Limits...
Instrumental variable analysis with a nonlinear exposure-outcome relationship.

Burgess S, Davies NM, Thompson SG, EPIC-InterAct Consorti - Epidemiology (2014)

Bottom Line: Our simulations suggest that linear instrumental variable estimates approximate a population-averaged causal effect.Estimates of localized average causal effects reveal the shape of the exposure-outcome relation for a variety of models.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.

View Article: PubMed Central - PubMed

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.

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.

Show MeSH

Related in: MedlinePlus

Mean level of cardiovascular risk factors stratified by quintile of body mass index against mean value of body mass index in quintile (lines are ±1.96 standard errors).
© Copyright Policy
Related In: Results  -  Collection


getmorefigures.php?uid=PMC4222800&req=5

Figure 1: Mean level of cardiovascular risk factors stratified by quintile of body mass index against mean value of body mass index in quintile (lines are ±1.96 standard errors).

Mentions: This study is illustrated using data on 8090 subcohort participants from the multicenter case-cohort study European Prospective Investigation into Cancer and Nutrition (EPIC)-InterAct, the diabetes-focused component of the EPIC.9 We use data on BMI (kg/m2) and a range of cardiovascular risk factors: systolic blood pressure (mmHg), C-reactive protein (mg/L, log-transformed), uric acid (μmol/L), glycated hemoglobin (HbA1c, %), total cholesterol (mmol/L), and triglycerides (mmol/L, log-transformed). Increases in BMI have been shown to have causal effects on each of these factors in previous Mendelian randomization studies.10–12 The observational association of each of the risk factors with BMI in a linear regression model, and with BMI and BMI-squared in a quadratic regression model, is given in Table 1. (BMI is centered before analysis, adjustment is made for age, sex, and center.) The mean levels and 95% confidence intervals (CIs) of the risk factors for each quintile of BMI are shown in Figure 1. The observational relations of BMI with several of the risk factors are nonlinear, although this does not necessarily imply that the causal relations will be nonlinear.


Instrumental variable analysis with a nonlinear exposure-outcome relationship.

Burgess S, Davies NM, Thompson SG, EPIC-InterAct Consorti - Epidemiology (2014)

Mean level of cardiovascular risk factors stratified by quintile of body mass index against mean value of body mass index in quintile (lines are ±1.96 standard errors).
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4222800&req=5

Figure 1: Mean level of cardiovascular risk factors stratified by quintile of body mass index against mean value of body mass index in quintile (lines are ±1.96 standard errors).
Mentions: This study is illustrated using data on 8090 subcohort participants from the multicenter case-cohort study European Prospective Investigation into Cancer and Nutrition (EPIC)-InterAct, the diabetes-focused component of the EPIC.9 We use data on BMI (kg/m2) and a range of cardiovascular risk factors: systolic blood pressure (mmHg), C-reactive protein (mg/L, log-transformed), uric acid (μmol/L), glycated hemoglobin (HbA1c, %), total cholesterol (mmol/L), and triglycerides (mmol/L, log-transformed). Increases in BMI have been shown to have causal effects on each of these factors in previous Mendelian randomization studies.10–12 The observational association of each of the risk factors with BMI in a linear regression model, and with BMI and BMI-squared in a quadratic regression model, is given in Table 1. (BMI is centered before analysis, adjustment is made for age, sex, and center.) The mean levels and 95% confidence intervals (CIs) of the risk factors for each quintile of BMI are shown in Figure 1. The observational relations of BMI with several of the risk factors are nonlinear, although this does not necessarily imply that the causal relations will be nonlinear.

Bottom Line: Our simulations suggest that linear instrumental variable estimates approximate a population-averaged causal effect.Estimates of localized average causal effects reveal the shape of the exposure-outcome relation for a variety of models.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.

View Article: PubMed Central - PubMed

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.

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.

Show MeSH
Related in: MedlinePlus