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Topic #4

Topic #4. Single-Locus Models & Power Analyses. University of Wisconsin Genetic Analysis Workshop June 2011. Outline. Case-Control Studies: Two-allele, single locus model Power for basic tests Quantitative Outcomes: Two-allele, single locus model Power for basic tests

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Topic #4

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  1. Topic #4 Single-Locus Models& Power Analyses University of Wisconsin Genetic Analysis Workshop June 2011

  2. Outline • Case-Control Studies: • Two-allele, single locus model • Power for basic tests • Quantitative Outcomes: • Two-allele, single locus model • Power for basic tests • Practical Assignment: Power Calculation in Quanto

  3. Biallelic Single-locus Model(Assumes Hardy-Weinberg Equilibrium – HWE) Where A2 is the minor allele, and q (< .50) is the minor allele frequency (MAF)

  4. Models for Association • Recessive: f0 = f1 < f2 • Dominant: f0 < f1 = f2 • Additive: f1 = ½(f2 + f0) • Logistic/Log-additive:

  5. Logistic/Log-additive Model

  6. Genetic Relative Risk (GRR) • Formally, GRR = Pr(D|g+)/Pr(D|g-) • In practice, because of the statistical advantages of the logistic model the genetic odds ratio is treated as if it is GRR • If the disease prevalence is low, then the odds ratio and risk ratio are roughly equivalent anyway

  7. Genetic Relative Risk (GRR) vs Familial Relative Risk (FRR) FRR for various GRR - Table 5.6 (p. 110) from Thomas, D. C. (2004). Statistical methods in genetic epidemiology. Oxford, UK: Oxford University Press. Estimates of FRR (SIR) for some common diseases: Hemminki, K. et al (2008). Familial risks for common diseases: Etiologic clues and guidance to gene identification. Mutation Research-Reviews in Mutation Research, 658(3), 247-258.

  8. Power Calculation in Simple Case-Control Design • Quanto (Morrison, J., & Gauderman, W. J. (2004). Quanto, version 0.5. University of Southern California: Author.) • Computes power for a range of G and E models. Here we will look at G main effect only: • In a study of 500 cases and 500 controls for a disease with population frequency .01, what is our power to detect a single locus effect? • Strength of genetic effect (GRR = Rg) • Risk allele frequency

  9. Quanto G Power Calculation • Outcome/Design: • Disease Case-Control 1 Control/Case • Hypothesis: • Gene Only • Gene: • Allele Frequency .10 to .90 by .20 • Log-additive model • Outcome Model: • Kp = .01 • Rg = 1.1 to 2.2 by 0.1 • Power: • Sample Size = 500 to 500 by 0 • Type I error rate = .05, two-sided • Calculate:

  10. Computed Power for N=500/500(Log-Additive Model) Genetic Odds Ratio

  11. Computed Power for N=500/500(Log-Additive Model) Adequate Power for OR > 1.3 if Moderate RAF Genetic Odds Ratio

  12. Computed Power for N=500/500(Log-Additive Model) Adequate Power for OR > 1.5 if RAF More Extreme Genetic Odds Ratio

  13. Computed Power for N=500/500(Log-Additive Model) Inadequate Power if RAF is Rare or Common Genetic Odds Ratio

  14. Computed Power for N=500/500(Dominant Model) Genetic Odds Ratio

  15. Computed Power for N=500/500(Recessive Model) Genetic Odds Ratio

  16. Power in Case-Control Design • For reasonably large samples (e.g., 500 cases and 500 controls) • Power is very poor if risk allele frequency is extreme • To detect ORs ~ 1.3, will need risk alleles to have intermediate frequencies • Power depends on the genetic model (i.e., recessive, dominant, log-additive) • Maximum if model fit corresponds to true alternative • In absence of knowledge about alternative, most use log-additive models

  17. Additional Considerations • Multiple Testing: If testing k variants may want to determine power at a significance level of .05/k • Noncausal Variant: • If N1 cases and N1 controls are needed to give desired power for a causal variant with an OR of, say, 1.5. • Then N2= N1 /.80 would give desired sample size for tagging SNP at r2 = .80.

  18. Single-locus Quantitative Model

  19. Reparameterized Single-locus Model

  20. Genotypic Values A2A2 A1A1 A1A2 u11 u12 u22 -a d a d is dominance parameter; when d = 0, locus is additive

  21. Additive Genetic Variance Note: d contributes to additive variance whenever q is not equal to .5

  22. Dominance Genetic Variance Note: There is dominance variance only when d is not 0

  23. Some Examples (all q = .5)

  24. Complete Additivity Slope of regression line =a Additive genetic variance = regression variance 1 0 2

  25. Partial Dominance Slope of regression line = a Dominance = Residual Variance Additive genetic variance = regression variance 1 0 2

  26. Complete Dominance Dominance = Residual Variance Slope of regression line = a Additive genetic variance = regression variance 1 0 2

  27. Some Examples

  28. Some Conclusions • Dominance effects contribute to additive genetic variance • Even with complete Mendelian dominance, additive variance typically exceeds dominance variance (exception would be overdominance)

  29. Power Calculation in Quanto for Quantitative Trait • In a study of 1000 unrelated individuals, what is our power to detect a single locus effect? • Strength of genetic effect (R2g) • Risk allele frequency?

  30. Quanto G Power Calculation • Outcome/Design: • Continuous  Independent Individuals • Hypothesis: • Gene Only • Gene: • Allele Frequency .10 to .90 by .20 • Additive model • Outcome Model: • R2g = .001 to .019 by .002 • Power: • Sample Size = 1000 to 1000 by 0 • Type I error rate = .05, two-sided • Calculate:

  31. Computed Power for N=1000(Minor Allele = Risk Allele) % Variance Accounted For

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