Developing Odds Ratio Estimation under a Multistage Design

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Developing Odds Ratio Estimation under a
Multistage Design

• Judy Zhong

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Outline

• Background
• Multistage Design
• Estimation under Multistage Design
• Simulation Results

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Background, readiness, potential

• Genome-wide association studies are now underway,
  enabled by
• Rapidly decreasing genotyping costs
• Genotyping costs in the vicinity of 0.01/SNP.
  May continue to fall?
• Massively multiplexed genotyping technologies
• Large-scale SNP discovery
• For example, David Cox and Perlegen Sciences have
  identified 250K tagging SNPs having estimated
  minor allele frequencies of 10 or larger across
  genome. (Perlegen now uses a 360K tag SNP set,
  informed by HapMap2).
• Could be used to provide insights into disease
  processes and mechanisms to examine genotype
  interactions with preventive interventions to
  identify susceptibles for targeted disease
  screening efforts.
• From Dr. Ross Prentice

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Association study sample size

• For some diseases preceding linkage study
  results may suggest absence of strong
  associations
• Hence need large sample sizes, e.g., OR 1.5 for
  presence of minor SNP allele (genotype risk
  ratio) n number of cases ( number of
  controls)
• 
  Test Size
• Test Power 0.05 0.01
• minor allele frequency 0.1
• ß 0.80 763 1211
• ß 0.95 1301 1875
• minor allele frequency 0.5
• ß 0.80 325 515
• ß 0.95 553 797
• (from Breslow and Day, 1987, V2)
• From Dr. Ross Prentice

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Association study genotyping costs and Approaches
to reducing genotyping costs

• 1000 cases, 1000 controls, 250K SNPs at 0.01/SNP
  gives genotyping costs of 5 million.
• Also, conventional testing, even at 0.01
  gives an expected 2500 false positives, under
  global null hypothesis, implying the need for a
  larger sample size.
• Approaches to reducing genotyping costs
• Reduced costs/SNP through further technology
  developments
• Reduce number of SNPs, perhaps restricted to SNPs
  in coding or regulatory regions of known genes
• Multistage design, perhaps testing at more
  extreme significance levels at later stages
• From Dr. Ross Prentice

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2-Stage Design
Random select a proportion cases controls
Remaining Cases Controls
genotyping
SNPs in 1st stage
genotyping
SNPs in 2nd stage
Significant SNPs
meet test criteria
meet test criteria

• e.g., 500 cases and 500 controls at first stage
  with 0.05 on 250K SNPs
• followed by 1000 cases and 1000 controls at a
  second stage using the approximately 12,500 SNPs
  significant at first stage and 0.001).
• Under global null hypothesis 12.5 false
  positives, and genotyping costs of 2.625 million.

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Association Testing Under a Multistage Design

• Individual-level data, observe x 0, 1, 2
  according to the number of minor alleles present
  for a SNP
• Logistic regression of case vs control status on
  x (and potential confounding factors) / s
• LR comparison of distribution of x between cases
  and controls
• Test statistic used on the data from stages 1, 2,
  , i or based on separate testing at each design
  stage.
• Testing at stage i can either be based on an
  inverse variance weighted log-odds ratio
• From Dr. Ross Prentice

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Combined odds-ratio testing in a two-stage design
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Summary From Prentice et al (2006)

• Hence, in summary, we are able to recommend a
  multistage design for high-dimensional SNP
  association studies.
• Testing from such a multistage design can take
  place with good power by considering log-odds
  ratio test statistics in an inverse variance
  weighted fashion from each design stage.

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Odds-ratio estimation under a two stage design

• 1. Use final stage estimator
• 2. Use combined-stage estimator

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Correction Essential
Significant
H2gtC2
H2 in 2nd stage
H1 in 1st stage
H1gtC1
H2lt-C2
Significant
Significant
H2gtC2
H1lt-C1
H2 in 2nd stage
H2lt-C2
Significant
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Correction Essential
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Correction
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Correction
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Correction Essential
Significant
H2gtC2
H2 in 2nd stage
H1 in 1st stage
H1gtC1
H2lt-C2
Significant
Significant
H2gtC2
H1lt-C1
H2 in 2nd stage
H2lt-C2
Significant
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Correction
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Confidence Interval

• Use a bootstrap method to get the confidence
  interval for the uncorrected combined log-OR
  estimator
• Resample Nn0n1 patients (with replacement)
  from the original sample, get a new combined
  log-OR estimator (sometimes the new samples fail
  to go through the two stages, ignore them)
• Repeat the above procedure B times, and get the
  empirical distribution of
• Therefore, we get
• Using the correction equation

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Simulation

• Simulate a SNP having two alleles N and D, with
  minor allele D frequency p10 and D is
  associated with a higher risk of getting disease
• X number of minor allele, X 0, 1, or 2
• Assuming Hardy-Weinberg equilibrium, thus in the
  control group
• Assume Ds genetic effect is additive (on
  log-scale)
• Assume Risk ratioOdds ratio for this rare
  disease
• log OR associated with X is 1/2log(1.35) 0.15
• In the case group

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Simulation

• Control group and Case group each has 2000
  patients
• Two stage design
• Randomly select 1000 cases the matching controls
  for the 1st stage, and the remaining 1000 samples
  for the 2nd stage.
• At each stage, observe x 0, 1, 2 according to
  the number of minor alleles present for a SNP.
  Logistic regression of case vs control status on
  x (and potential confounding factors)

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Bias
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Correction curve and its sensitivity to sigma
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Correction
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95 Confidence interval
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Simulation Results based on 1000 95 Confidence
Intervals
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Future Work

• Is it appropriate to use Bootstrap method with
  the presence of selection? Will it cause bias?
  May solve the problem of the CI length and
  conservative coverage rate.
• Asymptotic distribution of the corrected Log-OR
• Generalize the correction method to various
  multistage design, including those use pooling at
  the first stage
• Apply the correction method on genome-wide scan
  in theWomens Health Initiative
• Develop correction methods to multistage
  biomarker studies or other settings of multistage
  designs