Optimal%20designs%20for%20one%20and%20two-colour%20microarrays%20using%20mixed%20models

1
Optimal designs for one and two-colour
microarrays using mixed models

• A comparative evaluation of their efficiencies
• Lima Passos, Winkens, Tan and Berger
• DEMA 2008

Maastricht University Department of Methodology
and Statistics
2
(No Transcript)
3
Current situationOne versus two colour
comparisons
Background

• Woo et al, 2004
• We observed good concordance in both estimated
  expression levels and statistical significance of
  common genes.
• Smyth, 2005
• All four platforms reasonably precise (cDNA,
  oligo, Agilent, Affymetrix)
• Broadly agree
• Disagreement due to sequence differences, not to
  noise.
• John Hopkins Press release, 2005
• Different microarray systems more alike than
  previously thought
• Patterson et al., 2006
• The quality of the data stemming from one and
  two-colour arrays are equivalent in terms of
  reproducibility, sensitivity, specificity and
  accuracy
• highly concordant results regarding detection of
  differentially expressed genes

4
Current opinionsOne or Two?
Background

• Hardiman, 2004
• The choice of platform should be guided by the
  content on that platform and the amount of RNA
  available for experimentation.
• Agilent technologies
• Both one and two colour have their places in
  scientific research
• One provide much quicker analysis, more efficient
  method for analysing a large number of samples or
  those that span long time frames
• Two provide the most accurate results, helping
  identify small incremental changes in sample to
  further specific investigations
• Patterson et al. 2006
• The decision to used one or two will be
  determined by cost, experimental design
  considerations and personal preference
• Platform type should not be considered a primary
  factor in decisions regarding experimental
  microarray design

5
Optimal designsOne versus two?
Objective

• The majority of papers addressing microarray
  design questions - fixed effects models
• They are all specifically directed to two-colour
  microarrays
• Design papers with mixed models (also two-colour)
  are less abundant (Cui and Churchill, 2003
  Landgrebe et al., 2004 Tempelman, 2005 Bueno
  Filho et al., 2006 and Tsai et al., 2006)
• Is the choice of platform an important design
  issue?
• Main question
• What is exactly the impact the choice of a
  platform can have on the precision of model
  parameters?
• If any, which are the financial implications?

6
Design issues at stake
Design

• Two colour
• which pair-samples (the design points) to
  distribute across the slides together with their
  label assignment?
• One colour
• design points consists of the groups themselves,
  and not their pair-wise combinations
• ???

7
Mixed models
Premises

• One colour
• Two colour

8
Covariance structure
Premises

• Block diagonal, compound symmetric structure of
  V
• Dye swap is made at the level of technical
  replication with identical sample pairs. If not,
  i.e. lj with lk, with k ? k, the block diagonal
  of the final covariance matrix V will be lost.

9
Further premises
Premises

• Contrasts - T CT (first order interactions or
  main effects)
• Optimality criteria
• Sequential search yields an approximate
• Exact designs rounding up/down to the closest
  integer
• Relative efficiency one versus two

10
The cost function
Premises

• Given the prohibitive costs, it is recommendable
  to have an estimation of the costs of different
  microarray designs for comparative purposes
• cost njc1 nkSc2

11
Ceteris paribusAssumptions/limitations
Premises

• To warrant comparability and fair assessment
  between the two platforms
• model parameters and contrasts (common research
  questions) for the one and two-colour arrays are
  given on the same scale
• number of technical replicates was held constant
  (2), and the search of optimal designs focused on
  the distribution of biological replicates
• homogeneity of biological variances of
  experimental groups as well as independence and
  homogeneity of residual error variances were
  assumed to hold
• Variance components were restricted to a random
  intercept model with compound symmetric,
  block-diagonal covariance matrix (dye-swap with
  identical sample pairs!)
• subjects price was constant over all biological
  groups and the one- and two-colour arrays cost
  the same

12
Results
Results

• 3 x 3 factorial experiment

13
? and ?I - Two colour
Results
14
The design measure ? D-optimal design
main effects only
Results
Pmf
Directed graph
wd
xd
wd
xd
15
One versus two?? Subjects to groups allocation
Results
How many subjects?
11
8
5
12
16
One versus two?? Subjects to groups allocation
Results

17
Results
Efficiency comparison
N ? I
? N I
18
Results
Cost comparison
Cost 1 Cost 2
N ? I
? N I
Cost 1 Cost 2!!!
19
Results
Cost comparison adjusted for efficiency
20
Final remarks
Conclusion
Optimal allocation of subjects to experimental
groups is much concordant between the two
platforms - Hence the choice of platform will not
affect the subjects to groups optimal allocation
By varying number of subjects and arrays, while
holding statistical precision of parameter
estimates comparable, the choice of the one over
the two-colour platform or vice-versa will be
determined the subject to arrays cost ratio
On the grounds of statistical efficiency and
under the condition that the acquisition of
arrays outstrips that of subjects financially,
two-colour arrays should be considered an
efficient alternative over the one-colour,
specifically for studies involving class
comparisons.
21
(No Transcript)