developing economies, but there is evidence that the positive association in advanced economies is due to endogeneity bias. The core of our identification strategy relies on the idea that population age structure influences savings, but not total investment directly. Specifically, we use the share of adults in the [35-49] years of age bracket as an instrument for savings. Our estimates pass weak-instruments robust inference.

Identifying Modern Macro Equations with Old Shocks*

Despite decades of research, the consistent estimation of structural forward-looking macroeconomic equations remains a formidable empirical challenge because of pervasive endogeneity issues. Prominent cases—the estimation of Phillips curves, Euler equations, or monetary policy rules—have typically relied on using predetermined variables as instruments, with mixed success. In this work, we propose a new approach that consists in using sequences of independently identified structural shocks as instrumental variables. Our approach is robust to weak instruments and is valid regardless of the shocks’ variance contribution. We estimate a Phillips curve using monetary shocks as instruments and find that conventional methods substantially underestimate the slope of the Phillips curve.

Estimating the effect of lipids on IGF axis and subsequent breast cancer risk

Circulating lipids have been associated with breast cancer (BCa). This association may, in part, be due to an effect of lipids on insulin-like growth factors (IGFs), which have been reliably associated with BCa. In two-sample Mendelian randomization (MR) analyses, we found that low density lipoprotein (LDL-C) was associated with IGFBP-3 (beta:0.08 SD; 95%CI:0.02,0.15; p = 0.01, per SD increase in LDL-C) and IGFBP-3 was associated with postmenopausal BCa (OR:1.09; 95%CI:1.00,1.19; p = 0.05, per SD increase in IGFBP-3). We also found that triglycerides were associated with IGF-I (beta:-0.13SD; 95%CI:-0.22,-0.03, per SD increase in triglycerides) and that IGF-I was associated with overall BCa (OR:1.10;95%CI:1.02,1.18, per SD increase in IGF-I). Taken together, these results suggest that IGFBP-3 may be a potential causal step between LDL-C and postmenopausal BCa and IGF-I a potential causal for triglycerides. Our two-step MR results build on evidence linking circulating lipids and IGFs with BCa, however, multivariable MR analyses are currently unable to support this relationship due to weak instruments.

Testing and Correcting for Weak and Pleiotropic Instruments in Two-Sample Multivariable Mendelian Randomisation

Multivariable Mendelian Randomisation (MVMR) is a form of instrumental variable analysis which estimates the direct effect of multiple exposures on an outcome using genetic variants as instruments. Mendelian Randomisation and MVMR are frequently conducted using two-sample summary data where the association of the genetic variants with the exposures and outcome are obtained from separate samples. If the genetic variants are only weakly associated with the exposures either individually or conditionally, given the other exposures in the model, then standard inverse variance weighting will yield biased estimates for the effect of each exposure. Here we develop a two-sample conditional F-statistic to test whether the genetic variants strongly predict each exposure conditional on the other exposures included in a MVMR model. We show formally that this test is equivalent to the individual level data conditional F-statistic, indicating that conventional rule-of-thumb critical values of F > 10, can be used to test for weak instruments. We then demonstrate how reliable estimates of the causal effect of each exposure on the outcome can be obtained in the presence of weak instruments and pleiotropy, by re-purpousing a commonly used heterogeneity Q-statistic as an estimating equation. Furthermore, the minimised value of this Q-statistic yields an exact test for heterogeneity due to pleiotropy. We illustrate our methods with an application to estimate the causal effect of blood lipid fractions on age related macular degeneration.