An Integrated Approach to the Meta-Analysis of Genetic Association Studies using Mendelian Randomization
Cosetta Minelli ,
John R. Thompson ,
Martin D. Tobin and
Keith R. Abrams
From the Centre for Biostatistics and Genetic Epidemiology, Department of Health Sciences, Leicester Medical School, University of Leicester, Leicester, United Kingdom.
Received for publication August 20, 2003; accepted for publication March 18, 2004.
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ABSTRACT
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A natural randomization process, sometimes called Mendelian randomization, occurs at conception to determine a persons 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.
epidemiologic methods; genetic epidemiology; genetics; genotype; meta-analysis; phenotype
Abbreviations:
Abbreviations: CI, confidence interval; MTHFR, methylenetetrahydrofolate reductase.
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INTRODUCTION
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With the recent growth in knowledge about the human genome, there has been a dramatic increase in the number of genetic epidemiologic studies of the association between specific genes and diseases and between those genes and the risk factors or phenotypes that are thought to be intermediates on the causal pathway to disease. In many instances, these studies have supplemented preexisting research on the association between the phenotype and the disease. For instance, many recent studies have evaluated the associations between polymorphisms in the methylenetetrahydrofolate reductase (MTHFR) gene and coronary heart disease and between the MTHFR gene and homocysteine level. These studies have been motivated, in part, by the preexisting evidence of an association between homocysteine level and coronary heart disease. Similarly, there have been many studies of polymorphisms in the apolipoprotein E gene and coronary heart disease or stroke and many studies of the apolipoprotein E gene and lipid levels, stemming from epidemiologic evidence of an association between lipids and coronary heart disease or stroke.
As the number of genetic studies has grown, so have meta-analyses been produced to synthesize the evidence and overcome the limitations of power found in even moderate-sized studies (1). Two factors are evident from reviewing these meta-analyses: first, studies of the relation between a gene and an intermediate phenotype (hereafter referred to simply as phenotype) tend to be less common than studies of a gene and a disease; and second, evidence for a genotype-phenotype association is often obtained as a spin-off of a study aimed primarily at investigating the genotype-disease relation, and thus this information is often obtained only on a subset of the subjects. Where there is a strong reason to suppose that the phenotype is intermediate on the causal pathway from gene to disease, it would be sensible to perform a meta-analysis that in some way integrates the evidence for all three relations: genotype-phenotype, genotype-disease, and phenotype-disease. The logic behind this approach is greatly strengthened by an appeal to Mendelian randomizationthat is, the fact that ones genes are inherited at conception through a seemingly random process. Accordingly, epidemiologic studies of genotype-phenotype and genotype-disease associations show strong parallels with randomized trials and should not be affected by confounding or reverse causation in the way that makes classical epidemiologic phenotype-disease studies so difficult to interpret (24). In theory, the genotype acts as an instrumental variable, and by combining the information obtained from genotype-disease and genotype-phenotype studies, it should be possible to derive an unconfounded estimate of the phenotype-disease association. Integrated meta-analyses may be able to take advantage of Mendelian randomization in order to test whether the phenotype is actually on the causal pathway and to obtain an unconfounded estimate of the size of the effect of phenotype on disease.
In this paper, we present a framework for an integrated meta-analytical approach to the study of genotype-disease and genotype-phenotype associations that takes advantage of the benefits of Mendelian randomization to derive an indirect estimate of the phenotype-disease relation. To illustrate the methods involved, we use the example of an integrated meta-analysis of studies on MTHFR and coronary heart disease and MTHFR and homocysteine level.
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METHODS
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Mendelian randomization
In order to use genetic studies to quantify the relation between phenotype and disease, the estimate of the genotype-disease association must be combined with the estimate of the genotype-phenotype association (figure 1). Suppose that a mutant genotype (GG) causes an increased risk of disease in comparison with the wild type (gg) and that this effect is measured by the odds ratio, ORGG vs. gg. Further suppose that GG compared with gg causes a mean difference,
P, in the level of the intermediate phenotype. Then, under the assumptions required for Mendelian randomization and assuming linearity of the relation between phenotype difference and log odds ratio for the disease, ORGG vs. gg1/
P is an unconfounded estimate of the odds ratio of disease resulting from a unit change in the phenotype.

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FIGURE 1. Calculation of an unconfounded estimate of the effect of a change in phenotype on a disease based on the concept of Mendelian randomization. OR, odds ratio.
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Sources of evidence
When one is searching for evidence on genotype-phenotype and genotype-disease associations, three different types of genetic studies are likely to be identified: those evaluating only the genotype-phenotype association, those evaluating only the genotype-disease association, and those evaluating both. In addition to noting the usual estimates of effect and their precision, it is important to record when both associations are measured in the same study. It might be that studies classified as providing only genotype-phenotype information in fact also evaluated the genotype-disease association but used a different disease definition, so that this genotype-disease result cannot be pooled with the results of other studies. When collecting data on genotype-phenotype, it is important to note whether the information on the phenotype difference comes from cases, from controls, or from a mixture of both. Whenever possible, data from cases and data from controls should be analyzed separately. If the disease itself affects the level of the phenotype in a way that is not simply linear, the data on the genotype-phenotype effect collected from cases may be less reliable because of reverse causation.
Meta-analytical approaches
If the genotype-phenotype evidence and the genotype-disease evidence come from unrelated sources, separate meta-analyses will provide estimates of the pooled effects that can, by using Mendelian randomization, be combined to estimate the size of the phenotype-disease association. In practice, there is likely to be a mixture of studies that measured the genotype-phenotype effect, studies that measured the genotype-disease effect, and studies that measured both. Studies that measured both associations need to be modeled correctly in order to properly account for the correlation in their estimates of the genotype-phenotype and genotype-disease associations (5).
Consider first a meta-analysis in which all available studies measured both genotype-phenotype and genotype-disease. We could proceed as before and separately pool the genotype-phenotype estimates and genotype-disease estimates before combining the pooled values in order to estimate the effect of phenotype on disease. However, the likely correlation in the sizes of pairs of estimates from the same study would affect the size of the confidence interval for the derived phenotype-disease effect and the validity of any hypothesis test. A better procedure would be to combine the genotype-phenotype and genotype-disease estimates separately within each study to obtain study-specific estimates of the phenotype-disease effect. These study-specific estimates could be graphed in their own forest plot and pooled to obtain an overall estimate.
In the more realistic situation in which some studies measured both genotype-disease and genotype-phenotype and some measured one or the other, we need to proceed with caution. Most important features of the data will be evident from a forest plot with two columns, one for genotype-disease and the other for genotype-phenotype, in which paired estimates from within the same study are aligned in the same row (see figure 2). The forest plot is organized in three blocks, representing the studies that measured both the odds ratio and the mean difference, the studies that measured only the odds ratio, and the studies that measured only the mean difference. Within blocks, the studies are ordered by size of effect. Where both estimates were obtained in the same study, the studies are ordered by the size of the genotype-disease odds ratio. Having drawn the plot, the next stage should be to check that the genotype-disease estimates from studies that also reported data on genotype-phenotype are consistent with the estimates from studies that did not report data on genotype-phenotype. Similarly, genotype-phenotype estimates should be compared between studies that also reported data on genotype-disease and those that did not.

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FIGURE 2. Two-column forest plot and pooled estimates for genotype-disease and genotype-phenotype associations. A, Asians; E, Europeans; F, females; M, males. Horizontal bars, 95% confidence interval. (For references, see the technical report by Minelli et al. (5).)
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Funnel plots can be used to search for the presence of publication bias (6, 7). However, genetic studies may also be affected by a form of reporting bias in which both the odds ratio and the mean difference are measured but only one is reported because the other contradicts the anticipated relation. Moreover, it is possible that the reporting of data on both associations is a marker for some feature such as study quality. It is very difficult to detect this bias from the reported data; but a careful reading of the studys methods section may show whether data were collected but not reported, and it may be informative to distinguish studies that reported data on only one of the two associations using a different symbol on the funnel plots.
When the phenotype does indeed lie on the causal pathway between gene and disease, studies carried out in populations with a large genotype-phenotype difference might be expected to show a large genotype-disease odds ratio. This can be investigated by plotting the findings from each study on a graph of the log odds ratio of genotype-disease against the average difference in phenotype with genotype. A similar graphic approach was used previously in the meta-analysis of randomized trials (8, 9). This graph would be expected to show a monotonic trend if the phenotype is intermediate on the etiologic pathway to disease, and the line should pass through the origin. Lack of any correlation would cast doubt on whether the phenotype is truly intermediate. A line that does not pass through the origin might indicate that there is another intermediate phenotype through which the gene under study exerts its effect on disease (a special case of pleiotropy) or that the gene is in linkage disequilibrium (associated at population level) with a gene which also affects the risk of disease, or that there is differential publication bias for the two associations (7, 10). This graph will also show gross departures from linearity of the relation between phenotype difference and log odds ratio of disease, as approximate linearity is an assumption behind the averaging across studies to obtain an estimate of the pooled phenotype-disease association.
If it appears that genotype-phenotype and genotype-disease associations are consistent across all studies, we may pool all genotype-phenotype estimates and all genotype-disease estimates before combining these overall estimates to derive a figure for the phenotype-disease association. The effect of the correlation on the confidence interval and hypothesis test will depend on the proportion of studies that reported on both genotype-disease and genotype-phenotype associations. The studies that provided both estimates can now be used as described above to provide a comparison with studies reporting one of the estimates and to investigate the consistency of the study-specific phenotype-disease estimates. Methods for the adjustment of confidence intervals and hypothesis tests that allow for between-study correlation have been described elsewhere (5).
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EXAMPLE
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MTHFR, homocysteine, and coronary heart disease
A recent nongenetic meta-analysis of individual patient data from epidemiologic studies showed a decrease of 11 percent in coronary heart disease for a 25 percent decrease in homocysteine level (odds ratio = 0.89, 95 percent confidence interval (CI): 0.83, 0.96) (11). The meta-analysis showed that heterogeneity between studies was partly explained by study design. Retrospective studies yielded higher estimates of risk, perhaps because of reverse causation and/or unadjusted confounding. In particular, two major confounding factors were suggested: smoking and blood pressure. These factors are both strongly correlated with homocysteine level and are known risk factors for coronary heart disease. The strong possibility of unadjusted confounding makes it very difficult to be sure that the relation between homocysteine and coronary heart disease is causal.
A common polymorphism in the gene for the MTHFR enzyme leads to reduced enzyme activity, a lower folate level, and consequently a higher homocysteine level (12). The polymorphism involves a C
T base pair substitution at nucleotide 677, so the wild-type homozygous genotype is referred to as CC and the mutant homozygous genotype as TT. This polymorphism can be used, together with the idea of Mendelian randomization, to indirectly assess the effect of homocysteine on coronary heart disease.
A recent genetic meta-analysis of individual patient data has shown an increased risk of coronary heart disease of approximately 16 percent associated with genotype TT as compared with CC (odds ratio = 1.16, 95 percent CI: 1.05, 1.28) (13). This result was similar to that of another meta-analysis published at the same time but carried out on aggregated data, which showed a pooled odds ratio of 1.21 for the TT genotype (95 percent CI: 1.06, 1.39) (14). The latter paper also mentioned those studies that evaluated the association between genotype and phenotype. Wald et al. (14) found an average difference of 2.7 µmol/liter in homocysteine concentration (95 percent CI: 2.1, 3.4) between the TT and CC genotypes.
Sources of evidence
When the two meta-analyses by Wald et al. (14) and Klerk et al. (13) were combined, a total of 66 genetic studies were identified. Classifying the studies that reported both the estimate and its precision, 32 evaluated only the genotype-disease association, 16 evaluated only the genotype-phenotype association, and 18 evaluated both. The definition of coronary heart disease used in our analysis was myocardial infarction or angiographically confirmed coronary artery occlusion (>50 percent of the luminal diameter). Genotype-disease associations were reported in an additional 13 studies in the original meta-analyses, but this information was not included because of either a different disease definition or a restricted study population (5).
Among the 18 studies that evaluated both associations, nine measured the mean difference in phenotype level with genotype in both cases and controls (four reporting only combined means); four studies measured homocysteine only in cases and three only in controls, and two reports were unclear.
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RESULTS
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Figure 2 shows the two-column forest plot, with the first column representing the genotype-disease log odds ratio and the second representing the genotype-phenotype mean difference. It is clear that there is considerable variation between studies, with some even reporting average odds ratios less than 1 or mean homocysteine differences in the direction opposite that anticipated.
Parts a and b of figure 3 show the funnel plots for the genotype-disease and genotype-phenotype associations, respectively. For the genotype-disease association, there seems to be no evidence of either publication bias, indicated by an overall lack of symmetry in the funnel plot, or reporting bias, suggested by a discrepancy in the shape of the funnel plot between studies reporting on both associations and those reporting on only one association. For the genotype-phenotype association, the funnel plot is suggestive of possible publication bias, while there appears to be little evidence of reporting bias.

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FIGURE 3. Funnel plots for genotype-disease (a) and genotype-phenotype (b) associations. Different symbols are used for those studies that measured both associations (triangles) and those that measured only the association of interest (circles).
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All of the following meta-analyses were based on random-effects models, which take into account between-study heterogeneity (6). The pooled odds ratio estimate for the effect of genotype on coronary heart disease based on studies that also reported on the homocysteine change was 1.17 (95 percent CI: 0.93, 1.48), and where data on homocysteine were not reported, the pooled odds ratio was 1.24 (95 percent CI: 1.04, 1.48). The difference was not statistically significant (p = 0.68). Similarly, the mean change in homocysteine level in studies that also reported on coronary heart disease was 2.14 µmol/liter (95 percent CI: 1.37, 2.91), and in studies that did not report data on coronary heart disease it was 3.34 µmol/liter (95 percent CI: 2.10, 4.59). The direction of the difference is consistent with the presence of publication bias, whereby results from studies evaluating the genotype-phenotype association alone are published only if the effect size detected is large. However, this difference was not statistically significant (p = 0.11). The lack of significant differences justified pooling all of the odds ratio estimates to obtain an odds ratio of 1.21 (95 percent CI: 1.06, 1.40) and all mean differences in homocysteine to obtain a difference of 2.71 µmol/liter (95 percent CI: 2.02, 3.41). Combining the two estimates, we obtain an estimate of the odds ratio for coronary heart disease per unit (1.0-µmol/liter) change in homocysteine level of 1.07. If, for the moment, we ignore the correlation between the studies that measured both, we obtain the 95 percent confidence interval 1.02, 1.14. It may be more informative to rescale this odds ratio for increments other than a unit increase in homocysteine level. For instance, the odds ratio for coronary heart disease for a standard reference increment of 5 µmol/liter, as used by Wald et al. (14), is 1.43 (95 percent CI: 1.10, 1.95), while for an increment of 3 µmol/liter, considered to reflect the possible size of a homocysteine-lowering intervention with folic acid supplementation (15), the odds ratio is 1.24 (95 percent CI: 1.06, 1.49).
The next step is to investigate more fully the findings of the 18 studies that reported both an odds ratio and a mean difference. Figure 4 shows the forest plot of the study-specific estimates of the coronary heart disease odds ratio associated with a 5-µmol/liter increase in homocysteine level. Because, on a log odds ratio scale, the derived phenotype-disease association is obtained by division, when study results suggest that the homocysteine difference could reasonably be on either side of zero, the confidence interval for the ratio could stretch to plus or minus infinity (16, 17). In some cases, this infinite range is accompanied by a gap or clearing in the forest plot associated with values that the ratio is very unlikely to take. The most important feature of figure 4 is the poor precision in the derived estimate that can be obtained from most individual studies. Indeed, several derived estimates have infinite variance.

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FIGURE 4. Forest plot of the derived study-specific estimates of the odds ratio for the effect of phenotype on disease (per 5-µmol/liter difference in homocysteine level). A, Asians; E, Europeans. Horizontal bars, 95% confidence interval. (For references, see the technical report by Minelli et al. (5).)
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Parts a and b of figure 5 show the log odds ratio of genotype-disease plotted against the mean difference in homocysteine level, separately for homocysteine measured in cases and in controls. The two parts of the figure include all studies that either measured homocysteine only in cases or controls or measured it in both and reported separate estimates for the two groups. To allow for the large differences in the precision of the different studies, the individual estimates are plotted as ellipses, with their axes inversely proportional to the standard error of the log odds ratio of genotype-disease and the mean change in homocysteine level. Both figures show an approximately linear relation, with the line passing close to the origin. As anticipated, the pattern is somewhat clearer when control data are used.

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FIGURE 5. Plot of the log odds ratio for the effect of the methylenetetrahydrofolate reductase gene on coronary heart disease risk against the mean difference in homocysteine level between genotypes, separately for studies in which phenotype was measured among cases (a) and controls (b). The axes of the ellipses are inversely proportional to the standard errors of the respective associations.
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The unweighted correlations observed in parts a and b of figure 5 are 0.37 (p = 0.29) and 0.78 (p = 0.01), respectively. Adjusting for the correlation in the 18 studies reporting data on both measures would alter our odds ratio estimate and confidence interval for the effect of a 5-µmol/liter increase in homocysteine level on coronary heart disease risk from 1.43 (95 percent CI: 1.10, 1.95) to 1.54 (95 percent CI: 1.17, 2.06) (5).
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DISCUSSION
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Although genotype-disease associations are becoming better understood, it is only when we also have information about the causal pathway that we open up the possibility of preventive or therapeutic intervention. Thus, while the association between MTHFR polymorphisms and coronary heart disease is scientifically interesting, disease prevention becomes possible when we understand that this effect acts, at least in part, through homocysteine. Dietary folate supplementation is a relatively simple intervention that can be implemented at a population level to lower homocysteine level and thereby reduce coronary heart disease risk. This intervention was introduced in the United States in the late 1990s with the fortification of cereals and grains (18). Classical epidemiologic studies may provide evidence about the phenotype-disease association, but it will almost certainly be affected by confounding and/or reverse causation. The use of Mendelian randomization offers a novel way of deriving unconfounded estimates, although Mendelian randomization makes its own assumptions about the pathway from gene to disease (4). The most crucial assumption is that the genotype influences disease risk only through modification of the specific phenotype. If the genetic polymorphism also alters the risk of the same disease via other pathways, the estimate of a specific phenotype-disease association might be seriously biased. In the example of homocysteine and coronary heart disease, this is probably not a problem; but, for instance, polymorphisms of the apolipoprotein E gene affect several different intermediate phenotypes related to lipid metabolism and atherosclerosis (4). Consequently, it is advisable to limit the use of Mendelian randomization to studies where there is good biologic knowledge of the genotype-phenotype-disease pathway.
The approach proposed in this paper stresses the need for investigators conducting meta-analyses to review simultaneously the stages in the genotype-phenotype-disease pathway, and it implies that individual studies of genotype-disease associations should collect information on intermediate phenotypes whenever possible. In fact, the analysis of studies that measured both associations allows insight into the interrelations between genotype, phenotype, and disease and gives researchers an opportunity to check the assumptions of the analysis. In this respect, a meta-analysis of small studies might be more informative than a single large prospective study. In some meta-analyses, inconsistencies across studies could result in departures from the linear trend seen in figure 5. This might happen if study populations differed with respect to phenotype measurement, disease definition, gene-environment interactions, compensatory developmental processes (canalization), or linkage disequilibrium with functional alleles (4). Theoretical considerations and our example suggest that it may be safer for primary researchers to measure the phenotype in controls in order to avoid any possibility of bias due to reverse causation. If the phenotype level is measured in both cases and controls, two separate estimates should be reported. For meta-analyses, our recommendation is to perform sensitivity analyses, with phenotype data obtained on cases analyzed separately from phenotype data obtained on controls.
The need for an integrated meta-analytical approach to genetic studies when using Mendelian randomization is particularly important. The uncertainty associated with the derived estimate of the phenotype-disease association can be large, since it depends on uncertainty in both the estimate of the genotype-phenotype association and the estimate of the genotype-disease association (19). It is crucial to the use of Mendelian randomization that both estimates are sufficiently precise, but especially that of the genotype-phenotype association. Such precision is only likely to be obtained through a meta-analysis of all available evidence. In fact, at present, almost all genetic studies lack the statistical power to detect the relatively small effects of the many gene variants that underlie common, complex diseases (20). Although massive reductions in genotyping costs offer the prospect of larger studies, study size remains limited by the cost of proper phenotyping (21).
While meta-analyses can (in theory, at least) partially alleviate the problem of inadequate statistical power, they cannot control the problems of publication and reporting bias (6, 7) that are thought to be particularly important in genetic epidemiology (1, 22). However, using an integrated meta-analytical approach, investigators can start to address these issues by comparing the pooled estimates for genotype-phenotype and genotype-disease associations in studies reporting on either one association only or both associations, and by drawing the funnel plots in a way that allows comparison between the two types of studies for each association.
Analysis of the correlation between the genotype-disease odds ratio and the genotype-phenotype difference, as typified by figure 5, must be done with care. The plot is based on data aggregated over studies and is analogous to an ecologic study that is potentially subject to the ecological fallacythat is, patterns seen in aggregate data do not necessarily translate to the individual. Thus, when we see an increase in the risk of disease in studies that show an increased difference in phenotype, it is probable but not certain that we would see a similar effect at the individual level. Equally, failure to see a pattern in aggregate data does not rule out the possibility of an individual-level effect. Obviously, an individual-level causal effect is required for an intervention on the phenotype to have an impact on the risk of disease.
It is tempting to add nongenetic studies of the phenotype-disease association to our integrated approach, if only to test whether they accord with the estimate derived from the application of Mendelian randomization. Unfortunately, the sample sizes required to establish equivalence of the measured and derived estimates are such that even a large meta-analysis may not suffice (19). This is clearly an area that requires more work, because our ultimate aim should be to produce an integrated meta-analysis that links together all relevant phenotypes, diseases, and genotypes, including the heterozygous group.
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ACKNOWLEDGMENTS
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This research was supported via a National Research Scientist in Evidence Synthesis Award to Dr. Cosetta Minelli from the UK Department of Health.
The authors thank Prof. Paul Burton for his comments on earlier drafts of the paper.
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NOTES
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Joint senior authors. 
Correspondence to Dr. Cosetta Minelli, Department of Health Sciences, Leicester Medical School, University of Leicester, 2228 Princess Road West, Leicester LE1 6TP, United Kingdom (e-mail: cm109{at}le.ac.uk). 
Joint senior authors. 
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