• http://sahirbhatnagar.com
• 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

• 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

• 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

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

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

• For example:

• \[H_0: \textrm{mean height}= 170 cm \rightarrow \textrm{``truth''} \]

• \[ \textrm{sample mean } \bar{X}=220cm\]

• \[ \textrm{sample sd } = 60cm \]

• 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

• 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

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

• 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)

• \[ \chi^2_{(TDT)} = \frac{(b-c)^2}{b+c} \sim \chi^2_{(1)} \]

• This is also known as a McNemar Test

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

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

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

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

1. Different genetic models
2. Sampling designs
3. Multiallelic markers
4. Quantitative traits
5. Missing parental genotype information

• 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

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

• \(X\): 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

• 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

• Recently developed imputation algorithms giving no Mendelian errors can lead to inflated TDT results
  
• These false positive signals can occur for example from
  • mistyping homozygote parents as heterozygotes
  • missed calls among heterozygotes
• PDT and FBAT were not sensitive to imputation
  • more informative families being used \(\rightarrow\) more power

• 3.3 million variants input (PDT Sequenced TRD p-value < 0.70)
• 2.2 million variants used
• 10,632 genes mapped
• 19 gene sets selected (GO terms related to biological mechanisms of TRD)
• 1 result (\(p<0.001\), \(FDR=0.0070\), )

• Family Based Tests: FBAT, PLINK 1.9, PDT command line tools
  
• GSEA-SNP: http://gsea4gwas.psych.ac.cn/
  
• Plots: qqman, ggplot2, kinship2 packages in R, cranefoot
  
• Data Cleaning: awk, bash, data.table package in R, GRinux
• Slides: R Markdown, pandoc
• Results App: Shiny package in R
• Code: available on GitHub
• Paper: LaTeX