Sampling Design in Regional Fine Mapping of a Quantitative Trait

Shelley B. Bull, Lunenfeld-Tanenbaum Research Institute,& Dalla Lana School of Public Health, University of Toronto

Banff International Research StationEmerging Statistical Challenges and Methods

Session 7: GWAS and Beyond II25 June 2014

Co-authors: Zhijian Chen and Radu Craiu Lunenfeld-Tanenbaum Research Institute & University of Toronto

OverviewOverview

Setting

Studies designed to follow up associations detected in a GWAS

Fine-mapping of a candidate region by sequencing

Aim to identify a functional sequence variant

Approach

Phase I: Quantitative trait with GWAS data (eg. N = 5000)

Phase II: Two stage designStage 1 sample (n1) – expensive sequencing to identify a

smaller set of promising variantsStage 2 sample (n2) – cost-effective genotyping of selected

variants in an independent group Stratification in Stage 1 according to a promising GWAS tag SNP

Bayesian analysis in Stage 1, incorporating genetic model selection

Two-phase Two-stage Design Two-phase Two-stage Design

BackgroundBackground

Two-phase designs +/- Stratification on tag SNPChen et al (2012), Schaid et al (2013), Thomas et al (2013)Earlier: case-cohort designs

Two-stage designsSkol et al (2007), Thomas et al (2009), Stanhope & Skol (2012)

Bayesian approaches to genetic associationStephens & Balding (2009), Wakefield (2009), WTCCC/Maller et al (2012)

Genetic model (mis)specificationJoo et al (2010), Spencer et al (2011), Vukcevic et al (2011), Faye et al (2013)

Sampling Designs & Sample Allocation Sampling Designs & Sample Allocation

Based on tag SNP (AA, Aa, aa) from the GWAS:(1) Simple random sampling (SRS) – ignores tagSNP information(2) Equal (ES) number from each stratum(3) Oversampled homozygous (HO) – number larger than under SRS

Example: N=5000, MAF=0.2

Quantitative Trait ModelQuantitative Trait Model

QT Model Parameters: θ = (β0 , β1 , σ 2 )

Genetic Models: M1= additive, M2= dominant, M3= recessive

Bayesian Inference: Stage 1 sampleBayesian Inference: Stage 1 sample

(1) Specify priors for the genetic models and the regression parametersp(Mj ) = ⅓ p( θ | Mj ) = p( θ ) p( θ ) = p(β0 , β1 | σ 2 ) p( σ 2 ) normal-inverse-gamma (NIG)

• Derive model-specific posterior for the regression parameters for a functional sequence variant – analytic when prior is NIG

• Select a genetic model for each seq variant according to the posterior probability wj = p(Mj | data )

• Given selection of a genetic model, compare all seq variants in the region by computing the posterior probability that variant k is functional given all the data, and rank them (the Bayes factor)

p(1) ≥ p(2) ≥ … ≥ p(m)

• Construct a 95% credible interval that includes all variants such that

p(1) + p(2) + … + p(k) ≥ 0.95 for minimum k

Criteria for a Good DesignCriteria for a Good Design

Higher probability that the correct genetic model is identified for the sequence variant

Fewer sequence variants selected into the credible set (number and %) * cost

Higher probability that the functional sequence variant is selected into the credible set * power

Higher probability that the functional sequence variant is top ranked in the credible set

Simulation Design (APOE gene region, Simulation Design (APOE gene region, 1KG) 1KG)

Quantitative trait model is

Y = β0 + β1 X + γ 1(X=1) + ϵ, Parameters specified by β0=5, β1=0.25, σ2 =0.1, 0.5, 1.5 and σ/β1 =1.3, 2.8, 4.9

Simulation Results: Genetic model Simulation Results: Genetic model selection selection

Data simulated under additive, dominant and recessive genetic models.

The rate of selecting the true genetic model for the functional variant using the strong criteria of wj >0.833.

Common seq variant (MAF=0.2)

1000 simulations

Designs: SRS ____ ES - - - - HO …..

Simulation Results: Size of the 95% Simulation Results: Size of the 95% credible set credible set

Data simulated under additive, dominant and recessive genetic models.

Upper panels: common variant (MAF=0.2) with σ/β1=4.9(m=201)

Lower panels:low frequency variant (MAF=0.02) with σ/β1=2.8 (m=332)

1000 simulations

Designs: SRS ____ ES - - - - HO …..

Simulation Results: Selection of Simulation Results: Selection of functional variant functional variant

Designs: SRS ____ ES - - - - HO ….. Data simulated under additive, dominant and recessive genetic models.

Upper panels: common variant (MAF=0.2) with σ/β1=4.9(m=201)

Lower panels:low frequency variant (MAF=0.02) with σ/β1=2.8 (m=332)

1000 simulations

Simulation Results: Functional variant Simulation Results: Functional variant top ranked top ranked

Designs: SRS ____ ES - - - - HO ….. Data simulated under additive, dominant and recessive genetic models.

Upper panels: common variant (MAF=0.2) with σ/β1=4.9(m=201)

Lower panels:low frequency variant (MAF=0.02) with σ/β1=2.8 (m=332)

1000 simulations

Simulation Results: Model selection Simulation Results: Model selection

Data simulated under additive, dominant and recessive genetic models. For cases without model selection (no MS), analysed under an additive model. Common seq variant (MAF=0.2), σ/β1=4.9, n1=600, 1000 simulations

Simulation Results: Cost Efficiency (CE) Simulation Results: Cost Efficiency (CE)

A total of m sequence variants are identified in n1 individuals in stage 1, and a proportion q = (m2 / m) are genotyped in n2=N-n1 in stage 2.

Cost depends on c1, the stage 1 per individual sequencing cost, and on c2, the stage 2 per individual per marker genotyping cost.

CE is defined as “Power” / Cost, where “Power” is estimated by the probability that a functional variant falls within the 95% credible set

e.g. if N = 5000, n1=500, c1=$1000, n2=4500, m2=100, and c2=$0.50, then the total two-stage cost is $500,000 + $225,000 = $725,000 compared to a one-stage cost of $5 million.

Comments and DiscussionComments and Discussion

• Incorporating Bayesian genetic model selection is worthwhile

• Selection of informative individuals for expensive data collection can be a useful strategy in statistical genetic design and analysis

• The simulations confirm the intuition that the efficiency of the tag-stratified sampling strategy increases with tag-seq correlation.

• Winner’s curse effects propagate from the GWAS, but are more complicated

• Cost-efficiency of a two-stage design depends on the relative costs of sequencing versus genotyping – will it remain practical?

• Analysis of the sequence data limited to low frequency and common variants – extensions to rare variants

• Other design options – trait-dependent sampling

• How to conduct joint Bayesian inference for stages 1 and 2?

AcknowledgementsAcknowledgements

Co-Authors:

Zhijian Chen, STAGE Post-doctoral Fellow

Radu Craiu, Dept of Statistical Sciences

Thanks to Laura Faye and Andrew Paterson for helpful discussions, and to referees for improvements to the paper.

To appear in Genetic Epidemiology

Funding

Thanks Thanks

Simulation Results SummarySimulation Results Summary

In stage 1, a total of m variants are sequenced in n1 = 500 individuals, with equal strata sampling (ES) and an additive genetic model.

Size is the number m2 of sequence SNPs in the 95% credible set (% or count). P(Select) is the probability the functional variant is selected into the credible set. P(Rank) is the probability the functional variant is top ranked in the credible set.

GWAS Sample Size GWAS Sample Size

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