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Studies of human traits and diseases are inherently confined to observational studies, known as epidemiological studies. This can make it very hard to determine what actually causes a particular disease or trait, and what is just a by-product or biomarker of the disease.

Mendelian randomization is a statistical technique used by genetic epidemiologists to determine causal effects, for instance whether a biomarker actually influences disease risk, or whether it is just a statistical association.

From basics, how can genetics be used to determine causal associations between traits (such as blood markers) and increased risk of disease, and on what assumptions is this based?

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Should it not be trigs ~ SNPs for the triangulation? –  user4493 Sep 18 '13 at 17:25
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Epidemiological studies analyze human observational cohort data to try to statistically link disease risk and biomarkers. For instance, it is know a well know fact that smoking increases the risk of lung cancer, yet before the 1950s it was widely considered otherwise until observational evidence proved irrefutable (Levin, 1950).

Confounding

However, inferring causality using observational data can be tricky. For instance, there is a very strong statistical association between ice-cream sales and risk of drowning in the UK. In this example it is quite clear that the association is confounded - that is, there is a 'hidden' variable we have not accounted for that links the 2. It is easy to infer that ice-cream sales don't increase your risk of drowning, but the 2 are correlated because both ice-cream sales and risk of drowning increase at the same time of year; both are positively correlated with 'nice weather' traits.

In the above example it is easy to say that the relationship is confounded. However, in a hypothetical study on type-2 diabetes that finds higher blood hematocrit (% volume of blood made up of red blood cells) is associated with increased odds of being diabetic, it is less clear whether higher hematocrit increases susceptibility/risk of becoming diabetic, or whether diabetes increases hematocrit. Longitudinal studies that follow the same individuals for many years help determine which came first - this is based on the assumption that if raised hematocrit is associated with increased risk of diabetes 5 years later, it is more likely that hematocrit is causal, and you have a biomarker for diabetes risk (although you still cannot say it is causal, it may just be a proxy for another 'hidden' trait, or the effect may be mediated by another unmeasured marker).

Causality

Genome-wide association (GWA) studies have become increasingly popular since the completion of the human genome project, and there are currently (15th August 2012) 7039 genetic variants (SNPs, single-nucleotide polymorphisms) documented in the catalogue of published GWA studies (www.genome.gov/gwastudies). These SNPs have been robustly associated with traits such as 'risk of type-2 diabetes', or 'blood adiponectin levels', by large genetic epidemiological studies, usually with many thousands of participants sampled.

The key point about SNP associations is that the direction of effect is always known; a particular SNP may affect your adiponectin levels, but adiponectin does not affect the SNPs you inherit.

Mendelian Randomization

In an observational study that finds an association between (for example) circulating triglyceride levels and type-2 diabetes (using fasting glucose and insulin as 'proxies') it is not possible to determine the causal direction; do triglycerides increase risk of diabetes or vice versa? (This is an actual case study by De Silva, et al. 2011).

Using the assumption that the inheritance of SNPs is essentially random (i.e. not affected by the trait you are measuring - in this example triglycerides) it is possible to determine the causal effect of triglycerides on the risk of diabetes. Note: this is only possible for traits (such as serum triglyceride levels) that have SNPs identified by GWA studies.

First of all, you have already calculated the association between triglyceride levels (in this study a 1 standard-deviation (SD) increase in triglycerides was associated, with an Odds Ratio (OR) of 2.68, with type-2 diabetes in almost 10,000 human participants). Because it is a cross-sectional study, only an association is reported, with no causal implications... yet!

Enter the SNPs

Having identified the SNPs that increase triglyceride levels (at the time of the study, 10 were reported in the literature), each participants genotype for these SNPs needs to be measured or inferred (generally this is performed in large cohort studies, which are then used for many different individual projects).

A combined 'score' is then derived for each individual. This is conceptually very simple; if an individual has 4 of the 10 triglyceride raising alleles, they are given a score or 4, and so on. This is complicated by the fact that the SNPs have different effects on the triglycerides, so a 'weighted allele score' is derived instead (simply put, the coefficient of the SNP~triglyceride association is taken into account when adding risk allele scores). By using this kind of score, a 'per allele' estimation of the effects can be estimated;

The association between the triglyceride levels and the allele score is then determined (by linear regression analysis - adjusted for age and sex, as these are known to affect triglycerides). There are actually 2 ways of performing the next analysis, the first of which is conceptually simpler, but the second of which is more robust.

Method 1: the 'triangulation' approach

The two observed associations calculated so far (per-SD trig. levels are associated with diabetes, and the per-allele SNP score are associated with per-SD trig. levels) can then be used to calculate an expected association. This is simply derived by multiplying the 2 coefficients together. Below is the 'triangulation' representation of this;

Triangulation approach for Mendelian Randomization

This expected association between the triglyceride-raising SNPs and risk of diabetes is only true if raised triglycerides increase the risk of diabetes. The observed association between the SNP-score and diabetes can then be calculated. If the expected and observed estimates are similar, then triglycerides raise diabetes risk, and are a causal biomarker. If the observed association is null (or, at least, much smaller), then triglycerides are likely to be secondary.

Method 2: the instrumental variable analysis

This method is for the more hardy statisticians. Instrumental variables are derived variables, and represent an intermediate between a proposed 'cause' and the 'effect', or outcome (in this case the triglyceride raising alleles are proposed to 'cause' diabetes, and this is mediated by the triglyceride levels themselves).

Using a linear regression, the "fitted values" from a model with triglyceride levels as the outcome, and the weighted SNP score as the only independent variable, are extracted. These fitted values represent the variance in the triglycerides that is predicted by the SNP score. We are using the SNPs as the instrument here, as they directly influence the biomarker (exposure, i.e. triglycerides), and are not affected by either the exposure or the outcome (diabetes). The important assumption here is that the effect of the SNPs on the outcome is not confounded, and can only be mediated by the exposure - this is true for genotypes (Lawlor, et al. 2008).

By then determining the association between the derived variable and diabetes, you will know whether the proportion of the triglyceride variance predicted by the SNPs is associated with diabetes - if so, then triglycerides increase the risk of diabetes.

Results

The study performed both types of Mendelian Randomization analysis and found no evidence to suggest a causal association between triglycerides and diabetes phenotypes.

So Mendelian Randomization is a useful tool for inferring causality with biomarkers. It is not necessarily conclusive evidence, but it can help distinguish biomarkers of particular importance and interest (with regard to interventions) from those that are just markers of the disease.

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Nice weather? In the UK? Ridiculous. –  Konrad Rudolph Aug 15 '12 at 21:06
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