Causal Inference in Genetics

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Causal Inference in Genetics
Wentian Li ???, Ph.D Robert S Boas Center for
Genomics and Human Genetics, Feinstein Institute
for Medical Research, North Shore LIJ Health
System, NY, USA
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Statistical Correlations

• Rain/sunshine and wet/dry ground
• Wrinkle/smooth face and chance to have cancer
• Genetic marker ?? and disease status (genetic
  association and genetic linkage)
• One genetic marker and another genetic marker
• Two biomarkers (indicators of a disease) of the
  same disease

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Causal correlations

• Rain causes the wet ground
• Wrinkle does not cause the cancer
• Genetic marker may or may not cause the disease
  (when it does, it is called functional)
• Two markers being close to each on a chromosome
  linkage disequilibrium. (The cause/effect
  framework does not apply? Either one is a cause
  of another)
• If two biomarkers are involved in a disease, the
  one upstream in a pathway is cause, and
  downstream is effect

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Causal inference in Genetics ???, Epidemiology
????,Genomics ???? Is It Necessary?

• Risk factors of a disease have to be evaluated.
  Concept of confounding factor ???? (variable that
  is related to one or more variables in the study)
• No need for causal inference in
  genotype-phenotype correlation (only if Larmarck
  were right, inheritance of acquired trait,
  there is a reversal)
• Im addressing the last example up/down stream
  in biochemical pathway of two biomarkers

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It may not be necessary IF

• Both biomarkers are followed in time
• If one biomarker becomes positive ?? first, it is
  the more upstream
• Unfortunately, temporal information is usually
  unavailable, and biomarkers are measured after
  the onset of the disease

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Causal inference for observed data is an active
topic outside genetics

• Machine Learning (e.g. causal relationship
  between words in a corpus ?? )
• Economics and Social Science
• Biology (Sewall Wrights path analysis)
• Computer science (Bayesian network)

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A typical graphic model
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More complicated
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Even more complicated
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Outline of the talk

• Introduction to the local causality discovery
• Introduction to the dataset
• Results

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• Introduction to the local causality discovery
• Introduction to the dataset
• Results

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Data Mining and Knowledge Discovery (2000) v4,
pp.163-192
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Problems with a Bayesian network modeling

• All relevant variables have to be included
• The emphasis is not on structure of the network
  (sometimes it is even given), but on quantitative
  modeling of the transition probabilities

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In reality

• We may not known which variables are relevant
  (part of the inference is to find out)
• Not all variables are measured
• We may just be interested in who is a cause, who
  is an effect, and not interested in quantitative
  conclusions

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Local causality discovery

• Focus on three variables only
• It is OK that other relevant variables are not
  included
• The principle of inference is the exclusion of
  causal models that are inconsistent with the data
• which may not be successful

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local causality discovery (LCD) (cont.)

• 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 to exist but not
  measured
• Determine six correlations unconditional C(x,y),
  C(y,z), C(x,z), and conditional ??? C(x,zy),
  C(y,zx), C(x,zy)

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An Example
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Between two variables, there are only 6 causal
relationships (allowing confounding variable), 4
if x can only be a cause
confounding
x
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 is not caused by y or z, and
  doesnt 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
• Applying all possible causal models to the six
  correlations (yes or no) and exclude inconsistent
  models, which lead to

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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 gt y gt z
• x lt h gt y gt z
• h gtx gt y gtz
• (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 words for 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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biomarker 2
z
x is not an effect
x
causal inference is certain
gene
?
y
biomarker 1
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• Introduction to the local causality discovery
• Introduction to the dataset
• Results

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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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An update of recent whole genome association of RA

• PTPN22 (ch1) (Begovich et al, AJHG 2004) has
  consistently replicated in Caucasian samples
• STAT4 (ch2) (Remmers et al, NEJM, to appear)
• (Plenge et al, submitted)
• Wellcome trust (Nature, June 7, 2007)

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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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• Introduction to the local causality discovery
• Introduction to the dataset
• Results

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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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biomarker 2
RF
z
SE
x
gene
anti-CCP
y
biomarker 1
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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 the data is case-only)
• 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 risk factor
  comes in

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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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• Bibliography on microarray data analysis
• www.nslij-genetics/microarray/ and
  www.cbi.pku.edu.cn/mirror/microarray/microarray.ht
  ml
• Bibliography on linkage disequilibrium mapping
  www.nslij-genetics.org/ld/
• Bibliography on computational gene recognition
  www.nslij-genetics.org/gene/
• Bibliography on features, patterns, correlations
  in DNA sequences www.nslij-genetics.org/dnacorr/
• Comprehensive list of genetic analysis programs
  www.nslij-genetics.org/soft/ and
  linkage.rockefeller.edu/soft/