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Theoretical and experimental comparisons of gene expression indexes for oligonucleotide microarrays

Theoretical and experimental comparisons of gene expression indexes for oligonucleotide microarrays. William J. Lemon, Jeffrey J.T. Palatini, Ralf Krahe, Fred A. Wright. Department of Biostatistics, University pf North Carolina, Chapel Hill

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Theoretical and experimental comparisons of gene expression indexes for oligonucleotide microarrays

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  1. Theoretical and experimental comparisons of gene expression indexes for oligonucleotide microarrays William J. Lemon, Jeffrey J.T. Palatini, Ralf Krahe, Fred A. Wright Department of Biostatistics, University pf North Carolina, Chapel Hill Division of Human Cancer GeneticsOhio State University

  2. polyA Coding portion of gene X Perfect Match (PM) Mismatch (MM) ... PM - 25 bases complementary to region of gene MM - Middle base is different Measuring gene expression with the Affymetrix GeneChip • cRNA from sample mRNA is put on the chip • intensity of binding reflects gene expression

  3. Reproducibility of Probe Sensitivities Li, C and Wong, WH, Proc. Natl. Acad. Sci. USA, 98:31-36, 2001.

  4. The Li-Wong Model Li-Wong Full (LWF) Identifiability constraint Li-Wong Reduced (LWR) Li, C and Wong, WH, Proc. Natl. Acad. Sci. USA, 98:31-36, 2001.

  5. The Li-Wong Model Li-Wong Full (LWF) ith array jth probe pair Identifiability constraint Total no. probe pairs Li-Wong Reduced (LWR) Li, C and Wong, WH, Proc. Natl. Acad. Sci. USA, 98:31-36, 2001.

  6. The Li-Wong Model Li-Wong Full (LWF) ith array jth probe pair Identifiability constraint Total no. probe pairs Li-Wong Reduced (LWR) Li, C and Wong, WH, Proc. Natl. Acad. Sci. USA, 98:31-36, 2001. expression sensitivities

  7. How to compare gene expression indexes? • We get maximum likelihood estimates for q using either full data (LWF) or reduced data (LWR) • The Affymetrix software computes: • Average Difference (AD) • Log-Average (LA) • The log-average might perform particularly poorly. Note that if n terms are small and error variance is small,

  8. We gain insight by assuming Li-Wong model is true. Then what are the consequences? • For large sample sizes, the a’s and f’s will be well-estimated

  9. Compare LW estimators directly: Comparing to AD is tricky, but with a correction factor AD is also an unbiased estimate of q :

  10. This also gives insight into “perfect match only” analyses: • RE(full, PM-only)= and Furthermore, PM-only is always at least twice as efficient as LWR

  11. Empirical Comparisons • We propose that an expression index is “good” if it has a high correlation with the underlying true expression (which is usually unknown). • this correlation can be estimated using a specially designed mixing experiment • if r is the correlation coefficient between the measured index and true expression, the “relative efficiency” of two indexes q and h can be estimated as

  12. Suppose the true underlying gene expression for a given gene is t. Consider two indices of gene expression is an unbiased estimate of t And we have

  13. Can we estimate this relative efficiency? • Suppose we could do a regression of on t. • the ratio of explained to residual variance in the model can be shown to be and similarly for , so

  14. Can we estimate r without ever knowing true expressions t? • Yes, with a specially designed mixing experiment • we seek two contrasting conditions in which many genes will be differentially expressed

  15. Experimental Design (6 replicates for each condition) Human Fibroblasts (GM 08330) 20% FBS Cell culture 5 passages 20% 0.1% FBS Serum starvation 48h 0.1% 20% FBS Harvest total RNA Serum stimulation 24h Harvest total RNA RNA extraction Produce 50:50 group Starved 50:50 Stimulated Produce duplicates each day for 3d Dap, Thr, Lys, Phe Add Bacterial Control Genes Dap, Thr Lys, Phe Synthesize cDNA, cRNA; fragment BioB, BioC, BioD, Cre Add Hybridization Control Genes HuGeneFL Hybridize Gene Expression Indexes Data Reduction

  16. BIN1 expression Stim Starved 50:50 True expression = average of Stim, Starved

  17. BIN1 expression Stim Starved 50:50 3 1 2

  18. Note that Where X=1, 2, 3 (say) for Stim, 50:50 Starved, respectively

  19. Overall intensity higher in Stimulated Mean probe intensity per array Stim 50:50 Starved

  20. Coefficients of variation for assay (individual probes) and gene expression indexes

  21. Correlation matrix of 18 arrays as a colorized image for each expression index. Starved LWR LWF 50:50 Stim Starved AD LA 50:50 Stim Stim 50:50 Starved Stim 50:50 Starved

  22. Comparing ModelsCluster Analysis Strv 3 Strv 4 Strv 6 Strv 5 Strv 2 Strv 1 Stim 2 Stim 1 Stim 4 Stim 5 Stim 6 Stim 3 50:50 5 50:50 4 50:50 2 50:50 1 50:50 6 50:50 3 Strv 1 Strv 4 Strv 2 Strv 5 Strv 3 Strv 6 50:50 3 50:50 5 50:50 4 50:50 2 50:50 1 50:50 6 Stim 4 Stim 6 Stim 5 Stim 3 Stim 1 Stim 2 Full Model Reduced Model Strv 2 Strv 3 Strv 1 Strv 6 Strv 5 Strv 4 Stim 2 Stim 4 50:50 1 Stim 1 Stim 6 Stim 3 Stim 5 50:50 3 50:50 5 50:50 4 50:50 2 50:50 6 Stim 2 Strv 1 Strv 3 Strv 2 Strv 6 Strv 5 Strv 4 Stim 1 Stim 6 Stim 3 Stim 5 Stim 4 50:50 5 50:50 4 50:50 3 50:50 2 50:50 1 50:50 6 Affymetrix Ave Diff Affymetrix Log Ave

  23. Relative Efficiency Unscaled Scaled Median(r2/(1-r2)) LA LA AD AD LWF LWF LWR LWR

  24. Correlation of duplicate measurements of 149 genes LWF median r=.74 LWR median r=.43 AD median r=.08 LA median r=.17

  25. Number of unexpressed genes • Only 0.2% of the LW estimates are negative • 50:50 group has fewest negative estimates • could this indicate very few unexpressed genes? Starved Stim 50:50

  26. A conservative approach to estimating number of unexpressed genes • Let U denote number of unexpressed genes • genes are ranked according to expression index • This is useful if we can get a random sample of unexpressed genes Unexpressed population Gene expression index

  27. We use the spiked-out bacterial control genes as a sample of “unexpressed” genes • the 4 genes are are represented 3 times each (different portions of mRNA), for a total of 12 probe sets • Based on this reasoning, we estimate that greater than 88% of the genes are expressed, even in the Starved samples

  28. AD LWF Very low estimated expression for truly absent genes when using LWF Rank of expression index variance across the 6 Stimulated arrays versus rank of index mean Truly absent in stim group

  29. Present/absent calls • We use the statistic • to declare genes present/absent (absolute call) • we find the vast majority of genes on the array appear to be present • for the spiked in/out genes, we find vastly improved present/absent calling using LW estimates

  30. ROC curve - spiked in/out genes LWF-Z LWR-Z Untrimmed AD LA Untrimmed LA AD Absolute Call

  31. Variability in estimates Reduced Model Full Model Stim log(variance) 50:50 Starved log(mean)

  32. Conclusions • Model-based estimators are superior to simple averaging • Full model superior to reduced • this does not necessarily mean that the mismatch probes are a good idea - but if they are present we should use them • we have demonstrated this using both analytic considerations and experimental data • a carefully designed experiment can be used to address many issues • Many more genes may be expressed than previously thought

  33. Other issues/ future work • Spiking genes might be used to calibrate and normalize arrays • relationship between variance and mean of expression indexes may be useful in planning experiments • our data may be useful for future work, especially in producing indexes that are resistant to probe saturation • all primary data, this Powerpoint presentation and a preprint are available at http://thinker.med.ohio-state.edu

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