the analysis of microarray data using mixed models david baird peter johnstone & theresa wilson...

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