Body: <p><em>after comments on my original <a href="https://biology.stackexchange.com/questions/89133/detect-differentially-expressing-cells?noredirect=1#comment158173_89133">post</a>, I will ask my question again here</em></p>
  
  <p>I have data (RNA expression values, obtained with multi-channel in situ hybridization) collected from 1mio human cells. For each cell, I have the expression value of a negative control (non-human RNA) and single-cell measures for different RNA species. I know that the expression level of the negative control correlate in a linear fashion with all the other RNA species when there is no real expression (non-expressing cells). For example, when a cell has a high expression value of the negative control, the signal for all other RNA species will also be high. I now want to detect the cells that express an RNA without having a high negative signal, e.g. the "real" expressing cells. </p>
  
  <p>One thing to have in mind is that some RNA species are abundantly expressed in many cells, other are very rare and have a low expression value. </p>
  
  <p>I tried to do this with a linear model (for each of the RNA species, negative control vs. single RNA), computing z-scores, infer p-values and correct for multiple testing. For some RNA species, it works just fine. As soon as I have many cells expressing a certain RNA, the thing gets more tricky because the slope of the linear model doesn't reflect the linear relationship of negative control vs. RNA species in non-expressing cells because it is more shifted towards the "real" expressing cells. </p>
  
  <p>To visualize the problem, I attached two plots. One plot showing high RNA expression many cells (left plot) and one from an RNA species which is expressed on a very low level in few cells (right plot). Blue colored dots are considered as expressing cells according to the linear model. As you can see, for the scenario shown on the left side, many "real" expressing cells (low expression level) are not detected. </p>
  
  <p><a href="https://i.sstatic.net/NdzZ6.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/NdzZ6.png" alt="enter image description here"></a></p>
  
  <p>Any ideas which statistical model would better fit to detect those cells? </p>
  
  <p>Thank you for your suggestions!</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2019-12-09T12:19:05.730Z
Comments.Text: Have you considered plotting the per-cell ratio of RNA species to negative control? What is the downstream goal of all of this?
Comments.UserDisplayName: Devon Ryan
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2019-12-09T12:50:19.917Z
Comments.Text: @DevonRyan I've tried this but the problem is that you still have to manually introduce a signal-to-noise cut-off to define expressing cells, which in my opinion is prone to experimenter bias. The downstream goal is to binary label cells for expression (0 no expression, 1 expression). So rather than doing it manually, I would prefer a model that accounts for the variable expression levels and the variable s/n ratios.
Comments.UserDisplayName: tebiwankenebi
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2019-12-09T13:07:34.393Z
Comments.Text: Do you only have a single negative control or do you have more than one? I assume a few of the RNA species (like the second one in your example) are rarely expressed, is that correct?
Comments.UserDisplayName: Devon Ryan
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2019-12-09T13:55:59.463Z
Comments.Text: @DevonRyan I have a single negative control (besides the targets of interest) that is measured in each individual cell. Your assumption is completely correct, some RNA species are rarely expressed and if they are, at a fairly low level (but still detectable and different from the negative control). To note is that both axes are asinh transformed (1=1.17 counts, 3=10 counts).
Comments.UserDisplayName: tebiwankenebi
Tags: <r><single-cell><modelling><linear-regression><multi-omics>
Title: Detect differentially expressing cells
ThreadText: # Detect differentially expressing cells
  
  (Asked by: username_0 on 2019-12-09)
  
  *after comments on my original [post](https://biology.stackexchange.com/questions/89133/detect-differentially-expressing-cells?noredirect=1#comment158173_89133), I will ask my question again here*
  
  I have data (RNA expression values, obtained with multi-channel in situ hybridization) collected from 1mio human cells. For each cell, I have the expression value of a negative control (non-human RNA) and single-cell measures for different RNA species. I know that the expression level of the negative control correlate in a linear fashion with all the other RNA species when there is no real expression (non-expressing cells). For example, when a cell has a high expression value of the negative control, the signal for all other RNA species will also be high. I now want to detect the cells that express an RNA without having a high negative signal, e.g. the "real" expressing cells.
  
  One thing to have in mind is that some RNA species are abundantly expressed in many cells, other are very rare and have a low expression value.
  
  I tried to do this with a linear model (for each of the RNA species, negative control vs. single RNA), computing z-scores, infer p-values and correct for multiple testing. For some RNA species, it works just fine. As soon as I have many cells expressing a certain RNA, the thing gets more tricky because the slope of the linear model doesn't reflect the linear relationship of negative control vs. RNA species in non-expressing cells because it is more shifted towards the "real" expressing cells.
  
  To visualize the problem, I attached two plots. One plot showing high RNA expression many cells (left plot) and one from an RNA species which is expressed on a very low level in few cells (right plot). Blue colored dots are considered as expressing cells according to the linear model. As you can see, for the scenario shown on the left side, many "real" expressing cells (low expression level) are not detected.
  
  [![enter image description here](https://i.sstatic.net/NdzZ6.png)](https://i.sstatic.net/NdzZ6.png)
  
  Any ideas which statistical model would better fit to detect those cells?
  
  Thank you for your suggestions!
  
  **Tags:** r, single-cell, modelling, linear-regression, multi-omics
  
  > **Comments:**
  > **username_1**: Have you considered plotting the per-cell ratio of RNA species to negative control? What is the downstream goal of all of this?  
  > **username_0**: @username_1 I've tried this but the problem is that you still have to manually introduce a signal-to-noise cut-off to define expressing cells, which in my opinion is prone to experimenter bias. The downstream goal is to binary label cells for expression (0 no expression, 1 expression). So rather than doing it manually, I would prefer a model that accounts for the variable expression levels and the variable s/n ratios.  
  > **username_1**: Do you only have a single negative control or do you have more than one? I assume a few of the RNA species (like the second one in your example) are rarely expressed, is that correct?  
  > **username_0**: @username_1 I have a single negative control (besides the targets of interest) that is measured in each individual cell. Your assumption is completely correct, some RNA species are rarely expressed and if they are, at a fairly low level (but still detectable and different from the negative control). To note is that both axes are asinh transformed (1=1.17 counts, 3=10 counts).  
  
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