Download Design of Genetical Genomics Studies Which Use Two

Statistical Analysis and Design
of Experiments for Large Data
Sets
Steven Gilmour
School of Mathematical Sciences
Centre for Statistics
Introduction
• I will discuss microarrays, but there are
many other possible biological applications
• Microarray experiments provide a
measure of gene activity
• Used to compare expression levels of
“treatment” groups
• Single channel (e.g. Afymetrix) arrays, or
two-colour platforms
False Discovery Rate
• Hypothesis test procedures for a single
response variable are unsuitable for screening
for thousands of genes
• Testing at 5% level of significance would imply
wrongly rejected very large numbers of null
hypotheses (declaring inactive genes to be
active)
• Traditional corrections, such as familywise error
rate are too conservative
• False discovery rate (FDR) ensures that a
suitably small proportion of genes declared
active are truly inactive.
Sample size calculations
• Many methods have been suggested for
determining an appropriate number of slides
• Assume fixed, unstructured, treatments
• Microarrays used recently in genetical genomics
studies to understand genetic mechanisms
governing variation in complex traits
• Treatments now have structure, e.g. family
structure, multiloci genotypic groups
• We have worked out better sample size methods
for such treatments
Design for Two-Colour Arrays
• Slides are blocks of size two, so
incomplete blocks are usually needed
• Two colours imply a row-column structure
• Designs suggested by several authors
• Examples for 4 and 9 treatments
Structured Treatment Effects
• Three possible genotypes, e.g. F2
populations and codominant markers
• Modelled by additive-dominance model
• Single locus, genotypes bb, Bb, BB
• Plot variance vs. proportion of each
homozygous group (r)
• Optimal treatment design and blocking for
10 slides: (a) additive effect; (b)
dominance effect; (c) both
bb
BB
bb
BB
Bb
bb
BB
Bb
• For multiple loci, factorial structures are
used
• Two-locus experiment in 10 slides
• Optimal treatment design and blocking
follow
AABB
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aaBB
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AABb
aaBb
AAbb
aaBB
AaBB
Aabb
AaBb
AABB
aabb
AABb
aaBb
AAbb
aaBB
AaBB
Aabb
AaBb
• Including epistatic effects
• Same design problem
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AaBB
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AaBb
Random Treatment Effects
• Aim to get good estimates of genetic
variances and heritabilities
• Designs to find BLUPs of breeding values,
given a known pedigree
• Two simple pedigree structures:
Progeny
1
2
3
4
5
6
7
8
9
Dam
1
2
3
4
5
6
7
8
9
Sire
1
1
1
2
2
2
3
3
3
Dam
1
2
3
1
2
3
1
2
3
Sire
1
1
1
2
2
2
3
3
3
• Optimal designs in 9 slides:
Discussion
• Consideration of different experimental
objectives should lead to different types of
design being used
• Often a search algorithm is needed to find
an optimal design – we have written an R
function
• There are still many open questions