Meta-analysis of Mendelian randomization studies incorporating all three genotypes

In Mendelian randomization a carefully selected gene is used as an instrumental variable in the estimation of the association between a biological phenotype and a disease. A study using Mendelian randomization will have information on an individual's disease status, the genotype and the phenotype. The phenotype must be on the causal pathway between gene and disease for the instrumental-variable analysis to be valid. For a biallelic polymorphism there are three possible genotypes with which to compare disease risk. Existing methods select two of the three possible genotypes for use in a Mendelian randomization analysis. Multivariate meta-analysis models for Mendelian randomization case-control studies are proposed, which extend previous methods by estimating the pooled phenotype-disease association across both genotype comparisons by using the gene-disease log odds ratios and differences in mean phenotypes. The methods are illustrated using a meta-analysis of the effect of a gene related to collagen production on bone mineral density and osteoporotic fracture.     

Upward bias in odds ratio estimates from genome-wide association studies

Genome-wide association studies are carried out to identify unknown genes for a complex trait. Polymorphisms showing the most statistically significant associations are reported and followed up in subsequent confirmatory studies. In addition to the test of association, the statistical analysis provides point estimates of the relationship between the genotype and phenotype at each polymorphism, typically an odds ratio in case-control association studies. The statistical significance of the test and the estimator of the odds ratio are completely correlated. Selecting the most extreme statistics is equivalent to selecting the most extreme odds ratios. The value of the estimator, given the value of the statistical significance depends on the standard error of the estimator and the power of the study. This report shows that when power is low, estimates of the odds ratio from a genome-wide association study, or any large-scale association study, will be upwardly biased. Genome-wide association studies are often underpowered given the low alpha levels required to declare statistical significance and the small individual genetic effects known to characterize complex traits. Factors such as low allele frequency, inadequate sample size and weak genetic effects contribute to large standard errors in the odds ratio estimates, low power and upwardly biased odds ratios. Studies that have high power to detect an association with the true odds ratio will have little or no bias, regardless of the statistical significance threshold. The results have implications for the interpretation of genome-wide association analysis and the planning of subsequent confirmatory stages.     

Bias in causal estimates from Mendelian randomization studies with weak instruments

Mendelian randomization studies using genetic instrumental variables (IVs) are now being commonly used to estimate the causal association of a phenotype on an outcome. Even when the necessary underlying assumptions are valid, estimates from analyses using IVs are biased in finite samples. The source and nature of this bias appear poorly understood in the epidemiological field. We explain why the bias is in the direction of the confounded observational association, with magnitude relating to the statistical strength of association between the instrument and phenotype. We comment on the size of the bias, from simulated data, showing that when multiple instruments are used, although the variance of the IV estimator decreases, the bias increases. We discuss ways to analyse Mendelian randomization studies to alleviate the problem of weak instrument bias.     

Meta-analysis of genetic studies using Mendelian randomization--a multivariate approach

In traditional epidemiological studies the association between phenotype (risk factor) and disease is often biased by confounding and reverse causation. As a person's genotype is assigned by a seemingly random process, genes are potentially useful instrumental variables for adjusting for such bias. This type of adjustment combines information on the genotype-disease association and the genotype-phenotype association to estimate the phenotype-disease association and has become known as Mendelian randomization. The information on genotype-disease and genotype-phenotype may well come from a meta-analysis. In such a synthesis, a multivariate approach needs to be used whenever some studies provide evidence on both the genotype-phenotype and genotype-disease associations. This paper presents two multivariate meta-analytical models, which differ in their treatment of the heterogeneities (between-study variances). Heterogeneities on the genotype-phenotype and genotype-disease associations may be highly correlated, but a multivariate model that parameterizes the heterogeneity directly is difficult to fit because that correlation is poorly estimated. We advocate an alternative model that treats the heterogeneities on genotype-phenotype and phenotype-disease as being independent. This model fits readily and implicitly defines the correlation between the heterogeneities on genotype-phenotype and genotype-disease. We show how either maximum likelihood or a Bayesian approach with vague prior distributions can be used to fit the alternative model.     

Severity of bias of a simple estimator of the causal odds ratio in Mendelian randomization studies

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 meta‐analyses. Many applications of Mendelian randomization dichotomize genotype and estimate the population causal log odds ratio for unit increase in exposure by dividing the genotype‐disease log odds ratio by the difference in mean exposure between genotypes. This ‘Wald‐type’ estimator is biased even in large samples, but whether the magnitude of bias is of practical importance is unclear. We study the large‐sample 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 data‐generating 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 individual‐level data they require are available. The Wald‐type estimator may retain a role as an approximate method for meta‐analysis based on summary data. Copyright © 2012 John Wiley & Sons, Ltd.     

Patterns of bias due to differential misclassification by case–control status in a case–control study

BACKGROUND: Case-control study is still one of the most commonly used study designs in epidemiological research. Misclassification of case-control status remains a significant issue because it will bias the results of a case-control study. There exist two types of misclassification, differential versus nondifferential. It is commonly accepted that nondifferential misclassification will bias the results of the study towards the null hypothesis. Conversely, no reports have assessed the impact and direction of differential misclassification on odds ratio (OR) estimate. The goal of the present study is to demonstrate by statistical derivation that patterns exist on the bias induced by differential misclassification. METHODS: Based on a 2 x 2 case-control study design, we derive the odds ratio without misclassification, and those with misclassification according to: (1) controls are misclassified as cases by exposure status; (2) cases are misclassified as controls by exposure status; and (3) both controls and cases are misclassified by exposure status simultaneously. Furthermore, mathematical derivations are shown for each of the ratios of the two odds ratios with and without misclassification. These methods are carried out by simulation analyses. RESULTS: Simulation analyses show that quite a number of biased odds ratios tend to move away from the null hypothesis and result in approaching zero or infinity with increasing proportion of misclassification among cases, controls, or both. These patterns are associated with the exposure status and the values of unbiased odds ratio (<1, 1, or >1). CONCLUSIONS: Our findings suggest that, unlike nondifferential misclassification, differential misclassification of case-control status in a case-control study may not weaken the exposure-outcome association towarding the null hypothesis. Care needs to be taken for interpreting the results of a case-control study when there exists differential misclassification bias, a practical issue in epidemiological research.     

Genetic effect estimates in case-control studies when a continuous variable is omitted from the model

Large-scale genome-wide analyses scans on massive numbers of various cases and controls are archived in the genetic databases that are publically available, for example, the Database of Genotypes and Phenotypes ( https://www.ncbi.nlm.nih.gov/gap/ ). These databases offer unprecscendented opportunity to study the genetic effects. Yet, the set of nongenetic variables in these databases is often brief. From the statistical literature, we know that omitting a continuous variable from a logistic regression model can result in biased estimates of odds ratios (OR), even when the omitted and the included variables are independent. We are interested in assessing what information is needed to recover the bias in the OR estimate of genotype due to omitting a continuous variable in settings when the actual values of the omitted variable are not available. We derive two estimating procedures that can recover the degree of bias based on a conditional density of the omitted variable given the disease status and the genotype or the known distribution of the omitted variable and frequency of the disease in the population. Importantly, our derivations show that omitting a continuous variable can result in either under- or over-estimation of the genetic effects. We performed extensive simulation studies to examine bias, variability, false-positive rate, and power in the model that omits a continuous variable. We show the application to two genome-wide studies of Alzheimer's disease.     

Competing risks of death and Hardy-Weinberg equilibrium in case-control studies of gene-disease association

OBJECTIVE: To study the impact of competing risks on Hardy-Weinberg equilibrium and their consequences in case-control studies of gene-late onset disease association. METHODS: Based on a population born in Hardy-Weinberg equilibrium for a particular gene, the genetic composition when the gene is associated with a lethal early-onset disease and its consequences on a late-onset disease can be deduced. Odds ratios estimates are unbiased in case-control studies when controls are sampled by density, even if the controls are in Hardy-Weinberg disequilibrium. RESULTS: An example in which a mutant gene is associated with early mortality is presented, producing a departure from Hardy-Weinberg equilibrium; as a result, controls in later ages are in disequilibrium, producing an odds ratio equal to 1.61. CONCLUSION: Although the main causes of Hardy-Weinberg disequilibrium in controls are selection bias or genotyping error, a competing risk of death associated with the mutant gene would also result in Hardy-Weinberg disequilibrium among controls.     

Recall bias in self-reported melanoma risk factors

The evidence implicating sun exposure in the etiology of melanoma derives largely from case-control studies in which the retrospective assessment of sun exposure suggests potential for significant recall bias. Previous attempts at characterizing and quantifying that bias have had significant methodological limitations. In the International Twin Study, a case-control study of melanoma risk factors in twins conducted from 1980 to 1991, the authors asked melanoma cases and their co-twins to quantify their own exposures and asked which twin had the greater exposure. Recall bias was investigated by assuming that, if bias had occurred, the odds ratio based on the case's response would differ significantly from the odds ratio based on the co-twin's response. Case-derived odds ratios were higher than the odds ratios for the controls for sunbathing in childhood and adulthood and for mole frequency and freckling in childhood, suggesting some recall bias. The odds ratios for ease of burning and tanning appeared unbiased. The belief that sunlight was a cause of melanoma appeared related to an increased odds ratio for sunbathing as a child. There is a continuing need to carefully assess recall bias in the study of melanoma risk factors.     

An integrated approach to the meta-analysis of genetic association studies using Mendelian randomization

A natural randomization process, sometimes called Mendelian randomization, occurs at conception to determine a person's genotype. By combining information from genotype-disease and genotype-phenotype studies, it is possible to use this Mendelian randomization to derive an estimate of the association between phenotype (risk factor) and disease that is free of the confounding and reverse causation typical of classical epidemiology. When one is synthesizing evidence, studies evaluating genotype-phenotype associations, studies evaluating genotype-disease associations, and studies evaluating both are encountered, and methods should be used that allow for this structure. Plotting the log odds ratio of genotype-disease against the mean genotype-phenotype difference may help investigators detect departures from the assumptions underlying Mendelian randomization. Testing for differences between studies reporting on only the genotype-phenotype or genotype-disease association and those reporting on both associations may help in detecting reporting bias. This integrated approach to the meta-analysis of genotype-phenotype and genotype-disease studies is illustrated here using the example of the methylenetetrahydrofolate reductase (MTHFR) gene, homocysteine level, and coronary heart disease. An integrated meta-analytical approach may increase the precision of this estimate and provide information on the assumptions underlying Mendelian randomization. Serious biases may arise if the assumptions behind the analysis based on Mendelian randomization are not met.     

Uncovering selection bias in case–control studies using Bayesian post‐stratification

Case–control studies are particularly prone to selection bias, which can affect odds ratio estimation. Approaches to discovering and adjusting for selection bias have been proposed in the literature using graphical and heuristic tools as well as more complex statistical methods. The approach we propose is based on a survey‐weighting method termed Bayesian post‐stratification and follows from the conditional independences that characterise selection bias. We use our approach to perform a selection bias sensitivity analysis by using ancillary data sources that describe the target case–control population to re‐weight the odds ratio estimates obtained from the study. The method is applied to two case–control studies, the first investigating the association between exposure to electromagnetic fields and acute lymphoblastic leukaemia in children and the second investigating the association between maternal occupational exposure to hairspray and a congenital anomaly in male babies called hypospadias. In both case–control studies, our method showed that the odds ratios were only moderately sensitive to selection bias. Copyright © 2013 John Wiley & Sons, Ltd.     

Phenotype validation in electronic health records based genetic association studies

The linkage between electronic health records (EHRs) and genotype data makes it plausible to study the genetic susceptibility of a wide range of disease phenotypes. Despite that EHR‐derived phenotype data are subjected to misclassification, it has been shown useful for discovering susceptible genes, particularly in the setting of phenome‐wide association studies (PheWAS). It is essential to characterize discovered associations using gold standard phenotype data by chart review. In this work, we propose a genotype stratified case‐control sampling strategy to select subjects for phenotype validation. We develop a closed‐form maximum‐likelihood estimator for the odds ratio parameters and a score statistic for testing genetic association using the combined validated and error‐prone EHR‐derived phenotype data, and assess the extent of power improvement provided by this approach. Compared with case‐control sampling based only on EHR‐derived phenotype data, our genotype stratified strategy maintains nominal type I error rates, and result in higher power for detecting associations. It also corrects the bias in the odds ratio parameter estimates, and reduces the corresponding variance especially when the minor allele frequency is small.     

Quantifying bias due to allele misclassification in case-control studies of haplotypes

OBJECTIVES: Genotyping errors can induce biases in frequency estimates for haplotypes of single nucleotide polymorphisms (SNPs). Here, we considered the impact of SNP allele misclassification on haplotype odds ratio estimates from case-control studies of unrelated individuals. METHODS: We calculated bias analytically, using the haplotype counts expected in cases and controls under genotype misclassification. We evaluated the bias due to allele misclassification across a range of haplotype distributions using empirical haplotype frequencies within blocks of limited haplotype diversity. We also considered simple two- and three-locus haplotype distributions to understand the impact of haplotype frequency and number of SNPs on misclassification bias. RESULTS: We found that for common haplotypes (>5% frequency), realistic genotyping error rates (0.1-1% chance of miscalling an allele), and moderate relative risks (2-4), the bias was always towards the null and increases in magnitude with increasing error rate, increasing odds ratio. For common haplotypes, bias generally increased with increasing haplotype frequency, while for rare haplotypes, bias generally increased with decreasing frequency. When the chance of miscalling an allele is 0.5%, the median bias in haplotype-specific odds ratios for common haplotypes was generally small (<4% on the log odds ratio scale), but the bias for some individual haplotypes was larger (10-20%). Bias towards the null leads to a loss in power; the relative efficiency using a test statistic based upon misclassified haplotype data compared to a test based on the unobserved true haplotypes ranged from roughly 60% to 80%, and worsened with increasing haplotype frequency. CONCLUSIONS: The cumulative effect of small allele-calling errors across multiple loci can induce noticeable bias and reduce power in realistic scenarios. This has implications for the design of candidate gene association studies that utilize multi-marker haplotypes.     

The performance of different propensity score methods for estimating marginal odds ratios

The propensity score which is the probability of exposure to a specific treatment conditional on observed variables. Conditioning on the propensity score results in unbiased estimation of the expected difference in observed responses to two treatments. In the medical literature, propensity score methods are frequently used for estimating odds ratios. The performance of propensity score methods for estimating marginal odds ratios has not been studied. We performed a series of Monte Carlo simulations to assess the performance of propensity score matching, stratifying on the propensity score, and covariate adjustment using the propensity score to estimate marginal odds ratios. We assessed bias, precision, and mean-squared error (MSE) of the propensity score estimators, in addition to the proportion of bias eliminated due to conditioning on the propensity score. When the true marginal odds ratio was one, then matching on the propensity score and covariate adjustment using the propensity score resulted in unbiased estimation of the true treatment effect, whereas stratification on the propensity score resulted in minor bias in estimating the true marginal odds ratio. When the true marginal odds ratio ranged from 2 to 10, then matching on the propensity score resulted in the least bias, with a relative biases ranging from 2.3 to 13.3 per cent. Stratifying on the propensity score resulted in moderate bias, with relative biases ranging from 15.8 to 59.2 per cent. For both methods, relative bias was proportional to the true odds ratio. Finally, matching on the propensity score tended to result in estimators with the lowest MSE.     

On the adjustment for covariates in genetic association analysis: a novel,simple principle to infer direct causal effects

In genetic association studies, different complex phenotypes are often associated with the same marker. Such associations can be indicative of pleiotropy (i.e. common genetic causes), of indirect genetic effects via one of these phenotypes, or can be solely attributable to non‐genetic/environmental links between the traits. To identify the phenotypes with the inducing genetic association, statistical methodology is needed that is able to distinguish between the different causes of the genetic associations. Here, we propose a simple, general adjustment principle that can be incorporated into many standard genetic association tests which are then able to infer whether an SNP has a direct biological influence on a given trait other than through the SNP's influence on another correlated phenotype. Using simulation studies, we show that, in the presence of a non‐marker related link between phenotypes, standard association tests without the proposed adjustment can be biased. In contrast to that, the proposed methodology remains unbiased. Its achieved power levels are identical to those of standard adjustment methods, making the adjustment principle universally applicable in genetic association studies. The principle is illustrated by an application to three genome‐wide association analyses. Genet. Epidemiol. 33:394–405, 2009. © 2009 Wiley‐Liss, Inc.     

Proper analysis of secondary phenotype data in case‐control association studies

Case‐control association studies often collect extensive information on secondary phenotypes, which are quantitative or qualitative traits other than the case‐control status. Exploring secondary phenotypes can yield valuable insights into biological pathways and identify genetic variants influencing phenotypes of direct interest. All publications on secondary phenotypes have used standard statistical methods, such as least‐squares regression for quantitative traits. Because of unequal selection probabilities between cases and controls, the case‐control sample is not a random sample from the general population. As a result, standard statistical analysis of secondary phenotype data can be extremely misleading. Although one may avoid the sampling bias by analyzing cases and controls separately or by including the case‐control status as a covariate in the model, the associations between a secondary phenotype and a genetic variant in the case and control groups can be quite different from the association in the general population. In this article, we present novel statistical methods that properly reflect the case‐control sampling in the analysis of secondary phenotype data. The new methods provide unbiased estimation of genetic effects and accurate control of false‐positive rates while maximizing statistical power. We demonstrate the pitfalls of the standard methods and the advantages of the new methods both analytically and numerically. The relevant software is available at our website. Genet. Epidemiol. 2009. © 2008 Wiley‐Liss, Inc.     

Variance estimation of allele-based odds ratio in the absence of Hardy–Weinberg equilibrium

In gene-disease association studies, deviation from Hardy–Weinberg equilibrium in controls may cause bias in estimating the allele-based estimates of genetic effects. An approach to adjust the variance of allele-based odds ratio for Hardy–Weinberg equilibrium deviation is proposed. Such adjustments have been introduced for estimating relative risks of genotype contrasts and differences in allele frequency; however, an adjustment of odds ratios for allele frequencies still does not exist. The approach was based on the delta method in combination with the Woolf’s logit interval method and the disequilibrium coefficient. The proposed variance adjustment provided better power than the unadjusted one to detect significant estimates of odds ratio and it improved the variance estimation.     

弓形虫感染与精神分裂症的两样本孟德尔随机化研究

目的 采用两样本孟德尔随机化方法探究弓形虫感染和精神分裂症之间的因果关系.方法 利用汇总的大样本GWAS数据提取与弓形虫血清抗体密切相关的遗传位点作为工具变量,分别运用MR-Egger回归、加权中位数和逆方差加权法进行孟德尔随机化分析,以OR值及95％CI评价弓形虫感染与精神分裂症之间是否存在关联.采用Egger-in...     

Carpet-dust chemicals as measures of exposure: Implications of variability

Background

There is increasing interest in using chemicals measured in carpet dust as indicators of chemical exposures. However, investigators have rarely sampled dust repeatedly from the same households and therefore little is known about the variability of chemical levels that exist within and between households in dust samples.

Results

We analyzed 9 polycyclic aromatic hydrocarbons, 6 polychlorinated biphenyls, and nicotine in 68 carpet-dust samples from 21 households in agricultural communities of Fresno County, California collected from 2003-2005. Chemical concentrations (ng per g dust) ranged from < 2-3,609 for 9 polycyclic aromatic hydrocarbons, from < 1-150 for 6 polychlorinated biphenyls, and from < 20-7,776 for nicotine. We used random-effects models to estimate variance components for concentrations of each of these carpet-dust chemicals and calculated the variance ratio, ??, defined as the ratio of the within-household variance component to the between-household variance component. Subsequently, we used the variance ratios calculated from our data, to illustrate the potential effect of measurement error on the attenuation of odds ratios in hypothetical case-control studies. We found that the median value of the estimated variance ratios was 0.33 (range: 0.13-0.72). Correspondingly, in case-control studies of associations between these carpet-dust chemicals and disease, given the collection of only one measurement per household and a hypothetical odds ratio of 1.5, we expect that the observed odds ratios would range from 1.27 to 1.43. Moreover, for each of the chemicals analyzed, the collection of three repeated dust samples would limit the expected magnitude of odds ratio attenuation to less than 20%.

Conclusions

Our findings suggest that attenuation bias should be relatively modest when using these semi-volatile carpet-dust chemicals as exposure surrogates in epidemiologic studies.     

Conditioning on the propensity score can result in biased estimation of common measures of treatment effect: a Monte Carlo study

Propensity score methods are increasingly being used to estimate causal treatment effects in the medical literature. Conditioning on the propensity score results in unbiased estimation of the expected difference in observed responses to two treatments. The degree to which conditioning on the propensity score introduces bias into the estimation of the conditional odds ratio or conditional hazard ratio, which are frequently used as measures of treatment effect in observational studies, has not been extensively studied. We conducted Monte Carlo simulations to determine the degree to which propensity score matching, stratification on the quintiles of the propensity score, and covariate adjustment using the propensity score result in biased estimation of conditional odds ratios, hazard ratios, and rate ratios. We found that conditioning on the propensity score resulted in biased estimation of the true conditional odds ratio and the true conditional hazard ratio. In all scenarios examined, treatment effects were biased towards the null treatment effect. However, conditioning on the propensity score did not result in biased estimation of the true conditional rate ratio. In contrast, conventional regression methods allowed unbiased estimation of the true conditional treatment effect when all variables associated with the outcome were included in the regression model. The observed bias in propensity score methods is due to the fact that regression models allow one to estimate conditional treatment effects, whereas propensity score methods allow one to estimate marginal treatment effects. In several settings with non-linear treatment effects, marginal and conditional treatment effects do not coincide.