Genetic Epidemiology

0 · How To Use Thisread first

This subject is a pipeline: UNDERSTAND (is there a genetic role? — aggregation, heritability) → DISCOVER (which variants? — LD, GWAS, MR) → CHARACTERISE (how risky? — penetrance, modifiers, G×E) → USE (screening). Side 1 = understand & discover; side 2 = characterise & use.

Assessment shape: online MCQ 10% (10 Qs, 1-week window) + written A1 40% (Modules 1–3) + A2 50% (Modules 4–8). All online / take-home — no invigilated exam.

Every assignment task is one of three: (a) calculate + interpret, (b) discuss findings, (c) critically appraise a design. So the two high-value moves are: plug the right formula, then judge the design's bias. A Stata .do file is even handed out for A1 Q1 — expect software-based calculation, then a written interpretation.

1 · Genetics PrimerExtra-Module 1

Locus = position on a chromosome. Allele = the base(s) there; minor allele = rarer one. Genotype = the pair (e.g. TT, TC, CC); homo- vs hetero-zygous.

• Polymorphism — common variant (>1% freq), e.g. a SNP; small/no effect
• Pathogenic mutation — major deleterious effect → big risk
• Germline = inherited, in every cell → familial risk (sample blood/buccal)
• Somatic = acquired, tumour only → not inherited (sample biopsy)
• Minor allele = the less common allele at the locus in the population

Mutation classes: silent (usually benign), missense (changes amino acid), nonsense (premature stop), frameshift indels (corrupt every downstream codon → usually pathogenic). CNV = larger gain/loss.

2 · Modes of Inheritancerisk inequalities

Defined on Pr(phenotype | # risk alleles), not on "having" the trait:

AutosomalDominant: Pr(2)=Pr(1) > Pr(0)
Recessive: Pr(2) > Pr(1)=Pr(0)
Codominant: Pr(2) > Pr(1) > Pr(0)

Carrier risk can be <1 (incomplete penetrance) and non-carrier risk >0 (phenocopies/sporadic). So a dominant variant can still have penetrance below 100%.

Segregation (Punnett)

Each parent passes one randomly-chosen allele. Aa×aa → ½ Aa, ½ aa (no AA). Aa×Aa → ¼ AA, ½ Aa, ¼ aa ⇒ P(child carries ≥1 A)=¾, P(AA)=¼.

Trap: the genotype gives the expected probability distribution, not the realised counts in a small sibship.

2b · Germline vs Somaticsample choice

• Inherited colorectal-cancer family risk → germline → sample blood / buccal swab
• Tumour responds differently to chemo, no family history → somatic → sample the tumour biopsy

3 · Allele & Genotype Freqcalculate

From counts n(AA), n(Aa), n(aa) in N people:

Allele frequency (per chromosome)p = [2·n(AA) + n(Aa)] / 2N · q = 1 − p

Worked: 100 people = 64 CC, 32 CT, 4 TT. T alleles = 2·4+32 = 40; total alleles = 2·100 = 200 ⇒ freq(T)=40/200=0.20, freq(C)=0.80 (20% of all alleles at this locus are T).

Carrier frequency (per person)carrier freq = p² + 2pq = 1 − q²

Worked: risk-allele freq 0.1 ⇒ 0.1² + 2(0.1)(0.9) = 0.01 + 0.18 = 0.19 (19% carry ≥1 copy). Equivalently 1 − q² = 1 − 0.81 = 0.19.

Why it matters: the variant is the exposure; carrier freq = exposure prevalence → drives sample size/power. Rare variants need huge or enriched samples. Trap: allele freq (per-chromosome, ÷2N) ≠ carrier/genotype freq (per-person, ÷N). At T freq 0.01, TT is very rare (q²=0.0001) yet carriers are ~2% — design power around the carrier count.

4 · Hardy–Weinbergcanon

Holds in a large, randomly-mating population with no selection, migration or mutation ⇒ genotype freqs are constant across generations & predicted by allele freqs. This is exactly the genotype split used for carrier frequency:

HWEp² + 2pq + q² = 1
AA=p² · Aa=2pq · aa=q²

Test (χ² goodness-of-fit)χ² = Σ (O − E)² / E · df = 1
significant if χ² > 3.84 (α=0.05)

df=1: 3 genotype classes − 1 − 1 (estimated allele freq). Deviation in CONTROLS ⇒ genotyping error / population stratification → GWAS QC check.

Worked: p(T)=0.20 in N=100 ⇒ expected 100·0.2²=4 TT, 100·2(0.2)(0.8)=32 TC, 100·0.8²=64 CC. Observed 4/32/64 match exactly ⇒ χ²≈0 ⇒ in HWE (QC passes).

If instead observed = 10 TT, 20 TC, 70 CC (allele freq still ≈0.20), then χ² = (10−4)²/4 + (20−32)²/32 + (70−64)²/64 ≈ 9 + 4.5 + 0.6 = 14.1 > 3.84 ⇒ reject HWE ⇒ in controls, suspect a genotyping error or population stratification and exclude/recheck the SNP.

Trap: HWE deviation in cases can be a real disease association — so test HWE conventionally in controls.

5 · Linkage Disequilibriumwhy GWAS works

Two loci in LD = their genotypes are statistically correlated in a random person; nearby loci co-inherited. A marker SNP associated with disease flags a nearby causal variant.

LD measuresD = P(AB) − P(A)P(B)
D' = D/D_max ∈ [−1,1] · D'=1 ⇒ complete LD
r² = D² / [P(A)P(a)P(B)P(b)] ∈ [0,1]

r² is the metric that matters for tagging/power: r²=1 ⇒ marker perfectly proxies the causal SNP; r²=0.5 ⇒ need ~2× the cases to detect the same indirect signal. A haplotype = the specific alleles inherited together on one chromosome.

Trap: D' and r² answer different questions. D'=1 (no recombination) can coexist with low r² when the two SNPs have different allele frequencies — for tagging/power it is r², not D', that counts.

6 · Familial AggregationModule 1

Families share genes + environment + can be followed over time. Stronger aggregation in genetically closer relatives ⇒ evidence for (not proof of) inherited aetiology — because closer relatives also share more environment.

Design → measure → bias

7 · Aggregation Measuresplug numbers

From the 2×2 (proband case/control × relative affected/unaffected), cells a,b,c,d:

Effect estimatesOR = (a·d)/(b·c)
RR = [a/(a+b)] / [c/(c+d)]
SMR = Observed / Expected
λ_R = risk in type-R relative / prevalence K
FRR = RR given affected 1st-degree relative

SMR worked: mothers of cases O=45, E (population rates × person-time) =17.7 ⇒ SMR ≈ 2.5. λ_R >1 and declining with relatedness ⇒ genetic; the rate of decline hints polygenic vs single-gene. OR ≈ RR only when disease is rare.

OR worked: any affected sister 13/462 in cases vs 1/405 in controls ⇒ OR = (13·404)/(449·1) ≈ 11.7 (95% CI 1.7–98.2). The very wide CI (only one exposed control) ⇒ imprecise — report the CI, not just the point estimate, and beware the small-cell instability.

8 · Migrant & FH Qualityinterpret

• Migrant rate stays like source ⇒ genetics (or similar env)
• Shifts toward host ⇒ environment
• Migrant vs descendants differ ⇒ a critical age of exposure

Family-history misclassification: non-differential (random) ⇒ bias toward null; differential (cases recall better) ⇒ bias away from null, inflating OR/RR. Fix with standardised questionnaires, multiple informants, validation against registries/pathology/death records, trained interviewers.

8b · Family DesignsM1 extras

Case-control-family / case-family: relatives directly interviewed ⇒ OR / RR / SMR; relatives of controls are hard to recruit, and the case-family design needs a population registry.

Outcome can be analysed as dichotomous (affected y/n), ordinal (number affected) or multinomial — match the analysis to how family history was coded.

9 · HeritabilityModule 2

= proportion of phenotypic variance due to genetic variance. A property of a population in an environment, not an individual. Variance = SD² (e.g. height SD 9.29 ⇒ variance ≈ 86).

Variance partitionVp = Vg + Ve
Vg = Va + Vd (+ Vi)
Broad-sense H² = Vg/Vp
Narrow-sense h² = Va/Vp (h² ≤ H²)

Narrow-sense (additive Va) predicts relative resemblance & response to selection; Vd = dominance, Vi = epistatic/interaction variance. Estimate variance separately by sex & zygosity (M>F; DZ>MZ spread).

10 · Twin Studiesthe engine

MZ share ~100% genes; DZ ~50% (like full sibs). Both share rearing env → comparing them isolates genetics; twins control for age & shared env.

Binary: concordance = proportion of pairs both affected; conc_MZ > conc_DZ ⇒ genetic. Continuous: correlate twin-1 vs twin-2.

Falconer's heritabilityh² = 2 (r_MZ − r_DZ) (continuous)
h² = 2 (conc_MZ − conc_DZ) (binary)

Worked: female height r_MZ=0.78, r_DZ=0.46 ⇒ h² = 2(0.78−0.46) = 0.64 — 64% of variance in female height is additively genetic. Interpret: "consistent with, but not proof of, an inherited genetic aetiology."

Genetic variance from heritability: Vg = h² × Vp. With Vp≈86 and h²=0.64 ⇒ Vg≈55. Opposite-sex DZ pairs & the twin–co-twin (TRA) design extend the model to probe shared-environment and sex effects.

11 · ACE Modelvariance components

Split Vp into A additive genetic, C common/shared env, E unique env + error. From twin correlations:

ACE from r_MZ, r_DZr_MZ = A + C · r_DZ = ½A + C
A = 2(r_MZ − r_DZ) (= Falconer)
C = 2·r_DZ − r_MZ · E = 1 − r_MZ

Worked: r_MZ=0.78, r_DZ=0.46 ⇒ A=2(0.78−0.46)=0.64; C=2(0.46)−0.78=0.14; E=1−0.78=0.22. Check: A+C+E = 0.64+0.14+0.22 = 1.00 ✓.

So C is the part of resemblance shared equally by both twin types; E (incl. measurement error) is the only thing that makes MZ co-twins differ. Trap — equal-environments assumption: if MZ pairs are treated more alike than DZ, shared env masquerades as genes ⇒ h² overestimated.

11b · Classic Twin Model4 assumptions

• MZ share A=1.0, DZ share A=0.5 (like full sibs)
• MZ & DZ share C equally (equal-environments)
• Random mating (no assortative mating inflating r_DZ)
• No gene–environment interaction/correlation
• Trait measured the same way in both twin types

Break any assumption ⇒ biased h². Concordance/correlation are estimated separately by sex & zygosity because variance differs.

Binary worked: conc_MZ=0.40, conc_DZ=0.15 ⇒ h²(liability) = 2(0.40−0.15) = 0.50. MZ>DZ concordance is the signal; near-equality (conc_MZ≈conc_DZ) ⇒ shared environment, not genes, drives the resemblance.

12 · Liability-Thresholdbinary traits

Assume an unobserved continuous liability (genes+env), ~Normal; disease occurs above a threshold set by prevalence. Puts yes/no disease onto a continuous scale so variance/heritability methods apply.

Tail area = prevalence. Relatives of cases sit at a right-shifted liability distribution ⇒ larger tail ⇒ higher risk, the model's link from heritability to a yes/no trait. Trap: heritability of liability ≠ heritability "of the disease," and is very sensitive to the assumed prevalence (which sets where T sits).

13 · Heritability Cautionsassignment gold

High h² does NOT mean: (a) the trait is unmodifiable; (b) genes cause between-group/between-population differences; or (c) anything about an individual. It is a population- & environment-specific quantity.

Missing heritability: GWAS-discovered SNPs explain far less variance than the twin-study h². Candidate causes: private (family-specific) mutations, rare moderate-risk variants, additional undiscovered common SNPs, gene–gene interactions, and non-genetic factors correlated within relatives.

So twin-estimated h² and GWAS-explained variance are different quantities — don't expect the discovered SNPs to "add up" to the twin h². High h² ≠ "untreatable": environment can still shift the whole distribution (height is highly heritable yet population mean rose with nutrition).

14 · Genetic AssociationModule 3

= a case-control study where the exposure is a genetic marker (a SNP). Association arises if the SNP causes disease, is in LD with a causal variant, or is confounded by ancestry (stratification).

Candidate-gene = a few pre-specified, biologically-motivated SNPs; GWAS = hundreds of thousands–millions of SNPs, scanned agnostically across the whole genome. The marker is the exposure; cases vs controls are compared on marker frequency, reported as an OR + 95% CI per SNP.

An association is useful for prediction even if non-causal. Three reasons a SNP associates with disease:

• the SNP causes disease (directly functional)
• it is in LD with a nearby causal variant (still useful for prediction)
• artefact of confounding by ancestry (stratification)

Only the first two replicate in an independent sample — the third is what replication + PC-adjustment are designed to kill.

A genetic/polygenic risk score sums many such SNPs and is ~Normal in the population, sliding people along a continuous risk axis rather than a single yes/no genotype — the basis for risk stratification in M8.

15 · Association Testsχ² / logistic

Chi-square & logistic ORχ² = Σ(O−E)²/E → large χ² → small p
logit P(D) = β₀ + β₁·genotype + covariates
OR = e^β₁ · OR = (a·d)/(b·c)

Per-allele coding (0,1,2) ⇒ OR per extra risk allele; adjust for ancestry principal components, age, sex. State the mode of inheritance up front; testing several models multiplies the tests and so needs a stricter threshold.

16 · Multiple Testingthe GWAS problem

Testing millions of SNPs hugely inflates the type-1 error / false-positive rate; at α=0.05, 1 in 20 truly-null SNPs looks "significant" by chance alone.

ThresholdsBonferroni: α = 0.05 / (# tests)
genome-wide significance = 5×10⁻⁸

5×10⁻⁸ ≈ 0.05 / 10⁶ independent common-variant tests; hits must replicate independently. Worked: a candidate study of 50 SNPs ⇒ Bonferroni α = 0.05/50 = 0.001 — a SNP at p=0.01 is not significant after correction. Trap: Bonferroni is conservative (LD makes tests correlated) but 5×10⁻⁸ is the field standard — use it for GWAS.

17 · Manhattan & QQread the plot

Manhattan: x = genomic position, y = −log₁₀(p). Peaks crossing −log₁₀(5×10⁻⁸) ≈ 7.3 = associated loci.

QQ plot: observed vs expected −log₁₀(p) under the null. On the diagonal = no inflation; an early, whole-line upward lift = stratification / cryptic relatedness / artefact (genomic inflation λ_GC; λ≈1 is good); a departure only in the extreme tail = genuine signal.

Trap: don't read a single Manhattan peak as "the causal gene" — the top SNP is usually the best tag in LD with the true causal variant, so fine-mapping is needed to localise the cause.

18 · Pop. Stratificationkey confounder

Cases & controls differ in ancestry; both allele freqs & disease rates vary by ancestry ⇒ spurious association (confounding). Fixes: match on ancestry, adjust for principal components, genomic control (λ_GC), or family-based designs; HWE deviation in controls helps flag it.

This is why a hit must replicate in an independent sample and why GWAS report λ_GC — a clean QQ plot (λ≈1) is the reassurance that genuine signal, not stratification, is driving the Manhattan peaks. λ > 1 ⇒ inflate-corrected before trusting any hit.

Formula Beltside 1

p=[2n(AA)+n(Aa)]/2N · carrier=p²+2pq
HWE p²+2pq+q²=1 · χ²=Σ(O−E)²/E df1
r²=D²/[P(A)P(a)P(B)P(b)] · OR=ad/bc
h²=2(r_MZ−r_DZ) · A=2(r_MZ−r_DZ)
SMR=O/E · λ_R=relative risk/K · GWS 5×10⁻⁸

19 · Mendelian RandomisationModule 4

Use a genetic variant as an instrumental variable (IV/proxy) for a modifiable exposure to test causation. Genotype is randomly allocated at conception ("nature's RCT") ⇒ not subject to reverse causation or conventional confounding.

It mimics an RCT's randomisation: alleles are dealt independently of the lifestyle/environmental confounders that wreck observational X–Y comparisons, and a fixed germline genotype can't be changed by the disease (no reverse causation). The question it answers is "does X cause Y," using a variant that proxies lifelong X.

20 · The 3 IV Assumptionsstate verbatim

1. Relevance — the proxy is robustly associated with the exposure (must be strong for adequate power)
2. Independence (exchangeability) — proxy independent of confounders of the X–Y relationship
3. Exclusion restriction — proxy affects the outcome only through the exposure (no direct or alternative path)

DAG & Wald estimateG → X → Y (G ⊥ U; no direct G → Y)
β(X→Y) = β(G→Y) / β(G→X)

If G associates with Y and all 3 hold, X likely causes Y — MR sits on a continuum convincing → not; assumptions are argued likely, never proven. Assumption 1 is testable (the G–X association); 2 and 3 are largely untestable and argued from biology, so MR conclusions are framed as supporting (not proving) a causal role.

21 · MR Threatsappraisal targets

• Horizontal pleiotropy — variant affects Y via another pathway ⇒ breaks exclusion (the #1 threat); probe with MR-Egger, weighted median
• Weak instrument — breaks relevance ⇒ low power, bias toward the confounded observational estimate
• Confounding via LD / stratification — instrument correlated with another causal variant
• Canalisation — developmental compensation; lifelong genetic exposure ≠ a short intervention

Trap: MR estimates a lifelong average effect — answers "does X cause Y," not "what if I change X for 6 months." Course examples: insulin-resistance gene scores → renal/pancreatic cancer; vitamin-B12 genes → lung cancer (supports a causal role).

21b · Wald Ratio Workedshow the number

The ratio (Wald) estimate divides the variant–outcome effect by the variant–exposure effect. Say G raises the exposure by β(G→X)=0.5 units per allele, and G is associated with the outcome at β(G→Y)=0.1 (log-odds per allele):

β(X→Y) = 0.1 / 0.5 = 0.2 per unit of X

Interpretation: each one-unit higher (genetically-predicted) exposure ⇒ 0.2 higher log-odds of disease — a causal estimate if the 3 assumptions hold. A weak instrument (small β(G→X)) blows up the ratio's variance ⇒ check the F-statistic. Combine many SNPs by inverse-variance weighting; MR-Egger & weighted-median are the robustness checks for pleiotropy.

22 · PenetranceModule 5

= probability of disease by a specific age (or over a period) for a person with a given genotype, possibly conditional on covariates. E.g. MSH6 variant → colorectal-cancer penetrance ≈ 50% by age 70 (males).

Complete = all carriers eventually affected; incomplete = penetrance <1 (most disease genes). Age-specific / cumulative = a curve of cumulative risk vs age, typically by survival analysis / Kaplan-Meier birth→diagnosis.

Expressivity (contrast): penetrance = whether disease occurs; variable expressivity = how severe / which features. Penetrance may also be reported by sex and conditional on covariates, and is the input to risk-based counselling.

23 · Estimating Penetrancedesign-specific

Case-control gives OR; convert to absolute (age-specific) risk using non-carrier / population incidence — penetrance needs external incidence data. Prospective carrier cohorts need large N because high-risk variants are rare ⇒ low power. Trap — ascertainment bias: clinic carriers are tested because of strong FH / young onset ⇒ not random ⇒ naïve estimates overestimate penetrance.

24 · Weighted CohortModule 6 · signature

Fix for non-random ascertainment — build a "synthetic cohort" mimicking carriers drawn randomly from the population by probability weighting:

1. Age/sex carrier incidence = population incidence × RR for carriers
2. Derive weights so affected:unaffected per age-stratum matches population proportions
3. Analyse weighted data ⇒ unbiased, generalisable penetrance

Also called modified segregation analysis when carrier status is inferred across the family rather than directly genotyped.

25 · Modifiers of PenetranceModule 6

Genetic/environmental factors that alter risk among carriers of the same variant — explaining why same-gene carriers span "modest" to "extreme" risk, not clustered at the average. Use for pathogenesis, risk reduction, individualised counselling + risk-based screening.

Trap: a modifier acts within carriers — distinct from a general-population main effect and from whole-population G×E (M7).

Modifiers explain the wide spread of carrier risk; the same weighted-cohort machinery (M6) estimates a modifier's effect by re-weighting clinic-ascertained carriers to a synthetic random cohort, then comparing risk across modifier strata. Output → risk-stratified screening & counselling.

26 · Gene–Environment InteractionModule 7

G×E exists when the exposure–disease association differs across genotypes (equivalently, the genotype effect differs across exposure levels). Statistical interaction = a departure from a specified no-interaction model ⇒ it is scale-dependent.

No interaction means…Multiplicative: RR_joint = RR_G × RR_E
Additive: RD_joint = RD_G + RD_E (RERI=0)

Multiplicative is the default output of logistic/Cox models (they multiply ORs/HRs); additive needs the absolute risk differences. Synergistic = joint effect bigger than expected; antagonistic = smaller — interpreted against the underlying biological pathways (shared vs independent mechanisms).

27 · The Classic Trapstate the scale

Worked. Disease risk by genotype × exposure:

RRs equal (2.0=2.0) ⇒ NO multiplicative interaction; RDs differ (0.03≠0.02) ⇒ additive interaction present. Same data, two answers — always state the scale. Additive (RD) is the public-health-relevant one (who gains most from removing the exposure); multiplicative is the default logistic/Cox output. Synergistic = bigger than expected; antagonistic = smaller. Check the joint cell (gene+/E+ = 0.06) against both the product and the sum.

28 · G×E Designsdetect it

• Case-control (standard) — include G, E and the G×E product term in logistic regression
• Case-only — cases only; test whether G and E are associated among cases. Under G⊥E in the source population, a G–E association estimates the multiplicative interaction efficiently (no controls)
• Cohort / family designs also detect G×E and G×G, with more power for rare exposures but higher cost

Trap: case-only is biased if G and E are correlated in the population and estimates only multiplicative interaction.

Implication: precision prevention — target modifiable environmental exposures in the genetically susceptible.

28b · The Other Casemultiplicative present

Contrast: if gene+ gave (E−=0.03, E+=0.12) ⇒ RR=4.0 while gene− RR=2.0 ⇒ RRs differ (4≠2) ⇒ multiplicative interaction present. Read RR-ratio across strata for multiplicative, RD-difference for additive — same data, two verdicts.

RERI (relative excess risk due to interaction) = RR₁₁ − RR₁₀ − RR₀₁ + 1; RERI=0 ⇒ no additive interaction, >0 ⇒ synergy, <0 ⇒ antagonism.

G×G (epistasis) is tested the same way — a gene–gene product term — and is one explanation for missing heritability. Report rule: always state the scale, give the RR-ratio (multiplicative) and the RD-difference (additive), then say which is relevant to the question (public-health ⇒ additive).

29 · ScreeningModule 8

Disease screening = a systematic test to find asymptomatic disease/precursors in people not seeking care. Genetic screening = find risk-raising variants in asymptomatic people so risk can be reduced/prevented; can be population-wide but is usually targeted to high-prior-risk groups (e.g. strong family history).

Course twist: a genetic test can be "once-and-for-all" (your germline doesn't change), unlike repeated disease screening. Two uses: screen for genetic risk, or use a genetic factor to screen for disease.

30 · Wilson–JungnerWHO 1968

The screening-evaluation checklist (the course adapts all 10 to genetics):

• Condition — important problem, recognisable latent/early stage, understood natural history
• Test — suitable, acceptable, accurate
• Treatment — accepted risk-reduction, agreed policy on whom to treat
• Facilities for diagnosis & treatment exist
• Cost economically balanced; case-finding a continuing process
• Agreed natural history & an agreed definition of who counts as a "case"

Trap: "we can test" ≠ "we should screen." A test only helps if knowing the result reduces disease/disability/death and benefits beat harms (psychological, social, insurance, variants of unknown significance, false positives). Example genes the course uses: BRCA1/2, the mismatch-repair (MMR) genes, HTT — note HTT (Huntington) has no risk-reduction, which weakens the case for screening.

31 · NNT & NNSquantify benefit

Two-step screening calcARR = carrier risk × proportion risk reduced
NNT = 1 / ARR
NNS = NNT / carrier frequency

Worked (BRCA1/2): carrier breast-cancer risk to 70 = 0.4; tamoxifen cuts risk 50% ⇒ ARR = 0.4×0.5 = 0.2 ⇒ NNT = 1/0.2 = 5 carriers treated to prevent one cancer.

Carrier freq 0.0067 (1 in 150) ⇒ NNS = 5/0.0067 ≈ 746 screened per cancer prevented. High-FH group (carrier freq 0.25) ⇒ NNS = 5/0.25 = 20 — far more efficient ⇒ justifies targeted screening.

Trap: NNS collapses for rare variants in the general population — raising the prior probability of carriage (targeting high-FH groups) is what makes genetic screening worthwhile.

31b · Harms Ledgerbenefits vs costs

Screening is only justified when benefit beats harm. Weigh against the NNT/NNS benefit:

• False positives → anxiety, over-treatment
• Variants of unknown significance → uninterpretable results
• Psychosocial → family, identity, fatalism
• Insurance / legal / discrimination risk
• Opportunity cost of the screening budget

32 · Test Performance2×2 metrics

From a 2×2 of test (+/−) × true status (D+/D−): TP, FP, FN, TN.

Accuracy metricsSensitivity = TP/(TP+FN) P(+|disease)
Specificity = TN/(TN+FP) P(−|healthy)
PPV = TP/(TP+FP) · NPV = TN/(TN+FN)

Sens & spec are intrinsic to the test; PPV rises & NPV falls as prevalence rises. In low-prevalence screening even a very specific test gives many false positives → low PPV.

Bayes formPPV = (Sens·Prev) /
  [Sens·Prev + (1−Spec)(1−Prev)]

33 · ROC & AUCdiscrimination

ROC: plot sensitivity (y) vs 1−specificity (x) as the cut-off moves. AUC = P(a random case scores higher than a random control): 0.5 = chance (the diagonal), 1.0 = perfect (top-left corner). In this course AUC appears for polygenic risk scores (e.g. coronary-artery-disease AUC ≈ 0.81).

Moving the threshold trades sensitivity against specificity. Trap: excellent sens/spec is useless for screening if prevalence is tiny (PPV near zero) — always tie performance back to prevalence / carrier frequency.

33b · PPV Workedprevalence bites

Sens=0.90, Spec=0.99. At prevalence 1%:

PPV = (0.9·0.01) /
 [0.9·0.01 + 0.01·0.99] = 0.009/0.0189 ≈ 48%

Half of positives are false — despite 99% specificity. At prevalence 10% the same test gives PPV ≈ 91%. Lesson: raise the prior (target high-risk) before screening, or most positives are false alarms.

Sens/spec are fixed properties of the test; only PPV/NPV move with prevalence — that single fact answers most "evaluate this screening test" questions. NPV is near-perfect when disease is rare (almost all test-negatives really are well), which is little comfort if the few positives are mostly false.

34 · Risk Reclassificationprecision prevention

Adding a genetic factor (e.g. a polygenic score) re-classifies individuals across an actionable risk threshold — some move up (newly flagged high-risk), some down (reassured). The value of genetic screening = how many it correctly reclassifies + NNS/NNT, not "we can test, so we should." Ties back to the Wilson–Jungner conditions (penetrance understood, accurate test, early actionable stage).

A reclassification is only worthwhile if a person moving above the threshold gains an effective action (screening, prophylaxis, risk-reducing surgery). Reclassifying with no actionable consequence adds anxiety without benefit.

34b · Disease Screeningusing genetics

Two distinct goals: (1) screen for genetic risk in the well → reduce future risk; (2) use a genetic factor to triage disease screening — e.g. start colonoscopy earlier / more often in MMR carriers. Both still demand an accurate test + an effective downstream action + favourable NNS in the targeted group.

35 · Appraisal ChecklistLO5 · every module

LO5 (appraisal) threads through every module. For any study, answer design → measure → strength → limitation → bias:

• Design? case-control / cohort / twin / GWAS / MR / family / weighted / case-only / screening
• Measure? OR vs RR/SMR/HR; h²; per-allele OR; Wald β; penetrance; NNT/NNS
• Confounding? shared environment (aggregation), ancestry/stratification (GWAS), pleiotropy (MR)
• Selection? ascertainment (penetrance), healthy-migrant, control recruitment
• Information bias? family-history recall (differential vs non-differential), misclassification direction
• Power? rare variant / weak instrument / low r²
• Generalisability? twins, clinic families, ancestry of the GWAS sample
• Causation? aggregation/association ≠ cause; MR / replication / dose-response strengthen it
• Precision/CI? a wide 95% CI (few exposed) = imprecise — don't over-read a point estimate

36 · Interpretation Hooksuse these phrasings

• Aggregation / MZ>DZ = "evidence for, not proof of, inherited aetiology"
• Heritability is a population-in-an-environment property; no individual/between-group claim
• An associated SNP is usually a tag in LD; r² governs power
• GWS = 5×10⁻⁸ + independent replication
• MR: relevance, independence, exclusion; chief threat = pleiotropy; conclusions likely
• Clinic cohorts overestimate penetrance without probability weighting (synthetic cohort)
• Interaction is scale-dependent — state additive vs multiplicative
• PPV depends on prevalence ⇒ screen the targeted high-risk
• OR ≈ RR only when disease is rare; report the 95% CI, not just the point estimate
• "We can test" ≠ "we should screen" — needs an effective downstream action

Calculation Beltside 2

β(X→Y) = β(G→Y)/β(G→X) (Wald)
ARR = carrier risk × % reduced · NNT = 1/ARR
NNS = NNT / carrier freq
Sens = TP/(TP+FN) · Spec = TN/(TN+FP)
PPV = TP/(TP+FP) · NPV = TN/(TN+FN)
multiplic RR_J=RR_G·RR_E · additive RD_J=RD_G+RD_E