<p>The benefit to additional samples is seen in your point 1. The likelihood of making a variant call is a function of (1) the depth of coverage supporting a given variant (ignoring mapping/base quality considerations) and (2) the likelihood of that variant existing given background knowledge. With low depth and no background knowledge, poorly covered variants will be assumed to be sequencing errors. Adding more samples can just serve then to increase the background knowledge on a position.</p>

CC BY-SA 3.0
2017-05-18T11:35:26.060Z
Thanks Devon, the question specifically targets genotyping i.e. you already have to think that there is a variant there.
llevar
CC BY-SA 3.0
2017-05-17T13:13:18.863Z
2017-05-17T13:13:18.863Z
Devon Ryan
<p>Say you are sequencing to 2X coverage. Suppose at a site, sample S has one reference base and one alternate base. It is hard to tell if this is a sequencing error or a heterozygote. Now suppose you have 1000 other samples, all at 2X read depth. One of them has two ALT bases; 10 of them have one REF and one ALT. It is usually improbable that all these samples have the same sequencing error. Then you can assert sample S has a het. Multi-sample calling helps to increase the sensitivity of not so rare SNPs. Note that what matters here is the assumption of error independency. Ancestry only has a tiny indirect effect.</p>

<p>Multi-sample calling penalizes very rare SNPs, in particular singletons. When you care about variants only, this is for good. Naively combining single-sample calls yields a higher error rate. Multi-sample calling also helps variant filtering at a later stage. For example, for a sample sequenced to 30X coverage, you would not know if a site at 45X depth is caused by a potential CNV/mismapping or by statistical fluctuation. When you see 1000 30X samples at 45X depth, you can easily know you are looking at a CNV/systematic mismapping. Multiple samples enhance most statistical signals.</p>

<p>Older methods pool all BAMs when calling variants. This is necessary because a single low-coverage sample does not have enough data to recover hidden INDELs. However, this strategy is not that easy to massively parallelized; adding a new sample triggers re-calling, which is very expensive as well. As we are mostly doing high-coverage sequencing these days, the old problem with INDEL calling does not matter now. GATK has this new single-sample calling pipeline where you combine per-sample gVCFs at a later stage. Such sample combining strategy is perhaps the only sensible solution when you are dealing with 100k samples.</p>

<p>The so-called haplotype based variant calling is a separate question. This type of approach helps to call INDELs, but is not of much relevance to multi-sample calling. Also, of the three variant callers in your question, only GATK (and Scalpel which you have not mentioned) use assembly at large. Freebayes does not. Platypus does but only to a limited extent and does not work well in practice.</p>

<p>I guess what you really want to talk about is imputation based calling. This approach further improves sensitivity with LD. With enough samples, you can measure the LD between two positions. Suppose at position 1000, you see one REF read and no ALT reads; at position 1500, you see one REF read and two ALT reads. You would not call any SNPs at position 1000 even given multiple samples. However, when you know the two positions are strongly linked and the dominant haplotypes are REF-REF and ALT-ALT, you know the sample under investigation is likely to have a missing ALT allele. LD transfers signals across sites and enhances the power to make correct genotyping calls. Nonetheless, as we are mostly doing high-coverage sequencing nowadays, imputation based methods only have a minor effect and are rarely applied.</p>

CC BY-SA 3.0
2017-05-18T11:16:23.740Z
Thanks, a few followups (broken out over several comments):

Top paragraph sounds more like variant calling than genotyping, which is somewhat infeasible in context of large scale high-coverage studies or ongoing clinical-focused sequencing. Do you see same logic applying to genotyping i.e. conditional on there being a variant at the locus? What I'm struggling with is understanding, batch effect detection aside, why we would trust information on AFS from a somewhat arbitrary collection of samples (genetically speaking) more than a large sample resource like gnomAD?
llevar
CC BY-SA 3.0
2017-05-18T11:18:16.403Z
I don't understand why " Naively combining single-sample calls yields a higher error rate. " Can you elaborate or provide an example, in the context of genotyping?
llevar
CC BY-SA 3.0
2017-05-18T11:32:46.813Z
wrt. to haplotype or assembly-based calling it's simply a reflection of the fact that best methods seem to reason over a region around a locus not just the locus itself, and me trying to figure out where in such a method information from multiple samples can be used. Specifically in the context of  high coverage whole genome sequencing where multiple batches of samples are periodically arriving for analysis and there isn't necessarily a final sample size .
llevar
CC BY-SA 3.0
2017-05-18T11:36:05.407Z
Top paragraph is about deciding the *genotype* of sample S - it's genotyping. When you know the site allele frequency (AFS is the wrong wording here) in a larger population, you have a better prior. This prior is less accurate across populations, but better than a wright fisher prior. All these theories are only useful to lowCov. For highCov, genotype likelihood has a much bigger effect than prior and cross-sample information.
user172818
CC BY-SA 3.0
2017-05-18T11:37:48.507Z
For the rest, you should ask separate questions. Pooling multiple topics under this one question is hard for you, for me and for readers to comprehend.
user172818
CC BY-SA 3.0
2017-05-18T11:53:43.463Z
Anyway... On assembly-based calling, I already said it has little to do with multi-sample calling. On combining single-sample calls, I already explained in the top paragraph that jointly considering multiple samples helps genotyping – which means not using the info hurts genotyping. BTW, the body of your question is mixing variant calling and genotyping (e.g. FDR is about variant calling), which is causing confusion to me and to Devon below.
user172818
CC BY-SA 3.0
2017-05-17T14:08:21.663Z
2017-05-17T14:08:21.663Z
user172818
<p>I am trying to understand the benefits of joint genotyping and would be grateful if someone could provide an argument (ideally mathematically) that would clearly demonstrate the benefit of joint vs. single-sample genotyping.</p>

<p>This is what I've gathered from other resources (Biostars, GATK forums, etc.)</p>

<ul>
<li>Joint-genotyping helps control FDR because errors from individually genotyped samples are added up, and amplified when merging call-sets (by Heng Li on <a href="https://www.biostars.org/p/10926/" rel="noreferrer">https://www.biostars.org/p/10926/</a>)</li>
</ul>

<p>If someone understands this, can you please clarify what is the difference on the overall FDR rate between the two scenarios (again, with an example ideally)</p>

<ul>
<li>Greater sensitivity for low-frequency variants - By sharing information across all samples, joint calling makes it possible to “rescue” genotype calls at sites where a carrier has low coverage but other samples within the call set have a confident variant at that location. (from <a href="https://software.broadinstitute.org/gatk/documentation/article.php?id=4150" rel="noreferrer">https://software.broadinstitute.org/gatk/documentation/article.php?id=4150</a>)</li>
</ul>

<p>I don't understand how the presence of a confidently called variant at the same locus in another individual can affect the genotyping of an individual with low coverage. Is there some valid argument that allows one to consider reads from another person as evidence of a particular variant in a third person? What are the assumptions for such an argument? What if that person is from a different population with entirely different allele frequencies for that variant?</p>

<p>Having read several of the papers (or method descriptions) that describe the latest haplotype-aware SNP calling methods (HaplotypeCaller, freebayes, Platypus) the overall framework seems to be:</p>

<ul>
<li><ol>
<li>Establish a prior on the allele frequency distribution at a site of interest using one (or combination) of: non-informative prior, population genetics model-based prior like Wright Fisher, prior based on established variation patterns like dbSNP, ExAC, or gnomAD.</li>
</ol></li>
<li><ol start="2">
<li>Build a list of plausible haplotypes in a region around the locus of interest using local assembly.</li>
</ol></li>
<li><ol start="3">
<li>Select haplotype with highest likelihood based on prior and reads data and infer the locus genotype accordingly.</li>
</ol></li>
</ul>

<p>At which point(s) in the above procedure can information between samples be shared or pooled? Should one not trust the AFS from a large-scale resource like gnomAD much more than the distribution obtained from other samples that are nominally party of the same "cohort" but may have little to do with each other because of different ancestry, for example?</p>

<p>I really want to understand the justifications and benefits offered by multi-sample genotyping and would appreciate your insights.    </p>

<genotyping><gatk>
Single-sample vs. joint genotyping
# Single-sample vs. joint genotyping

(Asked by: username_0 on 2017-05-17)

I am trying to understand the benefits of joint genotyping and would be grateful if someone could provide an argument (ideally mathematically) that would clearly demonstrate the benefit of joint vs. single-sample genotyping.

This is what I've gathered from other resources (Biostars, GATK forums, etc.)

* Joint-genotyping helps control FDR because errors from individually genotyped samples are added up, and amplified when merging call-sets (by Heng Li on <https://www.biostars.org/p/10926/>)

If someone understands this, can you please clarify what is the difference on the overall FDR rate between the two scenarios (again, with an example ideally)

* Greater sensitivity for low-frequency variants - By sharing information across all samples, joint calling makes it possible to “rescue” genotype calls at sites where a carrier has low coverage but other samples within the call set have a confident variant at that location. (from <https://software.broadinstitute.org/gatk/documentation/article.php?id=4150>)

I don't understand how the presence of a confidently called variant at the same locus in another individual can affect the genotyping of an individual with low coverage. Is there some valid argument that allows one to consider reads from another person as evidence of a particular variant in a third person? What are the assumptions for such an argument? What if that person is from a different population with entirely different allele frequencies for that variant?

Having read several of the papers (or method descriptions) that describe the latest haplotype-aware SNP calling methods (HaplotypeCaller, freebayes, Platypus) the overall framework seems to be:

* 1. Establish a prior on the allele frequency distribution at a site of interest using one (or combination) of: non-informative prior, population genetics model-based prior like Wright Fisher, prior based on established variation patterns like dbSNP, ExAC, or gnomAD.
* 2. Build a list of plausible haplotypes in a region around the locus of interest using local assembly.
* 3. Select haplotype with highest likelihood based on prior and reads data and infer the locus genotype accordingly.

At which point(s) in the above procedure can information between samples be shared or pooled? Should one not trust the AFS from a large-scale resource like gnomAD much more than the distribution obtained from other samples that are nominally party of the same "cohort" but may have little to do with each other because of different ancestry, for example?

I really want to understand the justifications and benefits offered by multi-sample genotyping and would appreciate your insights.

**Tags:** genotyping, gatk

---

## 2 answers

### Answer by username_2 on 2017-05-17. Score: 10 | Accepted answer

Say you are sequencing to 2X coverage. Suppose at a site, sample S has one reference base and one alternate base. It is hard to tell if this is a sequencing error or a heterozygote. Now suppose you have 1000 other samples, all at 2X read depth. One of them has two ALT bases; 10 of them have one REF and one ALT. It is usually improbable that all these samples have the same sequencing error. Then you can assert sample S has a het. Multi-sample calling helps to increase the sensitivity of not so rare SNPs. Note that what matters here is the assumption of error independency. Ancestry only has a tiny indirect effect.

Multi-sample calling penalizes very rare SNPs, in particular singletons. When you care about variants only, this is for good. Naively combining single-sample calls yields a higher error rate. Multi-sample calling also helps variant filtering at a later stage. For example, for a sample sequenced to 30X coverage, you would not know if a site at 45X depth is caused by a potential CNV/mismapping or by statistical fluctuation. When you see 1000 30X samples at 45X depth, you can easily know you are looking at a CNV/systematic mismapping. Multiple samples enhance most statistical signals.

Older methods pool all BAMs when calling variants. This is necessary because a single low-coverage sample does not have enough data to recover hidden INDELs. However, this strategy is not that easy to massively parallelized; adding a new sample triggers re-calling, which is very expensive as well. As we are mostly doing high-coverage sequencing these days, the old problem with INDEL calling does not matter now. GATK has this new single-sample calling pipeline where you combine per-sample gVCFs at a later stage. Such sample combining strategy is perhaps the only sensible solution when you are dealing with 100k samples.

The so-called haplotype based variant calling is a separate question. This type of approach helps to call INDELs, but is not of much relevance to multi-sample calling. Also, of the three variant callers in your question, only GATK (and Scalpel which you have not mentioned) use assembly at large. Freebayes does not. Platypus does but only to a limited extent and does not work well in practice.

I guess what you really want to talk about is imputation based calling. This approach further improves sensitivity with LD. With enough samples, you can measure the LD between two positions. Suppose at position 1000, you see one REF read and no ALT reads; at position 1500, you see one REF read and two ALT reads. You would not call any SNPs at position 1000 even given multiple samples. However, when you know the two positions are strongly linked and the dominant haplotypes are REF-REF and ALT-ALT, you know the sample under investigation is likely to have a missing ALT allele. LD transfers signals across sites and enhances the power to make correct genotyping calls. Nonetheless, as we are mostly doing high-coverage sequencing nowadays, imputation based methods only have a minor effect and are rarely applied.

> **Comments:**
> **username_0**: Thanks, a few followups (broken out over several comments):  Top paragraph sounds more like variant calling than genotyping, which is somewhat infeasible in context of large scale high-coverage studies or ongoing clinical-focused sequencing. Do you see same logic applying to genotyping i.e. conditional on there being a variant at the locus? What I'm struggling with is understanding, batch effect detection aside, why we would trust information on AFS from a somewhat arbitrary collection of samples (genetically speaking) more than a large sample resource like gnomAD?  
> **username_0**: I don't understand why " Naively combining single-sample calls yields a higher error rate. " Can you elaborate or provide an example, in the context of genotyping?  
> **username_0**: wrt. to haplotype or assembly-based calling it's simply a reflection of the fact that best methods seem to reason over a region around a locus not just the locus itself, and me trying to figure out where in such a method information from multiple samples can be used. Specifically in the context of  high coverage whole genome sequencing where multiple batches of samples are periodically arriving for analysis and there isn't necessarily a final sample size .  
> **username_2**: Top paragraph is about deciding the *genotype* of sample S - it's genotyping. When you know the site allele frequency (AFS is the wrong wording here) in a larger population, you have a better prior. This prior is less accurate across populations, but better than a wright fisher prior. All these theories are only useful to lowCov. For highCov, genotype likelihood has a much bigger effect than prior and cross-sample information.  
> **username_2**: For the rest, you should ask separate questions. Pooling multiple topics under this one question is hard for you, for me and for readers to comprehend.  
> **username_2**: Anyway... On assembly-based calling, I already said it has little to do with multi-sample calling. On combining single-sample calls, I already explained in the top paragraph that jointly considering multiple samples helps genotyping – which means not using the info hurts genotyping. BTW, the body of your question is mixing variant calling and genotyping (e.g. FDR is about variant calling), which is causing confusion to me and to Devon below.  

---

### Answer by username_1 on 2017-05-17. Score: 1

The benefit to additional samples is seen in your point 1. The likelihood of making a variant call is a function of (1) the depth of coverage supporting a given variant (ignoring mapping/base quality considerations) and (2) the likelihood of that variant existing given background knowledge. With low depth and no background knowledge, poorly covered variants will be assumed to be sequencing errors. Adding more samples can just serve then to increase the background knowledge on a position.

> **Comments:**
> **username_0**: Thanks Devon, the question specifically targets genotyping i.e. you already have to think that there is a variant there.  

---

