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Experimental Design and Differential Expression Class web site: Statistics for Microarrays

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Biological question Differentially expressed genes Sample class prediction etc. Testing Biological verification and interpretation Microarray experiment Estimation Experimental design Image analysis Normalization Clustering Discrimination R, G 16-bit TIFF files (Rfg, Rbg), (Gfg, Gbg)

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Some Considerations for cDNA Microarray Experiments (I) Scientific (Aims of the experiment) Specific questions and priorities How will the experiments answer the questions Practical (Logistic) Types of mRNA samples: reference, control, treatment, mutant, etc Source and Amount of material (tissues, cell lines) Number of slides available

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Some Considerations for cDNA Microarray Experiments (II) Other Information Experimental process prior to hybridization: sample isolation, mRNA extraction, amplification, labelling, … Controls planned: positive, negative, ratio, etc. Verification method: Northern, RT-PCR, in situ hybridization, etc.

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Aspects of Experimental Design Applied to Microarrays (I) Array Layout Which cDNA sequences are printed Spatial position Allocation of samples to slides Design layouts A vs B: Treatment vs control Multiple treatments Factorial Time series

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Aspects of Experimental Design Applied to Microarrays (II) Other considerations Replication Physical limitations: the number of slides and the amount of material Sample Size Extensibility - linking

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Layout options The main issue is the use of reference samples, typically labelled green. Standard statistical design principles can lead to more efficient layouts; use of dye-swaps can also help. Sample size determination is more than usually difficult, as there are 1,000s of possible changes, each with its own SD.

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Natural design choice Case 1: Meaningful biological control (C) Samples: Liver tissue from four mice treated by cholesterol modifying drugs. Question 1: Genes that respond differently between the T and the C. Question 2: Genes that responded similarly across two or more treatments relative to control. Case 2: Use of universal reference Samples: Different tumor samples. Question: To discover tumor subtypes. C T1 T2T3T4 T1T1 Ref T2T2 T n-1 TnTn

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Treatment vs Control Two samples e.g. KO vs. WT or mutant vs. WT TC TRef C Direct Indirect 2 /22222 average (log (T/C))log (T / Ref) – log (C / Ref )

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I) Common Reference II) Common reference III) Direct comparison Number of Slides Ave. variance Units of material A = B = C = 1A = B = C = 2 Ave. variance One-way layout: one factor, k levels CB A ref CBA CBA

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I) Common Reference II) Common reference III) Direct comparison Number of Slides N = 3N=6N=3 Ave. variance20.67 Units of materialA = B = C = 1A = B = C = 2 Ave. variance10.67 One-way layout: one factor, k levels CB A ref CBA CBA For k = 3, efficiency ratio (Design I / Design III) = 3. In general, efficiency ratio = 2k / (k-1). (But may not be achievable due to lack of independence.)

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Design I Design III A B C A Ref BC Illustration from one experiment Box plots of log ratios: direct still ahead

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CTL OSM EGF OSM & EGF Factorial experiments Treated cell lines Possible experiments Here interest is not in genes for which there is an O or an E (main) effect, but in which there is an O E interaction, i.e. in genes for which log(O&E/O)-log(E/C) is large or small.

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IndirectA balance of direct and indirect I)II)III)IV) # Slides N = 6 Main effect A NA Main effect B Int A.B x 2 factorial: some design options C A.BBA B C A B C A B C A Table entry: variance (assuming all log ratios uncorrelated)

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Some Design Possibilities for Detecting Interaction Samples: treated tumor cell lines at 4 time points (30 minutes, 1 hour, 4 hours, 24 hours) Question: Which genes contribute to the enhanced inhibitory effect of OSM when it is combined with EGF? Role of time? ctlOSM EGF OSM & EGF ctl OSM EGF OSM & EGF 22 Design A: Design B:

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Combining Estimates Different ways of estimating the same contrast: e.g. A compared to P Direct = A-P Indirect = A-M + (M-P) or A-D + (D-P) or -(L-A) - (P-L) How do we combine these? L P V D M A

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Time Course Experiments Number of time points Which differences are of highest interest (e.g. between initial time and later times, between adjacent times) Number of slides available

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Design choices in time series. Entry: variance t vs t+1t vs t+2t vs t+3 Ave T1T2T2T3T3T4T1T3T2T 4 T1T4 N=3A) T1 as common reference B) Direct Hybridization N=4C) Common reference D) T1 as common ref + more E) Direct hybridization choice F) Direct Hybridization choice T2 T3 T4 T1 T2 T3 T4 T1 Re f T2 T3 T4 T1 T2T3T4T1 T2T3T4T1 T2 T3 T4 T1

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Replication Why? To reduce variability To increase generalizability What is it? Duplicate spots Duplicate slides Technical replicates Biological replicates

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Technical Replicates: Labeling 3 sets of self – self hybridizations Data 1 and Data 2 were labeled together and hybridized on two slides separately Data 3 were labeled separately Data 1 Data 2 Data 3

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Sample Size Variance of individual measurements (X) Effect size(s) to be detected (X) Acceptable false positive rate Desired power (probability of detecting an effect of at least the specfied size)

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Extensibility “Universal” common reference for arbitrary undetermined number of (future) experiments Provides extensibility of the series of experiments (within and between labs) Linking experiments necessary if common reference source diminished/depleted

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Summary Balance of direct and indirect comparisons Optimize precision of the estimates among comparisons of interest Must satisfy scientific and physical constraints of the experiment

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Identifying Differentially Expressed Genes Goal: Identify genes associated with covariate or response of interest Examples: –Qualitative covariates or factors: treatment, cell type, tumor class –Quantitative covariate: dose, time –Responses: survival, cholesterol level –Any combination of these!

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Biological question Differentially expressed genes Sample class prediction etc. Testing Biological verification and interpretation Microarray experiment Estimation Experimental design Image analysis Normalization Clustering Discrimination R, G 16-bit TIFF files (Rfg, Rbg), (Gfg, Gbg)

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Differentially Expressed Genes Simultaneously test m null hypotheses, one for each gene j : H j : no association between expression level of gene j and covariate/response Combine expression data from different slides and estimate effects of interest Compute test statistic T j for each gene j Adjust for multiple hypothesis testing

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Test statistics Qualitative covariates: e.g. two-sample t-statistic, Mann-Whitney statistic, F- statistic Quantitative covariates: e.g. standardized regression coefficient Survival response: e.g. score statistic for Cox model

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Example: Apo AI experiment (Callow et al., Genome Research, 2000) GOAL: Identify genes with altered expression in the livers of one line of mice with very low HDL cholesterol levels compared to inbred control mice Experiment: Apo AI knock-out mouse model 8 knockout (ko) mice and 8 control (ctl) mice (C57Bl/6) 16 hybridisations: mRNA from each of the 16 mice is labelled with Cy5, pooled mRNA from control mice is labelled with Cy3 Probes: ~6,000 cDNAs, including 200 related to lipid metabolism

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Which genes have changed? This method can be used with replicated data: 1. For each gene and each hybridisation (8 ko + 8 ctl) use M=log 2 (R/G) 2. For each gene form the t-statistic: average of 8 ko Ms - average of 8 ctl Ms sqrt(1/8 (SD of 8 ko Ms) 2 + 1/8 (SD of 8 ctl Ms) 2 ) 3. Form a histogram of 6,000 t values 4. Make a normal Q-Q plot; look for values “off the line” 5. Adjust for multiple testing

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Histogram & Q-Q plot ApoA1

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Plots of t-statistics

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Assigning p-values to measures of change Estimate p-values for each comparison (gene) by using the permutation distribution of the t- statistics. For each of the possible permutation of the trt / ctl labels, compute the two-sample t-statistics t* for each gene. The unadjusted p-value for a particular gene is estimated by the proportion of t*’s greater than the observed t in absolute value.

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Apo AI: Adjusted and unadjusted p-values for the 50 genes with the larges absolute t-statistics

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Genes with adjusted p-value 0.01

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Single-slide methods Model-dependent rules for deciding whether (R,G) corresponds to a differentially expressed gene Amounts to drawing two curves in the (R,G)-plane; call a gene differentially expressed if it falls outside the region between the two curves At this time, not enough known about the systematic and random variation within a microarray experiment to justify these strong modeling assumptions n = 1 slide may not be enough (!)

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Single-slide methods Chen et al: Each (R,G) is assumed to be normally and independently distributed with constant CV; decision based on R/G only (purple) Newton et al: Gamma-Gamma-Bernoulli hierarchical model for each (R,G) (yellow) Roberts et al: Each (R,G) is assumed to be normally and independently distributed with variance depending linearly on the mean Sapir & Churchill: Each log R/G assumed to be distributed according to a mixture of normal and uniform distributions; decision based on R/G only (turquoise)

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Matt Callow’s Srb1 dataset (#8). Newton’s, Sapir & Churchill’s and Chen’s single slide method Difficulty in assigning valid p- values based on a single slide

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Another example: Survival analysis with expression data Bittner et al. looked at differences in survival between the two groups (the ‘cluster’ and the ‘unclustered’ samples) ‘Cluster’ seemed to have longer survival

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Kaplan-Meier Survival Curves, Bittner et al.

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unclustered cluster Average Linkage Hierarchical Clustering, survival only

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Kaplan-Meier Survival Curves, reduced grouping

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Identification of genes associated with survival For each gene j, j = 1, …, 3613, model the instantaneous failure rate, or hazard function, h(t) with the Cox proportional hazards model: h(t) = h 0 (t) exp( j x ij ) and look for genes with both: large effect size j large standardized effect size j /SE( j ) ^ ^^

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Findings Top 5 genes by this method not in Bittner et al. ‘weighted gene list’ - Why? weighted gene list based on entire sample; our method only used half weighting relies on Bittner et al. cluster assignment other possibilities?

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Limitations of Single Gene Tests May be too noisy in general to show much Do not reveal coordinated effects of positively correlated genes Hard to relate to pathways

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Some ideas for further work Expand models to include more genes and possibly two-way interactions Nonparametric tree-based subset selection – would require much larger sample sizes

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Acknowledgements Sandrine Dudoit Jane Fridlyand Yee Hwa (Jean) Yang Debashis Ghosh Erin Conlon Ingrid Lonnstedt Terry Speed

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