Shears are more powerful
scissors

-> Assumption: bulk=weights*single cells

We need to compute a weight for each single-cell and each bulk sample. This is similar to deconvolution, except we have a single-cell matrix instead of a signature matrix aggregated by cell types and can be solved with e.g. linear regression. Since we have way too many features, we apply a Ridge constraint to the regression.

Use an individual linear model per cell. Fit a model

-> Phenotype ~ cell_weight

for each cell. The coefficient of the model can be considered as the effect size measured for each cell. The problem with this approach is that a cell will be significantly associated, even if the effect could be explained with other cells. I’d expect this to be mostly a problem when using a correlation matrix instead of a weight matrix that already takes the importance of each cell into account.

• Quantile normalization to make bulk and single-cell comparable (as done by scissor)
• Ridge regression to estimate weights for the following equation

\[ B = w_1 S_1 + w_2 S_2 + \dots + w_n S_n \]

For each cell:

weight ~ condition + covariates

-> coefficient and p-value for condition

• Multicollinearity, i.e. can shears distinguish between similar cell-types?
• How to validate?
• Code is available at icbi-lab/shears