Mendelian Randomisation

1. Mendelian Randomisation
James McMurray
PhD Student
Department of Empirical Inference
29/07/2014

2. What is Mendelian Randomisation?

3. What is Mendelian Randomisation?
Approach to test for a causal effect from observational data in
the presence of certain confounding factors.

4. What is Mendelian Randomisation?
Approach to test for a causal effect from observational data in
the presence of certain confounding factors.
Uses the measured variation of genes of known function, to
bound the causal effect of a modifiable exposure
(environment) on a phenotype (disease).

5. What is Mendelian Randomisation?
Approach to test for a causal effect from observational data in
the presence of certain confounding factors.
Uses the measured variation of genes of known function, to
bound the causal effect of a modifiable exposure
(environment) on a phenotype (disease).
Fundamental idea is that the genotypes are randomly assigned
(due to meiosis).

6. What is Mendelian Randomisation?
Approach to test for a causal effect from observational data in
the presence of certain confounding factors.
Uses the measured variation of genes of known function, to
bound the causal effect of a modifiable exposure
(environment) on a phenotype (disease).
Fundamental idea is that the genotypes are randomly assigned
(due to meiosis).
This allows them to be used as an instrumental variable.

7. What is Mendelian Randomisation?: DAG

8. Motivation: Why Observational Data?

9. Motivation: Why Observational Data?
Randomised Control Trials (RCTs) are the gold standard for
causal inference.

10. Motivation: Why Observational Data?
Randomised Control Trials (RCTs) are the gold standard for
causal inference.
However, it is often not ethical or possible to carry out RCTs.

11. Motivation: Why Observational Data?
Randomised Control Trials (RCTs) are the gold standard for
causal inference.
However, it is often not ethical or possible to carry out RCTs.
E.g. we cannot randomly assign a lifetime of heavy smoking
and no smoking to groups of individuals.

12. Motivation: Why Observational Data?
Randomised Control Trials (RCTs) are the gold standard for
causal inference.
However, it is often not ethical or possible to carry out RCTs.
E.g. we cannot randomly assign a lifetime of heavy smoking
and no smoking to groups of individuals.
This leads to a need to use observational data.

13. Motivation: Why Observational Data?
Randomised Control Trials (RCTs) are the gold standard for
causal inference.
However, it is often not ethical or possible to carry out RCTs.
E.g. we cannot randomly assign a lifetime of heavy smoking
and no smoking to groups of individuals.
This leads to a need to use observational data.
But this requires many assumptions.

14. Instrumental Variables (IV)

15. Instrumental Variables (IV)
In the previous DAG, G is the instrumental variable
(instrument).

16. Instrumental Variables (IV)
In the previous DAG, G is the instrumental variable
(instrument).
Because it affects Y only through X (exclusively)

17. Instrumental Variables (IV)
In the previous DAG, G is the instrumental variable
(instrument).
Because it affects Y only through X (exclusively)
Therefore, under certain assumptions, if G is correlated with Y
then we can infer the edge X → Y

18. Instrumental Variables (IV)
In the previous DAG, G is the instrumental variable
(instrument).
Because it affects Y only through X (exclusively)
Therefore, under certain assumptions, if G is correlated with Y
then we can infer the edge X → Y
First we will consider an example

19. Instrumental Variables (IV): Example

20. Instrumental Variables (IV): Example
If the assumptions are met, then if we observe that an
increase in tax leads to a reduction in lung cancer, then one
could infer that smoking is a “cause” of lung cancer (though
possibly indirectly itself - i.e. it’s not “smoking” per se, but
the tar in the lungs, etc.).

21. Instrumental Variables (IV): Assumptions: Z → X

22. Instrumental Variables (IV): Assumptions: Z → X
We must know (a priori) that the causal direction is Z → X
and not X → Z.

23. Instrumental Variables (IV): Assumptions: Z → X
We must know (a priori) that the causal direction is Z → X
and not X → Z.
This is what makes the causal structure unique and
identifiable.

24. Instrumental Variables (IV): Assumptions: Z → X
We must know (a priori) that the causal direction is Z → X
and not X → Z.
This is what makes the causal structure unique and
identifiable.
Note this does not mean that the Z we choose has to be the
“true” cause of X. For example, if Z is a SNP, we can choose
a SNP in linkage disequilibrium with Z, so long as it is
independent of all the other variables but still correlated with
X.

25. Instrumental Variables (IV): Assumptions: Z → X
We must know (a priori) that the causal direction is Z → X
and not X → Z.
This is what makes the causal structure unique and
identifiable.
Note this does not mean that the Z we choose has to be the
“true” cause of X. For example, if Z is a SNP, we can choose
a SNP in linkage disequilibrium with Z, so long as it is
independent of all the other variables but still correlated with
X.
The more correlated Z is with X, the better.

26. Example: Can use associated SNP as instrument

27. Instrumental Variables (IV): Assumptions: Z ⊥⊥ U

28. Instrumental Variables (IV): Assumptions: Z ⊥⊥ U
No factor can affect both the instrument and the effects. For
example, there cannot be a factor that causes both higher
taxes and less cancer (e.g. differences in health awareness in
different countries).

29. Instrumental Variables (IV): Assumptions: No Z → Y

30. Instrumental Variables (IV): Assumptions: No Z → Y
Z cannot directly affect Y (or indirectly, except through X).

31. Instrumental Variables (IV): Assumptions: No Z → Y
Z cannot directly affect Y (or indirectly, except through X).
I.e. there cannot exist other mechanisms by which Z affects Y
(i.e. high tobacco tax increases substance abuse, leading to
higher rates of cancer)

32. Instrumental Variables (IV): Assumptions: Faithfulness

33. Instrumental Variables (IV): Assumptions: Faithfulness
Assume that the true underlying DAG manifests itself in the
observed data

34. Instrumental Variables (IV): Assumptions: Faithfulness
Assume that the true underlying DAG manifests itself in the
observed data
I.e. causal effects do not cancel out

35. Instrumental Variables (IV): Assumptions: Faithfulness
Assume that the true underlying DAG manifests itself in the
observed data
I.e. causal effects do not cancel out
Reasonable assumption, because the contrary would require
very specific parameters

36. Instrumental Variables (IV): Assumptions: Faithfulness
Assume that the true underlying DAG manifests itself in the
observed data
I.e. causal effects do not cancel out
Reasonable assumption, because the contrary would require
very specific parameters
But note that if relations are deterministic, implied
Conditional Independencies do not hold and faithfulness is
violated

37. Instrumental Variables (IV): Assumptions: Faithfulness
Assume that the true underlying DAG manifests itself in the
observed data
I.e. causal effects do not cancel out
Reasonable assumption, because the contrary would require
very specific parameters
But note that if relations are deterministic, implied
Conditional Independencies do not hold and faithfulness is
violated
Note that, in practice, the sample size is important in testing
the independencies in the data.

38. Instrumental Variables (IV): Assumptions: DAG

39. What is Mendelian Randomisation?: Original example

40. What is Mendelian Randomisation?: Original example
Katan MB (1986): Apolipoprotein E isoforms, serum
cholesterol, and cancer.

41. What is Mendelian Randomisation?: Original example
Katan MB (1986): Apolipoprotein E isoforms, serum
cholesterol, and cancer.
Do low serum cholesterol levels increase cancer risk?

42. What is Mendelian Randomisation?: Original example
Katan MB (1986): Apolipoprotein E isoforms, serum
cholesterol, and cancer.
Do low serum cholesterol levels increase cancer risk?
But maybe both cancer risk and cholesterol levels are affected
by diet (confounders)

43. What is Mendelian Randomisation?: Original example
Katan MB (1986): Apolipoprotein E isoforms, serum
cholesterol, and cancer.
Do low serum cholesterol levels increase cancer risk?
But maybe both cancer risk and cholesterol levels are affected
by diet (confounders)
Or latent tumours cause the lower cholesterol level (reverse
causation)

44. What is Mendelian Randomisation?: Original example
Katan MB (1986): Apolipoprotein E isoforms, serum
cholesterol, and cancer.
Do low serum cholesterol levels increase cancer risk?
But maybe both cancer risk and cholesterol levels are affected
by diet (confounders)
Or latent tumours cause the lower cholesterol level (reverse
causation)
But patients with Abetalipoproteinemia (inability to absorb
cholesterol) - did not appear predisposed to cancer

45. What is Mendelian Randomisation?: Original example
Katan MB (1986): Apolipoprotein E isoforms, serum
cholesterol, and cancer.
Do low serum cholesterol levels increase cancer risk?
But maybe both cancer risk and cholesterol levels are affected
by diet (confounders)
Or latent tumours cause the lower cholesterol level (reverse
causation)
But patients with Abetalipoproteinemia (inability to absorb
cholesterol) - did not appear predisposed to cancer
Led Katan to idea of finding a large group genetically
predisposed to lower cholesterol levels

46. What is Mendelian Randomisation?: Original example
Katan MB (1986): Apolipoprotein E isoforms, serum
cholesterol, and cancer.
Do low serum cholesterol levels increase cancer risk?
But maybe both cancer risk and cholesterol levels are affected
by diet (confounders)
Or latent tumours cause the lower cholesterol level (reverse
causation)
But patients with Abetalipoproteinemia (inability to absorb
cholesterol) - did not appear predisposed to cancer
Led Katan to idea of finding a large group genetically
predisposed to lower cholesterol levels
This is Mendelian Randomisation.

47. What is Mendelian Randomisation?: Original example
Katan MB (1986): Apolipoprotein E isoforms, serum
cholesterol, and cancer.
Do low serum cholesterol levels increase cancer risk?
But maybe both cancer risk and cholesterol levels are affected
by diet (confounders)
Or latent tumours cause the lower cholesterol level (reverse
causation)
But patients with Abetalipoproteinemia (inability to absorb
cholesterol) - did not appear predisposed to cancer
Led Katan to idea of finding a large group genetically
predisposed to lower cholesterol levels
This is Mendelian Randomisation.
Note this does not require that the genetic variants are direct
determinants of health. But, uses the association to improve
inferences of the effects of modifiable environmental risks on
health.

48. What is Mendelian Randomisation?: Original example

49. What is Mendelian Randomisation?: Original example
Apolipoprotein E (ApoE) gene was known to affect serum
cholesterol, with the ApoE2 variant being associated with
lower levels.

50. What is Mendelian Randomisation?: Original example
Apolipoprotein E (ApoE) gene was known to affect serum
cholesterol, with the ApoE2 variant being associated with
lower levels.
Many individuals carry ApoE2 variant and so have lower
cholesterol levels from birth

51. What is Mendelian Randomisation?: Original example
Apolipoprotein E (ApoE) gene was known to affect serum
cholesterol, with the ApoE2 variant being associated with
lower levels.
Many individuals carry ApoE2 variant and so have lower
cholesterol levels from birth
Since genes are randomly assigned during meiosis (due to
recombination), ApoE2 carriers should not be different from
ApoE carriers in any other way (diet, etc.), so there is no
confounding via the genome - note these assumptions.

52. What is Mendelian Randomisation?: Original example
Apolipoprotein E (ApoE) gene was known to affect serum
cholesterol, with the ApoE2 variant being associated with
lower levels.
Many individuals carry ApoE2 variant and so have lower
cholesterol levels from birth
Since genes are randomly assigned during meiosis (due to
recombination), ApoE2 carriers should not be different from
ApoE carriers in any other way (diet, etc.), so there is no
confounding via the genome - note these assumptions.
Therefore if low serum cholesterol is really causal for cancer,
the cancer patients should have more ApoE2 alleles than the
controls - if not then the levels would be similar in both
groups.

53. What is Mendelian Randomisation?: Original example

54. What is Mendelian Randomisation?: Original example
Katan only provided the suggestion, but the method has since
been used for many different analyses with some success, such
as the link between blood pressure and stroke risk.

55. What is Mendelian Randomisation?: Original example
Katan only provided the suggestion, but the method has since
been used for many different analyses with some success, such
as the link between blood pressure and stroke risk.
However, some conclusions have later been disproved by
Randomised Control Trials. To understand why, we must
consider the biological assumptions.

56. Panmixia

57. Panmixia
Recall the assumption that the genotype is randomly assigned
- this implies panmixia

58. Panmixia
Recall the assumption that the genotype is randomly assigned
- this implies panmixia
That is, there is no selective breeding (so random mating)

59. Panmixia
Recall the assumption that the genotype is randomly assigned
- this implies panmixia
That is, there is no selective breeding (so random mating)
Implies that all recombination is possible

60. Panmixia
Recall the assumption that the genotype is randomly assigned
- this implies panmixia
That is, there is no selective breeding (so random mating)
Implies that all recombination is possible
In our DAG, this means that G is not influences by Y (or other
variables)

61. Panmixia
Recall the assumption that the genotype is randomly assigned
- this implies panmixia
That is, there is no selective breeding (so random mating)
Implies that all recombination is possible
In our DAG, this means that G is not influences by Y (or other
variables)
Not entirely accurate, as demonstrated by Population
Stratification

62. Population Stratification

63. Population Stratification
Systematic difference in allele frequencies between
subpopulations, due to ancestry

64. Population Stratification
Systematic difference in allele frequencies between
subpopulations, due to ancestry
For example, physical separation leads to non-random mating

65. Population Stratification
Systematic difference in allele frequencies between
subpopulations, due to ancestry
For example, physical separation leads to non-random mating
Leads to different genetic drift in different subpopulations (i.e.
changes in allele frequency over time due to random sampling)

66. Population Stratification
Systematic difference in allele frequencies between
subpopulations, due to ancestry
For example, physical separation leads to non-random mating
Leads to different genetic drift in different subpopulations (i.e.
changes in allele frequency over time due to random sampling)
Means that the genotype is not randomly assigned when
considered across sub-populations

67. Population Stratification
Systematic difference in allele frequencies between
subpopulations, due to ancestry
For example, physical separation leads to non-random mating
Leads to different genetic drift in different subpopulations (i.e.
changes in allele frequency over time due to random sampling)
Means that the genotype is not randomly assigned when
considered across sub-populations
E.g. Lactose intolerance

68. Canalization

69. Canalization
Variation in robustness of phenotypes to genotype and
environments

70. Canalization
Variation in robustness of phenotypes to genotype and
environments
Waddington Drosophilia experiment:
Exposed Drosophilia pupae to heat shock
Developed Cross-veinless phenotype (no cross-veins in wings)
By selecting for this phenotype, eventually appears without
heat shock
Led to theory of organisms rolling downhill in to “canals” of
the epigenetic landscape with development, becoming more
robust to variation
Think of it like an optimisation problem

71. Canalization
Variation in robustness of phenotypes to genotype and
environments
Waddington Drosophilia experiment:
Exposed Drosophilia pupae to heat shock
Developed Cross-veinless phenotype (no cross-veins in wings)
By selecting for this phenotype, eventually appears without
heat shock
Led to theory of organisms rolling downhill in to “canals” of
the epigenetic landscape with development, becoming more
robust to variation
Think of it like an optimisation problem
Exact mechanisms unknown

72. Canalization
Variation in robustness of phenotypes to genotype and
environments
Waddington Drosophilia experiment:
Exposed Drosophilia pupae to heat shock
Developed Cross-veinless phenotype (no cross-veins in wings)
By selecting for this phenotype, eventually appears without
heat shock
Led to theory of organisms rolling downhill in to “canals” of
the epigenetic landscape with development, becoming more
robust to variation
Think of it like an optimisation problem
Exact mechanisms unknown
Acts as confounder between genotype, environment and
phenotype

73. Pleiotropy

74. Pleiotropy
One gene can affect many (even seemingly unrelated)
phenotypes

75. Pleiotropy
One gene can affect many (even seemingly unrelated)
phenotypes
Mendelian Randomisation makes the assumption of no
pleiotropy

76. Pleiotropy
One gene can affect many (even seemingly unrelated)
phenotypes
Mendelian Randomisation makes the assumption of no
pleiotropy
In this case, this means that we know the genotype is only
influencing the phenotype via the considered exposure

77. Pleiotropy
One gene can affect many (even seemingly unrelated)
phenotypes
Mendelian Randomisation makes the assumption of no
pleiotropy
In this case, this means that we know the genotype is only
influencing the phenotype via the considered exposure
I.e. ApoE2 only affects serum cholesterol levels, and cannot
affect cancer risk by other, unobserved means.

78. Pleiotropy
One gene can affect many (even seemingly unrelated)
phenotypes
Mendelian Randomisation makes the assumption of no
pleiotropy
In this case, this means that we know the genotype is only
influencing the phenotype via the considered exposure
I.e. ApoE2 only affects serum cholesterol levels, and cannot
affect cancer risk by other, unobserved means.
This is a big assumption, prior knowledge is necessary.

79. Pleiotropy
One gene can affect many (even seemingly unrelated)
phenotypes
Mendelian Randomisation makes the assumption of no
pleiotropy
In this case, this means that we know the genotype is only
influencing the phenotype via the considered exposure
I.e. ApoE2 only affects serum cholesterol levels, and cannot
affect cancer risk by other, unobserved means.
This is a big assumption, prior knowledge is necessary.
If possible, using multiple, independent SNPs (instruments)
helps to alleviate this issue (as if they are all consistent then it
is unlikely that they all have other pathways causing the same
change) - but note they must not be in Linkage
Disequilibrium!

80. The real underlying DAG?

81. Conclusion
Instrumental variables are a method to infer causal relations
from observational data, given certain assumptions.
Applied in Genetic Epidemiology with Mendelian
Randomisation.
Has had some success, but underlying biology poses problems.
Can we improve robustness with more measurements of
intermediate phenotypes? (gene methylation, RNAseq,
proteomics) - multi-step Mendelian Randomisation
Can we improve identification of appropriate instruments?
(e.g. whole genome sequencing makes it easier to identify
population stratification)
Thanks for your time
Questions?