Genetic Meta-Analysis and Mendelian Randomization

George Davey Smith

MRC Centre for Causal Analyses in Translational Epidemiology,

University of Bristol

RCT vs Observational Meta-Analysis: fundamental

difference in assumptions• In meta-analysis of observational studies

confounding, residual confounding and bias:

– May introduce heterogeneity

– May lead to misleading (albeit very precise) estimates

Relative risk

(95% confidence interval)

0.1 0.2 0.5 1 2 5 10

Trial (Year)

Barber (1967) Reynolds (1972)

Wilhelmsson (1974) Ahlmark (1974)

Multicentre International (1975) Yusuf (1979)

Andersen (1979)

Rehnqvist (1980) Baber (1980)

Wilcox Atenolol (1980)

Wilcox Propanolol (1980) Hjalmarson (1981)

Norwegian Multicentre (1981)

Hansteen (1982) Julian (1982) BHAT (1982) Taylor (1982)

Manger Cats (1983)

Rehnqvist (1983) Australian-Swedish (1983)

Mazur (1984) EIS (1984)

Salathia (1985)

Roque (1987) LIT 91987)

Kaul (1988) Boissel (1990)

Schwartz low risk (1992)

Schwartz high risk (1992) SSSD (1993)

Darasz (1995) Basu (1997)

Aronow (1997)

Overall (95% CI) 0.80 (0.74 - 0.86)

Mortality results from 33

trials of beta-blockers in

secondary prevention after

myocardial infarction

Adapted from Freemantle et al BMJ 1999

0.2 0.5 1 2 5 10

Study

Allen Barongo Bollinger Bwayo Bwayo Cameron Carael Chao Chiasson Diallo Greenblatt Grosskurth Hira Hunter Konde-Luc Kreiss Malamba Mehendal Moss Nasio Pepin Quigley Sassan Sedlin Seed Simonsen Tyndall Urassa 1 Urassa 2 Urassa 3 Urassa 4 Urassa 5 Van de Perre

Relative risk

(95% confidence interval)

Results from 29 studies examining the association between intact foreskin

and the risk of HIV infection in men

Adapted from Van Howe Int J STD AIDS 1999

Vitamin E supplement use and risk of Coronary Heart Disease

Stampfer et al NEJM 1993; 328: 144-9; Rimm et al NEJM 1993; 328: 1450-6; Eidelman et al Arch Intern Med 2004; 164:1552-6

0.3

0.5

0.7

0.9

1.1

Stampfer 1993 Rimm 1993 RCTs

1.0

Genetic meta-analysis, while of observational data, may be

analogous to RCT meta-analysis NOT conventional observational

meta-analysis

Clustered environments and randomised genes (93 phenotypes, 23 SNPs)

Phenotype / phenotype

4278 pairwise associations

Phenotype / genotype

2139 pairwise combinations

Genotype / genotype

253 pairwise combinations

43% significant at p<0.01

20 significant at p<0.01 vs 21 expected

4 / 253 significant at p<0.01 vs 3 expected

Davey Smith et al. PLoS Medicine 2007 in press

WTCCC: blood donors versus 1958 birth cohort controls

A leading epidemiologist speaks …

“Forget what you learnt at the London School of Hygiene and Tropical Medicine …. just get as many cases as possible and a bunch of controls from wherever you can ..”

Paul McKeigue, Nov 2002

Or the polite version …

“This approach allows geneticists to focus on collecting large numbers of cases and controls at low cost, without the strict population-based sampling protocols that are required to minimize selection bias in case-control studies of environmental exposures”

Am J Human Genetics 2003;72:1492-1504

If not confounding or selection bias, why have genetic

association studies such a poor history of replication?

Are genetic association studies replicable?

Hirschhorn et al reviewed 166 putative associations for which there were 3 or more published studies and found that only 6 had been consistently replicated (defined as “achieving statistically significant findings in 75% or more of published studies”)

Hirschhorn JN et al. Genetics in Medicine 2002;4:45-61

Reasons for inconsistent genotype – disease associations

True variation

Variation of allelic association between subpopulations

Effect modification by other genetic or environmental factors that vary between populations

Spurious variation

Misclassification of phenotypeConfounding by population structureLack of powerChancePublication bias

Colhoun et al, Lancet 2003;361:865-72

True variation in genotype and health outcome between populations

Disease-causing allele is in LD with a different allele at the marker locus in different groups

Allelic heterogeneity (different variants within the same gene) between ethnic groups

More likely when disease-causing variant is rare or has been subject to selection pressure

The association is modified by other genetic or environmental factors that vary between the groups studied

Effect modification by genes unlikely to account for failure to replicate studies in similar populations. Modification by environmental factors more likely, especially when absolute risk of disease varies

Differential misclassification of genotypes Avoided by appropriate laboratory procedures

Differential misclassification of outcome: possible if genotype is known when outcome is classified

Unlikely, because outcome is usually confirmed in advance of genotyping

Biases vary between studies

Population is divided into strata that vary by disease risk and by allele frequencies at the marker locus

Unlikely to be a serious problem in most studies: when confounding is a problem, it can be controlled in study design by restriction or use of family-based controls, or in the analysis by quantifying and controlling for substructure

Confounding by population substructure

Case mix heterogeneity in an apparently homogenous outcome between populations studied: for instance in a study of stroke, mix of haemorrhagic and thrombotic subtypes may vary between populations

Unlikely to be an explanation for failure to replicate studies in similar populations with similar case sampling strategies

Case-mix heterogeneity

Failure to consider that the initial effect size reported is an inflation of the true effect size

Replication studies should be powered to detect effect sizes that are smaller than the initial effect size reported, especially when the initial study had low power

Absence of power leading to false-negative results and failure to replicate

The Beavis effect

If the location of a variant and its phenotypic effect size are estimated from the same data sets, the effect size will be over-estimated, in many cases substantially. Statistical significance and the estimated magnitude of the parameter are highly correlated.

H Göring et al. Am J Hum Genetics 2001;69:1357-69

Multiple testing and publication bias: multiple loci are assessed in each study, many statistical tests are done, and multiple studies are undertaken but only positive results are reported

Perhaps the most likely reason for failure to replicate?

False positive results by chance in initial positive studies

What is being associated in genetic association studies?

• Estimates of 15M SNPs in human genome (rare allele frequency >1% in at least one population)

• Large number of outcomes (diseases and subcategories of particular disease outcomes)

• Large number of potential subgroups• Multiple possible genetic contrasts

Polymorphism really is associated with disease

Polymorphism is not associated with disease

Total

Result of experiment

Association declared to exist

80 45 125

Association not declared to exist

20 855 875

Total 100 900 1000

What percentage of associations that are studied actually exist? … 1 in 10? (at 80% power, 5% significance level)

Oakes 1986; Davey Smith 1998; Sterne & Davey Smith 2001

Power of study (% of time we reject null hypothesis if it is false)

P=0.05 P=0.01 P=0.001

20 69.2 31.0 4.3

50 47.4 15.3 1.8

80 36.0 10.1 1.1

Percentage of “significant” results that are false positives if 10% of studied associations actually exist

Sterne & Davey Smith BMJ 2001;322:226-231

Power of study (% of time we reject null hypothesis if it is false)

P=0.05 P=0.01 P=0.001

20 96.1 83.2 33.1

50 90.8 66.4 16.5

80 86.1 55.3 11.0

Percentage of “significant” results that are false positives if 1% of studied associations actually exist

Sterne & Davey Smith. BMJ 2001;322:226-231

P values often misinterpreted in both genetic and conventional

epidemiologyLow prior probability major issue in genetic epidemiology; meaningless (but real) associations a major issue

in conventional epidemiology

Why has replicationproved to be so difficult?

LOW STATISTICAL POWER A consistent feature of almost all analyses Fundamental to many of the explanations or

the approach needed to correct for them If we need 5,000 cases to test for a given

aetiological effect with a power of 80%, and with a critical p-value of 0.0001, how much power would there be for a study with 500 cases?

Why has replicationproved to be so difficult?

LOW STATISTICAL POWER!! A key feature of almost all proffered

explanations, and/or of the approach needed to correct for them

If we need 5,000 cases to test for a given aetiological effect with a power of 80%, and with a critical p-value of 0.0001, how much power would there be for a study with 500 cases? 0.008

Deducing “true numerical ratios” requires “the greatest possible number of individual values; and the greater the number of these the more effectively will mere chance be eliminated”.

Gregor Mendel 1865/6

Association of GNB3 and HypertensionBagos et al, J Hypertens March 2007

34 Studies

Cases = 14,094Controls = 17,760

Total = 21,654

¿ | α β γ | A B C | a b c | ?

Are genetic associations studies replicable: take two?

Joel Hirschhorn’s group selected 25 of the 166 genetic associations that they had studied and performed formal meta-analysis, claiming that 8 of these (one third) were robust.

“One third” claim widely welcomed!

Lohmueller KE et al. Nature Genetics 2003;33:177-182

Replicable Studies

ABCC8, type 2 diabetes 2.28 (1.27-4.10)

COL1A1, fracture 1.59 (1.36-1.86)

CTLA4, type 1 diabetes 1.27 (1.17-1.37)

DRD3, schizophrenia 1.12 (1.02-1.23)

GSTM1, head/neck cancer 1.20 (1.09-1.33)

HTR2A, schizophrenia 1.07 (1.01-1.14)

PPARG, type 2 diabetes 1.22 (1.08-1.37)

SLC2A1, type 2 diabetes 1.76 (1.35-2.31)

Are genetic associations studies replicable: take two?

“Low hanging fruit” and a best-case scenario.

Effect size estimates not so widely welcomed ..

Science, June 1, 2007

All Studies Combined14,585 cases

17,968 controls

1.17

1.12

1.13

1.20

1.12

1.14

1.12

1.37

1.14

1.14

TCF7

Nature, June 7, 2007

0

2

4

6

8

10

12

14

16

18

20

1.05 1.15 1.25 1.35 1.45 1.55 1.65 1.75 1.85 1.95

Distribution of OR’s for 70 Common Disease Variants

Odds Ratio

%

for exposures with small effect sizes it is very difficult to exclude

confounding and bias in conventional epidemiology, and level of statistical “significance”

does not help

statistical deviation from the null more important in

genetic epidemiology

Mendel on Mendelian randomization

“the behaviour of each pair of differentiating characteristics in hybrid union is independent of the other differences between the two original plants, and, further, the hybrid produces just so many kinds of egg and pollen cells as there are possible constant combination forms” (Sometimes called Mendel’s second law – the law of independent assortment) Gregor Mendel, 1865.

Mendel in 1862

Mendelian randomization Genotypes can proxy for some modifiable environmental factors, and there should be no confounding of genotype by behavioural, socioeconomic or physiological factors (excepting those influenced by alleles at closely proximate loci or due to population stratification), no bias due to reverse causation, and lifetime exposure patterns can be captured

Mendelian randomisation and RCTs

RANDOMISATION METHOD

RANDOMISED CONTROLLED TRIAL

CONFOUNDERS EQUAL BETWEEN

GROUPS

MENDELIAN RANDOMISATION

RANDOM SEGREGATION OF ALLELES

CONFOUNDERS EQUAL BETWEEN

GROUPS

EXPOSED: FUNCTIONAL ALLELLES

EXPOSED:

INTERVENTION

CONTROL: NULL ALLELLES

CONTROL: NO INTERVENTION

OUTCOMES COMPARED BETWEEN GROUPS

OUTCOMES COMPARED BETWEEN GROUPS