Verifying Sample Identities - Implementation - Revision history

Goncalo: /* Mathematical Details */

2010-04-29T14:25:28Z

Mathematical Details

← Older revision		Revision as of 10:25, 29 April 2010
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	<math>		<math>
	P(match) = P_{ibd} (1 - \epsilon) + (1 - P_{ibd}) ~~\epsilon~~		P(match) = P_{ibd} (1 - \epsilon) + (1 - P_{ibd}) P_A
	</math>		</math>

	<math>		<math>
	P(no match) = P_{ibd} \epsilon + (1 - P_{ibd}) (1 - ~~\epsilon~~)		P(no match) = P_{ibd} \epsilon + (1 - P_{ibd}) (1 - P_A)
	</math>		</math>

Goncalo: /* Mathematical Details */

2010-04-20T19:22:00Z

Mathematical Details

← Older revision		Revision as of 15:22, 20 April 2010
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	<math>		<math>
	P(no match) = P_{ibd} \epsilon + (1 - P_{ibd}) \epsilon ~~= \epsilon ?~~		P(no match) = P_{ibd} \epsilon + (1 - P_{ibd}) (1 - \epsilon)
	</math>		</math>

Pha: /* Mathematical Details */

2010-04-20T18:18:06Z

Mathematical Details

← Older revision		Revision as of 14:18, 20 April 2010
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	<math>		<math>
	P(no match) = P_{ibd} \epsilon + (1 - P_{ibd}) \epsilon		P(no match) = P_{ibd} \epsilon + (1 - P_{ibd}) \epsilon = \epsilon ?
			</math>

			For now, genotypeIDcheck uses:

			<math>
			P(no match) = 1 - P(match)
	</math>		</math>

Pha: /* Mathematical Details */

2010-04-13T20:24:18Z

Mathematical Details

← Older revision		Revision as of 16:24, 13 April 2010
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	<math>		<math>
	P(no match) = P_{ibd} \epsilon + (1 - P_{ibd}) \epsilon		P(no match) = P_{ibd} \epsilon + (1 - P_{ibd}) \epsilon
			</math>

			If we also wish to use heterozygous sites, rather than limiting our comparison to reference homozygous sites, we could use:

			<math>
			P(match) = P(no match) = P_{ibd} 0.5 + (1.0 - P_{ibd}) P_A
	</math>		</math>

Pha: /* Mathematical Details */

2010-04-13T20:20:51Z

Mathematical Details

← Older revision		Revision as of 16:20, 13 April 2010
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	c) Evaluate this log-sum assuming <math>P_{ibd} = 0.5</math>. This assumes we sequenced a sample that shares half the genome with the target sample, perhaps because it is a sibling or parent of the target sample.		c) Evaluate this log-sum assuming <math>P_{ibd} = 0.5</math>. This assumes we sequenced a sample that shares half the genome with the target sample, perhaps because it is a sibling or parent of the target sample.

	d) If desired, evaluate the same log-sum for other intermediate values of P_{ibd}. It may be interesting to set <math>P_{ibd} = 0.95</math> to allow for 5% of reads that are derived from a different sample, for example, due to contamination. It may be interesting to set <math>P_{ibd} = 0.05</math> to consider more distant relatives.		d) If desired, evaluate the same log-sum for other intermediate values of <math>P_{ibd}</math>. It may be interesting to set <math>P_{ibd} = 0.95</math> to allow for 5% of reads that are derived from a different sample, for example, due to contamination. It may be interesting to set <math>P_{ibd} = 0.05</math> to consider more distant relatives.

	Once the result of evaluating a), b), c) and d) are available, we can decide if the target sample has been sequenced. Sequencing the target sample will mean that the log-sum in a) is the largest. Sequencing a parent or offspring of the target sample will maximize c). Sequencing a completely incorrect sample will maximize b).		Once the result of evaluating a), b), c) and d) are available, we can decide if the target sample has been sequenced. Sequencing the target sample will mean that the log-sum in a) is the largest. Sequencing a parent or offspring of the target sample will maximize c). Sequencing a completely incorrect sample will maximize b).

	If all the log-sums are very similar, then we don't have enough information to make a clear cut decision. Typically, we thousands of genetic markers from a typical SNP chip and whole genome shotgun sequence data, most decisions should be very clear cut.		If all the log-sums are very similar, then we don't have enough information to make a clear cut decision. Typically, we thousands of genetic markers from a typical SNP chip and whole genome shotgun sequence data, most decisions should be very clear cut.

			== Implementation Details ==

			After loading genotypes, we generate a genome mask for each position. There are three outcomes of interest:

			; Known Genotypes
			: These are sites where we have a previously observed a genotype call and where we will be evaluating match / mismatch rates to determine sample identity.

			; dbSNP sites
			: These are sites that are known to vary among individuals, but for which a known genotype is not available.

			; Background sites
			: These are all other sites and can be used to estimate the <math>\epsilon</math> error rate parameter.

Pha: /* Mathematical Details */

2010-04-13T20:09:19Z

Mathematical Details

← Older revision		Revision as of 16:09, 13 April 2010
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	</math>		</math>

	For any given value of P_{ibd} we can calculate this quantity for each read that overlaps a site with a known homozygous genotype. In addition, we can take the product of this quantity across all sites examined -- because this product is likely to be very small, we actually sum the <math>log</math>s of the appropriate quantities rather than multiplying them together.		For any given value of <math>P_{ibd}</math> we can calculate this quantity for each read that overlaps a site with a known homozygous genotype. In addition, we can take the product of this quantity across all sites examined -- because this product is likely to be very small, we actually sum the <math>log</math>s of the appropriate quantities rather than multiplying them together.

	To decide if we have sequenced the correct sample, we should do the following:		To decide if we have sequenced the correct sample, we should do the following:

	a) Evaluate this log-sum assuming P_{ibd} = 1.0. This assumes that we have sequenced the target sample.		a) Evaluate this log-sum assuming <math>P_{ibd} = 1.0</math>. This assumes that we have sequenced the target sample.

	b) Evaluate this log-sum assuming P_{ibd} = 0.0. This assumes we sequenced a different sample, unrelated to the target.		b) Evaluate this log-sum assuming <math>P_{ibd} = 0.0</math>. This assumes we sequenced a different sample, unrelated to the target.

	c) ~~Evalute~~ this log-sum assuming P_{ibd} = 0.5. This assumes we sequenced a sample that shares half the genome with the target sample, perhaps because it is a sibling or parent of the target sample.		c) Evaluate this log-sum assuming <math>P_{ibd} = 0.5</math>. This assumes we sequenced a sample that shares half the genome with the target sample, perhaps because it is a sibling or parent of the target sample.

	d) If desired, evaluate the same log-sum for other intermediate values of P_{ibd}. It may be interesting to set P_{ibd} = 0.95 to allow for 5% of reads that are derived from a different sample, for example, due to contamination. It may be interesting to set P_{ibd} = 0.05 to consider more distant relatives.		d) If desired, evaluate the same log-sum for other intermediate values of P_{ibd}. It may be interesting to set <math>P_{ibd} = 0.95</math> to allow for 5% of reads that are derived from a different sample, for example, due to contamination. It may be interesting to set <math>P_{ibd} = 0.05</math> to consider more distant relatives.

	Once the result of evaluating a), b), c) and d) are available, we can decide if the target sample has been sequenced. Sequencing the target sample will mean that the log-sum in a) is the largest. Sequencing a parent or offspring of the target sample will maximize c). Sequencing a completely incorrect sample will maximize b).		Once the result of evaluating a), b), c) and d) are available, we can decide if the target sample has been sequenced. Sequencing the target sample will mean that the log-sum in a) is the largest. Sequencing a parent or offspring of the target sample will maximize c). Sequencing a completely incorrect sample will maximize b).

	If all the log-sums are very similar, then we don't have enough information to make a clear cut decision. Typically, we thousands of genetic markers from a typical SNP chip and whole genome shotgun sequence data, most decisions should be very clear cut.		If all the log-sums are very similar, then we don't have enough information to make a clear cut decision. Typically, we thousands of genetic markers from a typical SNP chip and whole genome shotgun sequence data, most decisions should be very clear cut.

Pha: /* Mathematical Details */

2010-04-13T20:03:43Z

Mathematical Details

@@ Line 34: / Line 34: @@
 <math>
 P(match) = P_{ibd} (1 - \epsilon) + (1 - P_{ibd}) \epsilon
 P(no match) = P_{ibd} \epsilon + (1 - P_{ibd}) \epsilon
 </math>

Pha: /* Mathematical Details */

2010-04-13T19:52:58Z

Mathematical Details

← Older revision		Revision as of 15:52, 13 April 2010
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	For each sample, we would like to calculate the likelihood of a set of reads assuming that we sequenced the correct sample, assuming we sequenced a sample related to the correct sample, or assuming we sequenced an incorrect sample. We would then like to flag samples where it appears likely that the wrong sample has been sequenced.		For each sample, we would like to calculate the likelihood of a set of reads assuming that we sequenced the correct sample, assuming we sequenced a sample related to the correct sample, or assuming we sequenced an incorrect sample. We would then like to flag samples where it appears likely that the wrong sample has been sequenced.

	If we have a list of bases that overlap a known genotype, we can ~~calculate~~ the probability of a ~~match or mismatch at each~~ base as:		If we have a list of bases that overlap a known genotype, we can will
			describe the probability of a matching of mismatching base using the
			following notation:

	{\| width="100%" cellspacing="1" cellpadding="1" border="1" summary="Summary of Variables Used Below"		{\| width="100%" cellspacing="1" cellpadding="1" border="1" summary="Summary of Variables Used Below"
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	\| Definition		\| Definition
	\|-		\|-
	\| A/A		\| <span class="texhtml">''A/A''</span>
	\| Previously known genotype; we only consider homozygous sites.		\| Previously known genotype; we only consider homozygous sites.
	\|-		\|-
Line 27:		Line 29:
	\| Estimate error rate for the current base in the sequence data.		\| Estimate error rate for the current base in the sequence data.
	\|}		\|}

			Then, the probabilities of interest are:

			<math>
			P(match) = P_{ibd} (1 - \epsilon) + (1 - P_{ibd}) \epsilon
			P(no match) = P_{ibd} \epsilon + (1 - P_{ibd}) \epsilon
			</math>

Pha: /* Mathematical Details */

2010-04-13T19:49:48Z

Mathematical Details

← Older revision		Revision as of 15:49, 13 April 2010
Line 21:		Line 21:
	\| Frequency of allele A in the population		\| Frequency of allele A in the population
	\|-		\|-
	\| <span class="texhtml">''P''<sub>''~~i''''b''''d~~''</sub></span>		\| <span class="texhtml">''P''<sub>''ibd''</sub></span>
	\| Probability that the sequenced sample and the target sample share a chromosome. This should be 1.0 when we have sequenced the correct sample and 0.0 if we sequence an unrelated sample. If we sequence a related sample (e.g. a parent or sibling of the target sample), we will see intermediate values.		\| Probability that the sequenced sample and the target sample share a chromosome. This should be 1.0 when we have sequenced the correct sample and 0.0 if we sequence an unrelated sample. If we sequence a related sample (e.g. a parent or sibling of the target sample), we will see intermediate values.
	\|-		\|-

Pha at 19:49, 13 April 2010

2010-04-13T19:49:15Z

← Older revision		Revision as of 15:49, 13 April 2010
Line 9:		Line 9:
	If we have a list of bases that overlap a known genotype, we can calculate the probability of a match or mismatch at each base as:		If we have a list of bases that overlap a known genotype, we can calculate the probability of a match or mismatch at each base as:

	{\| width="~~200~~" cellspacing="1" cellpadding="1" border="1" summary="Summary of Variables Used Below"		{\| width="100%" cellspacing="1" cellpadding="1" border="1" summary="Summary of Variables Used Below"
	\|+ Notation		\|+ Notation
	\|-		\|-
	\| Variable		\| Variable
	\| Definition		\| Definition
	\|-		\|-
	\| A/A		\| A/A
	\| Previously known genotype; we only consider homozygous sites.		\| Previously known genotype; we only consider homozygous sites.
	\|-		\|-
	\| <~~math~~>~~P_A~~</~~math~~>		\| <span class="texhtml">''P''<sub>''A''</sub></span>
	\| Frequency of allele A in the population		\| Frequency of allele A in the population
	\|-		\|-
	\| <~~math~~>~~P_{ibd}~~</~~math~~>		\| <span class="texhtml">''P''<sub>''i''''b''''d''</sub></span>
	\| Probability that the sequenced sample and the target sample share a chromosome. This should be 1.0 when we have sequenced the correct sample and 0.0 if we sequence an unrelated sample. If we sequence a related sample (e.g. a parent or sibling of the target sample), we will see intermediate values.		\| Probability that the sequenced sample and the target sample share a chromosome. This should be 1.0 when we have sequenced the correct sample and 0.0 if we sequence an unrelated sample. If we sequence a related sample (e.g. a parent or sibling of the target sample), we will see intermediate values.
	\|-		\|-
	\| <math>\{epsilon}</math>		\| <math>\epsilon</math>
	\| Estimate error rate for the current base in the sequence data.		\| Estimate error rate for the current base in the sequence data.
	\|}		\|}