title: Instrumental variable analysis with a nonlinear exposure-outcome relationship.
abstract: BACKGROUND
  Instrumental variable methods can estimate the causal effect of an exposure on an outcome using observational data. Many instrumental variable methods assume that the exposure-outcome relation is linear, but in practice this assumption is often in doubt, or perhaps the shape of the relation is a target for investigation. We investigate this issue in the context of Mendelian randomization, the use of genetic variants as instrumental variables.
  
  
  METHODS
  Using simulations, we demonstrate the performance of a simple linear instrumental variable method when the true shape of the exposure-outcome relation is not linear. We also present a novel method for estimating the effect of the exposure on the outcome within strata of the exposure distribution. This enables the estimation of localized average causal effects within quantile groups of the exposure or as a continuous function of the exposure using a sliding window approach.
  
  
  RESULTS
  Our simulations suggest that linear instrumental variable estimates approximate a population-averaged causal effect. This is the average difference in the outcome if the exposure for every individual in the population is increased by a fixed amount. Estimates of localized average causal effects reveal the shape of the exposure-outcome relation for a variety of models. These methods are used to investigate the relations between body mass index and a range of cardiovascular risk factors.
  
  
  CONCLUSIONS
  Nonlinear exposure-outcome relations should not be a barrier to instrumental variable analyses. When the exposure-outcome relation is not linear, either a population-averaged causal effect or the shape of the exposure-outcome relation can be estimated.
authors.affiliation: From the aCardiovascular Epidemiology Unit, Department of Public Health and Primary Care, University of Cambridge, Cambridge, Cambridgeshire, United Kingdom; and bMedical Research Council Integrative Epidemiology Unit, School of Social and Community Medicine, University of Bristol, Bristol, United Kingdom.
authors.forename: Stephen
authors.initials: S
authors.lastname: Burgess
authors.forename: Neil M
authors.initials: NM
authors.lastname: Davies
authors.forename: Simon G
authors.initials: SG
authors.lastname: Thompson
mesh_terms: D015992:Body Mass Index; D002318:Cardiovascular Diseases / Q000453:epidemiology; D015984:Causality; D004812:Epidemiologic Methods; D005060:Europe / Q000453:epidemiology; D006801:Humans; D016014:Linear Models; D057182:Mendelian Randomization Analysis / Q000379:methods*; D015337:Multicenter Studies as Topic; D011446:Prospective Studies; D012307:Risk Factors