the analysis of microarray data using mixed models david baird peter johnstone & theresa wilson...
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The Analysis of The Analysis of Microarray data using Microarray data using Mixed Models Mixed Models
David Baird David Baird
Peter JohnstonePeter Johnstone& Theresa Wilson& Theresa Wilson
AgResearchAgResearch
David Baird 2002
Raw data – background (log2 scale)
Truncation of Red/Green at high levels
Limitation of Red & Green at low levels to stabilise ratio
David Baird 2002
Dye Bias
Differential binding or scanning levels of the two dyes
David Baird 2002
Visualization of SlideLog2(Red/Green) on Blue-Red spectrum
David Baird 2002
Spatial Effects (pins = 8 x 4)
Pins
Rows
Columns
Spatial auto-correlation
David Baird 2002
GenStat Spatial Model Analysis
Fixed effects (could be random) Pins Rows and columns within the slide
Random effects Cubic Smoothing Spline for Intensity
(log2(Red*Green)/2) AR1 autocorrelation process across
rows and columns within pins
(removes carry over effects, local trends)
David Baird 2002
Cubic Smoothing Spline B Spline Basis Basis
vectors fitted as random effects in a REML analysis
Alternatives:
Fixed knot cubic spline
Polynomial
David Baird 2002
Dye Bias Fits within Slide
Similar performance of two splines
Poor performance of polynomial (as expected)
Smoothing spline less responsive in left tail
David Baird 2002
Splines per Pin possibleOnly 3-5% extra variation explained
David Baird 2002
Pin Effects for First SlideLarge trend from one corner to the opposite diagonal
David Baird 2002
Pin Effects for 2nd Slide
Row/Col 1 2 3 4
8 0.53 0.65 0.80 1.02
7 0.42 0.47 0.61 0.58
6 0.62 0.70 0.73 0.67
5 0.19 0.35 0.47 0.53
4 0.00 0.13 0.21 0.20
3 0.41 0.02 0.18 0.04
2 0.57 0.60 0.73 0.75
1 0.31 0.64 0.71 0.43
David Baird 2002
Slide Row & Column Effects
Effects were highly significant (P<0.001)
In addition, within each pin there wasa significant autocorrelation for both columns = 0.2 - 0.3, and rows = 0.05 - 0.1.(Spots printed within columns)
David Baird 2002
Row/Column Effects Slide 2
David Baird 2002
Residuals from Analysis Unequal variances
Variance stablises for log2 Intensity > 9
EST effects calculated from residuals
David Baird 2002
Background too low
David Baird 2002
Background too high
David Baird 2002
Rescaling of Residuals
Possible need for a weighted analysis
David Baird 2002
Dye Swaps for EST Dye Bias Some ESTs
preferentially bind to one of the dyes
Important to swap dyes between treatments to detect and adjust for this
Extreme ratio caused by Red dye always binding to this EST
David Baird 2002
Q-Q Plot of EST RatiosA large number of under expressed ESTs
David Baird 2002
Differenced Q-Q Plot
Blank Removed
Departures from Normal distribution occur after Normal Score of ~ 2.5 (0.6% = 60 ESTs)
No significant departures in positive ratios
David Baird 2002
Volcano Plot Developed an Index based on combination of T, mean Ratio and Intensity
Plot coloured by Index
Usually Y = –log(p)
David Baird 2002
Design of Experiments Side by side duplicate spots are not
useful Repeat printing of EST library with
randomisation on same slide is useful Importance of balancing dyes with
treatment effects Incomplete Block Designs of size 2
used Replicate slides required due to slide-
slide variation (3 - 4 reps per treatment comparison)
David Baird 2002
Time Course Experiment Initial state, and then state 1, 2 & 3
weeks after treatment (8 reps)
Time 0 Time 1 Time 2 Time 3
Treatment
Treatment Contrast VariancesTime 1 0.125Time 2 0.250 0.125 Time 3 0.375 0.250 0.125 Time 0 Time 1 Time 2
David Baird 2002
Time Course Experiment Standard Treatment (8 reps)
Time 0 Time 1 Time 2 Time 3
Treatment
Treatment Contrast VariancesTime 1 0.125Time 2 0.125 0.250 Time 3 0.125 0.250 0.250 Time 0 Time 1 Time 2
David Baird 2002
Time Course Experiment Loop Design (6 reps)
Time 0 Time 1 Time 2 Time 3
Treatment
Treatment Contrast VariancesTime 1 0.125Time 2 0.167 0.125 Time 3 0.125 0.167 0.125 Time 0 Time 1 Time 2
David Baird 2002
Time Course Experiment Full incomplete block design (4 reps)
Time 0 Time 1 Time 2 Time 3
Treatment
Treatment Contrast VariancesTime 1 0.125Time 2 0.125 0.125 Time 3 0.125 0.125 0.125 Time 0 Time 1 Time 2
David Baird 2002
Analysis of Spot Shape
David Baird 2002
Analysis of pin accuracy