Lecture 3 quantitative traits and heritability full
- 1. This session • The theory behind quantitative traits • Heritability – definition and estimation • Data preparation • Lab on data preparation
- 2. Learning objectives • Primary • Know what a quantitative vs. a categorical trait is. • Be able to calculate heritability from twin correlations • Explain why heritability is population specific • Be able to transform a variable to a normal distribution • Secondary • Explain why we think quantitative traits are caused by many genetic variants. • Evaluate why heritability estimates may not be accurate • Discuss the importance of sample and trait characteristics.
- 3. Part 1 The theory of quantitative traits
- 4. Qualitative traits • PKU • Deficiency of phenylalanine hydroxylase. • Characterized by – Intellectual disability – microcephaly – delayed speech – seizures – eczema – behavior abnormalities
- 5. Qualitative traits • Qualitative trait: PKU • 12q23.2
- 6. Qualitative traits • “You have it or you don’t” 0 5 10 15 20 25 30 Affected Not Affected PKU
- 7. Qualitative traits – Not “a bit pregnant” 0 5 10 15 20 25 30 Not Somewhat Pregnant Very pregnant
- 8. Qualititative traits – Not “a bit pregnant” 0 5 10 15 20 25 30 Not Somewhat Pregnant Very pregnant
- 9. Quantitative traits • Attention Deficit Hyperactivity Disorder • Characterized by developmentally inappropriate – Hyperactivity / impulsivity – Inattentiveness • Ever said: I am sure I am ‘a bit ADHD’?
- 10. Quantitative traits – A bit ADHD
- 11. Qualitative vs. Quantitative traits • Qualitative • Categorical • Dichotomous • Quantitative • Continuous • Dimensional Is it easy to decide whether traits are qualitative or quantitative? Autism Type II Diabetes Eating disorders Dissociation disorders
- 12. “Traits are influenced by many variants of small effect, no one variant being necessary, nor sufficient, for the disorder”. Implications of the dimensional approach for genetics Quantitative Trait Loci approach: Quantitative trait loci (QTLs) are stretches of DNA containing or linked to the genes that underlie a quantitative trait
- 13. • Imagine 1 locus contributing to a trait • Each locus has 2 Alleles, one of which is the risk allele • The presence of each copy of the risk allele conveys an additional ‘score’ on the trait • What happens are you add loci? Why QTLs give rise to a normal distribution
- 14. • 1 locus. Aa. • How many genotypes? • AA • Aa • aa Why QTLs give rise to a normal distribution
- 15. • Given our genotypes, each risk allele gives you a score of +1 on the phenotype • If A is the risk allele, what are our phenotype scores? • AA • Aa • aa Why QTLs give rise to a normal distribution +2 +1 +0 20 21 19 .5 .25 .25 Genotype Effect Trait Frequency
- 16. Why QTLs give rise to a normal distribution 0 0.5 1 1.5 2 2.5 19 20 21
- 17. • 2 locus. Aa / Bb • 2 risk alleles (A and B) • Aa / Bb take a value of 20 • Fill in Table 1 Why QTLs give rise to a normal distribution
- 18. Why QTLs give rise to a normal distribution Genotypes Effect Trait Frequency AA/BB +4 21 1/16 AA/Bb +3 20 2/16 aA/BB +3 20 2/16 AA/bb +2 19 1/16 aA/Bb +2 19 4/16 aa/BB +2 19 1/16 Aa/bb +1 18 2/16 aa/Bb +1 18 2/16 aa/bb +0 17 1/16
- 19. • 2 locus. Aa / Bb • 2 risk alleles (A and B) • Aa / Bb take a value of 20 • Fill in Table 1 • Sketch out a graph (assuming 16 individuals) Why QTLs give rise to a normal distribution
- 20. 17 18 19 20 21 2 4 6 8 10 12 14 16
- 22. 17 18 19 20 21 2 4 6 8 10 12 14 16 2 loci
- 23. What do you notice about the trait as the number of loci increases? *Note: this shows additive genetic variance. Dominant genetic variance calculations are in the resources section.
- 24. Quantitative traits – A bit ADHD
- 25. • Waiting for ‘proof’ that the phenotypes & genes are the same • Does not mirror how clinicians work Controversies of the QTL
- 26. • Much easier to find study participants • Can be more powerful Advantages of the QTL approach
- 27. • Quantitative traits are normally distributed traits • Assumed that these arise from the combined effects of multiple genetic variants • Assumption is that finding variants associated with traits will find genes associated with disease: • Attentiveness -> ADHD • Blood sugar -> T2DM Quantitative traits in genetic research
- 29. Heritability is an estimation of the proportion of observed trait variance, attributable to genetic influences. What is heritability? Trait variance (Vp) Vp = Variance due to genetics (Vg) + variance due to non genetics (VE)
- 30. • Twin studies • Vp = A + C + E • A = Genes • C = Common environment • E = Unique environment How do we calculate heritability?
- 31. • Assumptions of Twin studies • MZ twins correlate (rMZ) 100% A • DZ twin correlate (rDZ) 50% A • MZ and DZ correlate 100% C • MZ and DZ correlate 0% for E How do we calculate heritability?
- 32. • A = h2 = 2 (rMZ – rDZ) • C = rMZ – A • E = 1- rMZ • If rMZ = .8, and rDZ = .4 • A = 2 (.8 - .4 ) = .8 • C= .8 - .8 = 0 • E = 1 = .8 = .2 How do we calculate heritability?
- 33. Calculate the heritability rMZ rDZ A C E .5 .3 .5 .4 .7 .7 .1 .1 .9 .6 .2 .1 .9 .8
- 34. Calculate the heritability rMZ rDZ A C E .5 .3 .4 .1 .5 .5 .4 .2 .3 .5 .7 .7 .0 .7 .3 .1 .1 .0 .1 .9 .9 .6 .6 .3 .1 .2 .1 .2 .0 .8 .9 .8 .2 .7 .1
- 35. • The equal environments assumption (EEA) (including prenatal) • Assortative mating • Generalizability. Assumptions of the twin method
- 36. • Gene environment correlation (rGE) • Passive rG • Increase C • Active rG • Increases or decreases heritability • (why does this increase with age?) • Evocative rG • Increases or decreases heritability • Gene environment interaction (G*E) – Increases E Limitations of the twin method
- 37. Our concept of heritability is tied up with variation, and with our population. What is heritability?
- 38. A thought experiment: • Where do our hearts come from? If you have a heart, is this from your genetics? Or from the environment? • What is the heritability of having a heart? Heritability & Variation
- 39. • Tonsillectomies (NG martin, 1991) • Thought experiment: Reading ability Population specific heritability
- 40. 1. How much genetics contributes to some trait that an individual shows. Heritability?
- 41. 2. Proportion of trait variation between individuals in a given population due to genetic variation. Heritability?
- 42. 2 definitions: 1. How much genetics contributes to some trait that an individual shows. 2. Proportion of trait variation between individuals in a given population due to genetic variation. What is heritability? What is the difference?
- 43. Question: Does a high heritability for a disease mean that we should target our treatments at genetics? What is heritability?
- 44. Qualitative traits • PKU • Deficiency of phenylalanine hydroxylase. • Characterized by – Intellectual disability – microcephaly – delayed speech – seizures – eczema – behavior abnormalities
- 45. • Parent-offspring Heritability estimates in non twins Mid-parent phenotypic trait value Offspringphenotypictraitvalue Slope = 0.89 h2= 0.89
- 46. • If offspring do not resemble parents then best fit line has a slope of approximately zero. • Slope of zero indicates most variation in individuals due to variation in environment. • If offspring strongly resemble parents then best fit line will be close to 1. Heritability estimates in non twins
- 47. • Most traits in most populations fall somewhere in the middle with offspring showing moderate resemblance to parents. Heritability estimates in non twins
- 48. • Heritability can be ascertained from twin correlations, and parent- offspring data • The point heritability is estimate is not exact (not like a mean) • Furthermore, it applies only to your population, at your time. Heritability summary
- 49. Part 3 Lab: Using phenotype data
- 50. The world of quantitative genetics • Genetics… without genotype data. Phenotype data 1. Sample characterization 2. Quantitative trait distribution 3. Heritability Genotype data – Variant description – Missing data – HWE – LD and haplotypes
- 51. • Make a table of sample characteristics • Prepare a quantitative trait for genetic analysis Goals of this lab
- 52. Summarize the sample characteristics (covariates) for our population, often broken down by gender or ethnicity. Summarize trait distribution 1. Summarize data characteristics Why?
- 53. – Define the population parameters for comparison of results with those from other samples (i.e. gender, age, health) – Help to identify biases in the data Why summarize sample characteristics? LOOK AT THE TABLE CLOSELY!!!
- 54. – Population definition – Generalizability Why summarize trait distribution? LOOK AT THE TABLE CLOSELY!!!
- 55. ‘Table 1’
- 56. ‘Table 1’
- 57. 1. Is the distribution normal? 2. Are there outliers? 2. Prepare a quantitative trait for genetic analysis
- 58. 1. What is a normal distribution? For continuous data we don’t have equally spaced discrete values so instead we use a curve or function that describes the probability density over the range of the distribution. Continuous data
- 59. Normal distribution describes a special class of continous distributions that are symmetric and can be described by two parameters (i) μ = The mean of the distribution (ii) σ = The standard deviation of the distribution Changing the values of μ and σ alter the positions and shapes of the distributions. The normal distribution
- 61. Deviations from normal - skew The normal distribution will have a skew of 0
- 62. Deviations from normal - Kurtosis ‘Tails’ are misshapen The normal distribution will have a kurtosis of 0
- 63. Why we care about the normal distribution • Assumption of most (including genetic association) tests.
- 64. How do we test for a normal distribution? • The Chi-square and KS GOF test (low power). • Eyeball methods: look at histogram & look for a skew and kurtosis -1 - +1 • Shapiro and Wilk formal test What is the Ho for Shapiro Wilk?
- 65. What do we do about non normal distributions • Run a monotonic transformation • You can try • Log • Square root • Cube root • Reciprocal • STATA: lnskew0 command which does it for you!
- 66. Example of a log transformation Pre transformation Log transformed
- 67. NOTE ALWAYS check the correlation of the transformed variable with the original variable.
- 68. Screening outliers Screen ‘odd’ or extreme values Subjective definition: sometimes values 3 or 4 +/- the mean Contentious. Positives and negatives. My personal recommendation ‘sensitivity analysis’
- 69. Summary Normal distribution is a symmetrical distribution Skew and kurtosis represent a deviation from normality Most genetic tests require a normal distribution Therefore we try to transform our distributions
- 70. Lab Goals Going to prepare three variables for analysis: fasting VLDL, LDL and HDL particle size (cardiovascular disease risk factors) 1. Prepare a summary table, split by gender, for the trait and relevant covariate characteristics of the sample 2. Decide if the variables need to be transformed, and transform if so. 3. Prepare a variable with no outliers (using 2 definitions)
- 71. Learning objectives • Primary • Given an example of a qualitative trait • Give an example of a quantitative trait • With rMz = 6 and rDz = 6, what is the heritability? • Why is heritability is population specific? • How would you recognize a non-normal variable and transform it to a normal distribution • Secondary • Explain why we think quantitative traits are caused by many genetic variants. • Given one reason why heritability estimates may not be accurate • Why do we need to include covariate characteristics?
- 72. Slide graveyard
- 73. Lab Goals Going to prepare three variables for analysis: fasting VLDL, LDL and HDL particle size. Prepare a summary table, split by gender of the trait distributions and relevant
- 74. Implications of the dimensional approach 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 AA/BB AA/BB Column1 Column2 Column3 Column4