1. Finding associated genes in large collections of microarrays

2. Produce hypothesis of functional relations between genes
Positive correlation: Co-regulated genes or positive modulator
Negative correlation: Co-regulated genes or inhibitor.
Used to derive networks of gene interactions.

3. 4 simple ways of finding association
Pearson correlation coefficient.
Spearman’s rank correlation coefficient.
Probabilistic approach (Present/Absent).
Mutual information (Present/Absent)

4. Pearson correlation coefficient
Varies between -1 and 1:
Between 0.6 and 1: strong positive correlation.
Between -0.6 and -1: strong negative correlation.
-1 is perfect negative correlation
1 is perfect positive correlation
Assumes linear relation between variables.

5. Pearson correlation coefficient
Step 1: Prepare data.
Step 2: Compute Pearson coefficient between pairs of probes of interest.
Step 3: Assess significance.
Step 4: Multiple testing correction.

6. Pearson correlation coefficient
Step 1: Prepare data:
Chips are normalized with MAS 5.0 or other procedure.
Scale probes in each chip dividing by mean.
Center and standardize each probe distribution: z-scores.

7. Pearson correlation coefficient
Step 2: Compute Pearson coefficient between pairs of probes:
when z-scores are pre-computed:
n: number of chips

8. Pearson correlation coefficient
Step 3: Assess significance:
Randomize if possible. Good for less than 20 chips or
Use t-Student distribution with n-2 degrees of freedom:
ρ: correlation coefficient
n: number of chips

9. Pearson correlation coefficient
Step 4: Multiple testing correction

10. Spearman’s rank correlation coefficient
Non parametric method:
Less power but more robust.
Does not assume normal distribution.
Also varies between -1 and 1

11. Spearman’s rank correlation coefficient
Step 1: Prepare data.
Step 2: Compute Spearman’s rank correlation coefficient between probe of interest and the rest.
Step 3: Assess significance.
Step 4: Multiple test correction.

12. Spearman’s rank correlation coefficient
Step 1: Prepare data:
Same as Pearson.
Order the values of the probes by increasing hybridization values.
Construct the rank vectors.

13. Spearman’s rank correlation coefficient
Step 2: Compute coefficient between probe sets of interest:
d: differences between the ranks of the two probes
n: number of chips

14. Spearman’s rank correlation coefficient
Step 3: Assess significance: Same as Pearson.
Randomize if possible. Less than 20 chips or
Use t-Student distribution with n -2 degrees of freedom:
ρ: correlation coefficient
n: number of chips

15. Spearman’s rank correlation coefficient
Step 4: Multiple testing correction.

16. Binary probabilistic approach based on Present/Absent
Approach adapted from:
“Computational methods for the identification of differential and coordinated gene expression.” Claverie JM Hum Mol Genet. 1999;8(10):
Use MAS 5.0 calls of Present-Marginal-Absent for each probe.
Good for heterogeneous microarray collections.

17. Binary approach based on Present/Absent
Step 1: Prepare data.
Step 2: Compute p-value of # of observed matches.
Step 3: Multiple test correction.

18. Binary approach based on Present/Absent
Step 1: Obtain P/M/A calls for probes:
Each call is associated to a p-value. Filter can be applied.
Codify P/M/A calls as binary vectors:
Encode P as 1 and M/A as 0

19. Binary approach based on Present/Absent
Step 2: Compute p-value of # of matches
probe x:
probe y:
probe z:
Find improbably high number of matches (or miss-matches).
probe x & y: 11 out of 12 matches
probe x & z: 11 out of 12 miss-matches

20. Binary approach based on Present/Absent
Step 2: Compute probability for observing by chance x matches or more from the binomial distribution B(n,p). First, probability of a match.
: fraction of 1s (Present) probe x.
: fraction of 1s (Present) probe y.

21. Binary approach based on Present/Absent
Step 2: Compute probability for observing by chance x matches or more from the binomial distribution:
For n large one can use the normal distribution:
n: number of chips.

22. Binary approach based on Present/Absent
Step 3: Multiple test correction.

23. Mutual information based on Present/Absent
Step 1: Prepare data.
Step 2: Compute MI value for pairs of probes.
Step 3: Use of a threshold for MI

24. Mutual information based on Present/Absent
Step 1: Obtain P/M/A calls for probes:
Each call is associated to a p-value. Filter can be applied.
Codify P/M/A calls as binary vectors:
Encode P/M as 1 and A as 0 OR
Encode P as 1 and M/A as 0

25. Mutual information based on Present/Absent
Step 2: Compute MI value for probes X and Y:
p(.) frequencies of observed Ps and As
p(x,y) frequencies of the joint distribution

26. Mutual information based on Present/Absent
Step 3: Use a threshold: probes X and Y are correlated if:
MI(X, Y) >1/n * log(1/P)
n: number of chips.
P: 1/p^2 (with p number of probes).
“A simple method for reverse engineering causal networks”
M. Andrecut and S. A. Kauffman
J. Phys. A: Math. Gen. 39 No 46.

27. Try Pearson method in Stembase!
Implemented by Reatha Sandie