Some thought about statistical analysis of gene-gene interaction in gwas
- 1. Some thoughts about Gene-gene interaction Nelson Tang CUHK
- 5. What is the subject matter for analysis ? • 3 x 3 table (9 wells checkers, 9口井) Case Control
- 6. Multilocus interaction model by MDR • Limitation of MDR • No formal statistical basis
- 7. Classical Statistical analysis • 1. Case only analysis • 2. Logistic regression analysis
- 8. Classical 1. Case-only analysis • 2 unrelated SNPs (no LD), • expectation : independent Case Control 3 x 3 chi square test simple
- 9. Classical 2. Logistic Regression • PLINK: default approach
- 10. Limitation of logistic Reg • 1. Iterative method to solve and obtain parameters (time) – PLINK is relatively fast – But not solving the the full logistic eqn • 2. b3 coefficient term
- 11. Limitation of logistic Reg • Without and with interaction Rearrange Effect of x1 on y is related to dosage effect of x2 Limitation in both logistic regression and log-linear models
- 12. Limitation of logistic Reg • Existing analysis approach only allow a allele dosage related interaction • i.e. x2=(0,1,2) for (RR,RQ,QQ) • QQ should have double the interaction effect of RQ Interaction effect is allele dose related 0 1 2X2=
- 13. Huge number of tests • 330K chips • Will have 330,000 ^2 interactions • 1 x 10^11 test • Problems • 1. speed • 2. type 1 error
- 14. Early attempts • Yu Weichuan et al in UST • Information theory • Some try • Limitation: too many variables and not statistically based.
- 15. Log-linear regression • First developed by LA Goodman in 1970’s • Further extended by Bishop, Finberg & Holland 1975; Haberman 1975 • Model the counts (no. Of subjects in each wells of a table)
- 16. Log-linear regression • Probability Observed counts y11 y12 y21 y22 𝝅𝟏𝟏 𝝅12 𝝅21 𝝅22 Unknown Observed
- 17. Log-linear regression • Statistical inference by comparison of nested models • Simplest model: no association (independent) • Saturated model: with association 𝝅𝟏𝟏 𝝅12 𝝅21 𝝅22 A1 A2 B1 B2 S B
- 18. Log-linear regression • The saturated model fits the data best • Step by step to remove terms • Ask if the more simple (nested) model significantly fit worse Test statistics: likihood ratio test Follow chi-square distribution
- 19. CONTROL Log-linear regression • 1. can expand to nth dimension – E.g. 3-way table – Allow potential study of n-SNP interaction – Here we still restrict to 2-SNP interaction – Which is a 3-way table ( 3 x 3 x 2) CASE
- 20. Log-linear regression • 2. Equivalent to logistic regression Similar to PLINK (test for b3) Will be compare model Ms to MH No need to iterate for model Approximation by closed form equation (available for most log-linear models )
- 21. Analysis of WTCCC dataset • T1D • Known SNP-SNP interaction in HLA loci • HLA region shown • Single SNP association • Interaction analysis (log- linear) shows interacting pairs within 31 Mb to 33Mb, p<1e-15
- 22. Example of an interaction pair • (a) Case, (b) control, (c) Odds • Double heterozygotes have increased risk
- 23. • Boolean Operation-based data coding • Log-linear model test Wan, X., Yang, C., Yang, Q., Xue, H., Fan, X., Tang, N. L., & Yu, W. (2010). BOOST: A fast approach to detecting gene- gene interactions in genome-wide case-control studies. American journal of human genetics, 87(3), 325– 340. https://doi.org/10.1016/j.ajhg.2010.07.021
- 24. • AJHG paper : narrow- sense interaction • Broad-sense Interaction • Ms – Mp
- 25. Acknowledge • Colleagues in UST • Wan X, Yang C, Yang Q, Xue H, Fan X, Yu W • Kadoorie grant