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Improved normalisation of microarray data by optimised iterative local regression Matthias E. Futschik Department of Information Science University of Otago New Zealand

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Normalisation by local regression and problem of model selection Example: Correction of intensity-dependent bias by loess (MA-regression: A=0.5*(log 2 (Cy5)+log 2 (Cy3)); M = log 2 (Cy5/Cy3); Raw data Local regression Corrected data However, local regression and thus correction depends on choice of parameters. Correction: M- M reg ? ? ? Different choices of paramters lead to different normalisations.

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Optimising by cross-validation and iteration Iterative local regression by locfit (C.Loader): 1) GCV of MA-regression 2) Optimised MA-regression 3) GCV of MXY-regression 4) Optimised MXY-regression 2 iterations generally sufficient GCV of MA

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Optimised local scaling Iterative regression of M and spatial dependent scaling of M: 1) GCV of MA-regression 2) Optimised MA-regression 3) GCV of MXY-regression 4) Optimised MXY-regression 5) GCV of abs(M)XY-regression 6) Scaling of abs(M)

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Comparison of normalisation procedures MA-plots: 1) Raw data 2) Global lowess (Dudoit et al.) 3) Print-tip lowess (Dudoit et al.) 4) Scaled print-tip lowess (Dudoit et al.) 5) Optimised MA/MXY regression by locfit 6) Optimised MA/MXY regression with scaling => Optimised regression leads to a reduction of variance (bias)

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Comparison II: Spatial distribution => Not optimally normalised data show spatial bias MXY-plots can indicate spatial bias MXY-plots:

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Averaging by sliding window reveals un- corrected bias Distribution of median M within a window of 5x5 spots: => Spatial regression requires optimal adjustment to data

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Statistical significance testing by permutation test M Original distribution What is the probabilty to observe a median M within a window by chance? Comparison with empirical distribution => Calculation of probability (p-value) using Fisher’s method M r1 M r2 M r3 Randomised distributions

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Statistical significance testing by permutation test Histogram of p-values for a window size of 5x5 Number of permutation: 10 6 p-values for negative M p-values for positive M

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Statistical significance testing by permutation test MXY of p-values for a window size of 5x5 Number of permutation: 10 6 Red:significant positive M Green:significant negative M

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References M. Futschik and T. Crompton, Model selection and efficiency testing for improved normalisation of microarray data by iterative local regression (in preparation)

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