Methods for identifying DNA copy number changes

A method for estimating copy number for each allele of a biallelic SNP using the following equation:

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• where the parameters of the model are estimaed using a training set of samples of known genotype and where
• Ia,m=(Ia,1m,Ia,2m, . . . ,Ia,rm, . . . ,Ia,RM);
• Ib,l=(Ib,1m,Ib,2m, . . . ,Ib,rm, . . . ,Ib,RM)
• Ca,m=(Ca,1m,Ca,2m, . . . ,Ca,rm, . . . ,Ca,RM);
• Cb,l=(Cb,1m,Cb,2m, . . . ,Cb,rm, . . . ,Cb,RM)
• Ia,m=αa0,m+αa1,mln(Ca,m+δa,m)+εa,m
• Ib,m=αb0,m+αb1,mln(Cb,m+δb,m)+εb,m
• where Ia,rm is the perfect match intensity for the A allele and Ib,rm is the perfect match intensity for the B allele of reference sample r on SNP m and Ca,rm and Cb,rm are the known copy numbers on the A and B alleles of reference sample r on SNP m.

A method of estimating in a sample the copy number of a genomic region containing a first single nucleotide polymorphism (SNP) from a plurality of SNPs, wherein each SNP in the plurality has an A and a B allele, said method comprising:

• (a) genotyping the sample using a high density genotyping array comprising a plurality of perfect match and mismatch probes for the A allele of each SNP in a plurality of SNPs (PMA and MMA) and a plurality of perfect match and mismatch probes for the B allele (PMB and MMB) to obtain a raw intensity measurement for each PMA, MMA, PMB and MMB probe for each SNP in the plurality and to obtain a genotyping call for each SNP in the plurality;
• (b) transforming each raw intensity measurement to its natural log to obtain a transformed intensity value for each probe;
• (c) normalizing the transformed intensity values using the MMB transformed intensity values for all SNPs from the plurality that are called BB in the sample to obtain normalized PMA intensities;
• (d) normalizing each PMB transformed intensity using the MMA transformed intensities for all SNPs from the plurality that are called AA in the sample to obtain normalized PMB intensities;
• (e) using a plurality of reference samples identify a set of PMA probes and a set of PMB probes for each SNP that show linear correlation between copy number and intensity;
• (f) for each SNP calculate an average of the PMA probes in the set of PMA probes and an average of the PMB probes in the set of PMB probes to obtain a PMA average intensity and a PMB average intensity for each SNP;
• (g) performing linear regression against a model equation derived from a plurality of reference samples to obtain an estimated A allele copy number and an estimated B allele copy number;
• and
• (h) adding estimated A allele copy number to the estimated B allele copy number to obtain an estimated total copy number of the genomic region.

A method for estimating the copy number of a genomic region in an experimental sample comprising:

• (a) isolating nucleic acid from the experimental sample;
• (b) fragmenting the nucleic acid sample with a restriction enzyme;
• (c) ligating an adaptor to the fragments
• (d) amplifying at least some of the adaptor ligated fragments
• (e) labeling the amplified products;
• (f) hybridizing the labeled amplified products to an array to obtain a hybridization pattern, wherein the array comprises a plurality of genotyping probe sets for a plurality of SNPs, wherein a probe set comprises:
• (i) a plurality of perfect match probes to a first allele of a SNP,
• (ii) a plurality of perfect match probes to a second allele of the SNP,
• (iii) a plurality of mismatch probes to the first allele of the SNP, and
• (iv) a plurality of mismatch probes to the second allele of the SNP,
• (g) obtaining a raw intensity measurement for each perfect match and each mismatch probe in each probe set for each SNP
• (h) calculating the natural log (ln) of the raw intensity measurement for each probe;
• (i) standardizing the natural log of the raw intensity measurement for each probe using as background the mismatch probe intensities from the opposite allele in SNPs with a genotype call homozygous for the opposite allele;
• (j) obtaining a standardized measurement for each perfect match probe by a method comprising obtaining a first background intensity by calculating an average of a plurality of B allele mismatch probes for a plurality of SNPs called homozygous A in the sample, obtaining a second background intensity by calculating an average of a plurality of A allele mismatch probes for a plurality of SNPs called homozygous B in the sample,
• (k) standardize the PMa probes so that the MMa probes for SNPs with BB genotype calls have a variance of one and a mean of zero;
• (l) standardize the PMb probes so that the mismatch B probes for homozyous A SNPs have a variance of one and a mean of zero;
• (m) select probes to be included in calculation by identifying probes that show a linear response between copy number and intensity above a threshold and calculate an average intensity across selected probes in a probe set;
• (n) perform regression analysis on the reference set mean intensities for a given probe set and genotype for each SNP;
• (o) compare the intensity of the target sample against the mean intensity values of smaples from the reference set with the same genotype call;
• (p) apply a linear regression to adjust the target intensity so that it falls on the line Y+X, perform separately on PMA and PMB probe intensities;
• (q) model copy number from the reference samples using the following equations
• ln(Ca,rm+δa,m)=γa0,m+γa1,mIa,rm+εa,rm
• ln(Cb,rm+δb,m)=γb0,m+γb1,mIb,rm+εb,rm
• (r) use the values of 65 ao,m, γa1,m, γbo,m, γb1,m, obtained in (q) to estimate copy number of the unknown sample for each allele of each SNP using the following equation
• {circumflex over (C)}a,lm=max(exp({circumflex over (γ)}a0,m+{circumflex over (γ)}a1,mIa,lm)−{circumflex over (δ)}a,lm,0) and
• {circumflex over (C)}b,lm=max(exp({circumflex over (γ)}b0,m+{circumflex over (γ)}b1,mIb,lm)−{circumflex over (δ)}b,lm,0)
• (s) perform kernel smooting on the estimated copy number applying significance with a 1 Mb window and Gaussian kernel.

A computer program product for estimating the copy number of a genomic region, the computer program product stored on a computer readable medium and configured to cause a processor to execute the steps of:

• (a) obtaining a copy number model for each allele of each SNP in a plurality of SNPs using a reference set of probe hybridization intensity data from samples of known genotypes;
• (b) estimating a reference mean and variance of allele specific probe intensity for each SNP across a subset of the reference set, wherein individuals in the subset have the same genotype at that SNP;
• (c) estimating allele-specific and total copy number for each SNP in the reference set;
• (d) using the reference mean and variance from (b) to obtain an adjusted intensity value for each SNP from an unknown sample;
• (e) using the adjusted intensity value obtained in (d) and the copy number model obtained in (a) to estimate allele-specific and total copy number for each SNP;
• (f) comparing the total copy number estimate from (e) for each SNP to the total copy number estimate from (c) to determine a significance value;
• and (g) performing kernel smoothing on the values obtained from (e) and (f) to obtain smoothed valued for allele-specific and total copy number for each SNP and total significance.

A system for identifying regions of copy number variation in a test sample comprising:

• a computer that receives a plurality of probe intensity values;
• a computer software program product to execute on the computer the method of calculating an intensity value for a first allele of a first polymorphism and an intenstiy value for a second allele of the first polymorphism using one or more of the probe intensity values associated with the polymorphism;
• normalizing the probe intensity value for the first allele using a normalization value for the first allele obtained from a reference set of samples of known genotype;
• normalizing the probe intensity value for the second allele using a normalization value fro the second allele obtained from a reference set of samples of known genotype;
• estimating copy number for said first allele;
• estimating copy number for said second allele;
• and estimating total copy number for said genomic region containing said polymorphism by combining the estimated copy number for said first allele and the estimated copy number for said second allele.