1. A Method for Analyzing Time Course Multi-factor Expression Data with Applications to A Burn Study Baiyu Zhou Department of Statistics Stanford University 12/08/2008

2. Outline Motivations Brief review: methodology Tissue data analysis Age impact on survival in adult burn patients

3. Data: gene expression at different times after burn injury Tissue data (blood, skin, muscle and fat): Questions: 1. what tissue is most affected by burn injury? 2. what tissue contributes most to pediatric and adult differences in burn patients? 3. For a given gene, how is its expression affected in different tissues? Age impact on survival in burn patients: Reported dramatically increasing death rate in burn patients over 48 years old ( Muller MJ, Pegg SP, Rule MR. Determinants of death following burn injury. Br J Surg. 2001 Apr;88(4):583-7. ) The explanation on gene express level? Data and Questions These questions can be addressed by our method !

4. Brief Review: Methodology (1) A novel approach to analyze longitudinal multi-factorial data Example: time course measurements of gene expressions from each patients. longitudinal: time course multi-factorial: factor 1: burn/control ; factor 2: gender (male/ female) Classify genes into different gene sets. Each gene set represents a different ANOVA structure. Example: C1: interaction. Gender related burn responsive C2: additive. Burn and gender effects are independent C3: only have burn effect, no gender differences C4: only have gender differences, no burn effect C5: constant genes

5. Brief Review: Methodology (2) Gene classification is based on information pooling from time course measurements. Each gene is associated with an ANOVA direction (in time space), which captures gene specific response features. Response timing (when to respond): The magnitude of each component of the ANOVA direction reflects the intensity of ANOVA signal at the corresponding time points. Response pattern (how to respond): Negative signs in the ANOVA directions indicate the ANOVA signal is embedded into the expression change between time points. Examples (Burn+Age, time course data)

6. Application beyond time course data : Tissue Data Analysis Tissue data : Gene expressions in blood, skin, muscle and fat were measured for burn patients and controls. Two factors : burn/control and age (children ( =22 yr)). Questions: Which tissue is mostly affected by burn injury? Which tissue is perturbed most differentially in children and adults? For a gene of interest, how is its expression affected in different tissues? Analysis longitudinal multi-factorial data Treat tissue measurements as a vector Estimate ANOVA directions in ‘ tissue space ’ BurnControl Children79 Adults114 Data :

7. Tissue Data Analysis (1) The total of 11027 probe sets are classified into five gene sets (FDR=0.05). C1C2C3C4 236919520521 Examples: A gene ’ s ANOVA direction reflects the ANOVA signal intensity in different tissues of that gene

8. Tissue Data Analysis (2) Question: Which tissue contributes most to age related differences in burn patients? Weight matrix First eigen-gene (first right singular vector of W) captures weight distribution among tissues for a gene set.

9. Tissue Data Analysis (3) Age differences are strong in muscle, fat and skin after burn injury (C1 and C2 genes) Gene expressions in blood are perturbed most by burn injury (C3) Blood Muscle Fat Skin 20 12 11 5 6 8 18 19 15 14 17 9 13 4 10 1 3 7 16 2 21 Weight Matrix (C4) 01 Row Z-Score Color Key

10. Tissue Data Analysis (4) A gene is assigned to a tissue if the tissue receives the largest weight in the ANOVA direction. The gene sets are divided into four tissue subsets. TissueFunctional groups (GO: BP_5)pathways C3 (5205 probe sets) Blood (2242)Apoptosis (8.7E-8) Cell death (3.7E-7) Protein kinase cascade (4.5E-6) Natural killer cell mediated cytotoxicity (8.0E-4) GnRH signaling pathway (1.3E-3) T cell receptor signaling pathway (1.3E-3) Skin (1513)Vasculature development (4.2E-7) Blood vessel development (9.1E-7) Blood vessel morphogenesis (1.8E-5) Organ morphogenesis (8.4E-5) Focal adhesion (2.1E-5) Regulation of actin cytoskeleton (4.9E-4) Muscle (799)Cellular protein catabolic process (1.1E-3) Modification-dependant macromolecule catabolic process (2.4E-3) Protein catabolic process (2.9E-3) Tight junction (1.9E-2) Valine, leucine and isolecine degradation (1.9E-2) Fat (651)Tissue development (9.3E-3) Icosanoid metabolic process (2.7E-2) Fatty acid metabolic process (4.4E-2) Valine, leucine and isolecine degradation (3.6E-3) Fatty acid metabolism (4.0E-3) Sulfer metabolism (8.9E-3) Example: functional analysis on tissue subsets of C3.

11. Extension to Cross-sectional Time Course Data Longitudinal: time course measurements are from the same experimental units Cross-sectional : time course measurements are not from the same experimental units. Different numbers of measurements are allowed at each time points. Method for cross-sectional data: Assume gene specific variance. No correlations over time points. Estimate mean vectors for conditions Estimate ANOVA directions based on s Estimate gene specific variance by pooling information from all arrays

12. An Example : Impact of Age on Survival After Burn Injury One factor : Died/Survived Three time points (age groups) Two data sets: (1) early stage data (2) middle stage data Question: The impact of age on survival after burn injury. The data are cross-sectional Age group 1 (18- 39 year-old) Age group 2 (40- 54 year-old) Age group 3 (>=55 year-old) Data set 1 (early stage) Died8610 Survived493411 Data set 2 (middle stage) Died757 Survived38267

13. Impact of Age on Survival After Burn Injury (1) 1236 (early stage ) and 1171 (middle stage) probe sets are differentially expressed between survival & non survival populations (FDR=0.05). Early Stage Data

14. Impact of Age on Survival After Burn Injury (2) Middle Stage Data

15. Impact of Age on Survival After Burn Injury (3) Weight matrix: Weight matrix reflects the impact of age groups for each gene. The first right singular vector of W ( ‘ first eigen-gene ’ ) reflects the impact of age on the gene set. Early data: age group 2 (40-54 yo) Middle data: age group 2 (40-54 yo) and 3 (>=55 yo)

16. Impact of Age on Survival After Burn Injury (4) The result coincide with the reported increasing death rate in burn patients over 48 year-old (7.3 time more likely to die after burn injury) Some significant pathways: Early Stage Data Middle Stage Data

17. Summary A novel approach for analyzing time course multi-factor expression data (1) Classify genes into different gene sets based on factor effects, suited for explorative study (2) The estimated ANOVA directions capture gene specific response features: response timing and response pattern Applications (1) Burn + Age (pediatric/adult), time course data (2) Burn + Gender, time course data (3) Burn + Tissue (early stage) (4) Age impact on adult survival (early stage & middle stage) (5) Survival + Gender, time course data Results are available: http://gluegrant1.stanford.edu/~DIC/burn.html

18. Acknowledgements Professor Wing Wong Weihong Xu, Wenzhong Xiao from Davis lab

19. Thanks!