Method and system for genotyping samples in a normalized allelic space

Abstract

Aspects of the present invention describe an apparatus and method for generating genotype calls for a sample. The genotyping initially models allelic signal response into an allelic model having one or more model parameters for an identified one or more sources of systematic variation. The model and parameters are then used to transform the allelic signals to a normalized normalized allelic space that serves to compensate for the one or more sources of systematic variation. By compensating for the systematic variation in this manner, the genotype for the sample is readily determined based upon its relationship to the representation of the allelic signals in normalized allelic space and in accordance with the allelic model.

1 . A computer implemented method of generating genotype calls for a sample comprising:
 generating allelic signal response into an allelic model having one or more model parameters for an identified one or more sources of systematic variation;   transforming the allelic signals through the one or more model parameters of the allelic model to a normalized allelic space, wherein the normalized allelic space includes compensation for the one or more sources of systematic variation;   measuring a Cartesian distance from a sample included in the normalized allelic space to an expected one or more genotype coordinates, wherein the expected one or more genotype coordinates are determined from a normalized training set of genotype data;   calling a genotype for the sample that represents the shortest measured Cartesian distance between the sample and one of the expected one or more genotype coordinates.   
     
     
         2 . (canceled) 
     
     
         3 . The method of  claim 2  wherein the expected one or more genotype coordinates is selected from a set of genotype coordinates including: a homozygous allele A, a heterozygous allele AB and a homozygous allele B having corresponding coordinates (1, 0), (½, ½) and (0, 1) respectively. 
     
     
         4 . The method of  claim 1  wherein the probability distributions are based upon elliptical Gaussian probability distributions. 
     
     
         5 . The method of  claim 1  wherein the elliptical Gaussian probability distribution for the set of alleles normalized in the normalized allelic space is represented by the following equations:
   Homozygous aa ( a,b )= Fe   −(a−1)     2     /s     a       2     −(b−0)     2     /s     b       2      
   Heterozygous ab ( a,b )= Fe   −(a−1/2)     2     /s     a       2     −(b−1/2)     2     /s     b       2      
   Homozygous bb ( a,b )= Fe   −(a−0)     2     /s     a       2     −(b−1)     2     /s     b       2      Equation 8
 
 where: 
 a is a normalized allele A in the allelic space; 
 b is a normalized allele B in the allelic space; 
 s b   2  is a measure of the dimension of the ellipse along the axis of allele b in allelic space; and 
 s a   2  is is a measure of the dimension of the ellipse along the axis of allele a in allelic space. 
 
     
     
         6 . The method of  claim 1  wherein the systematic variation in allelic signals is selected from a set of systematic factors including: a sample variability, an experimental run variability and an allelic imbalance. 
     
     
         7 . The method of  claim 1  wherein the parameter associated with each source of systematic variation is modified to minimize overall variation in the allelic signals and a model of the alleles in a training population. 
     
     
         8 . The method of  claim 1  wherein the model of the alleles in the training population arc assigned a unit probability of occurrence in the allele space of homozygous and heterozygous alleles. 
     
     
         9 . The method of  claim 7  wherein the model of the alleles Aij and Bij in the training population are fit to a linear function as follows:
   γα i β j ( A   ij /δ i +δ i   B   ij )=1
 
 where: 
 A ij  and B ij  are the measured allele signals for SNP assay i and sample j 
 γis a parameter to compensate for variability in the overall run 
 α i  is a parameter to compensate for variability in the SNP assay i 
 β i  is a parameter to compensate for variability in the sample j 
 δ i  is a parameter to compensate for allele imbalance for a SNP assay i and sample j 
 
     
     
         10 . A computer program product for generating genotype calls for a sample, comprising instructions operable to cause a programmable processor to:
 generate allelic signal response into an allelic model having one or more model parameters for an identified one or more sources of systematic variation;   transform the allelic signals through the one or more model parameters of the allelic model to a normalized allelic space that serves to compensate for the one or more sources of systematic variation;   determine a genotype for the sample based upon its relationship to the representation of the allelic signals in the normalized allelic space and in accordance with the allelic model;   measure a Cartesian distance from a sample represented in the normalized allelic space to an expected one or more genotype coordinates; and   call a genotype for the sample that represents the shortest measured Cartesian distance between the sample and one of the expected one or more genotype coordinates.   
     
     
         11 . The computer program product of  claim 10  wherein the expected one or more genotype coordinates is selected from a set of genotype coordinates including: a homozygous allele A, a heterozygous allele AB and a homozygous allele B having corresponding coordinates (1, 0), (½, ½) and (0, 1) respectively. 
     
     
         12 . The computer program product of  claim 10  wherein the instructions that determine the genotype for the sample further comprises instructions when executed that,
 create a fixed prior probability distribution of normalized allele signals from a statistically significant training set of genotype data by fitting a normalized training set of genotype data to probability distributions that reflect a set of allowed genotypes in the normalized allelic space; 
 transform ordinary allelic signals through the one or more model parameters of an allelic model to the normalized allelic space that serves to compensate for the one or more sources of systematic variation; and 
 call the genotype for the sample based upon a greatest prior probability as reflected by the fitted probability distribution and applied to the sample normalized in the normalized allelic space. 
 
     
     
         13 . The computer program product of  claim 12  wherein the probability distributions are based upon elliptical Gaussian probability distributions. 
     
     
         14 . The computer program product of  claim 13  wherein the elliptical Gaussian probability distribution for the set of alleles normalized in the normalized allelic space is represented by the following equations:
   Homozygous aa ( a,b )= Fe   −(a−1)     2     /s     a       2     −(b−0)     2     /s     b       2      
   Heterozygous ab ( a,b )= Fe   −(a−1/2)     2     /s     a       2     −(b−1/2)     2     /s     b       2      
   Homozygous bb ( a,b )= Fe   −(a−0)     2     /s     a       2     −(b−1)     2     /s     b       2      Equation 8
 
 where: 
 a is a normalized allele A in the allelic space; 
 b is a normalized allele B in the allelic space; 
 s b   2  is a measure of the dimension of the ellipse along the axis of allele b in allelic space; and 
 
       s a   2  is is a measure of the dimension of the ellipse along the axis of allele a in allelic space. 
     
     
         15 . An apparatus for generating genotype calls for a sample, comprising:
 a processor; and   a memory encoded with instructions executable by the processor, the instructions including instructions for:   modeling allelic signal response into an allelic model having one or more model parameters for an identified one or more sources of systematic variation;   transforming the allelic signals through the one or more model parameters of the allelic model to a normalized allelic space that serves to compensate for the one or more sources of systematic variation; and   determining a genotype for the sample according to a clustering of allelic data signals as represented in the normalized allelic space;   measuring a relative angular offset of values for the allelic data signals in the normalized allelic space; and   calling a genotype for the sample based upon its proximity to the different angular offsets of values and their corresponding genotype classifications.   
     
     
         16 . The apparatus of  claim 15  wherein the expected one or more genotype coordinates is selected from a set of genotype coordinates including: a homozygous allele A, a heterozygous allele AB and a homozygous allele B having corresponding coordinates (1, 0), (½, ½) and (0, 1) respectively. 
     
     
         17 . The apparatus of  claim 15  wherein determining the genotype for the sample further comprises,
 means for presenting the cluster of allelic data signals in a diagram along with a confidence factor for the sample and genotype classification.