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A Simple Method for
Computationally Inferring
Microarray Sensitivity
Toni Reverter and Brian Dalrymple
Bioinformatics Group
CSIRO Livestock Industries
Queensland Bioscience Precinct
306 Carmody Rd., St. Lucia, QLD 4067, Australia
BioInfoSummer, ANU 1-5/12/2003, Reverter
Empirical Distribution of Tags
MPSS Paper, Jongeneel et al.
PNAS 03, 100:4702
tpm
>
1
5
10
50
100
500
1,000
5,000
10,000
N Tags
(0.0)
(0.7)
(1.0)
(1.7)
(2.0)
(2.7)
(3.0)
(3.7)
(4.0)
27,965
15,145
10,519
3,261
1,719
298
154
26
7
%
100.00
54.16
37.61
11.66
6.15
1.07
0.55
0.09
0.02
MPSS Test Data
No Tags = 25,503
cDNA Noise Paper
PNAS 02, 99:14031
S1
S2
 2x2 

f ( x)  exp  
1

x


100.00
57.14
36.11
10.89
5.73
1.21
0.57
0.15
0.05
100.00
49.87
33.66
10.74
5.67
1.13
0.55
0.11
0.05
100.00
56.19
36.79
11.76
6.95
1.94
1.11
0.29
0.16
BioInfoSummer, ANU 1-5/12/2003, Reverter
Empirical Distribution of Tags
1.
Universal distribution associated
with stochastic processes of gene
expression (Kuznetsov, 2002)
2.
Framework for a mapping function:
Concentration  Signal
BioInfoSummer, ANU 1-5/12/2003, Reverter
Concentration  Signal
f ( x)  e
x
0.0
0.7
1.0
1.7
2.0
2.7
3.0
3.7
4.0
2 x2

1 x
%
100.00
56.19
36.79
11.76
6.95
1.94
1.11
0.29
0.16
Arrays 97
Signals 3,544,000
Mean 1,724
Intensity
%
>
100.0
56.4
36.6
12.1
6.7
0.9
0.4
0.2
0.1
1
280
560
2,800
5,600
28,000
40,000
55,000
65,000
BioInfoSummer, ANU 1-5/12/2003, Reverter
Sensitivity (Definition of)
References:
• Not from Confidence (1 – )
• Not from Formulae: Sn 
Kane et al. 2000
TP
1

TP  FN 1     
• More like Minimum Detectable Concentration/Activity
“The smallest concentration of radioactivity in a sample that
can be detected with a 5% Prob of erroneously detecting
radioactivity, when in fact none was present (Type I Error)
and also, a 5% Prob of not detecting radioactivity when in
fact it is present (Type II Error).”
Lemon et al. 2003
Zien et al. 2003
Brown et al. 1996
O’Malley & Deely,
2003
• If  = , then Sensitivity = Confidence
BioInfoSummer, ANU 1-5/12/2003, Reverter
Economics 101
Quantity
Supply
Demand
Market
Equilibrium !
$ Price
BioInfoSummer, ANU 1-5/12/2003, Reverter
Sensitivity (Process for)
…for a given microarray experiment:
1.
2.
3.
2 x2

1 x
From all the genes, find the intensity thresholds that define f ( x)  e
Apply these same threshold to the set of Differentially Expressed Genes.
The ratio of 2./1. Meets at the Equilibrium defining Sensitivity.
…example:
164,318 Records
6,051 Total Genes
183 Diff. Expressed Genes
x
0.0
0.7
1.0
1.7
2.0
2.7
3.0
3.7
4.0
Threshold
1
312
566
3,417
5,414
13,936
17,096
26,477
30,378
All Genes
100.00
54.16
37.61
11.66
6.15
1.07
0.55
0.09
0.02
DE
100.00
99.45
97.81
46.45
27.32
5.46
3.83
0.00
0.00
% DE
3.02
5.55
7.87
12.05
13.44
15.45
21.03
0.00
0.00
BioInfoSummer, ANU 1-5/12/2003, Reverter
…example:
All Genes
6051 x 0.0615 = 372
183 x 0.2752 = 50
50/372 = 13.44%
Cat_1 (1)
Cat_2 (5)
Cat_3 (10)
Cat_4 (50)
Cat_5 (100)
Cat_6 (500)
Cat_7 (1000)
Cat_8 (5000)
Cat_9 (10000)
100.00
54.16
37.61
11.66
6.15
1.07
0.55
0.09
0.02
DE
% DE
100.00
99.45
97.81
46.45
27.32
5.46
3.83
0.00
0.00
3.02
5.55
7.87
12.05
13.44
15.45
21.03
0.00
0.00
BioInfoSummer, ANU 1-5/12/2003, Reverter
Sensitivity (Inferential Validity)
Let
NT = N of “Total” Genes
ND = N of “Differentially Expressed” Genes (ND  NT)

nt  xi 
f (x ) 
e
%
t
N D f ( xd )
NT f ( xt )
ND
NT
 f ( xd

nd  xi 
)
ND
ND

 f ( xd )  f ( xt )
NT
Flat line (except Upper Bound)
x
1.
2.
NT
2 x2

1 x
N D f ( xd )
 f ( xt )
NT f ( xt )

nd  xi 
 xi  f ( xt ) 
nt  xi 
The relevance of f(xi) is limited to the Concentration  Signal mapping.
At equilibrium the probability of an error either way equals.
BioInfoSummer, ANU 1-5/12/2003, Reverter
Sensitivity (Mechanics for)
INPUT: (1) Gene ID – (2) Avg Intensity – (3) DE Flag
i=1
cat_nde(i) = nde
! For each category compute
cat_pde(i) = 100.0 * nde/ntot
! N and Prop of DE Genes
DO i = 2, 9
j = ntot - int(ntot*cat(i)/100.00) ! Pointer Location of threshold
m=0
! Counter for DE genes found so far
DO k = 1, ntot
IF( gene(k)%deflag > 0 )THEN
m=m+1
IF( gene(k)%intens > int(gene(j)%intens) )THEN
cat_nde(i) = nde-m+1
cat_pde(i) = 100.0*(cat_nde(i)/(ntot*(cat(i)/100.0)))
EXIT
ENDIF
ENDIF
ENDDO
WRITE(10,1000)i,cat(i),100.0*cat_nde(i)/nde,cat_pde(i)
ENDDO
BioInfoSummer, ANU 1-5/12/2003, Reverter
Sensitivity (Material for)
…from CSIRO Livestock Industries:
ARRAYS
1.
2.
3.
4.
Wool Follicles
Beef Cattle Diets
Pigs Pneumonia
M Avium ss avium
10
14
16
13
GENES
Total
DE
6,051
6,816
6,456
132
183
450
307
47
…from Non-CSIRO Livestock Industries:
5.
6.
7.
Callow et al. (2000)
Lin et al. (2002)
Lynx MPSS test data
16
2
2
6,384
320
27,007 1,350
25,503 8,284
BioInfoSummer, ANU 1-5/12/2003, Reverter
Sensitivity (Results)
BioInfoSummer, ANU 1-5/12/2003, Reverter
Sensitivity (Results)
130 tpm …..I’ve seen them worse
80 tpm …..a ball-park figure
40 tpm …..possibly real
25 tpm …..possibly optimistic
5 tpm …..as Lynx claims
BioInfoSummer, ANU 1-5/12/2003, Reverter
Sensitivity (Inferential Validity)
 < 
Not many DE genes
High Confidence
Few False +ve
 = 
 > 
Lots of DE genes
High Power
Few False -ve
BioInfoSummer, ANU 1-5/12/2003, Reverter
Sensitivity (Conclusions)
1. We are looking at the Sensitivity of the Experiment,
not the Sensitivity of the Microarray Technology.
2. The proposed method is Very Simple and Very Fast.
3. Results acceptable but could be affected by:
a.
b.
c.
d.
e.
N Arrays in a given experiment
Quality of the Arrays themselves
Quality of the RNA extracted
Statistical approach to identify DE
Degree of Dissimilarity between samples
4. The impact of (3.a … 3.e) is not necessarily bad.
BioInfoSummer, ANU 1-5/12/2003, Reverter
Acknowledgements
Beef and Meat
Quality CRC
Sheep Industry CRC
Christian D. Haudenschild
Lynx Therapeutics, Inc.
Innovative Dairy
Products CRC
BioInfoSummer, ANU 1-5/12/2003, Reverter