Association Testing in Related Individuals

Family data is correlated that could lead to inflation in test statistics if not accounted for. Many genetic studies contain related individuals. Family-based studies were developed to avoid bias due to population structure; Biological family members are genetically matched.

Most behavioral and environmental factors do not alter DNA, so SNP associations are unlikely to be confounded EXCEPT confounding by ancestry.

Population Stratification Bias

• For case control studies, population structure means bad matching; cases and controls come from different genetic populations.
• For cohort/cross-sectional studies with quantitative phenotypes, if the phenotype and genotype distributions both differ by population then population stratification bias can occur.
• If a population consists of a mixture of subpopulations and it is not accounted for in the analysis, false evidence for association may result.
• Spurious association only occurs when there is a difference in BOTH genotype and phenotype distribution with subpopulations.

Designs for Family-Based Studies

• Early-onset phenotypes:
  • Case-parent trios (where child is effected) - Transmission disequilibrium test (TDT)
• Late-onset phenotypes:
  • Discordant siblings - sub-TDT/conditional logistic regression
• General designs
  • Nuclear or extended families - Family-based association test (FBAT)

We'll mostly focus on case-parent trios and TDT tests.

Case-Parent Trios

In this design we collect samples of trios; Two parents and one affected child (affection status of parents are not considered). The idea is under Mendels laws, heterozygous parents transmit each allele with equal probability (1/2) regardless of population structure. If there is preferential transmission of a specific allele from parents to affected offspring it indicates that allele is associated with the disease.

Transmission Disequilibrium Test (TDT)

Tests whether a particular marker allele is transmitted to affected offspring more frequently than expected. Non-transmitted alleles act as matched controls.

H₀: No association or no linkage
H_a: Variant is associated with disease/trait (and is not due to population structure)

Notation:

• a = number of AA parents
• b + c = number of AB parents
  • b = Number of AB parents transmitting B to affected child
  • c = Number of AB parents transmitting A to affected child
• d = number of BB parents

Under the null we would expect:

The test statistic follows a McNemar test:

We observe this is only a function of the heterozyzgous parents, homozygous parents provide no information.

Discordant Siblings

• TDT unit of analysis is affected child + parents.
• Discordant siblings - unit of analysis is sibships with at least one affected and one unaffected sibling
• Analysis possibilities:
  • Cochram-Maentel-Haenszel test
  • Conditional Logistic Regression
• Like TDT these tests are conditioning on the genotypes in the family
  • TDT: conditioning on the parent's alleles
  • Sibs: conditioning on the observed genotypes in the sibship

General Family Structures

• Family Based Association Test (FBAT) and other similar tests (requires specialized software)
• Determine the expected genotypes of the affected individuals conditional on the family structure
• Use this to create a score test comparing observed and expected genotypes
• Same idea as parent-offspring trios or case-control sibships: conditioning on the observed genotypes

Unconditional Tests

• TDT, sTDT, FBAT and other family based association tests are conditional tests
• These tests are immune to population structure bias but often ignore information that can be used to assess association when population structure is not a concern
  • Homozygous parents
  • Sibships where the case and control have the same genotype
• Modern analyses can account for population structure using ancestry information available with genome-wide data
• Unconditional analyses account for the family correlation and make use of all the observed data
• These analyses tend to be more powerful than the conditional family-based tests

Review: For unrelated (independent) subjects we can use standard linear or logistic regression. Including related individuals in the analysis violates the assumption of independence, causing inflation in the test statistics.

Where X_i1 is the genotype of the i^th person and beta1 is the fixed affect of the SNP. X_i2 and X_i3 are covariates.

For related data there are specific methods we can use:

• For quantitative traits use Linear mixed effects models are frequently used for corrected observations for an individual or related individuals.
• Pedigree-specific methods use a variance component that is dependent on the kinship matrix for individuals.

We can see the mixed effects model adds a G variable to account for genetic variance component.

For association analysis of quantitative traits, if X₁ is the SNP then the test H₀: Beta1 = 0 is a test of association just as for the linear model for unrelated subjects. The regression estimate beta is exactly the same as in simple linear regression.

In either case G is not tested for significance. If we want to test for heritability we estimate variance of G.

Common software: GCTA, SOLAR, R GMMAT package, Genesis R/Bioconductor package.

Dichotomous Traits

• Logistic mixed effects can be used to account for relationships
  • Fit using penalized quasi-likelihood method
  • Requires iterative matrix inversion - can be very slow
• Alternative: Logistic model with Generalized Estimating Equations (GEE)
  • Accounts for correlated observations in a general way
  • Produces a "robust" variance estimate to account for correlation
  • Tends to result in inflated Type-I error
    • Low frequency SNPs primary probelm
    • Extent of inflation varies

In this course we focus on quantitative traits to keep things simple.