The Analysis of Microarray data using Mixed Models David Baird Peter Johnstone & Theresa Wilson AgResearch

David Baird 2002 Raw data – background (log 2 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 Slide Log 2 (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 (log 2 (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 possible  Only 3-5% extra variation explained

David Baird 2002 Pin Effects for First Slide Large trend from one corner to the opposite diagonal

David Baird 2002 Pin Effects for 2 nd Slide

David Baird 2002 Slide Row & Column Effects Effects were highly significant (P<0.001) In addition, within each pin there was a significant autocorrelation for both columns  = , and rows  = (Spots printed within columns)

David Baird 2002 Row/Column Effects Slide 2

David Baird 2002 Residuals from Analysis  Unequal variances  Variance stablises for log 2 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 Ratios  A 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 0Time 1Time 2Time 3 Treatment Treatment Contrast Variances Time Time Time Time 0 Time 1 Time 2

David Baird 2002 Time Course Experiment Standard Treatment (8 reps) Time 0Time 1Time 2Time 3 Treatment Treatment Contrast Variances Time Time Time Time 0 Time 1 Time 2

David Baird 2002 Time Course Experiment Loop Design (6 reps) Time 0Time 1Time 2Time 3 Treatment Treatment Contrast Variances Time Time Time Time 0 Time 1 Time 2

David Baird 2002 Time Course Experiment Full incomplete block design (4 reps) Time 0Time 1Time 2Time 3 Treatment Treatment Contrast Variances Time Time Time Time 0 Time 1 Time 2

David Baird 2002 Analysis of Spot Shape

David Baird 2002 Analysis of pin accuracy