AlgebraicHaploPackage— The package haplotype a contingency of two pairs of snips of a sample.

Description

Assume a group of patients of an unordered pair of data per snips. The contingency table of 2 snips on diffrent positions are calculated. A haplotype 2x2 most likely contingency table is guessed.

Details

Author(s)

Jan Wolfertz.

Maintainer: jan.wolfertz@uni-duesseldorf.de

References

[1] David Clayton. "An r package for analysis of whole-genome association studies."Human Heredity, 64(1):45 - 51, 2007. doi: doi:10.1001/archgenpsychiatry.2010.25. http://archpsyc.jamanetwork.com/article.aspx?articleid=210679. [2] Nathan Jacobson. Basic Algebra I: Second Edition (Dover Books on Mathematics). Dover Publication, 2009. [3] Montgomery Slatkin Laurent Excofie. Maximum-likelihood esti-mation of molecular haplotype frequencies in a diploid population. Molecular biology and evolution, 12(5):921 - 927, 1995. URL http://mbe.oxfordjournals.org/content/12/5/921.full.pdf. [4] Tianhua Niu. Algorithms for inferring haplotypes. Genetic Epidemiology, 27:334347, 2004. doi: DOI: 10.1002/gepi.20024. URL http://biostat.gru.edu/Journal [5] Werner A. Stahel. Statistische Datenanalyse Eine. Vieweg Verlag, 2002.

Examples

print("The second example: \n")
dd=matrix(c(1212, 2, 0, 679, 0,0,75,0,0), byrow=TRUE, nrow=3)
colnames(dd)=c("CC","CT","TT")
rownames(dd)=c("CC","CT","TT")
callhaplotype(dd)
### Check the result of the cubic equation of the second example
print("##############################")
print("Check the result of the cubic equation of the second example: \n")
temp2haplo =as.numeric(t(dd));
t2h=temp2haplo
haplotypeit(t2h[1],t2h[2],t2h[3],t2h[4],t2h[5],t2h[6],t2h[7],t2h[8],t2h[9]);
rm(temp2haplo)
rm(t2h)
### Third example
print("##############################")
print("Third example : \n")
dd3=matrix(c(1030,678,123,1,1,0,0,0,0),ncol=3,byrow=TRUE)
colnames(dd3)=c("AA","AG","GG")
rownames(dd3)=c("CC","CT","TT")
callhaplotype(dd3)
###  Check for alternative solutions
print("##############################")
print("Check for alternative solutions: \n")
temp2haplo =as.numeric(t(dd3));
t2h=temp2haplo;
haplotypeit(t2h[1],t2h[2],t2h[3],t2h[4],t2h[5],t2h[6],t2h[7],t2h[8],t2h[9]);
rm(temp2haplo)
rm(t2h)
print("##############################")
print("##############################")
print("This tests the result of the first example of the article \n")
dd2=matrix(c(4,0,0,0,30,0,0,0,23),ncol=3,byrow=TRUE)
callhaplotype(dd2)
callhaplotype(dd2)/(2*57)
print("##############################")

calcultes the cotigency table of the haplotypes

Description

It starts with a contigency table of pairs of haplotypes and ends up with the haplotypes one. The heterocygote cases are the middle of the column and rows.

Usage

callhaplotype(dd)

Arguments

Details

A 2x2 contingency table of haplotypes is calculated. The most likely solution had been choosen.

Value

The haplotype contingency table is returned. All entries are numeric.

Note

The differences are the coice of the solution of the cubic equations. About 4 percent differences and about 7 assuming 1 per thousand. For data export or import you can use a different package.

Author(s)

Jan Wolfertz

References

David Clayton. "An r package for analysis of whole-genome association studies." Human Heredity, 64(1):45 - 51, 2007. doi: doi:10.1001/archgenpsychiatry.2010.25. URL http://archpsyc.jamanetwork.com/article.aspx?articleid=210679. Jan Wolfertz(in press.):""

Examples

print("###########################")
dd2=matrix(c(4,0,0,0,30,0,0,0,23),ncol=3,byrow=TRUE)
callhaplotype(dd2)
callhaplotype(dd2)/(2*57)

### The second example
print("##############################")
print("The second example: \n")
dd=matrix(c(1212, 2, 0, 679, 0,0,75,0,0), byrow=TRUE, nrow=3)
colnames(dd)=c("CC","CT","TT")
rownames(dd)=c("CC","CT","TT")
callhaplotype(dd)
print("##############################")

Function that can resolve the cubic equation numerical stable and any lower dimensional case except unsolvable cases.

Description

A*x^3+B*x^2+C*x+D=0. All coefficients had to be numeric or integers. This function calculates from 4 coefficient all possible and senfully solutions. D=0 returns no values at all. This would be a impossibel case. It returns upto 3 potential complex solutions. Less solutions are copied to get the tripple solution format.

Usage

cubic(A, B, C, D)

Arguments

Details

This function is called by haplotypeit. The results are returned as vector of the three possible solutions: output[1],output[2],output[3]. Further data for checks of the roots. p,q and the discriminat. 10 and 11 are only usable for symmetry checks.

Value

Returns cubic(A,B,C,D)[c(1:3)] roots of the at most cubic equation.

Note

Using cardenian formular, a well known method.

Author(s)

Jan Wolfertz

References

Cardans formular as in e.g. The Mathematical Gazette (1993); 77 (Nov, No 480), 354-359 (jstor) http://www.nickalls.org/dick/papers/maths/cubic1993.pdf or any other book for algebraic solutions. See also : http://de.wikipedia.org/wiki/Cardanische_Formeln and http://en.wikipedia.org/wiki/Cubic_equation

See Also

haplotypeit,callhaplotype

Examples

cubic(1,0,0,-1)[c(1:3)]
cubic(1,1,0,0)[c(1:3)]

Chose the most likely solution of the three potential onces.

Description

Starting with a 3x3 matrix, three potential haplotypes 2x2 matrices will be calculted and evaluated. The most likly one is choosen. A dicrete solution values are not enforced. This reduces increases the right prediction on real data.

Usage

findoptimal(A, B, C, D, mmorg, exact = 1e-05)

Arguments

Details

It chose the 2x2 model of haplotypes with the smallest prediction error.

Value

Author(s)

Jan wolfertz

Examples

dd2=matrix(c(4,0,0,0,30,0,0,0,23),ncol=3,byrow=TRUE)
A=c(38+0i,2+12.1655i,2-12.1655i)
B=c(0+0i,36-12.1655i,36+12.1655i)
C=c(0+0i,36-12.1655i,36+12.1655i)
D=c(76+0i,40+12.1655i,40-12.1655i)

Haplotype a 3 x 3 counting matrix.

Description

This functions recalculates the potential 2x2 haplotype matrics. It gets a 3x3 matrixs and returns a list A,B,C,D of vectors. A[1],B[1],C[1],D[1] is the first solution of the matrix. There are always three solutions.

Usage

haplotypeit(a, b, c, d, e, f, g, h, i)

Arguments

Details

The software automatically resolves the cases e=0 by circumventing the cubic equation. If the degree of the equation is lower additional copies of some solution will be made to produce the outputformat. The output format is a list of four vectors of copefficients. Each vector contains three complex numbers.

Value

output$A is a vector of length 3. output$B,Output$C, output$D is eighter of length 3. One potential solution is A[1],B[1],C[1],D[1].

Author(s)

Jan wolfertz

References

This methods refers to an article: David Clayton. An r package for analysis of whole- genome association studies. Human Heredity, 64(1):45 - 51, 2007. doi: doi:10.1001/archgenpsychiatry.2010.25. URL http://archpsyc.jamanetwork.com/article.aspx?articleid=210679.

See Also

callhaplotype

Examples

haplotypeit(4,0,0,0,30,0,0,0,23)
print("##############################")
print("This tests the cubic routine")
haplotypeit(4,0,0,0,30,0,0,0,23)
### Formated of 4 digits
print("Formated of 4 digits")
round(as.numeric(Re(haplotypeit(4,0,0,0,30,0,0,0,23)$A)),digit=4)
round(as.numeric(Re(haplotypeit(4,0,0,0,30,0,0,0,23)$B)),digit=4)
round(as.numeric(Re(haplotypeit(4,0,0,0,30,0,0,0,23)$C)),digit=4)
round(as.numeric(Re(haplotypeit(4,0,0,0,30,0,0,0,23)$D)),digit=4)
### 

Evaluate potential haplotypes.

Description

Calculate the difference of a known haplotype and the resulting unordered pair of snip pairs.

Usage

optimalfrequency(mm, mmorg)

Arguments

Details

The average squared distance to the expected result 3x3 table is used as a T statistic. The p value not to be zero is calculated. The higher the p value the more exact is the haplotype.

Value

A list of values is returned.

Author(s)

Jan wolfertz.

References

Stahel: Statistik fuer Naturwissenschaftler und Medizinier, pp. 107-120.

See Also

findoptimal