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The many weak instruments problem and Mendelian randomization.

ABSTRACT: Instrumental variable estimates of causal effects can be biased when using many instruments that are only weakly associated with the exposure. We describe several techniques to reduce this bias and estimate corrected standard errors. We present our findings using a simulation study and an empirical application. For the latter, we estimate the effect of height on lung function, using genetic variants as instruments for height. Our simulation study demonstrates that, using many weak individual variants, two-stage least squares (2SLS) is biased, whereas the limited information maximum likelihood (LIML) and the continuously updating estimator (CUE) are unbiased and have accurate rejection frequencies when standard errors are corrected for the presence of many weak instruments. Our illustrative empirical example uses data on 3631 children from England. We used 180 genetic variants as instruments and compared conventional ordinary least squares estimates with results for the 2SLS, LIML, and CUE instrumental variable estimators using the individual height variants. We further compare these with instrumental variable estimates using an unweighted or weighted allele score as single instruments. In conclusion, the allele scores and CUE gave consistent estimates of the causal effect. In our empirical example, estimates using the allele score were more efficient. CUE with corrected standard errors, however, provides a useful additional statistical tool in applications with many weak instruments. The CUE may be preferred over an allele score if the population weights for the allele score are unknown or when the causal effects of multiple risk factors are estimated jointly.

SUBMITTER: Davies NM

PROVIDER: S-EPMC4305205 | biostudies-literature | 2015 Feb

REPOSITORIES: biostudies-literature

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The many weak instruments problem and Mendelian randomization.

Davies Neil M NM von Hinke Kessler Scholder Stephanie S Farbmacher Helmut H Burgess Stephen S Windmeijer Frank F Smith George Davey GD

Statistics in medicine 20141110 3

Instrumental variable estimates of causal effects can be biased when using many instruments that are only weakly associated with the exposure. We describe several techniques to reduce this bias and estimate corrected standard errors. We present our findings using a simulation study and an empirical application. For the latter, we estimate the effect of height on lung function, using genetic variants as instruments for height. Our simulation study demonstrates that, using many weak individual var ...[more]

PMID: 25382280

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Project description:Although experimental studies are regarded as the method of choice for determining causal influences, these are not always practical or ethical to answer vital questions in health and social research (e.g., one cannot assign individuals to a "childhood trauma condition" in studying the causal effects of childhood trauma on depression). Key to solving such questions are observational studies. Mendelian Randomization (MR) is an influential method to establish causality in observational studies. MR uses genetic variants to test causal relationships between exposures/risk factors and outcomes such as physical or mental health. Yet, individual genetic variants have small effects, and so, when used as instrumental variables, render MR liable to weak instrument bias. Polygenic scores have the advantage of larger effects, but may be characterized by horizontal pleiotropy, which violates a central assumption of MR. We developed the MR-DoC twin model by integrating MR with the Direction of Causation twin model. This model allows us to test pleiotropy directly. We considered the issue of parameter identification, and given identification, we conducted extensive power calculations. MR-DoC allows one to test causal hypotheses and to obtain unbiased estimates of the causal effect given pleiotropic instruments, while controlling for genetic and environmental influences common to the outcome and exposure. Furthermore, the approach allows one to employ strong instrumental variables in the form of polygenic scores, guarding against weak instrument bias, and increasing the power to detect causal effects of exposures on potential outcomes. Beside allowing to test pleiotropy directly, incorporating in MR data collected from relatives provide additional within-family data that resolve additional assumptions like random mating, the absence of the gene-environment interaction/covariance, no dyadic effects. Our approach will enhance and extend MR's range of applications, and increase the value of the large cohorts collected at twin/family registries as they correctly detect causation and estimate effect sizes even in the presence of pleiotropy.

Project description:BACKGROUND:Mendelian randomization (MR) studies use genetic variants mimicking the influence of a modifiable exposure to assess and quantify a causal association with an outcome, with an aim to avoid problems with confounding and reverse causality affecting other types of observational studies. AIM:We evaluated genetic markers that index differences in 25-hydroxyvitamin D (25(OH)D) as instruments for MR studies on vitamin D. METHODS AND FINDINGS:We used data from up-to 6,877 participants in the 1958 British birth cohort with information on genetic markers and 25(OH)D. As potential instruments, we selected 20 single nucleotide polymorphisms (SNP) which are located in the vitamin D metabolism pathway or affect skin pigmentation/tanning, including 4 SNPs from genome-wide association (GWA) meta-analyses on 25(OH)D. We analyzed SNP associations with 25(OH)D and evaluated the use of allele scores dividing genes to those affecting 25(OH)D synthesis (DHCR7, CYP2R1) and metabolism (GC, CYP24A1, CYP27B1). In addition to the GWA SNPs, only two SNPs (CYP27B1, OCA2) showed evidence for association with 25(OH)D, with the OCA2 association abolished after lifestyle adjustment. Per allele differences varied between -0.02 and -0.08 nmol/L (P?0.02 for all), with a 6.1 nmol/L and a 10.2 nmol/L difference in 25(OH)D between individuals with highest compared lowest number of risk alleles in synthesis and metabolism allele scores, respectively. Individual SNPs but not allele scores showed associations with lifestyle factors. An exception was geographical region which was associated with synthesis score. Illustrative power calculations (80% power, 5% alpha) suggest that approximately 80,000 participants are required to establish a causal effect of vitamin D on blood pressure using the synthesis allele score. CONCLUSIONS:Combining SNPs into allele scores provides a more powerful instrument for MR analysis than a single SNP in isolation. Population stratification and the potential for pleiotropic effects need to be considered in MR studies on vitamin D.

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The many weak instruments problem and Mendelian randomization.

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The many weak instruments problem and Mendelian randomization.

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