1. Evaluation of power for linkage disequilibrium mapping2 4
Basics 2: p-value, power, df=1
Power when surrogate marker is used.
When a table of df=2 is tested with a test of df=1;
eg. Additive test on 2x3 tables in case-control association studies with SNPs.
p-value
power
Yamada, R., Terao C., Kawaguchi T., Narahara, M.
(2)Unit of Statistical Genetics, Center for Genomic Medicine, Kyoto University, Kyoto, Japan
September 18-20, 2011 Strasbourg, Germany(IGES 2011)
Probability
Probability
we appreciate any comments or questions on this poster :
Power when the null hypothesis is tested compared with an alternative hypothesis of df=1.
When a surrogate marker is used to test, the cut-off line is oblique to the direction to the true alternative hypothesis.
SUMMARY 1
Basics 1: Multiple df=1 tests on NxM table
Statistics
Statistics
When cut-off value of null-hypothesis test is equal to the value of alternative hypothesis
Genetic factors of various diseases have been studied with SNP chips and next generation sequencing technology is now being utilized for the purpose. Although polymorphic and potentially affecting markers distribute along the chromosomes with relatively even density in the studies with SNP chips and sequence data, the number of markers and their density as well as linkage disequilibrium pattern in each gene or locus varies substantially.
In this poster we propose a novel method which handles multiple marker tests for a set of categorical phenotypes in the context of geometric statistics so that we are abele to estimate power when multiple tests are applied to identify association between a locus with multiple markers and a phenotype that might have multiple surrogating phenotype-related criteria. First of all, we introduced a method to define multiple tests in a higher dimensional space. Secondly, we studied power when one surrogating marker was applied with our geometric approach. Thirdly, we designed models of condition of multiple tests and evaluated the effect of relation between the power and pattern of linkage disequilibrium. The result suggested some loci with higher variation in linkage disequilibrium might have several times higher power than less variable loci.
LD mapping for case-control association studies.
N: No. samples
M: No. SNPs
N x M table is observed.
M tests are applied to the N x M table.
Observations in the shape of NxM table can be expressed in df-dimensional space.
All df=1 tests on the table are directions in the space.
power = 0.5
Cumulative Prob.
Probability
Statistics
Statistics 3
Power is higher, when df is larger:
in case of df=2
Prob of blue area = 0.5
Power =Prob of blue area < 0.5
Alternative hypothesis
Cut-off
TAKE-HOME MESSAGES
Dimension of data affects on the way surrogate markers influences on the power of tests.
When the dimension is higher, weaker correlation between surrogate markers and the true marker increases the power.
When surrogate markers correlate with the true marker in higher variation in terms of the strength and the direction, the power gets higher.
Angle
Surrogate
Truth
Power π 2
Power is measured geometrically, when surrogate marker is used.
Prob of blue area = 0.5
Power =Prob of blue area > 0.5
0.5
Angle between “TRUTH” and “SURROGATE” 5
Comparison of powers when 1, 2 or infinite surrogate markers are tested together with the test in the direction of alternative hypothesis. 6
Dimensions = dfs and power and best angle to maximize power
Power is the sum of probability of observations outside of the 3-dimensional figures.
Visual image of the borders when df=3
Direction of alternative hypothesis a b a
b-1
b-2
Infinite ... ie. df=2
Two surrogates
One surrogate
Best angle to increase power
Angle between “TRUTH” and “SURROGATE” π 2
Angle a
b-2
Horizontal lines :
Curves :
dfs: 64 32 16 8 4 2
df=4
Finer coverage with more markers increases power.
b-3
The best angle is wider when No. marker gets more.
With higher df = dimension, power increases and the best angle gets wider.
Angle
Surrogate
Truth π 2
Angle
Power 7
Multi-marker coverage and LD plot π 2
b-3
b-2