Composite interval mappingSignificance thresholds
Confidence intervalsExperimental design
Association between genotype and phenotype
Individual Marker 1 Marker 2 Marker 3 Marker 4 Marker 5 Marker 6 Phenotype
A 1 1 1 1 1 1 1 1 1 1 1 1 0.07
B 1 1 1 1 1 1 1 1 1 1 1 1 0.35
C 2 2 2 2 2 2 2 2 2 2 2 2 0.46
D 2 2 2 2 2 2 2 2 2 2 2 2 0.67
E 1 2 1 2 1 2 1 2 1 2 1 2 0.41
F 1 2 1 2 1 2 1 2 1 2 1 2 0.30
Interval mapping vs. Composite interval mapping
Interval mapping• Uses flanking marker genotypes to infer
probability of genotype at intervals between the markers
• Associates probability of genotype with phenotype
Composite interval mapping• Uses markers in addition to flanking markers to
control for QTL located elsewhere
Composite interval mapping
Composite interval mapping• Uses markers in addition to flanking markers
to control for QTL located elsewhere• including linked markers accounts for linked
QTL- improved localisation of QTL• including unlinked markers reduces variation
(noise) due to other QTL, and so increases power.
Zeng 1994; Genetics 136:1457-1468
Composite interval mapping
• There is a trade-off between estimation of QTL location (esp. if linked QTL) and power to detect QTL with small effects.
• QTL cartographer
Significance thresholds
• How do you determine whether a QTL is statistically significant?
• Problem with multiple tests• Arbitrary threshold OR• Obtain an empirical distribution for the test
statistic under the null hypothesis• Permutation tests
Permutation test• Permute genotypes/phenotypes (removes any
real association)
Individual Marker 1 Marker 2 Marker 3 Marker 4 Marker 5 Marker 6 Phenotype
A 1 1 1 1 1 1 1 1 1 1 1 1 0.07
B 1 1 1 1 1 1 1 1 1 1 1 1 0.35
C 2 2 2 2 2 2 2 2 2 2 2 2 0.46
D 2 2 2 2 2 2 2 2 2 2 2 2 0.67
E 1 2 1 2 1 2 1 2 1 2 1 2 0.41
F 1 2 1 2 1 2 1 2 1 2 1 2 0.30
Permutation test• Permute genotypes/phenotypes (removes any
real association)
Individual Marker 1 Marker 2 Marker 3 Marker 4 Marker 5 Marker 6 Phenotype
A 1 1 1 1 1 1 1 1 1 1 1 1 0.67
B 1 1 1 1 1 1 1 1 1 1 1 1 0.35
C 2 2 2 2 2 2 2 2 2 2 2 2 0.30
D 2 2 2 2 2 2 2 2 2 2 2 2 0.07
E 1 2 1 2 1 2 1 2 1 2 1 2 0.46
F 1 2 1 2 1 2 1 2 1 2 1 2 0.41
Permutation test• Permute genotypes/phenotypes (removes any
real association)
Individual Marker 1 Marker 2 Marker 3 Marker 4 Marker 5 Marker 6 Phenotype
A 1 1 1 1 1 1 1 1 1 1 1 1 0.41
B 1 1 1 1 1 1 1 1 1 1 1 1 0.67
C 2 2 2 2 2 2 2 2 2 2 2 2 0.46
D 2 2 2 2 2 2 2 2 2 2 2 2 0.35
E 1 2 1 2 1 2 1 2 1 2 1 2 0.07
F 1 2 1 2 1 2 1 2 1 2 1 2 0.30
Permutation test• Permute genotypes/phenotypes (removes any
real association)• Rerun genome-wide scan analysis, and
calculate the highest test statistic across the genome
• Repeat many times
Example
Permuted data
Distribution of test statistic by permutation
Permutation results
Traditional statistical analysis of real data
Confidence intervals
• How do you assess uncertainty in the location of a QTL?
• 1 LOD support interval– LOD-based intervals are often too narrow
• Bootstrappig
Bootstrapping• want to know what would happen if you
repeated the experiment many times• use existing data set, and use it to create new,
bootstrap, datasets by random sampling with replacement
Marker 1 Marker 2 Pheno
AA Aa 4
Aa aa 5
Aa Aa 8
AA Aa 6
aa Aa 9
Marker 1 Marker 2 Pheno
AA Aa 4
AA Aa 4
aa Aa 9
aa Aa 9
AA Aa 6
Marker 1 Marker 2 Pheno
Aa Aa 8
Aa Aa 8
Aa Aa 8
AA Aa 4
aa Aa 9
Bootstrapping• want to know what would happen if you repeated
the experiment many times• use existing data set, and use it to create new,
bootstrap, datasets by random sampling with replacement– a given observation may appear more than once– bootstrap datasets have the same sample size as the real
data set
• Repeat QTL analysis with each bootstrapped data set• Bootstrapping is more robust/ conservative
Experimental design
• Phenotyping – what phenotype to measure?– Endophenotypes
Schmidt et al. 2003 JOURNAL OF BONE AND MINERAL RESEARCH 18: 1486-1496
Experimental design
• Phenotyping – what phenotype to measure?• Type of cross
– Pedigree vs. cross– Inbred vs. outbred– F2 vs. backcross
Experimental design
• Phenotyping – what phenotype to measure?• Type of cross• Sample size and power• Beavis effect• Marker density