Which SNP genotyping errors are most costly and when

1
Which SNP genotyping errors are most costly and
when?

• Stephen J. Finch
• Stony Brook University

2
Acknowledgments

• Joint work
• Derek Gordon (Rockefeller University)
• Sun Jung Kang (Duke University)
• Five papers are the material for this talk with
  additional coauthors
• Michael Nothnagel and Jurg Ott in paper 1
• Mark Levenstien and Jurg Ott in paper 2
• Abe Brown and Jurg Ott in paper 4

3
Acknowledgments

• Colleagues
• Nancy Mendell
• Kenny Ye
• Stony Brook students (work in progress)
• Nathan Tintle (repeated sampling)
• Qing Wang (LRT for mixtures)
• Kwangmi Ahn, Rose Saint Fleur
• Undergraduates Alex Borress, Josh Ren, Jelani
  Wiltshire

4
First Paper

• Gordon, D., Finch, S.J., Nothnagel, M., Ott, J.
  (2002). Power and sample size calculations for
  case-control genetic association tests when
  errors are present application to single
  nucleotide polymorphisms. Human Heredity, 54,
  22-33.

5
Second Paper

• Gordon D., Levenstien M.A., Finch S.J., and Ott
  J. (2003). Errors and linkage disequilibrium
  interact multiplicatively when computing sample
  sizes for genetic case-control association
  studies. Pacific Symposium on Biocomputing
  490-501.

6
Third Paper

• Kang, S.J., Gordon, D., Finch, S.J. (2004). What
  SNP Genotyping Errors Are Most Costly for Genetic
  Association Studies. Genetic Epidemiology, 26,
  132-141.

7
Fourth Paper

• Kang, S.J., Gordon, D., Brown, A.M., Ott, J.,
  Finch, S.J. (2004). Tradeoff between No-Call
  Reduction in Genotyping Error Rate and Loss of
  Sample Size for Genetic Case/Control Association
  Studies. Pacific Symposium on Biocomputing

8
Fifth Paper

• Kang, S.J., Finch, S.J., Gordon, D. (2004).
  Quantifying the cost of SNP genotyping errors in
  genetic model based association studies. Human
  Heredity, In press.

9
PAWE Web Site

• http//linkage.rockefeller.edu/pawe/pawe.cgi

10
Review Paper

• Gordon, D., Finch, S.J. (2004). Factors affecting
  statistical power to detect genetic association.
  Submitted for publication.

11
Background

• Definition of SNPs
• SNP genotyping measurements
• Specification of error models
• Tests of association
• Two supplementary measurement approaches

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Definition of SNP

• A gene with two possible alleles (here A and B)
• A is the more common allele in the controls
• Three possible genotypes
• AA, index1 (more common homozygote)
• AB, index2 (heterozygote)
• BB, index3 (less common homozygote)

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Measure of Cost

• The percentage increase in the minimum sample
  size necessary to maintain constant Type I and
  Type II error rates associated with an increase
  of 1 in a genotyping error rate is our measure
  of the cost of a genotyping error.
• MSSN is our abbreviation for this measure.

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SNP Genotyping Measurements

• Two die intensities are measured R and G.
• Measurements are typically taken at two or three
  time points.
• Ratio FR/(RG) is used to classify into
  genotypes.
• Genotyping error event in which an observed
  genotype is different from the true genotype.

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SNP Genotyping Measurements (Raw Data)
16
Scatterplot of SNP Dye Intensities
17
Scatterplot of SNP Fraction by Cycle Time
18
Approaches to Replication

• Sutcliffe studied the reclassification of
  subjects using the same classification procedure
  at all remeasurements.
• Tenenbein studied the reclassification of
  subjects using a virtually perfect instrument for
  the second reclassification.

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Regenotyping Results

• There is a common perception that genotyping
  error is negligible.
• One test is to regenotype a set of data.
• COGA provided such data to last GAW.
• Tintle et al. (2004) analyzed it.

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Regenotyping Results Summed over All SNPs(COGA
GAW Data)
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Observations on Table

• Homozygote to homozygote inconsistencies are
  extremely rare.
• CIDR missing rate is 6.7.
• Affymetrix missing rate is 6.1
• Double missing rate is 1.7, much higher than the
  0.4 expected under independence, suggesting some
  subjects may be consistently more difficult to
  genotype.

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Regenotyping Definitions

• Consistency Two genotypes on a SNP for a
  regenotyped subject exist and are the same.
• Nonreplication One genotype on a SNP for a
  regenotyed subject exists, and data is missing
  for the other genotype. Note that we treat two
  missing genotypes as replicated.
• SNP nonreplication rate the number of
  non-replications divided by the sum of the number
  of replications and the number of non
  replications.

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Critical assumptions about errors

• Regardless of nature of errors, they are random
  and independent
• Error model is same for cases (affecteds) and
  controls (unaffecteds)

25
Mote-Anderson Model 1965 Penetrance Table
(most general)

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Simple but Realistic Error Model

• Homozygote to homozygote error rates set to zero
• All other error rates set to equal error rate

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Three Component Normal Mixture

• Given AA, F is normal(-?, 1)
• Given AB, F is normal(0, 1)
• Given BB, F is normal(?,1)
• Symmetric cutpoints create an error model that
  has equal error rates for all errors except
  homozygote to homozygote errors.

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Tests of Association

• Case-control study. The ratio of number of
  controls to number of cases is k.
• We use the 2x3 chi-squared test of independence
  (simplest non-trivial case).
• Mitra found the noncentrality parameter of the
  chi-squared test of association which is needed
  for power and sample size calculations
• Recommended (Sasieni) test is test of trend
  (Armitage).

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Test Statistic

• Pearsons on 2 3 tables
• Example Table

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Effect of Misclassification Errors on Tests of
Association

• Bross found that level of significance is
  unchanged when the same error mechanism affects
  cases and control and that parameter estimates
  are biased.
• Mote and Anderson found that the power is reduced
  (level of significance constant) when there are
  misclassification errors.

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Notation

• Count parameters
• NA number of cases in the absence of errors
• NU number of controls in the absence of errors
• NA number of cases in the presence of errors
• NU number of controls in the presence of
  errors

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What is needed for asymptotic power calculations?
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Genetic model free parameterization

• Specify the genotype probabilities directly
• Assuming Hardy Weinberg Equilibrium (HWE), all
  probabilities specified with two parameters ( p,
  q )

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Genetic model free parameterization

• Specify the genotype probabilities directly
• Not assuming HWE, can specify all probabilities
  with four parameters

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Genetic Model Specification

• p1 allele frequency of SNP marker 1 allele
• p2 allele frequency of SNP marker 2 allele 1-
  p1
• pd allele frequency of disease locus d allele
• p allele frequency of disease wild-type allele
  1- pd

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Genetic Model Specification

• D disequilibrium (non-scaled as defined in Hartl
  and Clark
• DMAX min (p1 pd, p2 p)
• DD/ DMAX

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Genetic Model Specification (penetrance
parameters)
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Results

• Demonstrate analytic solution of asymptotic
  power using standard chi-square test of genotypic
  association

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Genotype Frequencies in the Presence of Errors
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Noncentrality Parameter

• We assume NU kNA.
• Using Mitras work (1958),

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Noncentrality Parameter

• Let ?kNAg, where g is the bracketed function for
  genotypes measured without error.
• Let ?kNAg, where g is the bracketed function
  using frequencies for genotypes observed with
  error.

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To maintain constant asymptotic power

• We choose NA so that ? ?.

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Paper 1 Findings

• Noncentrality parameter for the 2x3 chi-squared
  test of independence from Mitra to describe
  asymptotic power.
• Increase in error rate (three error models)
  requires a corresponding increase in sample size
  to maintain Type I and Type II error rates.
• Regression analysis of increase in MSSN as
  function of error rate in a number of published
  models.
• Interaction of linkage disequilibrium (D) and
  measure of overall error rate (S).

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Paper 2 Findings

• Linkage Disequilibrium (LD) and errors interact
  in a non-linear fashion.
• The increase in sample size necessary to maintain
  constant asymptotic power and level of
  significance as a function of S (sum of error
  rates) is smallest when D 1 (perfect LD).
• The increase grows monotonically as D decreases
  to 0.5 for all studies.

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Paper 3 Method

• Saturated error model (called Mote-Anderson in
  PAWE software).
• Taylor series expansion of the ratio of sample
  sizes expressed with the non-centrality
  parameters.
• The coefficients of each error parameter give the
  MSSN for a 1 increase in that error rate.

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Recall the Noncentrality Parameters

• Let ?kNAg, where g is the bracketed function.
• Let ?kNAg, where g is the bracketed function
  using frequencies for genotypes observed with
  error.
• Then, when ? ? (that is, equal power for both
  specifications), NA/NAg/g.

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MSSN Function

• ( NA / NA ) 1 C12e12 C13e13 C21e21
  C23e23 C31e31 C 32e32.
• Suppose C13 7. Then every 1 increase in e13
  requires a 7 increase in sample size to maintain
  constant power

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MSSN Coefficients

• The MSSN coefficient associated with the error
  rate of misclassifying the more common homozygote
  as the heterozygote is given by

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MSSN Coefficients

• Similar expressions hold for the other five MSSN
  coefficients.

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Example of Sample Size increase in presence of
errors

• Suppose we have

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Example Error Model Penetrance
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Comparison of Genotype Frequencies

• Without error With 1 error With 3 error

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Sample size in presence of errors

• Assume we want 0.80 power at 0.05 level of
  significance. Let k 1.

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Cost coefficients for our example

• Coefficient Type of error
• More common hom to het
• Het to more common hom
• Het to less common hom
• Less common hom to het

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Simplest non-trivial case to develop insights

• Assume HWE, cases and controls
• pa 0.2, 0.3, 0.4, 0.5
• pu pa d, d 0.01
• P01 (1- pa )2 , P02 2(1- pa ) pa , P03 (pa
  )2
• P11 (1- pu )2 , P12 2(1- pu ) pu , P13 (pu
  )2

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Results for MSSN Coefficients d 0.01
Cost
Case SNP minor allele frequency
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Conclusion What happens to MSSN coefficients as
minor SNP allele frequency approaches 0?
Costly errors are those made on the more common
homozygote
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Extension to non-HWE generalizing example

• MSSN coefficients C12 and C13 have infinite
  limits.
• Additionally, C23 may have infinite limit.

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How to perform calculations in practice?

• Use PAWE webtool.

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Paper 5 Findings

• MSSN coefficients with infinite limit hold when
  studying usual genetic models.
• Recessive models can have C23 with infinite limit
  as minor SNP allele frequency goes to zero.
• Dominant models have a notably different behavior
  with fewer MSSN coefficients with infinite
  limit. Behavior can be more problematic.
• MSSN coefficients are complex functions that
  should be studied on a case-by-case basis.

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Paper 5 Definitions

• Total MSSN is defined to be

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Total MSSN by Freq of Disease Allele and Minor
SNP Allele
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Coefficient of Heterozygote to Less Common
Homozygote Error
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Dominant Model, Total MSSN
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Possible Strategies to Counter Effects of SNP
Genotyping Errors

• Increase sample size to compensate for loss of
  power. Use small Type I and Type II error rates
  in designing studies. (This works.)
• When a three component normal mixture describes
  the measurements that are the basis of
  genotyping, use no-call rules to lessen error
  rates and reduce consequent cost.

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Possible Strategies to Counter Effects of SNP
Genotyping Errors

• Use the same genotyping classification procedure
  and regenotype subjects (Tintles problem).
• Use a perfect genotyping classification procedure
  on some of the subjects (Gordon et al.)

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Increase sample size

• Use PAWE software to identify whether the problem
  under consideration has the possibility of large
  MSSN coefficients.
• Good design (using small Type I and Type II error
  rates) can yield protocols that are less
  sensitive to the consequences of SNP genotyping
  errors.

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Power in presence of errors
A study design in which type I error rate is low
and power is high is less sensitive to genotyping
error rate
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No Call Regions for Three Component Normal
Mixture Model
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Power Using No Call Rules
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No-Call Rules (Paper 4)

• The gain (less reduction in power) from a reduced
  error rate using no call is almost exactly
  balanced by the loss of power due to reduced
  sample size.
• That is, there is only so much information in the
  sample.
• Conclusion Use all of the data without resorting
  to no call procedures.

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Regenotype Subjects

• Tintle will report on this approach in the next
  seminar.

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Double Sampling

• See the following paper.
• Gordon, D., Yang, Y., Haynes, C., Finch, S.J.,
  Mendell, N.R., Brown, A.M., Haroutunian, V.
  (2004) "Increasing power for tests of genetic
  association in the presence of phenotype and/or
  genotype error by use of double-sampling."
  Statistical Applications in Genetics and
  Molecular Biology.

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Summary

• 1. We have described quantitatively the magnitude
  of the effect of genotype errors on case/control
  association studies How much power or
  (equivalently) how much increase in sample size
  necessary to maintain constant power
• - We have quantified this magnitude for the
  chi-square test of independence
  (http//linkage.rockefeller.edu/pawe)

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Summary

• 2. Under HWE, cost coefficients of both error
  types made on the more common homozygote have
  infinite limits as SNP minor allele frequency
  approaches 0

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Recommendations

• 1. Researchers should increase sample size to
  maintain specification of type I error rate and
  power in case/control studies
• A study design in which type I error rate is low
  and power is high is less sensitive to genotyping
  error rate

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Recommendations

• 2. Researchers designing SNP genotyping
  technologies should avoid designs where
  homozygote-gthomozygote misclassifications might
  occur with non-zero probability

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References

• Armitage, P., Tests for linear trends in
  proportions and frequencies. Biometrics, 1955.
  11 p. 375-386.
• Bross, I., Misclassification in 2 x 2 tables.
  Biometrics, 1954. 10 p. 478-486.
• Hartl, D.L. and A.G. Clark, Principles of
  population genetics. 2nd ed. 1989, Sunderland
  Sinauer Associates.
• Mitra, S.K., On the limiting power function of
  the frequency chi-square test. Annals of
  Mathematical Statistics, 1958. 29(4) p.
  1221-1233.
• Mote VL, Anderson RL (1965) An investigation of
  the effect of misclassification on the properties
  of chisquare-tests in the analysis of categorical
  data. Biometrika 5295-109

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References

• Sasieni, P.D., From genotypes to genes doubling
  the sample size. Biometrics, 1997. 53(4) p.
  1253-61.
• Sutcliffe, J.P. (1965) A probability model for
  errors of classification. I. General
  considerations. Psychometrika, 30, 73-96.
• Sutcliffe, J.P. (1965) A probability model for
  errors of classification. II. Particular cases.
  Psychometrika, 30, 129-155.

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References

• Tenenbein, A. 1970. A double sampling scheme for
  estimating from binomial data with
  misclassifications. Journal of the American
  Statistical Association 651350-1361.
• Tenenbein, A. 1972. A double sampling scheme for
  estimating from misclassified multinomial data
  with applications to sampling inspection.
  Technometrics 14187-202.
• Tintle, N., Ahn, K., Mendell, N.R., Gordon, D.,
  Finch, S.J. (2004). Using Replicated SNP
  Genotypes for CoGA. Genetics Analysis Workshop
  contribution.