Using instrumental variables to estimate the attributable fraction

• In order to design efficient interventions aimed to improve public health, policy makers need to be provided with reliable information of the health burden of different risk factors. For this purpose, we are interested in the proportion of cases that could be prevented had some harmful exposure been eliminated from the population, i.e. the attributable fraction. The attributable fraction is a causal measure; thus, to estimate the attributable fraction from observational data, we have to make appropriate adjustment for confounding. However, some confounders may be unobserved, or even unknown to the investigator. A possible solution to this problem is to use instrumental variable analysis. In this work, we present how the attributable fraction can be estimated with instrumental variable methods based on the two-stage estimator or the G-estimator. One situation when the problem of unmeasuredconfounding may be particularly severe is when assessing the effect of low educational qualifications on coronary heart disease. By using Mendelian randomization, a special case of instrumental variable analysis, it has been claimed that low educational qualifications is a causal risk factor for coronary heart disease. We use Mendelian randomization to estimate the causal risk ratio and causal odds ratio of low educational qualifications as a risk factor for coronary heart disease with data from the UK Biobank. We compare the two-stage and G-estimator as well as the attributable fraction based on the two estimators. The plausibility of drawing causal conclusion in this analysis is thoroughly discussed and alternative genetic instrumental variables are tested.

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