1. Genetical Genomics in the Mouse
Finding Genes with Microarray Expression Data

2. Genetical Genomics
Jansen, R.C. and J.P. Nap (2001). Genetical genomics: the added value from segregation. Trends Genet 17(7):

3. Mouse Genetical Genomics
BXD recombinant inbred lines
21 strains + parents and F1
genotypes
508 markers
traits
forebrain RNA assayed by Affymetrix U74Av2
PM probe sequences
MM probe sequences
1 to 4 microarrays per RI line (average 2.5)

4. QTL mapping by regression
Trait vs genotype association
Genetically determined difference
in expressed RNA level
in hybridization of probe sequence
in competing hybridization
Measured by LRS (likelihood ratio statistic)

5. BXD Marker Distribution
Distribution of 508 markers on the BXD genome. Marker location (recombination-based map distance) is plotted against marker number across the whole genome, and the location of the most proximal marker on each chromosome is given a location of 0. If markers were perfectly evenly distributed, they would form straight parallel lines with no gaps.

6. Trait Data Preparation
12,422 probesets (traits)
16 PM & 16 MM probes (oligonucleotides)
average PM-MM difference
log2-transform average difference
normalize data of each microarray to common mean and standard deviation
average replicate microarrays
400,000 PM & MM probes (cells)
log2-transform cell intensity
normalize and average replicate arrays
Log-transformed data was normalized by subtracting the chip mean from each value, multiplying by (2/chip standard deviation), then adding 8. This gives values with a chip mean of 8.0 and a chip standard deviation of 2. Values from replicate chips were then averaged.

7. Multiple testing problem
Two levels of multiple testing
Each trait or probe vs 508 loci
12,422 traits or 400,000 probes
Strategy
Empirical p-value for multiple loci
measures significance of single best association
Benjamini-Hochberg procedure for multiple traits or probes
may declare many significant associations
assumes at least one significant association
There are two levels of multiple testing in this analysis and we use different methods for dealing with each one. To handle the fact the we are testing multiple loci, we choose the single best association from each genome scan and establish its p-value by comparing it with a distribution of p-values generated by a permutation test. This converts the multiple test into a single test of the maximum p-value against the appropriate null distribution. To handle the multiple trait tests, we apply a Benjamini-Hochberg procedure to the p-values from each test. This test applies graduated significance threshold; the most significant cases are tested stringently, but as more cases are declared significant, the test becomes more lenient. The Benjamini-Hochberg method has one potential trap; it assumes that at least one case will be declared significant.

8. Empirical p-value Measures genome-wide significance
converts multiple test into single test
significance of best association among all loci
Permutation test for distribution under null
up to 106 scans with permuted trait values
record largest LRS for each permutation
Find p-value of original regression from its rank in the null distribution

9. Outliers Examine permutation test distribution for bimodality
Compare 37th and 95th percentile values
Find outlier and assign next most extreme value
Redo permutation test and regression
Among probeset data, about 5% of cases are corrected for an outlier. Among analyses with individual probes, about 12% of cases are corrected, but among individual probes declared significant, the rate is about 4%.

10. Benjamini-Hochberg test
Test of 100 uniformly distributed p-values (p-values from non-significant results)
P-values as blue dots
Significance threshold for FDR = 0.2 as red line
An idealized experiment in which 100 cases, none of which are significant, are tested with the Benjamini-Hochberg procedure, controlling the false discovery rate at 20%. The blue dots are the ranked p-values from the 100 cases, and the red line is the significance threshold established by the Benjamini-Hochberg procedure. None of the cases can be declared significant.

11. Benjamini-Hochberg test
Test of 10 low p-values (significant results) mixed with 90 p-values from non-significant results
P-values as blue dots
Significance threshold for FDR = 0.2 as red line
Eleven cases declared significant
Declare significant
An idealized experiment in which 10 cases with significantly low p-values are mixed with 90 cases that are not significant. All cases can be declared significant up to the highest-ranked case that falls below the significance threshold.

12. Empirical P-value Calculation
500x Permutation test
Marker regression mapping ?
p-value
5000x Perm
Maximum genome-wide LRS ?
p-value
50000x Perm ?
p-value
x Perm
p-value

13. Trait-locus associations
Ranked P-values as blue dots (90 smallest from 12,422)
Significance threshold as red line
Cases below red line are significant for FDR = 0.2
75 significant trait-locus associations
Sorted p-values from about 12,000 QTL scans with microarray trait data. In the figure, blue dots show p-value plotted against rank. The red line shows the significance threshold established by the Benjamini-Hochberg procedure for a false discovery rate of 20%, declaring 75 trait-locus associations as significant.

14. Probe-locus associations
Ranked P-values as blue dots (600 smallest from ~400,000)
Significance threshold as red line
Cases below red line are significant for FDR = 0.2
576 significant probe-locus associations
Sorted p-values from about 400,000 QTL scans with data from individual microarray cells. In the figure, blue dots show p-value plotted against rank. The red line shows the significance threshold established by the Benjamini-Hochberg procedure for a false discovery rate of 20%, declaring 576 cell-locus associations as significant. P-values up to a rank of 419 are established by 106 permutations; beyond that, most p-values are established by 50,000 permutations.

15. QTLs from MM probes 576 QTLs defined by single microarray probes
454 (79%) by PM probes
122 (21%) by MM probes
Proportion of PM probes QTLs declines as p-value increases A B C
The 576 QTLs defined by single-cell QTL mapping include both QTLs defined by match cells and QTLs defined by mismatch cells. Overall, 79% of the QTLs are defined by match cells. The figure shows a moving-window average of the proportion of cell QTLs defined by match cells across cases ranked by increasing p-value. The proportion of QTLs defined by match cells for those with the smallest p-values (the most significant associations).
The larger deviations from linearity may be artifacts of the fact that the data were sorted both by p-value and by LRS and the fact that p-values were defined by differnet numbers of permutations. Three lettered regions in the figure show how these conditions apply. Cases in region A had p-values that were less than 10-6 and not well defined; in this region cases were sorted by likelihood ratio statistic. Cases in regions A & B had p-values established with 1,000,000 permutations; those in region C were mostly established with 50,000 permutations.

16. QTLs from cell-level mapping
576 cell-marker associations (QTLs)
339 traits (probesets) represented
most probesets represented by a single probe
rarely, two or more significant probes from same probeset
all probes from one probeset identify same locus
79% of probes are PM

17. QTLs from PM cells only 454 PM cells defining QTLs
288 traits (probesets) represented
184 controlled by location on the same chr
88 controlled by location on different chr
16 unknown location for probeset
147 locations (marker loci) with nearby QTLs, distributed on all chromosomes

18. Probe-locus associations among traits
339 traits (probesets) with probes identifying significant QTLs
186 traits represented by a single probes
2 traits represented by 10 probes

19. QTL distribution among marker loci
147 loci identified by at least one significant probes-locus association
multiple associations to one locus
multiple probes from one probeset
multiple QTL near locus
This chart shows the distribution of QTLs among marker loci, where each marker locus represents the QTLs near it. Of the 508 loci distinguishable in this data set, 147 have at least one QTL nearby and 67 have exactly one QTL nearby.

20. Profiles of probe sensitivity
Li and Wong reported a year and a half ago that different probes within a probeset differed greatly in their ability to detect the target sequence for which they were designed.
Li, C & Wong, WH (2001) Model-based analysis of oligonucleotide arrays: Expression index computation and outlier detection. PNAS 98: 31-36

21. Probe profiles (best) LRS vs probe number
Probesets with highest significance in probeset-level mapping
Comparison of probe-level mapping and probeset-level mapping. The four probesets were among the most significant of the 74 declared significant by probeset-level mapping. The charts show LRS for each probe as a function of probe number.
Circled probes were significant when tested as single probes. Note that one MM probe has a higher LRS than the corresponding PM probe and that both achieved significance as single probes. For each probesets, significant probes (including MM probes) had regression coefficients of the same sign; coefficients were positive for 93269, negative for the others
PM MM

22. Probe profiles (worst)
LRS vs probe number
Probesets with lowest significant association in probeset-level mapping
Comparison of probe-level mapping and probeset-level mapping. The four probesets were among the least significant of the 74 declared significant by probeset-level mapping. The charts show LRS for each probe as a function of probe number. The LRS scores are generally lower than those on the previous slide and MM probe sometimes has stronger association than the PM probe. None of these probes achieved significant LRS scores when tested as single probes.
PM MM

23. Distribution of controlled loci
Distribution across chromosomes of 256 probes detecting a QTL (having a significant association with a marker locus). “Syn” and “Nonsyn” indicate those probes for which the detected QTL is syntenic and nonsyntenic, respectively. The number of probes on each chromosome is normalized to the approximate genetic length of the chromosome, with syntenic and nonsyntenic cases normalized separately. Lengths used, from L. Silver, “Mouse Genetics”, are:
107, 107, 85, 85, 107, 77, 77, 85, 77, 77, 77, 68, 77, 68, 68, 68, 55, 55, 55, 77
for chrs 1 through X, respectively.

24. Distribution of controlling loci
Distribution across chromosomes of 272 QTLs. Sixteen QTLs for which the probe location is unknown are included in the nonsyntenic class. Frequencies are normalized to chromosome length as on the previous slide. Chr 9 appears to have a higher frequency of nonsyntenic QTLs than any other chromosome. Of the 21 sequences affected by chr 9 QTLs, 18 are distributed across 11 chromosomes and 3 have unknown locations.

25. Chr 9 QTLs
Unusual number of chr 9 QTLs (22) controlling sequences on other chrs
Normalized frequency 3-fold greater than average chr
Many of these QTLs cluster near 2 loci on chr 9

26. Acknowledgments Jintao Wang Robert W Williams Ram Varma Jianxin Wang
Lu Lu
S Shou
Yanhua Qu
Elissa Chesler
John D Mountz
Hui Chen Hsu
David Threadgill
Gene Hwang
Dan Nettleton
Jintao Wang
Ram Varma
Jianxin Wang
Mark Brady
Gene Sobel
U Tennessee, Memphis
Gene Expression Core
Bioinformatics
U Alabama, Birmingham
GOG
U North Carolina
Cornell U
Iowa State U