I have data (RNA expression values, obtained with 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 values from the negative control correlate in a linear fashion with all the other RNA species. 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 are not detected.

enter image description here

Any ideas which statistical model would better fit to detect those cells?

Thank you for your suggestions!

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    $\begingroup$ Have you tried just substracting the values for the negative control from each RNA species X? I think that should both improve your actual measurement and make it easier to detect with cells have non-detectable levels of the RNA. $\endgroup$ – Nicolai Dec 8 '19 at 11:16
  • $\begingroup$ good point @Nicolai, I will try that.. but how would you then define expressing cells? with a manual cut-off? I have to say that I'm not a big fan of manually defining things for such analyses because I think that will just introduce an unnecessary bias. $\endgroup$ – tebiwankenebi Dec 8 '19 at 14:46
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    $\begingroup$ You can try linear mixed effects model. I'm not 100% sure if it would help but the cell to cell variability of the slope/intercept can be modelled as the random effect. $\endgroup$ – WYSIWYG Dec 8 '19 at 15:29
  • $\begingroup$ Welcome to Biology.SE! This question seems like it might be a better fit for the Bioinformatics site. $\endgroup$ – tyersome Dec 8 '19 at 18:37
  • $\begingroup$ @tyersome may be a better fit at Cross Validated but this isn't really a bioinformatics question. $\endgroup$ – WYSIWYG Dec 8 '19 at 19:24

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