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Mendelian Randomisation
James McMurray
PhD Student
Department of Empirical Inference
29/07/2014
What is Mendelian Randomisation?
What is Mendelian Randomisation?
Approach to test for a causal effect from observational data in
the presence of certain co...
What is Mendelian Randomisation?
Approach to test for a causal effect from observational data in
the presence of certain co...
What is Mendelian Randomisation?
Approach to test for a causal effect from observational data in
the presence of certain co...
What is Mendelian Randomisation?
Approach to test for a causal effect from observational data in
the presence of certain co...
What is Mendelian Randomisation?: DAG
Motivation: Why Observational Data?
Motivation: Why Observational Data?
Randomised Control Trials (RCTs) are the gold standard for
causal inference.
Motivation: Why Observational Data?
Randomised Control Trials (RCTs) are the gold standard for
causal inference.
However, ...
Motivation: Why Observational Data?
Randomised Control Trials (RCTs) are the gold standard for
causal inference.
However, ...
Motivation: Why Observational Data?
Randomised Control Trials (RCTs) are the gold standard for
causal inference.
However, ...
Motivation: Why Observational Data?
Randomised Control Trials (RCTs) are the gold standard for
causal inference.
However, ...
Instrumental Variables (IV)
Instrumental Variables (IV)
In the previous DAG, G is the instrumental variable
(instrument).
Instrumental Variables (IV)
In the previous DAG, G is the instrumental variable
(instrument).
Because it affects Y only thr...
Instrumental Variables (IV)
In the previous DAG, G is the instrumental variable
(instrument).
Because it affects Y only thr...
Instrumental Variables (IV)
In the previous DAG, G is the instrumental variable
(instrument).
Because it affects Y only thr...
Instrumental Variables (IV): Example
Instrumental Variables (IV): Example
If the assumptions are met, then if we observe that an
increase in tax leads to a red...
Instrumental Variables (IV): Assumptions: Z → X
Instrumental Variables (IV): Assumptions: Z → X
We must know (a priori) that the causal direction is Z → X
and not X → Z.
Instrumental Variables (IV): Assumptions: Z → X
We must know (a priori) that the causal direction is Z → X
and not X → Z.
...
Instrumental Variables (IV): Assumptions: Z → X
We must know (a priori) that the causal direction is Z → X
and not X → Z.
...
Instrumental Variables (IV): Assumptions: Z → X
We must know (a priori) that the causal direction is Z → X
and not X → Z.
...
Example: Can use associated SNP as instrument
Instrumental Variables (IV): Assumptions: Z ⊥⊥ U
Instrumental Variables (IV): Assumptions: Z ⊥⊥ U
No factor can affect both the instrument and the effects. For
example, ther...
Instrumental Variables (IV): Assumptions: No Z → Y
Instrumental Variables (IV): Assumptions: No Z → Y
Z cannot directly affect Y (or indirectly, except through X).
Instrumental Variables (IV): Assumptions: No Z → Y
Z cannot directly affect Y (or indirectly, except through X).
I.e. there...
Instrumental Variables (IV): Assumptions: Faithfulness
Instrumental Variables (IV): Assumptions: Faithfulness
Assume that the true underlying DAG manifests itself in the
observe...
Instrumental Variables (IV): Assumptions: Faithfulness
Assume that the true underlying DAG manifests itself in the
observe...
Instrumental Variables (IV): Assumptions: Faithfulness
Assume that the true underlying DAG manifests itself in the
observe...
Instrumental Variables (IV): Assumptions: Faithfulness
Assume that the true underlying DAG manifests itself in the
observe...
Instrumental Variables (IV): Assumptions: Faithfulness
Assume that the true underlying DAG manifests itself in the
observe...
Instrumental Variables (IV): Assumptions: DAG
What is Mendelian Randomisation?: Original example
What is Mendelian Randomisation?: Original example
Katan MB (1986): Apolipoprotein E isoforms, serum
cholesterol, and canc...
What is Mendelian Randomisation?: Original example
Katan MB (1986): Apolipoprotein E isoforms, serum
cholesterol, and canc...
What is Mendelian Randomisation?: Original example
Katan MB (1986): Apolipoprotein E isoforms, serum
cholesterol, and canc...
What is Mendelian Randomisation?: Original example
Katan MB (1986): Apolipoprotein E isoforms, serum
cholesterol, and canc...
What is Mendelian Randomisation?: Original example
Katan MB (1986): Apolipoprotein E isoforms, serum
cholesterol, and canc...
What is Mendelian Randomisation?: Original example
Katan MB (1986): Apolipoprotein E isoforms, serum
cholesterol, and canc...
What is Mendelian Randomisation?: Original example
Katan MB (1986): Apolipoprotein E isoforms, serum
cholesterol, and canc...
What is Mendelian Randomisation?: Original example
Katan MB (1986): Apolipoprotein E isoforms, serum
cholesterol, and canc...
What is Mendelian Randomisation?: Original example
What is Mendelian Randomisation?: Original example
Apolipoprotein E (ApoE) gene was known to affect serum
cholesterol, with...
What is Mendelian Randomisation?: Original example
Apolipoprotein E (ApoE) gene was known to affect serum
cholesterol, with...
What is Mendelian Randomisation?: Original example
Apolipoprotein E (ApoE) gene was known to affect serum
cholesterol, with...
What is Mendelian Randomisation?: Original example
Apolipoprotein E (ApoE) gene was known to affect serum
cholesterol, with...
What is Mendelian Randomisation?: Original example
What is Mendelian Randomisation?: Original example
Katan only provided the suggestion, but the method has since
been used ...
What is Mendelian Randomisation?: Original example
Katan only provided the suggestion, but the method has since
been used ...
Panmixia
Panmixia
Recall the assumption that the genotype is randomly assigned
- this implies panmixia
Panmixia
Recall the assumption that the genotype is randomly assigned
- this implies panmixia
That is, there is no selecti...
Panmixia
Recall the assumption that the genotype is randomly assigned
- this implies panmixia
That is, there is no selecti...
Panmixia
Recall the assumption that the genotype is randomly assigned
- this implies panmixia
That is, there is no selecti...
Panmixia
Recall the assumption that the genotype is randomly assigned
- this implies panmixia
That is, there is no selecti...
Population Stratification
Population Stratification
Systematic difference in allele frequencies between
subpopulations, due to ancestry
Population Stratification
Systematic difference in allele frequencies between
subpopulations, due to ancestry
For example, p...
Population Stratification
Systematic difference in allele frequencies between
subpopulations, due to ancestry
For example, p...
Population Stratification
Systematic difference in allele frequencies between
subpopulations, due to ancestry
For example, p...
Population Stratification
Systematic difference in allele frequencies between
subpopulations, due to ancestry
For example, p...
Canalization
Canalization
Variation in robustness of phenotypes to genotype and
environments
Canalization
Variation in robustness of phenotypes to genotype and
environments
Waddington Drosophilia experiment:
Exposed...
Canalization
Variation in robustness of phenotypes to genotype and
environments
Waddington Drosophilia experiment:
Exposed...
Canalization
Variation in robustness of phenotypes to genotype and
environments
Waddington Drosophilia experiment:
Exposed...
Pleiotropy
Pleiotropy
One gene can affect many (even seemingly unrelated)
phenotypes
Pleiotropy
One gene can affect many (even seemingly unrelated)
phenotypes
Mendelian Randomisation makes the assumption of n...
Pleiotropy
One gene can affect many (even seemingly unrelated)
phenotypes
Mendelian Randomisation makes the assumption of n...
Pleiotropy
One gene can affect many (even seemingly unrelated)
phenotypes
Mendelian Randomisation makes the assumption of n...
Pleiotropy
One gene can affect many (even seemingly unrelated)
phenotypes
Mendelian Randomisation makes the assumption of n...
Pleiotropy
One gene can affect many (even seemingly unrelated)
phenotypes
Mendelian Randomisation makes the assumption of n...
The real underlying DAG?
Conclusion
Instrumental variables are a method to infer causal relations
from observational data, given certain assumption...
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Mendelian Randomisation

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Mendelian Randomisation

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Mendelian Randomisation

  1. 1. Mendelian Randomisation James McMurray PhD Student Department of Empirical Inference 29/07/2014
  2. 2. What is Mendelian Randomisation?
  3. 3. What is Mendelian Randomisation? Approach to test for a causal effect from observational data in the presence of certain confounding factors.
  4. 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. 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. 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. 7. What is Mendelian Randomisation?: DAG
  8. 8. Motivation: Why Observational Data?
  9. 9. Motivation: Why Observational Data? Randomised Control Trials (RCTs) are the gold standard for causal inference.
  10. 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. 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. 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. 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. 14. Instrumental Variables (IV)
  15. 15. Instrumental Variables (IV) In the previous DAG, G is the instrumental variable (instrument).
  16. 16. Instrumental Variables (IV) In the previous DAG, G is the instrumental variable (instrument). Because it affects Y only through X (exclusively)
  17. 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. 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. 19. Instrumental Variables (IV): Example
  20. 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. 21. Instrumental Variables (IV): Assumptions: Z → X
  22. 22. Instrumental Variables (IV): Assumptions: Z → X We must know (a priori) that the causal direction is Z → X and not X → Z.
  23. 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. 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. 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. 26. Example: Can use associated SNP as instrument
  27. 27. Instrumental Variables (IV): Assumptions: Z ⊥⊥ U
  28. 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. 29. Instrumental Variables (IV): Assumptions: No Z → Y
  30. 30. Instrumental Variables (IV): Assumptions: No Z → Y Z cannot directly affect Y (or indirectly, except through X).
  31. 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. 32. Instrumental Variables (IV): Assumptions: Faithfulness
  33. 33. Instrumental Variables (IV): Assumptions: Faithfulness Assume that the true underlying DAG manifests itself in the observed data
  34. 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. 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. 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. 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. 38. Instrumental Variables (IV): Assumptions: DAG
  39. 39. What is Mendelian Randomisation?: Original example
  40. 40. What is Mendelian Randomisation?: Original example Katan MB (1986): Apolipoprotein E isoforms, serum cholesterol, and cancer.
  41. 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. 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. 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. 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. 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. 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. 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. 48. What is Mendelian Randomisation?: Original example
  49. 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. 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. 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. 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. 53. What is Mendelian Randomisation?: Original example
  54. 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. 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. 56. Panmixia
  57. 57. Panmixia Recall the assumption that the genotype is randomly assigned - this implies panmixia
  58. 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. 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. 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. 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. 62. Population Stratification
  63. 63. Population Stratification Systematic difference in allele frequencies between subpopulations, due to ancestry
  64. 64. Population Stratification Systematic difference in allele frequencies between subpopulations, due to ancestry For example, physical separation leads to non-random mating
  65. 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. 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. 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. 68. Canalization
  69. 69. Canalization Variation in robustness of phenotypes to genotype and environments
  70. 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. 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. 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. 73. Pleiotropy
  74. 74. Pleiotropy One gene can affect many (even seemingly unrelated) phenotypes
  75. 75. Pleiotropy One gene can affect many (even seemingly unrelated) phenotypes Mendelian Randomisation makes the assumption of no pleiotropy
  76. 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. 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. 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. 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. 80. The real underlying DAG?
  81. 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?

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