Causal Inference

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Causal Inference????

• Of Intermediate ?? Phenotypes?? and Biomarkers
  ???? in Rheumatoid Arthritis ??????
• An Application of Machine Learning ????
  Techniques to Genetic Epidemiology ??????

Wentian Li ???, Ph.D Feinstein Institute for
Medical Research
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Genetic Association

• Association ?? is not equivalent to causal ???
  relationship
• Wrinkle-Cancer risk association does not mean one
  causes ?? another
• Age is a confounding factor ????

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When do we need to know cause and effect?

• Rarely discussed in genetic analysis because
  genotype is always the cause ??, and phenotype is
  always the effect ??
• In epidemiology ???? factor ??-disease ??
  association can belong to three situations (1)
  factor is a cause (2) reverse causality (3) a
  third confounding factor
• For two intermediate phenotypes (biomarkers),
  causal arrow can point either way

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Causal Inference in Machine Learning

• Large text database (e.g. google)
• Observational data (no controlled experiment, and
  no other approaches to determine causality)
• Two-point association indeed cannot be used to
  claim causality
• The key is a third variable, as well as
  conditional ??? association based on the third
  variable

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Data Mining and Knowledge Discovery (2000) v4,
pp.163-192
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An Example
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Coopers Local Causality Discovery (LCD) Rule

• Six assumptions 1.database completeness. 2.
  discrete variables. 3. Bayesian network model
  (directed acyclic ???? graph no loops). 4. 5.
  no selection bias. 6. valid statistical testing.
• Three variables x,y,z
• Hidden ??? variable is allowed (but not in the
  dataset)
• Determine three correlations unconditional
  C(x,y), C(y,z) and conditional C(x,zy)

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Between two variables, there are only 6(4) causal
relationships (allowing confounding variable)
confounding
no relationship
confoundingcausing
causing
NO
NO
confounding plus rev causing
Reverse causing
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Number of causal relationships among three
variables

• 6x6x6216 possibilities
• 4x4x696 if x is not caused by either y or z (but
  can receive an arrow from a hidden variable)
  Cooper97 paper
• 2x2x624 if x doesnt even receive an arrow from
  hidden confounding variables Li and Wang,
  unpublished

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Given a causal model

• Unconditional ??? association between any two
  variables can be determined by whether they are
  connected by a path
• Conditional ??? association can be determined by
  the so-called d-separation rule

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CCC causal inference rule

• (Cooper version) if C(x,y), C(y,z), but
  C(x,zy)-,
• then there are only three possible causal
  models x y z
• x y z
• h x y z
• (Silverstein et al. version) if C(x,y), C(y,z),
  C(x,z), but C(x,zy)-, C(x,yy), C(y,zx),
  then...

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In a three-way correlated set

• If one of the variable (x) is not an effect (only
  a cause)
• AND
• If correlation is lost between x and z
  conditionally,
• THEN
• y causes z

x gene y,z two intermediate phenotypes
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The use of a not-a-effect variable has an amazing
parallel in epidemiology

• Called instrumental variable
• Martjin Katans idea on cholesterol ???
• cancer ?? association he proposed to use a
  genotype (apoliprotein ???? E) as the third
  variable (Lancer 1986, i507-508)
• Katan did not use conditional correlation
• This idea is now called Mendelian randomization

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Rheumatoid Arthritis (RA)

• An autoimmune ????? disease
• Chronic inflammation ?? of joints ??
• Three times more likely to occur in women than
  men
• Age of onset 40-60
• Twin ??? concordance rates 12-15 for
  MZ???,????, 5 for DZ ????
• Genetic and environmental (e.g. smoking) risk
  factors

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MHC/HLA the main genetic contribution of RA

• MHC (Major Histocompatibility Complex??????????)
  or HLA (Human leukocyte antigens ???????)
  HLA-DRB1 gene on chromosome 6 (6p21.3)
• The RA associated alleles are HLA-DRB10401,
  0404, 0408 (Caucasian), not 0402, 0403, 0407
• In Asian population, different DRB1 alleles are
  associated with RA (e.g. 0405, 0901)
• A group of DRB1 risk alleles are called shared
  epitope (SE) ????, or rheumatoid epitope, code
  position 70-74 amino acids in the third
  hypervariable region

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Two Auto-antibodies are strongly associated with
RA RF and anti-CCP

• RF (rheumatoid factor ?????) 80 of RA patients
  are RF positive
• anti-CCP (anti-cyclic citrullinated peptide
  antibody ????????,?CCP??) even better predictor
  of RA in early stage
• HLA-DRB1, RF, anti-CCP are all associated with
  the RA disease, and they are associated with each
  other. CCC rule can be applied!
• ???,???,???,?, ??????????????????????,
  ?????,2004,2052-57

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Q Between RF and anti-CCP, which one is the
cause and which is the effect?
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1723 Caucasian RA patients
anti-CCP positive
anti-CCP negative
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Association between RF and DRB1 genotype is lost
conditional on anti-CCP
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By the CCC rule, anti-CCP is the cause, RF is the
effect

• Or, anti-CCP is upstream and RF is downstream in
  a pathway

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Discussions/Issues

• There are evidences that RA patients become
  anti-CCP positive before becoming RF positive
• The three-way correlation might be lost in normal
  controls (here we have a case-only analysis)
• In-between anti-CCP and RF, other factors are
  possible (so the cause-effect may not be direct)
• It is not clear where the smoking factor comes in
  (could be an intriguing analysis with smoking
  data!)

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Revisit Katans Mendelian Randomization (MR) by
LCD Wang, Li, unpublished

• MR needs a not-an-effect variable (gene)
• Conditional association is not used
• Only need a counter example (e.g. Apo E2 samples
  have low cholesterol, but NOT high cancer risk)

• LCD needs a variable that is not a cause
• Conditional association is used
• Complete information of (G, IP, D) trio for all
  samples (e.g. Apo genotype, cholesterol level,
  cancer status)

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Co-Authors

• Mingyi WANG (Zhejiang Univ, Computer Science
  Department, causal inference)
• Patricia Irigoyen, Peter Gregersen (North Shore
  LIJ, RA data)

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