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Abstract
Mendelian randomization studies estimate causal effects using genetic variants as instruments. Instrumental variable methods are straightforward for linear models, but epidemiologists often use odds ratios to quantify effects. Also, odds ratios are often the quantities reported in metaanalyses. Many applications of Mendelian randomization dichotomize genotype and estimate the population causal log odds ratio for unit increase in exposure by dividing the genotypedisease log odds ratio by the difference in mean exposure between genotypes. This Waldtype' estimator is biased even in large samples, but whether the magnitude of bias is of practical importance is unclear. We study the largesample bias of this estimator in a simple model with a continuous normally distributed exposure, a single unobserved confounder that is not an effect modifier, and interpretable parameters. We focus on parameter values that reflect scenarios in which we apply Mendelian randomization, including realistic values for the degree of confounding and strength of the causal effect. We evaluate this estimator and the causal odds ratio using numerical integration and obtain approximate analytic expressions to check results and gain insight. A small simulation study examines finite sample bias and mild violations of the normality assumption. For our simple datagenerating model, we find that the Wald estimator is asymptotically biased with a bias of around 10% in fairly typical Mendelian randomization scenarios but which can be larger in more extreme situations. Recently developed methods such as structural mean models require fewer untestable assumptions and we recommend their use when the individuallevel data they require are available. The Waldtype estimator may retain a role as an approximate method for metaanalysis based on summary data. Copyright (c) 2012 John Wiley & Sons, Ltd.
Original language  English 

Pages (fromto)  12461258 
Number of pages  13 
Journal  Statistics in Medicine 
Volume  32 
Issue number  7 
Early online date  18 Oct 2012 
DOIs  
Publication status  Published  30 Mar 2013 
Keywords
 Mendelian randomization
 instrumental variables
 causal inference
 binary outcomes
 odds ratios
 INSTRUMENTALVARIABLE ESTIMATION
 CORONARYHEARTDISEASE
 OBSERVATIONAL EPIDEMIOLOGY
 PLASMAFIBRINOGEN
 BAYESIAN METHODS
 MODELS
 INFERENCE
 METAANALYSIS
 RISK
 ASSOCIATION
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 1 Finished

CENTRE FOR CASUAL ANALYSES IN TRANSLATIONAL EPIDEMIOLOGY (CAiTE)
Davey Smith, G. (Principal Investigator)
1/09/07 → 1/09/13
Project: Research