Illustration of the Mendelian randomization framework.

<p>In Mendelian randomization, if there is a causal effect of the exposure (e.g., smoking heaviness) that is being captured by the genotype on the outcome (e.g., lung cancer), then an association of genotype with the outcome should be detectable in a sufficiently large unstratified GWAS (panel A). This can be confirmed in a stratified analysis, where an association of genotype with the outcome should only be seen in the exposed group (i.e., smokers, panel B) and not the unexposed group (i.e., never-smokers, panel C). This is a special case of gene × environment (G × E) interaction, where both G and E are known, although it will not always be possible to stratify on the exposure, and stratification (which can be considered a form of statistical adjustment) can introduce other potential biases in certain circumstances (see <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1005765#pgen.1005765.box003" target="_blank">Box 3</a>).</p

Hierarchy of evidence.

<p>Hierarchy of evidence.</p

Association of <i>ADH1B</i> genotype with risk of upper aerodigestive cancer.

<p>Risk of upper aerodigestive cancer by <i>ADH1B</i> genetic variation, stratified by drinking intensity and smoking status, is shown as the odds ratio (OR) of upper aerodigestive cancer by re1229984 (<i>ADH1B</i>) genotype comparing rare allele (dominant model) carriers versus common allele homozygous genotype. ORs are standardised by age, sex, study centre, cumulative alcohol consumption, and, when relevant, smoking. ORs and 95% CI are derived from fixed effects models. <i>Figure adapted from Hashibe et al</i>. <i>(2008)</i> [<a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1005765#pgen.1005765.ref057" target="_blank">57</a>] <i>with permission granted by Nature Publishing Group</i>.</p

Illustration of collider bias.

<p>Panel A shows the basic premise of collider bias. In this example, a bell is sounded whenever either coin come up “heads.” The result of one coin toss is independent of the other. However, if we stratify on the bell ringing, seeing “heads” on both coins is not independent and a spurious correlation is induced. Panel B shows this with the example of stratifying on smoking status. If the variant used as an instrument for heaviness of smoking is also associated with smoking status (i.e., ever-smoker versus never-smoker), and if BMI also influences smoking status, then there is a risk of collider bias if we stratify on smoking status. Panel C shows an example where stratification will not introduce collider bias, as sex is not an effect of either possession of a genetic variant that predicts alcohol consumption or of blood pressure.</p

PRISMA Flow chart of literature search and data extraction.

<p>Flow chart of literature search, selected meta-analyses papers, selection of sub-analyses and selection of final data sets.</p

Relationship Between Number of Foci and Sample Size per Study.

<p>Scatter plot of foci and sample size from all data sets (N = 1778) within all meta-analyses.</p

Relationship Between Sample Size and Number of Clusters in Simulated fMRI Data.

<p>Relationship between sample size and number of clusters in simulated fMRI data.</p

Relationship Between Number of Meta-Analytic Foci, Sample Size and Number of Studies per Meta-Analysis.

<p>2A - Scatter plot of foci (per meta-analysis) and studies per meta-analysis. 2B - scatter plot of foci (per meta-analysis) and sample size per meta-analysis.</p