Consequences Of Mis-Adjustment Of Instrumental Variables And The Application Of Multiple Instrumental Variables

In observational epidemiology studies,one leading cause for biased estimation of the exposure effect is confounding.When adjusting for the observed confounders,the instrumental variable(Ⅳs)may be mistakenly regarded as a con founder and then begs to be adjusted,since it is hard to distinguish between Ⅳs and confounders in the aspect of statistical properties.Recent studies have shown that mistaking instrumental variables for confounders to implementing regression adjustment would lead to an increase in bias and variance of exposure effect estimate.Nevertheless,most of these works just provide theoretical framework or give results mainly under linear systems.Therefore,this study based on Logistic regression models,four simulations were performed to explore the effects of adjusting for Ⅳs,near-Ⅳs(variables that are strongly associated with exposure and weakly associated with outcome through unmeasured confounders),and confounders,further to explore the effects of adjusting for Ⅳs on selection bias,where the exposure and outcome were set to be binary.On the other hand,if the role of the Ⅳ was confirmed,Ⅳs can be used to obtain an unbiased estimate of exposure effect in the presence of unmeasured via the Ⅳmethods.For instance,Mendelian randomization analyses is a method which use genetic variants as Ⅳs to estimate causal effects of exposures on outcomes.Since that genetic variants typically explain a small proportion of the variability in exposure,hence Mendelian randomization analyses can require large sample sizes to improve power.It has been found that using multiple genetic variants as instrumental variables can improve the accuracy of effect estimation,but it is still not clear about how to use multiple genetic variants efficiently.Therefore,based on the two-stage least squares model,simulations were performed to examine the effect of different multiple genetic variates combining strategy on precision and bias,where the exposure and outcome were set to be continuous and all relationships are assumed to be linear.Result:(1)①Adjusting for variables that meet all criterions of a perfect Ⅳ Z would increase the confounding bias and the standard error of exposure effect estimate,but these increases were generally small.②For the performance of adjusting for a near-Ⅳthat are strongly associated with exposure and related to outcome through unmeasured confounders,the role of near-Ⅳ Z is determined by the association between Z and outcome,it would turn from a bias-amplifier to a bias-reducer with such association getting stronger.③Adjusting for a confounder Z that influence both exposure and outcome directly would reduce the bias of exposure effect estimate even though the direct association between Z and outcome was weak.④Adjusting for an Ⅳ had no effects on the selection bias as long as the bias contains no confounding component.(2)①When the SNP is a strong instrumental variable,using a single Ⅳ can get close to unbiased estimate of effect,and increasing the number of SNPs,can reduce the standard error of the effect estimation.LD structure will not significantly influence the bias of effect estimation.②When there are weak instrumental variables in the selected SNPs,using a single weak Ⅳ will produce a weak instrumental variable bias,and the stronger the LD of the SNPs,the smaller the bias of the effect estimation.Using multiple SNP IVs or using combined multiple gene variants as a single Ⅳ can reduce the weak instrumental variable bias and improve the accuracy of effect estimation,to a certain extent.The two stage least squares model which is based on weighted allele score is better than that of based on the allele score model and that of based on principal component analysis model.And the two stage least squares based on PCA method is not applicable to lowLD situation.When multiple SNPs are combined into a single IV based on allele scoring method,weighted allele scoring method and principal component analysis method,adding two more SNPs all can reduce the bias of causal effect estimation.(3)As for the real data analysis,①the estimated value of the BMI to the high blood pressure with adjusting for instrumental variable was slightly less than the estimated value without adjusting for the instrumental variable,and the difference was small.②the effect estimations value of BMI on systolic and diastolic blood pressure obtained by Mendel’s randomization analysis were greater than that of ordinary linear regression.Increasing the number of instrumental variables could reduce the standard error of effect estimation.Using the allele score,weighted allele score and the first principal component of multiple SNPs as a single instrumental variable got the similar effect estimations,which is consistent with the simulation results of this study.Conclusions:(1)The effect of adjusting possible I Vs on the bias of exposure estimates is not constant as the change of the association between IVs and outcomes.The results indicated that covariates should be chosen for control based on their importance with respect to the outcome,rather than the exposure.Firstly,variables that meet all criterions of a perfect IV should be discarded to prevent bias amplification.Secondly,covariates that have strong effects on the outcome are unlikely to be IVs,they are beg to be adjusted to reduce confounding bias.Furthermore,variables that influence exposure and outcome directly even though weakly should also be included for adjustment in the logistic regression model.Finally,within the context of scenarios considered in our simulation studies,the increased biases of exposure effect estimate due to inadvertently adjusting for an IV are usually small.Thus in the case of binary exposure and outcome,if the causal structure of the problem cannot be figured out,the need to control residual confounding bias greatly outweighed bias amplification caused by adjusting for an Ⅳ.(2)When a single SNP is a strong instrumental variable,using a single IV could obtain the asymptotic unbiased estimation.And the bias is affected by the LD between SNPs,the stronger the LD,the smaller the estimation bias.It is recommended to use multiple SNPs or combine multiple gene variants as a single instrumental variables,as for the method of combining multiple gene variants,the weighted allele score method is recommended.(3)The real data analysis results are consistent with the simulation results,and the mis-adjustment of the instrumental variables will cause deviation of the effect estimatin,and the deviation is usually small.The results of Mendel randomization analysis were similar with the allele score,the weighted allele score and the first principal component of multiple SNPs as instrumental variables.