Posted by: Greg Gloor
I've been thinking a bit about distance metrics for compositional data, and in particular about the Jensen-Shannon distance (JSD) metric used in the famous Enterotypes paper. While, in my opinion and others, enterotypes are the result of measuring abundance not variance, the Jensen-Shannon distance has been of interest to me because it is based on Kullback-Leibler divergence which has log-ratios as a term. Others have noted that the JSD is not quite as consistent as the Aitchison distance for compositional data, but I decided to look for myself. There is a nice tutorial about how to implement JSD and identify enterotypes, which was posted to convince people of the validity of the JSD and the approach used to determine enterotypes.
I've written before about why high throughput sequencing data are compositions, and was thinking about how to test if JSD is a valid compositional distance metric when I came across this working paper from the Proceedings of the IAMG in 1998. The paper gives a very simple set of tests, and I thought that they could easily be applied to JSD and Bray-Curtis dissimilarity.
The approach is very simple. It depends on the distance metric giving the same answer when the data are permuted (rearranged), scaled, perturbed (rotated), or subset (one OTU left out). A useful distance metric should give the same answer regardless of these alterations. The test is simple, given two pairs of compositions:
x1 = [0.1,0.2,0.7] and x2 = [0.2,0.1,0.7]
or
x3 = [0.3,0.4,0.3] and x4 = [0.4,0.3,0.3]
and the subset of them s1, s2, s3,s4 (the first two parts of the compositions), or a perturbation of them, p1,p2,p3,p4, (multiplication by a constant, which rotates the data), the distance should be the same.
The paper tested a broad range of distances including the Aitchison distance, which is the Euclidian distance determined on the centred log-ratio data. The conclusion of the paper was that the Aitchison distance was the only one that gave consistent answers. In the table below, d() is the distance for the pairs of compositions, x is the original composition, s is the subset and p is the perturbed data.
On to the test:
d(x1,x2) d(s1,s2) d(p1,p2) d(x3,x4) d(s3,s4) d(p3,p4)
Aitchison 0.98 0.98 0.98 0.41 0.41 0.41
JSD 0.13 0.13 0.15 0.08 0.08 0.06
Bray-Curtis 0.10 0.33 0.20 0.10 0.14 0.07
So what does this mean?
The Aitchison distance, which is used for compositional biplots, or for clustering gives a consistent answer whether the data is complete, subset or rotated.: it is the same for d(x), d(s) and d(p). Yay!
The JSD used in the enterotypes paper and others by the same group does pretty well, but is not as consistent as the Aitchison distance. The JSD gives the same answer for the complete data and for the subset, but a different answer when he data are perturbed. So, changes in the scale of the data in one or more dimensions, or which rotate the data around one or more parts will give a different answer with this metric.
The Bray-Curtis difference fails miserably when the variables are altered in any way. This metric is not reproducible in a compositional context, and so will give potentially different answers when the data are subset (maybe let's remove those rare OTUs or leave them in - which plot looks better?), or rotated (maybe we had a different amplification efficiency in this tube than that one?). This surprised me a bit, since we had previously shown that the Bray-Curtis metric was fairly consistent when the samples were subset.
In the end, this confirms in my mind that the Aitchison distance is the one that we should be using whenever possible for compositional data such as 16S rRNA gene sequencing data, transcriptome data, metagenomic data, etc for distance-based metrics like clustering. We have seen in the past that this is true empirically, eg. in the cross-sectional study of microbiome v. age in China.
Thursday, 9 February 2017
Thursday, 7 April 2016
Sequencing is not counting!
Posted by: Greg Gloor
The idea of using compositional data analysis approaches (CoDa) to examine microbiome samples appears to be gaining traction. There have been a recent spate of papers (and not just from us) that are going in the right direction by acknowledging that we have compositional data.
However, to my mind, most papers do go far enough, and still make strong assumptions about the data. I want to briefly outline why we must embrace the idea of CoDa in its entirety.
Fundamentally, sequencing is not counting. To see this, lets set up a very simple thought experiment. In ecology, it is common to count species within some area, and then to use these counts for the analysis.
In the counting example, we have 5 tigers and 20 ladybugs in some defined area which is a random sample of the environment. We can assume that the animals are free to move both within the box and between the box and the environment, and that the density of animals inside and outside the box is about the same. Therefore, if one more tiger should wander in from the outside, that not alter the number of ladybugs and vice-versa. Moreover, if a space alien happens to land in the counting box, it will likely not alter the count of tigers or ladybugs (unless it lands on and squishes one!). We can see that the abundance of tigers and ladybugs can be essentially treated as uncorrelated. In addition, we can normalize for different box sizes rather simply by scaling the size of the box. So if one student measures a box of size 1, and another a box of size 2, we can adjust for sampling effort fairly simply. This is the rationale behind normalizing for sequencing depth, and if we had counts would work marvelously for sequencing data.
This problem generalizes to any number of species, and is not alleviated by increasing the number of cells in the grid. Attempts to normalize read counts, which are the same as normalizing the number of squares in the grid are doomed to fail because of this property.
So what can we do? We have to embrace the idea that the actual numbers we observe from a sequencing run are irrelevant, and the only information available is relative information: that is, that the ratios between the ladybugs and tigers is the only measurable property. We have begun the process of adapting the full measure of CoDa tools to microbiome studies and our first paper is just out in Annals of Epidemiology: It's all relative: analyzing microbiome data as compositions, and I hope you give it a read. There is also a supplement that contains all the code used to generate the paper.
Although there are many issues to be resolved, mainly because sparse data can be problematic with CoDa approach, I think that it is worth checking out for your datasets. In a later post, I will outline how the general approach we use to account for the sparsity problem.
However, to my mind, most papers do go far enough, and still make strong assumptions about the data. I want to briefly outline why we must embrace the idea of CoDa in its entirety.
Fundamentally, sequencing is not counting. To see this, lets set up a very simple thought experiment. In ecology, it is common to count species within some area, and then to use these counts for the analysis.
In the counting example, we have 5 tigers and 20 ladybugs in some defined area which is a random sample of the environment. We can assume that the animals are free to move both within the box and between the box and the environment, and that the density of animals inside and outside the box is about the same. Therefore, if one more tiger should wander in from the outside, that not alter the number of ladybugs and vice-versa. Moreover, if a space alien happens to land in the counting box, it will likely not alter the count of tigers or ladybugs (unless it lands on and squishes one!). We can see that the abundance of tigers and ladybugs can be essentially treated as uncorrelated. In addition, we can normalize for different box sizes rather simply by scaling the size of the box. So if one student measures a box of size 1, and another a box of size 2, we can adjust for sampling effort fairly simply. This is the rationale behind normalizing for sequencing depth, and if we had counts would work marvelously for sequencing data.
But, this is not the case with sequencing. Every DNA sequencing instrument has a fixed upper limit on the number of reads that can be delivered, and this is illustrated by having exactly 25 cells inside the box. Visualized in this way, we can see the difference in how the same counts of 5 tigers and 20 ladybugs must behave in the face of a perturbation. Either a tiger or a ladybug must be displaced if another tiger wanders onto the sequencing grid. Another way of saying this is that the tiger and ladybug numbers observed are correlated, since an increase in one necessarily involves a decrease in the other. If the space alien now enters the sequencing grid, we see that again we must displace a tiger or a ladybug. This causes all manner of problems for traditional approaches because of spurious correlation, negative correlation bias and sub-compositional correlation effects.
This problem generalizes to any number of species, and is not alleviated by increasing the number of cells in the grid. Attempts to normalize read counts, which are the same as normalizing the number of squares in the grid are doomed to fail because of this property.
So what can we do? We have to embrace the idea that the actual numbers we observe from a sequencing run are irrelevant, and the only information available is relative information: that is, that the ratios between the ladybugs and tigers is the only measurable property. We have begun the process of adapting the full measure of CoDa tools to microbiome studies and our first paper is just out in Annals of Epidemiology: It's all relative: analyzing microbiome data as compositions, and I hope you give it a read. There is also a supplement that contains all the code used to generate the paper.
Although there are many issues to be resolved, mainly because sparse data can be problematic with CoDa approach, I think that it is worth checking out for your datasets. In a later post, I will outline how the general approach we use to account for the sparsity problem.
Tuesday, 12 January 2016
Tuesday, 27 October 2015
Wading through the deluge of scientific literature
Posted by: Jean M Macklaim
The amount of science published every day is massive, making it extremely difficult to keep up with literature in your given field. I used to rely on keyword searches and RSS feeds or email updates on specific topics ("microbiome", "bacterial vaginosis", "probiotics", etc.) but this becomes a chore to keep up, and missing a day or two leave you with dozens of emails to catch up with. Not only that, but each weekly update on a topic will consist of 50-80 article titles that you have to read and sort and determine which are relevant enough to follow up on. I stumbled across this article in Nature (How to tame the flood of literature, Elizabeth Gibney) outlining some of these issues and suggested solutions.
So *is* there a better solution? Maybe not a catch-all tool, but here are some tools and software that have helped me out.
Google Scholar (online)
Google scholar is my primary tool for searching and finding publications. Once you make a scholar profile (linked to your Google account), you'll get an automated list of your own publications and citations (see mine here), including some metrics on your citation rate. Once you have a profile, Google will automatically suggest publications that are related to your work (they appear under "My Updates"). I find these updates are the most relevant to my research and what I am interested in.
Additionally, you can save articles you find via Google Scholar to "My Library". This keeps a list with links to the articles, along with citation metrics and information. However, this does not replace a citation manager as there is currently no way to export your list of articles, or automatically insert citations into a manuscript.
PubChase (online)
Papers (Mac and iOS only; $)
Zotero (Mac, Windows, Linux; free)
Cross-platform, and free. Does the job, but the interface is not as clean as I'd like (seems a little 90s Windows-esque). Ability to insert citations and build reference lists for most document types.
Mendeley (Mac, Windows, Linux, iOS, Android; free)
Evernote (Mac, iOS, Windows, Linux, Android; free)
A multi-multi-purpose digital notebook. I use this for everything in my life, and it has become my digital lab book. You can add notes, PDFs, images, code, basically anything you want. You can compile notes into notebooks and tag topics. You can share with your workmates. It basically keeps my scientific life organized. Did I mention its FREE (I've found no need to pay for the premium subscriptions).
Blogs and social networking sites
The amount of science published every day is massive, making it extremely difficult to keep up with literature in your given field. I used to rely on keyword searches and RSS feeds or email updates on specific topics ("microbiome", "bacterial vaginosis", "probiotics", etc.) but this becomes a chore to keep up, and missing a day or two leave you with dozens of emails to catch up with. Not only that, but each weekly update on a topic will consist of 50-80 article titles that you have to read and sort and determine which are relevant enough to follow up on. I stumbled across this article in Nature (How to tame the flood of literature, Elizabeth Gibney) outlining some of these issues and suggested solutions.
So *is* there a better solution? Maybe not a catch-all tool, but here are some tools and software that have helped me out.
Automated recommendation tools
Google Scholar (online)
Google scholar is my primary tool for searching and finding publications. Once you make a scholar profile (linked to your Google account), you'll get an automated list of your own publications and citations (see mine here), including some metrics on your citation rate. Once you have a profile, Google will automatically suggest publications that are related to your work (they appear under "My Updates"). I find these updates are the most relevant to my research and what I am interested in.
Additionally, you can save articles you find via Google Scholar to "My Library". This keeps a list with links to the articles, along with citation metrics and information. However, this does not replace a citation manager as there is currently no way to export your list of articles, or automatically insert citations into a manuscript.
PubChase (online)
This is a new tool I am using, but I already see the potential. Like Google Scholar, it uses information about what you've published, but with the addition of articles you've saved to your Library as a resource to recommend articles relevant to you. Your Library can be populated by uploading a BibTeX (.bib) file, which nearly any reference manager will export for you.
Pubchase has some other useful features I haven't yet explored. It automatically links your library entries to PDF files (where possible) so you can read papers directly from your account. They also provide tablet, mobile, and computer apps for OSX, iOS, and Android, allowing you to read and access your library from any device. You can also make your library public for other members to follow, or follow someone else's library.
Pubchase has some other useful features I haven't yet explored. It automatically links your library entries to PDF files (where possible) so you can read papers directly from your account. They also provide tablet, mobile, and computer apps for OSX, iOS, and Android, allowing you to read and access your library from any device. You can also make your library public for other members to follow, or follow someone else's library.
Reference managers
A reference manager is essential for writing a manuscript and keeping track of citations. I don't have a favourite yet, but here are a few I've tried and liked:
Papers (Mac and iOS only; $)
An app you can install on your Mac and iPhone/iPad to access and view citations, and make notes and mark up PDF articles. It had a nice interface, and easily links to most word processing software (citations can be added to Word, plain text apps, Google Docs, etc.). The one major downside is this software has a cost, although there is a student discount rate.
Zotero (Mac, Windows, Linux; free)
Cross-platform, and free. Does the job, but the interface is not as clean as I'd like (seems a little 90s Windows-esque). Ability to insert citations and build reference lists for most document types.
Mendeley (Mac, Windows, Linux, iOS, Android; free)
Another nice looking application. It manages papers and citations. Has more functionality than I need though, and I find myself lost in menus sometimes. Seems to currently only support adding citations and building reference lists in Microsoft Word documents.
Other tools
Evernote (Mac, iOS, Windows, Linux, Android; free)
A multi-multi-purpose digital notebook. I use this for everything in my life, and it has become my digital lab book. You can add notes, PDFs, images, code, basically anything you want. You can compile notes into notebooks and tag topics. You can share with your workmates. It basically keeps my scientific life organized. Did I mention its FREE (I've found no need to pay for the premium subscriptions).
Blogs and social networking sites
Another source I use to keep up-to-date. A number of researchers maintain blogs with current information about their research or research in the field. I recommend using an RSS reader to receive the posts as they become live. Some I recommend:
CommaFeed (online)
Feedly (online, and available apps)
Also, the current Safari and Chrome browsers have RSS functionality built in.
Other sources include Facebook, Twitter, ResearchGate, and Google+. I find it's only useful to follow these if you are already an avid user. It's not feasible for me to check with every social networking site every day, and so I don't rely on these to keep up.
In case you are interested, here are some of the blogs I follow:
Not Exactly Rocket Science (Ed Yong)
Microbiome Digest – Bik's Picks (Elisabeth Bik)
Simply Statistics (Jeff Leek, Roger Peng, and Rafa Irizarry)
Bits of DNA (Lior Pachter)
Musings from an unlikely candidate (Dave Tang)
What You're Doing is Rather Desperate (Neil Saunders)
Please comment below on any other software tools that make your research life easier!
Monday, 24 August 2015
Science is hard
Posted by: Jean M Macklaim
An interesting article on Christie Aschwanden on FiveThirtyEight - worth a read!
Wednesday, 20 May 2015
From the blogosphere - batch effects in sequence data
Posted by: Jean M Macklaim
We've performed a number of sequencing runs lately in replicates (replicated in PCR amplification, library preparation, sequencing run, and sequencing platform) to explore the technical variation, including batch effects. We know technical variation can change your results in big ways.
A good example of batch effect has been brought to attention recently:
http://simplystatistics.org/2015/05/20/is-it-species-or-is-it-batch-they-are-confounded-so-we-cant-know/
http://www.the-scientist.com/?articles.view/articleNo/43003/title/Batch-Effect-Behind-Species-Specific-Results-/
In summary, two major papers (1 and 2) nearly a decade apart report the same conclusion: human tissues are more similar in gene expression to any other human tissue than to the equivalent tissue in mouse.
Whoa, what?
So human lung tissue is more similar to human eye tissue than to mouse lung?
As it turns out, this likely isn't true. The observation is due to the confounding batch effect. In other words, what the authors thought was explained by differences in species was actually confounded by the differences in platforms/analyses (in the first case e.g. a different microarray with a different set of probes were used for mouse vs human). The most recent 2014 study has been refuted for confounding batch effect too in at least one publication.
So how does one deal with confounding variables?
The most robust way is to sufficiently randomize your samples so technical parameters don't line up with the biological parameters you are testing, and ensure you maintain a consistent protocol throughout.
This, of course, does not guarantee you won't confound your data, but it should help prevent a systemic bias in sample preparation. If you process all your controls on Tuesdays and your affected samples on Fridays, you won't be able to determine if the effect is due to the condition or the day of the week. As another example, it's important to randomize sample loadings to ensure you don't line up all of condition1 in row 1 of your 96-well plate, and condition2 in row 2 etc. This is where is is essential to collect sufficient metadata about your samples in order to explicitly examine confounding variables.
And of course, ALWAYS look at your data
A good example of batch effect has been brought to attention recently:
http://simplystatistics.org/2015/05/20/is-it-species-or-is-it-batch-they-are-confounded-so-we-cant-know/
http://www.the-scientist.com/?articles.view/articleNo/43003/title/Batch-Effect-Behind-Species-Specific-Results-/
In summary, two major papers (1 and 2) nearly a decade apart report the same conclusion: human tissues are more similar in gene expression to any other human tissue than to the equivalent tissue in mouse.
Whoa, what?
So human lung tissue is more similar to human eye tissue than to mouse lung?
As it turns out, this likely isn't true. The observation is due to the confounding batch effect. In other words, what the authors thought was explained by differences in species was actually confounded by the differences in platforms/analyses (in the first case e.g. a different microarray with a different set of probes were used for mouse vs human). The most recent 2014 study has been refuted for confounding batch effect too in at least one publication.
So how does one deal with confounding variables?
The most robust way is to sufficiently randomize your samples so technical parameters don't line up with the biological parameters you are testing, and ensure you maintain a consistent protocol throughout.
This, of course, does not guarantee you won't confound your data, but it should help prevent a systemic bias in sample preparation. If you process all your controls on Tuesdays and your affected samples on Fridays, you won't be able to determine if the effect is due to the condition or the day of the week. As another example, it's important to randomize sample loadings to ensure you don't line up all of condition1 in row 1 of your 96-well plate, and condition2 in row 2 etc. This is where is is essential to collect sufficient metadata about your samples in order to explicitly examine confounding variables.
And of course, ALWAYS look at your data
Tuesday, 12 May 2015
The count you get is just a guideline - part 2
Posted by: Greg Gloor
In previous posts I have shown the effect of sequencing on the underlying shape of the data, and that the data are better thought of as likelihoods of observing a particular count for a particular gene or OTU. Now I'm going to show you the effect of combining those two ideas into an approach to examine datasets of this type that minimizes false positives while maintaining power.
The two-step method is implemented in the ALDEx2 package on Bioconductor. Step one is to model the technical variance by sampling instances from the Dirichlet distribution. This distribution is essentially a multivariate Poisson distribution, and is a good estimator for the underlying technical variation that we have seen in previous blog posts. Step two is to use the centered log-ratio transformation to re-capitulate the underlying shape of the data. These two steps are implemented in the aldex.clr function.
We can now use these transformed instances for standard statistical tests. Below shows an example for a dataset where we are interested in knowing which variants differ in abundance between two conditions. What we want is to find out which variants will give us the same answer regardless of the underlying technical variation. The way we do this is to calculate P values, and Benjamin-Hochberg adjusted P values for each Dirichlet instance, and then to tabulate the mean values. The mean P value for random data should converge on 0.5. The mean P value (and BH adjusted values) for real differences should be relatively invariant to technical replication. That is, we should make the same conclusions if we sequence today or tomorrow.
The figure shows four plots of what we get from a different numbers of Dirichlet instances (number on the left), coupled with a histogram of the P values and the number of BH adjusted values that pass a threshold of <0.05 (number on the right). P values <0.05 are in orange, BH <0.05 are in red. As you can see we start off with 138 'significant' variants with a single instance, this is also about what we get if we just use our raw data. After only 5 Dirichlet instances we have reduced this to 80 'significant' variants, and by 100 or so, we stabilize on a value of 75 or so.
In previous posts I have shown the effect of sequencing on the underlying shape of the data, and that the data are better thought of as likelihoods of observing a particular count for a particular gene or OTU. Now I'm going to show you the effect of combining those two ideas into an approach to examine datasets of this type that minimizes false positives while maintaining power.
The two-step method is implemented in the ALDEx2 package on Bioconductor. Step one is to model the technical variance by sampling instances from the Dirichlet distribution. This distribution is essentially a multivariate Poisson distribution, and is a good estimator for the underlying technical variation that we have seen in previous blog posts. Step two is to use the centered log-ratio transformation to re-capitulate the underlying shape of the data. These two steps are implemented in the aldex.clr function.
We can now use these transformed instances for standard statistical tests. Below shows an example for a dataset where we are interested in knowing which variants differ in abundance between two conditions. What we want is to find out which variants will give us the same answer regardless of the underlying technical variation. The way we do this is to calculate P values, and Benjamin-Hochberg adjusted P values for each Dirichlet instance, and then to tabulate the mean values. The mean P value for random data should converge on 0.5. The mean P value (and BH adjusted values) for real differences should be relatively invariant to technical replication. That is, we should make the same conclusions if we sequence today or tomorrow.
The figure shows four plots of what we get from a different numbers of Dirichlet instances (number on the left), coupled with a histogram of the P values and the number of BH adjusted values that pass a threshold of <0.05 (number on the right). P values <0.05 are in orange, BH <0.05 are in red. As you can see we start off with 138 'significant' variants with a single instance, this is also about what we get if we just use our raw data. After only 5 Dirichlet instances we have reduced this to 80 'significant' variants, and by 100 or so, we stabilize on a value of 75 or so.
Below is an animated gif that walks through 2000 instances. It is pretty clear that inferred technical variation has a large effect on what is called 'significant', and that we can remove at least some of this stochastic noise quite simply. Also it is clear that the number of significant variants stabilizes and is not affected by further random sampling.
(Click the image to restart the gif animation)
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