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enter image description here

I have counts (from multiple cell types) here only tumor is shown. I want to quantitatively define the clusters below as tumor rich/tumor poor based on tumor count. Tumor count represents no. of tumor cells in these clusters.

What is the appropriate statistical test I should use to say e.g. Cluster 0 is tumor rich compared to rest of the clusters?

Is there a way to do it across the groups to define e.g. clusters 0,4 and 7 are tumor rich compared to other clusters?

Would doing this for multiple cell-types together change what statistical test we use?

PS: Each dot here on the violin plot is a spot/grid hexagon (indicating how many cells in each grid are tumor likewise for other celltype not shown here).

Thank you!

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First, this is a parallel strip plot (there's no violin). I think a parallel violin plot would be better. Or, if you keep this plot, I'd make the dots unfilled circles, or maybe points. Right now, you have a lot of overplotting that obscures what is going on.

Then, I think you have to define more clearly what you mean by "tumor rich" (or any other type of condition rich). A higher mean? A higher median? Higher outliers? Or what? That will affect what exact type of plot you do and what test (if any) you do. You can emphasize different aspects of the data in a plot. E.g. you could make a red horizontal line at the 90th percentile.

That might speak for itself. But, if you do want some sort of test, you can do regression where the DV is count and the IV is cluster. If each cluster has different numbers of people, you will need to account for that, possibly with an offset. It might be OLS regression, or quantile regression, or something else.

If you do decide to do a test, I would not emphasize p values, as you have a large sample size and that will make even small difference very significant.

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