In my experiment I have a number of clusters of cells from an unsupervised clustering. Each cluster represents a cell type, and can be seen as random samples from a large pool of possible cell types that could have ended up in the experiment. The clusters are very different in size, say between 10 and 10000 cells. The total number of cells is maybe 50000 and the number of clusters 20. For each cell I have a measurement of a gene X. I would like to know if the expression of gene X is significantly different in cluster Y compared to all other clusters. The clustering can be seen as independent of the expression level of X. For technical reasons the variances in the clusters are very different. The number of cells in each cluster is irrelevant and can be seen as a technical effect, but clusters with many cells would of course have better estimates of their means.

For simplicity we can assume that the expression values are normally distributed within each cluster.

The simplest approach would be to pool all the cells in the non-Y clusters and then do, say, a t-test. However, that would weigh clusters with many cells more heavily and that's something I'd like to avoid. A group should be considered the experimental unit, not the cell.

Any hints would be welcome! Thanks!


closed as unclear what you're asking by SmallChess, Michael Chernick, mdewey, kjetil b halvorsen, Jeremy Miles Sep 13 '18 at 4:04

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  • $\begingroup$ It's unclear how the mixed-model tag would apply: could you explain? This seems instead like a straightforward application of a negative binomial GLM with fixed effects. $\endgroup$ – whuber Sep 10 '18 at 14:59
  • $\begingroup$ That was probably wrong, so I removed it. I was thinking along the lines of the samples being dependent observations in each group and that I would be able to test for the significance of the random effects. Could you please explain in some more detail how I would formulate it as a GLM model? You can ignore the negative binomial part, I think I need help getting the problem formulation right. Note that the thing I don't know how to approach is how to test one mean against a set of means. $\endgroup$ – Rasmus Sep 10 '18 at 15:35
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    $\begingroup$ It's really no different than the usual ANOVA, and is carried out in essentially the same way but using a GLM to account properly for the negative binomial response and performing an "analysis of deviance." $\endgroup$ – whuber Sep 10 '18 at 15:37
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    $\begingroup$ That's called a "contrast." It can be handled with ANOVA, but is easiest to deal with in the regression setting, which is mathematically the same as ANOVA and generalizes to GLMs, etc. $\endgroup$ – whuber Sep 10 '18 at 15:50
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    $\begingroup$ Was expression of gene X used as part of the clustering process? If so, would the clustering have been different had gene X been omitted from the process? It's best to edit the question with such information as comments sometimes get lost and aren't necessarily examined carefully by new readers of the post. $\endgroup$ – EdM Sep 10 '18 at 17:55

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