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Calculation of MAX test P value with geometric characterization of 2x3 table tests. 2010 Joint Statistical Meetings Vancouver, Canada 2010/08/05 Ryo Yamada Kyoto Univ. Kyoto Japan. Case-Control x MM,Mm,mm genotypes Genetic models Dominant Recessive Somewhere between them. - PowerPoint PPT Presentation
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Calculation of MAX test P value with geometric characterization of
2x3 table tests
2010 Joint Statistical Meetings Vancouver, Canada2010/08/05
Ryo YamadaKyoto Univ. Kyoto Japan
• Expected values determine shape of ellipsoid
Pearson’s chi-sq values draws ellipsoid contour lines,
which can be spherized
Tables on a contour line have the same statistic value
Spherization
Spherization
Any test of 1 df is a plane tangent to the ellipsoid or the spher
e• Tables with the same Psn’s chi-sq are ellipsoid/sphere.• Tables with the same stat value of test of 1 df are a plan
e.
Any test of 1 df = a vector in the space
a
b
• In the spherized coordinate, the radius to the tangent point is perpendicular to the plane.
• In the coordinate with ellipsoid, NOT perpendicular.
Test Vector
Tangent point to the smaller
sphere.
MAX3 test for 2x3 table• 3 tests of 1 df in matrix-form and vector-form
– Find tangent points for three test planes.
dom
recadd
To which model fit most?It depends where the observed
table locates.
DominantDominant
Recessive
Recessive
Additive
Additive
How to integrate?
• For 2x3 tables (df=2),
• Sum of the probabilities in evenly spaced multiple directions gives the good approximation of the integral.
How to integrate?
• For NxM tables (df=(N-1)x(M-1)),
• Sum of the probabilities in evenly spaced multiple directions gives the good approximation of the integral.
How to integrate?
• For NxM tables (df=(N-1)x(M-1)),
• Sum of the probabilities in evenly spaced multiple directions gives the good approximation of the integral.
How to integrate?
• For NxM tables (df=(N-1)x(M-1)),
• Sum of the probabilities in randomly spaced multiple directions gives the good approximation of the integral.
How to integrate?
• For NxM tables (df=(N-1)x(M-1)),
• Sum of the probabilities in randomly spaced multiple directions gives the good approximation of the integral.
P-value estimation using random points on the sphere fits well with
the permutation method
Black : Permutation
Red : Sphere method
• Collaborators– Graduate school of Medicine, Kyoto University, Kyoto, Japan
• Takahisa Kawaguchi• Katsura Hirosawa• Meiko Takahashi• Fumihiko Matsuda
– Lab for Autoimmune Diseases, CGM, RIKEN, Yokohama, Japan• Yukinori Okada• Yuta Kochi• Akari Suzuki• Kazuhiko Yamamoto
R code and web-based calculator of the method for 2x3 table presented are available at;
http://www.genome.med.kyoto-u.ac.jp/wiki_tokyo/index.php/Estimate_of_P-value_of_MAX_for_2x3_tables
Comments and questions are welcome → [email protected]