Transcript Significance analysis of microarrays (SAM)

Significance analysis of microarrays
(SAM)
•
SAM can be used to pick out significant
genes based on differential expression
between sets of samples.
Currently implemented for the following
designs:
-
two-class unpaired
two-class paired
multi-class
censored survival
one-class
SAM
• SAM gives estimates of the False Discovery Rate
(FDR), which is the proportion of genes likely to
have been wrongly identified by chance as being
significant.
• It is a very interactive algorithm – allows users to
dynamically change thresholds for significance
(through the tuning parameter delta) after looking
at the distribution of the test statistic.
SAM designs
Two-class unpaired: to pick out genes whose
mean expression level is significantly
different between two groups of samples
(analogous to between subjects t-test).
Two-class paired: samples are split into two
groups, and there is a 1-to-1
correspondence between an sample in
group A and one in group B (analogous to
paired t-test).
SAM designs
Multi-class: picks up genes whose mean
expression is different across > 2 groups of
samples (analogous to one-way ANOVA)
Censored survival: picks up genes whose
expression levels are correlated with duration
of survival.
One-class: picks up genes whose mean
expression across experiments is different
from a user-specified mean.
SAM Two-Class Unpaired
1. Assign experiments to two groups, e.g., in the expression matrix
below, assign Experiments 1, 2 and 5 to group A, and
experiments 3, 4 and 6 to group B.
Group A
Exp 1 Exp 2 Exp 3 Exp 4 Exp 5 Exp 6
Exp 1 Exp 2 Exp 5
Gene 1
Gene 1
Gene 2
Gene 2
Gene 3
Gene 3
Gene 4
Gene 4
Gene 5
Gene 5
Gene 6
Gene 6
2. Question: Is mean expression level of a gene in group A
significantly different from mean expression level in group B?
Group B
Exp 3
Exp 4 Exp 6
SAM Two-Class Unpaired
Permutation tests
i) For each gene, compute d-value (analogous to t-statistic). This is
the observed d-value for that gene.
ii) Rank the genes in ascending order of their d-values.
iii) Randomly shuffle the values of the genes between groups A and B,
such that the reshuffled groups A and B respectively have the same
number of elements as the original groups A and B. Compute the
d-value for each randomized gene
Group A
Group B
Exp 1 Exp 2 Exp 5
Exp 3
Exp 4 Exp 6
Original grouping
Gene 1
Group A
Exp 3 Exp 2
Gene 1
Group B
Exp 6
Exp 4 Exp 5 Exp 1
Randomized grouping
SAM Two-Class Unpaired
iv) Rank the permuted d-values of the genes in ascending order
v) Repeat steps iii) and iv) many times, so that each gene has many
randomized d-values corresponding to its rank from the observed
(unpermuted) d-value. Take the average of the randomized d-values
for each gene. This is the expected d-value of that gene.
vi) Plot the observed d-values vs. the expected d-values
“Observed d = expected d” line
SAM Two-Class Unpaired
Significant negative genes
(i.e., mean expression of group A > mean
expression of group B)
Significant positive genes
(i.e., mean expression of group B >
mean expression of group A)
The more a gene deviates
from the “observed =
expected” line, the more
likely it is to be
significant. Any gene
beyond the first gene in
the +ve or –ve direction
on the x-axis (including
the first gene), whose
observed exceeds the
expected by at least delta,
is considered significant.
SAM Two-Class Unpaired
For each permutation of the data, compute the
number of positive and negative significant
genes for a given delta as explained in the
previous slide. The median number of
significant genes from these permutations is
the median False Discovery Rate.
The rationale behind this is, any genes
designated as significant from the randomized
data are being picked up purely by chance (i.e.,
“falsely” discovered). Therefore, the median
number picked up over many randomizations
is a good estimate of false discovery rate.