
Martin’s key concepts
The 20 concepts on the key-concepts list for GWAS, Mendelian randomization and proteomics, one module each
On 2 October the course published Martin’s key concepts, a list of 20 concepts for the GWAS, Mendelian randomization (MR) and proteomics part of the course (Lectures 4–6, 8 and 9). When the lecture pages were written this list did not exist, so the material is spread across many sections and some concepts only got a sentence or two.
This page collects the list into 20 short modules, in the list’s own order. Each module gives an exam-ready definition you can say in one or two sentences, the common confusion to avoid, a quick check, and links to the lecture sections that go deeper. Three concepts that were thin in the lectures get more space here: additive, dominant and recessive models (K.4), colocalization (K.19) and biomarker vs causal protein (K.20).
Mark each module Reviewed or Confident as you go. The status is saved in this browser and counted on the dashboard under 🔑.
Source: “Martins part key_concepts.docx” (course material, uploaded 2 October), a list of 20 concept names without further text. The definitions, examples and questions on this page are written for this app.
Changes elsewhere: lecture sections that cover these concepts now carry the badge 🔑 Martin’s key concepts instead of ❔ or 🗣️. Seminar topics (🗣️) are no longer described as “not on the written exam”: seminar content can also come on the exam. The seminar’s own questions are on Seminar questions.
Part 1: From SNP to GWAS
K.1 SNP (single-nucleotide polymorphism)
- Usually biallelic: two alleles, often called the reference/other and the effect allele in GWAS files.
- “Polymorphism” traditionally means common enough to be a normal variant in the population (often minor allele frequency ≥ 1%). A rare change in one family is usually called a variant or mutation.
- SNPs are what SNP arrays genotype and what GWAS tests, one at a time.
Don’t confuse: a SNP is a position with variation in the population; an allele is one of the possible bases at that position; a genotype is the pair of alleles one person carries.
Deeper: 3.3c dbSNP and rs numbers · 4.2 SNPs, alleles, MAF
K.2 Genotype and allele dosage (0/1/2)
| Genotype (effect allele = T) | CC | CT | TT |
|---|---|---|---|
| Dosage | 0 | 1 | 2 |
- Imputed SNPs give an expected dosage between 0 and 2 (for example 1.7), because the genotype is predicted with uncertainty.
- The dosage only means something once you know which allele is counted. Swap the effect allele and every dosage becomes 2 − dosage, and β changes sign.
Don’t confuse: dosage counts the effect allele, which is not always the minor allele or the “risk” allele.
Deeper: 4.4 The additive model · A3 Reading association output
K.3 Minor allele frequency (MAF)
- Computed from genotype counts: each heterozygote contributes one copy, each homozygote two. With \(n_{AA}, n_{Aa}, n_{aa}\): \(f_a = (2n_{aa} + n_{Aa}) / (2N)\).
- Low MAF means low power: few people carry the allele, so β is estimated with a large SE. Rare variants are why GWAS QC often filters on MAF.
- MAF is population-specific. The minor allele in Europeans can be the major allele in another ancestry, which matters when combining datasets (seminar question on GLGC vs 1000 Genomes).
Don’t confuse: MAF is not the same as the effect allele frequency (EAF). If the effect allele is the major allele, EAF = 1 − MAF.
Deeper: 4.2 SNPs, alleles, MAF and genotype frequencies · 3.9 Hardy–Weinberg
K.4 Additive, dominant and recessive models
Coding of the same SNP under the three models (effect allele = T)
| Model | CC | CT | TT | What β means |
|---|---|---|---|---|
| Additive | 0 | 1 | 2 | Change in phenotype per extra copy of T |
| Dominant (T dominant) | 0 | 1 | 1 | Difference between carriers (one or two T) and non-carriers |
| Recessive (T recessive) | 0 | 0 | 1 | Difference between TT and everyone else |
Why GWAS use the additive model (Lecture 4, “Worth noting 2”): you test a million SNPs and do not know each one’s true pattern. The additive model is the simple default; it has reasonable power even when the true pattern is dominant or recessive, and it uses one degree of freedom. Dominant and recessive models are useful when you study one specific SNP or gene in depth.
Don’t confuse: dominance describes the genotype–phenotype relationship, not the allele. The same allele can act dominant for one phenotype and recessive for another (Lecture 4).
Deeper: 4.4 The additive model · 3.6 Mendelian genetics
K.5 Genome-wide association study (GWAS)
- Hypothesis-free: no candidate gene is chosen in advance.
- Output: one β, SE and p per SNP (summary statistics, K.11), shown as a Manhattan plot (position vs −log₁₀ p) and checked with a QQ plot.
- Continuous phenotype → linear regression (β = mean difference per allele); binary → logistic regression (β = log-odds per allele, OR = e^β).
- A GWAS finds associations. The top SNP is usually a tag in LD with the causal variant, and the association can still be confounded (population structure).
Don’t confuse: GWAS finds loci, not genes or mechanisms. Going from a hit to biology needs fine-mapping, QTL data, colocalization, MR or experiments.
Deeper: 4.6 The GWAS scan · 4.9 Population structure · 4.10 From hit to biology · 5.2 The full GWAS pipeline
K.6 Effect size, standard error and p-value
Example. β = 0.05 SD per allele, SE = 0.008.
| Step | Value |
|---|---|
| z = β / SE | 0.05 / 0.008 = 6.25 |
| Two-sided p | ≈ 4 × 10⁻¹⁰, below 5 × 10⁻⁸ |
| 95% CI | 0.05 ± 1.96 × 0.008 = 0.034 to 0.066 |
- SE shrinks with larger sample size, higher MAF and lower phenotype variance. That is why a tiny β can have a tiny p in a large GWAS.
- Binary outcome: β is a log(OR). OR per allele = e^β; for two copies under the additive model, OR = e^(2β).
- p measures evidence, not importance. A highly significant SNP can explain almost none of the phenotype variance.
Don’t confuse: a small p-value does not mean a large effect. Compare β (and its units) to judge size.
Deeper: 4.3 Phenotype types and the per-allele effect · 4.4 β, SE and p
K.7 Genome-wide significance
\[\frac{0.05}{1\,000\,000} = 5 \times 10^{-8}\]
- “Independent” is the key word: there are many more SNPs than that, but because of LD neighbouring SNPs are correlated, so the effective number of independent tests in European-ancestry genomes is about one million.
- It controls the family-wise error rate: the chance of even one false positive across the whole scan is about 5%.
- SNPs with 5 × 10⁻⁸ < p < 10⁻⁵ are sometimes called “suggestive”.
Don’t confuse: passing the threshold does not make a SNP causal, and failing it does not mean “no effect”; it may mean too little power.
Deeper: 4.7 Multiple testing, Manhattan and QQ plots · 7.11 FWER vs FDR · 7.12 Bonferroni
K.8 Linkage disequilibrium (LD; r²)
- LD exists because nearby SNPs are inherited together: recombination between them is rare, so the haplotypes they sat on are preserved over generations.
- r² = 1: one SNP perfectly predicts the other, so they give the same GWAS signal. r² ≈ 0: independent.
- LD is population-specific. Compute it in a reference panel that matches the ancestry of the GWAS (for example the European part of 1000 Genomes).
- LD generally decays with distance, but physical distance is not LD: two close SNPs can have low r², and LD blocks vary in size.
Don’t confuse: linkage is about co-inheritance within families (recombination frequency); LD is the correlation of alleles across a population.
Deeper: 3.7 Linkage, recombination and LD · 4.8 Lead SNP and r² · 5.4b r² bands
K.9 Lead SNP and GWAS locus
- A locus is defined around the lead SNP, by a distance window (for example ± 500 kb) and/or by LD with the lead SNP.
- The lead SNP is the best statistical tag, not necessarily the causal variant. The causal variant can be any SNP in strong LD with it, or one that was not genotyped at all.
- One locus can contain more than one independent signal (conditional analysis or clumping can reveal a secondary signal).
Don’t confuse: “lead SNP” (strongest p in the region) ≠ “causal SNP” (the variant that changes the biology) ≠ “nearest gene” (often assumed, not proven).
Deeper: 4.8 Lead SNP and r² · 4.10 Locus, lead SNP, QTLs · 5.4 Finding the causal SNP
K.10 LD clumping and independent genetic signals
The algorithm
| Step | Action |
|---|---|
| 1 | Sort significant SNPs by p, smallest first |
| 2 | Take the top SNP as an index SNP |
| 3 | Remove SNPs within the window (for example 1,000 kb) with r² above the threshold (for example 0.01–0.1) |
| 4 | Repeat with the next remaining SNP until none are left |
- Why: correlated SNPs carry the same information. For MR you need independent instruments, otherwise the same signal is counted several times and the SE is too small. For PRS clumping avoids double-counting.
- Choices matter: a wider window compares more SNP pairs (slower, catches long-range LD, leaves fewer SNPs); a lower r² threshold removes more SNPs (stricter independence).
- More SNPs can survive clumping than there are causal variants: two weakly correlated tags of one causal variant can both pass a lenient threshold, and SNPs outside the window are never compared.
Don’t confuse: “independent” (low r² between the kept SNPs) is not “causal”. Each clump still represents a region.
Deeper: 5.4b r² bands and LD clumping · A5 Manual LD clumping · Seminar S.1 and S.5
K.11 GWAS summary statistics
- Before using them, check four things: which allele is the effect allele, whether β is OR or log(OR), the scale of the phenotype (SD units? log?), and the genome build (hg19/GRCh37 vs hg38/GRCh38).
- LD cannot be computed from summary statistics: they have no genotypes per person. Use a reference panel with matching ancestry.
- Two-sample MR needs two sets: one for the exposure, one for the outcome, matched on SNP and allele.
Don’t confuse: summary statistics are per SNP, not per person. You cannot rerun the regression with new covariates from them.
Deeper: 4.6 Summary statistics · 5.5 LD with summary statistics · 9.2 The data you need
Part 2: Mendelian randomization
K.12 Instrumental variable (IV)
flowchart TD Z["Z (instrument)"] --> X["X (exposure)"] X --> Y["Y (outcome)"] U["U (confounders)"] --> X U --> Y
- The idea comes from econometrics. The classic example is the randomization in an RCT: the coin flip shifts treatment and is independent of everything else.
- In MR the instrument is a genetic variant: alleles are allocated at conception, before the exposure and the disease, and independently of most lifestyle confounders.
Don’t confuse: an IV is not a confounder or a covariate to adjust for. Its job is to give variation in the exposure that confounders do not touch.
Deeper: 6.3 Genetic variants as instruments · 6.4 Why we need MR: confounding
K.13 Mendelian randomization (MR)
- “Nature’s randomized trial”: people who inherited exposure-raising alleles are, on average, like people who were randomized to a slightly higher exposure for life.
- One-sample MR: exposure and outcome in the same people. Two-sample MR: SNP–exposure and SNP–outcome effects from two different GWAS, using only summary statistics.
- The answer is the effect per unit of genetically predicted exposure, which is lifelong and usually small; it is not the same as the effect of a drug given in middle age.
Don’t confuse: MR is only as good as its three assumptions (K.14). A significant MR estimate with a pleiotropic instrument is not causal evidence.
Deeper: 6.4 Why we need MR · 9.1 Two-sample MR · 9.7 Interpreting an MR estimate
K.14 The three MR assumptions
| # | Assumption | How you check it | Typical threat |
|---|---|---|---|
| 1 | Relevance | p < 5 × 10⁻⁸ in the exposure GWAS; F-statistic > 10 | Weak instruments |
| 2 | Independence | Cannot be proven; adjust for ancestry, check associations with known confounders | Population stratification, assortative mating, selection |
| 3 | Exclusion restriction | Cannot be proven; biology of the gene, MR-Egger intercept, weighted median, outlier tests | Horizontal pleiotropy |
- Only assumption 1 can be tested directly. Assumptions 2 and 3 are made plausible, never proven, which is why MR uses several sensitivity analyses.
Don’t confuse: “the SNP is associated with the outcome” is not an assumption. That is what MR tests, and it is only interesting if the three assumptions hold.
Deeper: 6.5 The three MR assumptions · 6.8 Sensitivity analyses · 9.3 F-statistic
K.15 Horizontal vs vertical pleiotropy
Causal diagrams (each arrow means “directly affects”):
flowchart TD S1["SNP"] --> L1["LDL-C"] L1 --> A1["atherosclerosis"] A1 --> C1["CHD"]
flowchart TD S2["SNP"] --> L2["LDL-C"] L2 --> C2["CHD"] S2 --> I2["inflammation"] I2 --> C2 linkStyle 2,3 stroke:#c92a2a,stroke-width:2px,stroke-dasharray:6 4,color:#c92a2a
- Horizontal pleiotropy shows up as instruments whose Wald ratios disagree with the rest, an MR-Egger intercept away from zero, or IVW and weighted median giving different answers.
- trans-pQTLs and SNPs in genes with many functions are the usual suspects. cis instruments in the exposure’s own gene reduce the risk.
Don’t confuse: vertical pleiotropy is not a problem to remove. It is the causal chain MR is designed to detect.
Deeper: 6.6 Pleiotropy · 6.8 MR-Egger and weighted median · 9.8 Pleiotropy and pitfalls
K.16 Wald ratio and inverse-variance weighted (IVW) MR
\[\hat\beta_{\text{Wald}} = \frac{\beta_{\text{SNP}\to Y}}{\beta_{\text{SNP}\to X}}, \qquad SE_{\text{Wald}} \approx \frac{SE_{\text{SNP}\to Y}}{|\beta_{\text{SNP}\to X}|}\]
\[\hat\beta_{\text{IVW}} = \frac{\sum_j \beta_{X_j}\beta_{Y_j}/SE_{Y_j}^2}{\sum_j \beta_{X_j}^2/SE_{Y_j}^2}\]
Example. Three clumped SNPs (exposure in mmol/L, outcome log-odds).
| SNP | β exposure | β outcome | SE outcome | Wald ratio |
|---|---|---|---|---|
| 1 | 0.20 | 0.10 | 0.02 | 0.50 |
| 2 | 0.10 | 0.06 | 0.02 | 0.60 |
| 3 | 0.30 | 0.12 | 0.03 | 0.40 |
IVW numerator = (0.20·0.10 + 0.10·0.06)/0.0004 + 0.30·0.12/0.0009 = 65 + 40 = 105. Denominator = (0.04 + 0.01)/0.0004 + 0.09/0.0009 = 125 + 100 = 225. IVW = 105/225 ≈ 0.47 log-odds per mmol/L, OR ≈ e^0.47 ≈ 1.6.
- Before computing: harmonise the alleles so both β refer to the same effect allele, and for a binary outcome use log(OR).
- Through the origin = assumes no horizontal pleiotropy (zero exposure effect → zero outcome effect). MR-Egger frees the intercept to test that.
Don’t confuse: the Wald ratio is per unit of the exposure’s scale. An exposure in SD units and one in mmol/L give different numbers for the same biology.
Deeper: 6.7 The Wald ratio and IVW · 9.5 Harmonisation · 9.6 Wald ratio and IVW
Part 3: Proteomics and genetics
K.17 Proteomics and protein abundance
- Why proteins: they do the work in cells, change with disease, diet, drugs and age, and are the targets of most drugs.
- Why it is hard: plasma protein concentrations span about 10 orders of magnitude, so a few abundant proteins (albumin, immunoglobulins) dominate; one gene can give several proteoforms (isoforms, post-translational modifications).
- Platforms: affinity-based (Olink, SomaScan: antibodies or aptamers, thousands of proteins, relative units) and mass spectrometry (peptides, can see isoforms and give absolute amounts with internal standards).
- NPX is relative and log₂: +1 NPX = twice as much of that protein in that sample. It cannot be compared between different proteins.
Don’t confuse: abundance ≠ function. A variant can change what a protein does without changing how much there is, and an affinity assay can miss a form it does not bind.
Deeper: 8.1 Why study the proteome · 8.4 Three technology families · 8.5 Units and NPX · 8.13 Reading: comparing eight platforms
K.18 pQTLs: cis-pQTL and trans-pQTL
| cis-pQTL | trans-pQTL | |
|---|---|---|
| Location | Near the protein’s own gene | Far away (> 500 kb) or another chromosome |
| Likely mechanism | Direct: transcription, splicing, stability, secretion of that protein | Indirect: transcription factors, receptors, pathways |
| As MR instrument | Preferred: clear biology, less pleiotropy | Higher risk of horizontal pleiotropy |
- Found with a GWAS that has the protein level as the phenotype: protein = β₀ + β₁ × dosage + ε.
- Caution: a coding (missense) cis variant can change the epitope an antibody or aptamer binds and fake a pQTL: lower measured signal, unchanged amount.
Don’t confuse: cis is defined relative to the protein’s gene, not relative to any gene. A SNP next to gene A that changes protein B is trans for B.
Deeper: 8.9 pQTLs · 8.10 Protein MR · 8.11 Challenges of protein MR
K.19 Colocalization
The logic from the slides (Lecture 8): compare the pattern of association across the region for the protein and for the disease. If one shared variant drives both, SNPs in LD with it produce the same shape of signal for both traits: the same SNPs are strongest, and the association weakens in step as LD with the shared variant falls.

Why MR alone is not enough: if SNP A raises the protein and a different SNP B in LD with A raises disease risk through another mechanism, an MR using A will still find a “protein → disease” effect. That is LD confounding. Colocalization checks for it.
The widely used Bayesian method (the R package coloc) compares five hypotheses for a region: H0 no association with either trait, H1 only trait 1, H2 only trait 2, H3 both traits but different causal variants, H4 both traits and one shared causal variant. It reports a posterior probability for each, and PP.H4 above about 0.8 is often taken as evidence of colocalization. It needs only summary statistics for both traits in the region. The slides describe the idea; this formal version is background, not course material.
Don’t confuse: “both signals are in the same locus” is not colocalization. Two causal variants 50 kb apart can sit in one locus with overlapping towers of association.
Deeper: 8.11 Challenges of protein MR (colocalization) · 8.12 From association to mechanism
K.20 Biomarker vs causal protein
| Biomarker | Causal protein | |
|---|---|---|
| Question | Does it predict or reflect disease? | Does changing it change disease? |
| Evidence | Association, prediction (AUC), reproducibility | MR with cis-pQTLs, colocalization, experiments, trials |
| Useful for | Diagnosis, prognosis, risk prediction, monitoring treatment | Drug targets, understanding mechanism |
| Example type | Troponin after heart damage: excellent marker, consequence not cause | A protein whose cis-pQTL predicts disease in MR and colocalizes |
- A protein associated with disease in a PWAS can be (1) a cause, (2) a consequence of disease (reverse causation), or (3) a correlate sharing a confounder (smoking, BMI, inflammation).
- A good biomarker does not have to be causal; a causal protein is not always a good biomarker (it may vary little between people or be hard to measure).
- The route from biomarker to causal protein (Lecture 8): association → pQTL → MR and colocalization → experiments (CRISPR, cell models, animal models).
Don’t confuse: “strongly associated” and “predictive” do not mean “causal”. Lowering a consequence-marker does not undo the disease.
Deeper: 1.3b Biomarkers and their five roles · 8.7 PWAS · 8.8 Association is still not causation · 8.12 From association to mechanism