1. Statistical Analysis and Design of Experiments for Large Data Sets
Steven Gilmour
School of Mathematical Sciences
Centre for Statistics

2. 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

3. 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.

4. 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

5. 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

7. 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)

9. Optimal treatment design and blocking for 10 slides: (a) additive effect; (b) dominance effect; (c) both bb BB

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11. For multiple loci, factorial structures are used
Two-locus experiment in 10 slides
Optimal treatment design and blocking follow

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14. Including epistatic effects Same design problem
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15. 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:

16. Progeny
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Sire 1 2 3 4 5 6 7 8 9

17. Optimal designs in 9 slides:

19. 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