Transcript Slide 1
Sampling Design in Regional Fine Mapping of a Quantitative Trait
Banff International Research Station Emerging Statistical Challenges and Methods Session 7: GWAS and Beyond II 25 June 2014
Shelley B. Bull
, Lunenfeld-Tanenbaum Research Institute, & Dalla Lana School of Public Health, University of Toronto
Co-authors: Zhijian Chen and Radu Craiu
Lunenfeld-Tanenbaum Research Institute & University of Toronto
Overview
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 design Stage 1 sample (
n
1 ) – expensive sequencing to identify a smaller set of promising variants Stage 2 sample (
n
2 ) – 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
Background
Two-phase designs +/- Stratification on tag SNP
Chen
et al
(2012), Schaid
et al
(2013), Thomas
et al Earlier:
case-cohort designs (2013)
Two-stage designs
Skol
et al
(2007), Thomas
et al
(2009), Stanhope & Skol (2012)
Bayesian approaches to genetic association
Stephens & Balding (2009), Wakefield (2009), WTCCC/Maller
et al
(2012)
Genetic model (mis)specification
Joo
et al
(2010), Spencer
et al
(2011), Vukcevic
et al
(2011), Faye
et al
(2013)
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 Model
QT Model Parameters: θ = (
β
0 ,
β
1 ,
σ
2 ) Genetic Models: M 1 = additive, M 2 = dominant, M 3 = recessive
Bayesian Inference: Stage 1 sample
(1) Specify priors for the genetic models and the regression parameters
p
(M
j
)
= ⅓ p
( θ | M
j p
( θ ) =
p
(
β
0 ,
β
1 |
σ
2 ) =
p
( θ ) )
p
(
σ
2 ) normal-inverse-gamma (NIG) (2) Derive model-specific posterior for the regression parameters for a functional sequence variant – analytic when prior is NIG (3) Select a genetic model for each seq variant according to the posterior probability
w j
=
p
(M
j
| data ) (4) 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
) (5) 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 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, 1KG)
Quantitative trait model is
Y = β 0 + β 1 X + γ
Parameters specified by
β 0 =5, β 1 =0.25
,
σ 2 =0.1, 0.5, 1.5
and
σ/β 1 =1.3, 2.8, 4.9
1(X=1) + ϵ
,
Simulation Results: Genetic model selection
Designs: SRS ____ ES - - - HO …..
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
Simulation Results: Size of the 95% credible set
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: Selection of 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 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
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)
A total of
m
sequence variants are identified in
n 1
and a proportion
q
= (
m
2 /
m
) are genotyped in individuals in stage 1,
n 2
=
N
-
n 1
in stage 2. Cost depends on c 1 , the stage 1 per individual sequencing cost, and on c 2 , the stage 2 per individual per marker genotyping cost. e.g. if
N
= 5000,
n
1 =500, c 1 =$1000,
n
2 =4500,
m
2 =100, and c 2 =$0.50, then the total two-stage cost is $500,000 + $225,000 = $725,000 compared to a one-stage cost of $5 million. CE is defined as “Power” / Cost, where “Power” is estimated by the probability that a functional variant falls within the 95% credible set
Comments 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?
Acknowledgements
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
Simulation Results Summary
In stage 1, a total of
m
variants are sequenced in
n 1
= 500 individuals, with equal strata sampling (ES) and an additive genetic model.
Size
is the number
m 2
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.