August 7, 2014 Statistical Genetics Journal Club

About me

  • 2nd year PhD student (Biostatistics) with Celia
  • Im interested in
    • anything applied that can contribute to society
    • big data
    • reproducible research
    • how to give a good talk
  • Big believer in open source software


  1. I will ask alot of questions
  2. I need your help
  3. Your participation is necessary for this to be useful
  4. Interrupt me often


What is Transmission Ratio Distortion (TRD)

  • A statistical departure from the Mendelian 1:1 inheritance ratio
  • Occurs when one of the two alleles from either parent is preferentially transmitted to the offspring

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What is Transmission Ratio Distortion (TRD)

Properties of TRD

  • Can act independently of disease status
    • there are biological processes that cause TRD
    • leads to false positives in linkage/association studies
  • Extent of TRD and its influence in the human genome remains incomplete
    • we didn't find any studies that looked at TRD in WGS data

Biological Mechanisms of TRD

How can we assess TRD ?

The Transmission Disequilibrium Test (TDT)

Caveat of assesing TRD

  • Can only be observed in family-based studies
    • Costs
    • Not always feasible to genotype unaffected
    • Getting in touch with family members

A note on Test Statistics

Test Statistics

What we care about

Test Statistics

What they actually are

- A single measure of a sample
- It reduces the data to one value
- Need to know its sampling distribution to conduct hypothesis tests

\[ \textrm{Pearson} = \frac{(Observed - Expected)^2}{Expected} \sim \chi^2_{(df)} \]

\[ Z = \frac{\bar{X}-\mu}{\sigma} \sim \mathcal{N}(0,1) \]

Test Statistics

In general…

\[\textrm{Test Statistic} = \frac{\textrm{a measure of deviation from the "truth"}}{\textrm{a scaling factor to account for variability in your sample}} \]
  • For example:
  • \[H_0: \textrm{mean height}= 170 cm \rightarrow \textrm{``truth''} \]
  • \[ \textrm{sample mean } \bar{X}=220cm\]
  • \[ \textrm{sample sd } = 60cm \]

What do we mean by Chi-Square Test ?

  • Any statistical hypothesis test in which the sampling distribution of the test statistic is a chi-squared distribution when the null hypothesis is true
  • Chi-Square Test
    • Pearson's goodness of fit
    • McNemar's test
    • Tukey's test of additivity
    • Likelihood ratio test


Genetic Analysis Workshop 19 (GAW19)

  • GAW19 data drawn from T2D-GENES Project
  • Whole genome sequencing
    • 20 Mexican American Pedigrees from San Antonio
    • Enriched for type 2 diabetes
  • Genotype calls cleaned of mendelian errors for 959 individuals
    • 464 directly sequenced
    • 495 imputed
    • 8.4 million markers
    • odd-numbered autosomes

Genetic Analysis Workshop 19

20 Mexican American Pedigrees

Genetic Analysis Workshop 19

Imputation Procedure

A novel population-based imputation approach: Prephasing Imputation

  1. Haplotypes are estimated for each individual
  2. Estimated haplotypes used directly for imputation of sequence variants
  3. Imputation ignores family structure
    • to improve quality, data was cleaned for mendelian errors
  4. For each missing genotype:
    • the probabilities of each possible genotype were calculated in the context of the local haplotypes
    • the resulting probabilities were then used to generate an appropriately weighted
      gene dosage variable


GAW19 Objective

Identify potentially distorted regions in the genome using family based association methods

GAW19 Objective

My Reaction

GAW19 Objective: Take 2

  • See if this inflation in TRD \(p\) values is replicated in other Family Based Tests
    • Pedigree Disequilibrium Test (PDT)
    • Family Based Association Test (FBAT)
  • Compare methods across different subsets of the data
    • Everyone (n=1387)
    • Sequenced only (n=464)
    • 1 Nuclear family per pedigree (n=136)


Transmission Disequilibrium Test

  A non transmitted B non transmitted Total
A transmitted a b a+b
B transmitted c d c+d
Total a+c b+d 2n
  • \[ \chi^2_{(TDT)} = \frac{(b-c)^2}{b+c} \sim \chi^2_{(1)} \]
  • This is also known as a McNemar Test

Transmission Disequilibrium Test

Informative Trios

Need to have at least 1 heterozygous parent for trio to be informative

Transmission Disequilibrium Test

How to assess TRD

Pedigree Disequilibrium Test (PDT)

Consider a marker with two alleles \(A\) and \(B\).

Informative families are:

  1. At least one affected child, both parents genotypes, one heterozygous parent
  2. Discordant sibships (1 affected, 1 unaffected) with different genotypes, parental genotypes not required

Pedigree Disequilibrium Test (PDT)

Informative Trios

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Pedigree Disequilibrium Test (PDT)

Informative Discordant Sibships

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Pedigree Disequilibrium Test (PDT)

Within an informative nuclear family define:

  • \(X_T\) = (#\(A\) transmitted) - (#\(A\) not transmitted) \(\rightarrow\) \(n_T\) trios
  • \(X_S\) = (#\(A\) affected sib) - (#\(A\) unaffected sib) \(\rightarrow\) \(n_s\) sibships

\[D=\frac{1}{n_T + n_S} \left( \sum X_{T} + \sum X_{S} \right) \]

For \(k=1,\ldots,N\) unrelated informative pedigrees

\[ PDT_{test} = \frac{\sum D_k}{\sqrt{\sum D_k^2 }} \sim \mathcal{N}(0,1) \]

Family Based Association Test (FBAT)

A unified approach to family based tests of association that can handle:
  1. Different genetic models
  2. Sampling designs
  3. Multiallelic markers
  4. Quantitative traits
  5. Missing parental genotype information

Family Based Association Test (FBAT)

  • The FBAT statistic is based on the covariance between genotype and phenotype
  • What is covariance ?
  • A measure of how much two random variables change together
    • \(R^2\) is normalized version of the covariance

Family Based Association Test (FBAT)

Test Statistic

\[ U = \sum T^* \left[ X-E(X|P) \right] \rightarrow \textrm{Covariance} \] \[ FBAT = \frac{U^2}{var(U)} \sim \chi^2_{(1)} \rightarrow \textrm{Test Statistic} \]

  • \(X\): translates offspring's genotype to a numeric value e.g. count of A alleles (random)
  • \(P\): genotype of offspring's parents (fixed)
  • \(T\): offspring's trait (fixed)
  • summation is over all offspring in the sample

Family Based Association Test (FBAT)

Why so flexible ?

  • Of interest is the offspring's genotype
    • Missing parental genotypes are nuisance parameters
  • Standard approach to handling nuisance parameters:
    • Find sufficient statistics for them
    • Condition on the sufficient statistics
    • Conditional distribution does not depend on nuisance parameters

Family Based Association Test (FBAT)