Revealing the Mode of Inheritance in Genetic Association Studies

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UNIVERSITY OF THESSALY School of
Medicine Laboratory of Biomathematics

• Revealing the Mode of Inheritance in Genetic
  Association Studies

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• Genetics background
• Genetics is the science that studies the heredity
  of traits
• Genetic information is contained in DNA which
  consists of nucleotides
• Gene is a sequence of nucleotides that translates
  a protein
• Genes (through proteins) determine traits
  (phenotypes)
• A gene may have different forms called alleles
• An allele can be mutant type-mt (change in
  nucleotudes) or wild type-wt
• For each gene there are two alleles due to
  diploidy of humans (homologous chromosome pairs)
• In an individual the genotype distribution of
  gene can be homozygous (wtwt or mtmt) or
  heterozygous (wtmt)

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• Genetic association studies (GAS)
• The evaluation of possible associations between
  phenotypic traits (diseases) and genetic variants
  (gene polymorphisms) is carried out using GAS
• In the case of a genetic variant with two alleles
  (mutant type-mt and wild type-wt), where mt is
  thought to be associated with a disease, GAS will
  collect information on the numbers of diseased
  subjects and control subjects with each of the
  three genotypes (wt/wt, wt/mt, mt/mt)

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• In an illustrative example of GAS with 8261/4374
  cases/controls investigated the association
  between ACE D/I (wt/mt) and CAD, the genotype
  distribution was
• Genotype Cases with CAD Controls
• mt/mt 1788 874
• mt/wt 4145 2165
• wt/wt 2328 1335
• The association between disease status and the
• genetic variant is tested using a chi-squared
  (x2) test
• with (3-1)x(2-1)2 df

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• When the association is significant, various
  genetic models
• of genotypes are tested by merging genotypes
• These models include
• additive model homozygous for mt vs.
• homozygous for wt
• recessive model homozygous for mt vs.
  wt-carriers
• dominant model mt-carriers vs. non-mt-carriers
• co-dominant model heterozygous vs. all
  homozygotes

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• The significance of the genetic model is
  assessed using the respective odds ratio (OR) and
  its 95 confidence interval (CI).
• The OR for the additive model is
• For ORgt1 an mt subject has greater chance of
  being diseased than a wt subject
• If the 95 CI does not include 1, then, the OR
  is significant (Plt0.05) (i.e. the variant is
  associated with the disease).

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• ACE D/I (wtD/mtI) vs. CAD
• Genotype Cases with CAD Controls
• mt/mt 1788 874
• mt/wt 4145 2165
• wt/wt 2328 1335
• x29.42, Plt0.05
• (http//people.ku.edu/preacher/chisq/chisq.htm)
• There is significant association between ACE D/I
  gene variant and development of CAD

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• But, what is the mode of inheritance,
• or
• what is the real genetic model?

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• Recessive model
• Genotype Cases with CAD Controls
• mt/mt 1788 874
• mt/wtwt/wt 4145 23286473 216513353500
• Since 1 is not included in the 95 CI, we
  conclude that the OR is significant (Plt0.05).
• Since ORgt1, we conclude that homozygous for the
  mt allele have 11 greater risk for CAD than
  wt-carriers

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• Dominant model
• Genotype Cases with CAD Controls
• mt/mtmt/wt 178841455933 87421653039
• wt/wt 2328 1335
• Since 1 is not included in the 95 CI, we
  conclude that the OR is significant (Plt0.05).
• Since ORgt1, we conclude that carriers of the mt
  allele have 12 greater risk for CAD than
  homozygous for the wt allele

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• Additive model
• Genotype Cases with CAD Controls
• mt/mt 1788 874
• wt/wt 2328 1335
• Since 1 is not included in the 95 CI, we
  conclude that the OR is significant (Plt0.05).
• Since ORgt1, we conclude that homozygous for the
  mt allele have 17 greater risk for CAD than
  homozygous for the wt allele

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• Co-dominant model
• Genotype Cases with CAD Controls
• mt/wt 4145 2165
• mt/mtwt/wt 178823284116 87413352209
• Since 1 is included in the 95 CI, we conclude
  that the OR is not significant (P0.05).

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• Recessive model OR1.11 (1.01, 1.21),
  significant
• Homozygous for the mt allele have greater risk
  than wt-carriers
• Dominant model OR1.12 (1.03, 1.21), significant
• Carriers of the mt allele have greater risk
  than non-carriers
• Additive model OR1.17 (1.06-1.30), significant
• Homozygous for the mt allele have greater risk
  than homozygous for the wt allele
• Co-dominant model OR1.03 (0.96, 1.11), non-sign

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• Is the genetic model,
• recessive,
• dominant or
• additive?
• Mess!

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• The source of the problem
• The ORs of the genetic models
• (recessive, dominant, additive, co-dominant)
• are not independent
• the testing of association between genotype
• distribution and outcome (disease/controls) is
  based
• on 2 df (the df for the Chi-squared test)

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• How can we avoid the hash of possible genetic
  models making the interpretation of the results
  straightforward at the same time?

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• Zintzaras (2010, Stat Appl Genet) introduced the
  concept of a generalized odds ratio (ORG) as a
  metric for describing the association between
  disease status (disease vs. healthy or disease
  progression) and genotype (biallelic or
  multiallelic)

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• The ORG is a single statistic that utilizes the
  complete genotype distribution and provides an
  estimate of the overall risk effect
• General definition
• The ORG is the probability of a subject being
  more diseased relative to the probability of
  being less diseased, given that the more diseased
  subject has a higher mutational load

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• Definition for bi-allelic variant and binary
• phenotype
• ORG is the probability of a subject being
  diseased relative to probability of being free of
  disease, given that the diseased subject has a
  higher mutational load than the non-diseased
• When ORGgt1 then an increased genetic exposure
  (mutational load) implies disease

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• ORGGASMA a software for implementing the
  generalized odds ratio methodology for the
  analysis and meta-analysis of GAS
• The software ORGGASMA (together with
  instructions how to operate it) is freely
  available and it can be downloaded form the web
  site http//biomath.med.uth.gr

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• ACE D/I (wtD/mtI) vs. CAD
• Genotype Controls Cases with CAD
• mt/mt 1788 874
• mt/wt 4145 2165
• wt/wt 2328 1335
• Assumption Subjects who are homozygous for I
  allele have the highest mutational load, those
  homozygous for D allele have the lowest, and
  heterozygous have an intermediate level.
• ORG1.13 with 95 CI (1.08-1.19),

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• ORG1.13 with 95 CI (1.08-1.19)
• For any two subjects, diseased and healthy, the
  probability of being diseased is 13 higher
  (relative to the probability of being
  non-diseased) given that the diseased subject has
  higher mutational load than the healthy one.

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• Disease progression
• ADH2 2/1 Controls Alcoholics
  Alcoholicswith
• liver disease
• 1/1 188 874 321
• 2/1 145 265 456
• 2/2 238 135 231
• ORG 1.37 (1.10-1.72) Risk of disease
  progression is related to mutational load
• A subject has 37 higher risk of being more
  diseased (relative to the risk of being less
  diseased) given that the subject has a higher
  mutational load.
• Multiallelic variant
• APOE Controls CAD
• e2/e2 23 44
• e2/e3 45 65
• e2/e4 28 35
• e3/e3 32 21

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• The ORG is a good solution, but,
• it is not enough!
• Zintzaras and Santos (2010, Stat Med) provided
  the whole solution!
• Problem The ORs of the genetic models
• (recessive, dominant, additive, co-dominant)
• are not independent
• Solution Inferences should be based solely on
• the additive and co-dominant models

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• Instead of talking for
• recessive,
• dominant,
• additive,
• co-dominant models
• we could talk for
• Dominance and Co-Dominance
• or even better for
• Degree of dominance

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• Co-dominance
• In the extreme case where there is co-dominance
  (i.e., perfect additivity), the heterozygote wtmt
  lies exactly in the middle of the two
  homozygotes, with mtmt having the maximum
  susceptibility of being diseased and wtwt having
  the least

• Co-dominant model is non-significant (Pgt0.05)
• Additive model is highly significant (Plt0.01)

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• Dominance
• The heterozygote wtmt lies towards mtmt or wtmt

Co-dominant model is significant
(Plt0.05) Additive model can be significant
(Plt0.05) or non-significant (Pgt0.05)
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Degree of dominance

• The degree of dominance could be derived from
  the ratio of the logarithms of the OR of
  co-dominant vs. the OR of the additive model
• the sign of ln(?co) determines the direction of
  dominance, and the value of ln(?co) relative to
  the absolute value of ln(?a) the magnitude of
  dominance deviation (i.e. deviation from the
  middle)

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• -1lthlt0 wtmt is expected to have a risk of being
  diseased somewhere in between the middle of the
  two homozygotes and towards to wtwt
• 0lthlt1 wtmt is expected to have a risk of being
  diseased somewhere in between the middle of the
  two homozygotes and towards to mtmt
• hgt1 wtmt has a higher risk of being diseased
  than mtmt
• hlt-1 wtmt has least chance of being diseased
  than wtwt

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• Once significance in dominance is detected (i.e.
  co-dominant model has Plt0.05) and h is obtained,
  the degree of dominance is inferred as follows

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• To summarize, inferences regarding any
• degree of dominance are obtained from the
• following order
• If the co-dominant model is non-significant and
  the additive model is significant (i.e.
  co-dominance), the risk of disease for the
  heterozygote is in the middle of the two
  homozygotes.
• If the co-dominant model is significant (i.e.
  dominance), we then test for the direction of
  dominance.
• If 0lthlt1, wtmt has a risk of disease closer to
  mtmt or wtwt according to the sign ( or -,
  respectively) of h
• If hgt1 is significant then, there is over- or
  under-dominance.

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• ACE D/I (wtD/mtI) vs. CAD
• Genotype Cases with CAD Controls
• mt/mt 1788 874
• mt/wt 4145 2165
• wt/wt 2328 1335
• The co-dominant model is not significant (P0.05)
  and the additive model is significant (Plt0.05)
  the risk of disease for the heterozygote is in
  the middle of the two homozygotes.

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• A GAS investigating the association between the
  alleles ADH21 and ADH22 with alcoholism
  produced the following genotype distributions
• Both co-dominant and additive models are
  significant. Since the co-dominant model is
  significant, we proceed to inquiry about the
  degree of dominance, which here is
• indicating that the risk-associated allele 1 is
  dominant, or that dominance exists.

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• In other words, the homozygous 1/1 (mt/mt)
  has a greater risk of being alcoholic than the
  homozygous 2/2 (wt/wt), and the heterozygote
  2/1 has a risk of alcoholism closer to the
  homozygote 1/1 than to the midpoint between the
  two homozygotes.

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Ancient Theater of Larissa