Relationship between CI, minimal effect threshold, and FDR on plots$credible_intervals_1D

[Winbuntu]

Hi,

I was trying to understand the relationship between CI, minimal effect threshold, and FDR on plots$credible_intervals_1D. One example is given in the Readme:

For c_effects (on the left), "The dashed lines represent the minimal effect that the hypothesis test is based on. An effect is labelled as significant if bigger than the minimal effect according to the 95% credible interval", as you mentioned in Readme.

My understanding is that minimal effect = 0.2 by default. In general, a celltype whose CI is far away from 0 is considered as significant. That means, if a cell type has c_effect < 0, it will be signficant (c_FDR<0.05) if its c_upper < -0.2 ; if a cell type has c_effect > 0, it will be signficant (c_FDR<0.05) if its c_lower > 0.2.

However the plots$credible_intervals_1D shows differently than my understanding. i.e. I imagine NK cells in c typehealthy should be non-signficant, because its c_lower is less than 0.2 (as indicated by grey vertical line). But on the plots$credible_intervals_1D it turns out to be signficant.

Can you help me to clarify how should I understand the relationship between CI, minimal effect threshold, and FDR in general?

[stemangiola]

My understanding is that minimal effect = 0.2 by default. In general, a celltype whose CI is far away from 0 is considered as significant. That means, if a cell type has c_effect < 0, it will be signficant (c_FDR<0.05) if its c_upper < -0.2 ; if a cell type has c_effect > 0, it will be signficant (c_FDR<0.05) if its c_lower > 0.2.

Although this is roughly what happens intuitively, is not 1 to 1 link.

• probability: The probability of an effect occurring is calculated as the quantile of the posterior distribution that is left or right (exclusively) of the minimal effect threshold (e.g 0.2). Here, if the CI is outside the threshold range, it is significant.
• false-discovery rate: as explained in the paper, it is the cumulative mean of the probabilities (so FDR always < than the probability for each single cell type). So, the CI and FDR do not match perfectly. FDR is a cumulative statistic, and it is not about a single cell type.

Let me know if that was clear; with your help, we could add an explanation in the README to help users understand.

[stemangiola]

closing for inactivity, feel free to reopen it.