NMDP [002 SP_B]

Vidhi Lalchand, Ph.D.

 IMU Biosciences

April 29, 2026

[203 donors]

Depth-weighted pooling approach to modelling immue ratios 

How are the subtrees formed?

Each column of the megatable is mapped to a subtree label

"population","ratio_parent","hierarchical_path","subtree"

"Eosinophil_Tv5","Live_cells_Tv5","Total_Tv5/WBC_Tv5/Live_cells_Tv5/Eosinophil_Tv5","Granulocyte"

"Eosinophil/CD5p_Tv5","Eosinophil_Tv5","Total_Tv5/WBC_Tv5/Live_cells_Tv5/Eosinophil_Tv5/Eosinophil/CD5p_Tv5","Granulocyte"

"Eosinophil/HLADRp_Tv5","Eosinophil_Tv5","Total_Tv5/WBC_Tv5/Live_cells_Tv5/Eosinophil_Tv5/Eosinophil/HLADRp_Tv5","Granulocyte"

"Eosinophil/PD1p_Tv5","Eosinophil_Tv5","Total_Tv5/WBC_Tv5/Live_cells_Tv5/Eosinophil_Tv5/Eosinophil/PD1p_Tv5","Granulocyte"

"Neutrophil_Tv5","Live_cells_Tv5","Total_Tv5/WBC_Tv5/Live_cells_Tv5/Neutrophil_Tv5","Granulocyte"

"Neutrophil/BIG_Tv5","Neutrophil_Tv5","Total_Tv5/WBC_Tv5/Live_cells_Tv5/Neutrophil_Tv5/Neutrophil/BIG_Tv5","Granulocyte"

"Neutrophil/CD5p_Tv5","Neutrophil_Tv5","Total_Tv5/WBC_Tv5/Live_cells_Tv5/Neutrophil_Tv5/Neutrophil/CD5p_Tv5","Granulocyte"

"Neutrophil/HLADRp_Tv5","Neutrophil_Tv5","Total_Tv5/WBC_Tv5/Live_cells_Tv5/Neutrophil_Tv5/Neutrophil/HLADRp_Tv5","Granulocyte"

"Neutrophil/PD1p_Tv5","Neutrophil_Tv5","Total_Tv5/WBC_Tv5/Live_cells_Tv5/Neutrophil_Tv5/Neutrophil/PD1p_Tv5","Granulocyte"

"Neutrophil/SMALL_Tv5","Neutrophil_Tv5","Total_Tv5/WBC_Tv5/Live_cells_Tv5/Neutrophil_Tv5/Neutrophil/SMALL_Tv5","Granulocyte"

"Total_B_Tv5","Live_cells_Tv5","Total_Tv5/WBC_Tv5/Live_cells_Tv5/Total_B_Tv5","B_cell"

"Total_B/CD5p_Tv5","Total_B_Tv5","Total_Tv5/WBC_Tv5/Live_cells_Tv5/Total_B_Tv5/Total_B/CD5p_Tv5","B_cell"

"Total_B/CD27p_Tv5","Total_B_Tv5","Total_Tv5/WBC_Tv5/Live_cells_Tv5/Total_B_Tv5/Total_B/CD27p_Tv5","B_cell"

"Total_B/CD39p_Tv5","Total_B_Tv5","Total_Tv5/WBC_Tv5/Live_cells_Tv5/Total_B_Tv5/Total_B/CD39p_Tv5","B_cell"

"Total_B/CD57p_Tv5","Total_B_Tv5","Total_Tv5/WBC_Tv5/Live_cells_Tv5/Total_B_Tv5/Total_B/CD57p_Tv5","B_cell"

"Total_B/CD95p_Tv5","Total_B_Tv5","Total_Tv5/WBC_Tv5/Live_cells_Tv5/Total_B_Tv5/Total_B/CD95p_Tv5","B_cell"

"Total_B/CD103p_Tv5","Total_B_Tv5","Total_Tv5/WBC_Tv5/Live_cells_Tv5/Total_B_Tv5/Total_B/CD103p_Tv5","B_cell"

"Total_B/CXCR5p_Tv5","Total_B_Tv5","Total_Tv5/WBC_Tv5/Live_cells_Tv5/Total_B_Tv5/Total_B/CXCR5p_Tv5","B_cell"

"Total_B/ICOSp_Tv5","Total_B_Tv5","Total_Tv5/WBC_Tv5/Live_cells_Tv5/Total_B_Tv5/Total_B/ICOSp_Tv5","B_cell"

"Total_B/LAG3p_Tv5","Total_B_Tv5","Total_Tv5/WBC_Tv5/Live_cells_Tv5/Total_B_Tv5/Total_B/LAG3p_Tv5","B_cell"

"Total_B/PD1p_Tv5","Total_B_Tv5","Total_Tv5/WBC_Tv5/Live_cells_Tv5/Total_B_Tv5/Total_B/PD1p_Tv5","B_cell"

"Total_B/TIM3p_Tv5","Total_B_Tv5","Total_Tv5/WBC_Tv5/Live_cells_Tv5/Total_B_Tv5/Total_B/TIM3p_Tv5","B_cell"

  Total rows: 2342                            
  Number of subtrees: B = 8
                                                                         
  Columns:        
  - population        : Node name (e.g. Eosinophil_Tv5, VD1/PD1p_Tv5)    
  - ratio_parent      : Direct parent node, defines the tree edges      
  - hierarchical_path : Full path from root (e.g.                      
  Total_Tv5/WBC_Tv5/.../VD1_Tv5)                                        
  - subtree           : Which of the B=8 subtrees this node belongs to
                                                                         
  

Tree encoding: Aggregate ratios at each depth level to collapse noisy information

Below, is just to show how it happens for different types of tree topologies

Once we have access to this final embedding which has encoded all the subtrees, we can treat it as a flat embedding vector training any non-linear model on it to predict the binary response. 

Comparing with a flat neural network trained directly on the ratios, and Tree-LSTM embeddings (50-dim).

Interpretation. DWP answers the question: how much does each level of specificity in subtree b contribute to predicting the outcome?

The ratios at the leaves may be less important and more susceptible to gating noise: Depth 0 corresponds to the subtree root (most general population); increasing depth corresponds to increasingly specific subpopulations which may be less important. 

Parameter efficient: The non-linear predictor is trained on a much low-dimensional embedding than the original vector (~2.3k dims) -> 64-dims. So the first layer of the neural network now only has 64 neurons instead of 2.3k neurons, this reduces the noise introduced by the model across runs (400x compression of parameters in the model, tighter error bars)

Discussion points for 30/04

- Is there a relative ranking or importance score we can assign to the different subtrees?

- What about tree pruning, would it make sense to prune out nodes with a very small count or ratio under a certain threshold as a way to further control for inherent noise?

- Modelling with counts rather than ratios, as ratios obscure the effect of small counts?

Next steps on the modelling side: 

- Incorporate pairwise tree interaction terms which will measure covariance patterns between pairs of tree embeddings.

- Incorporate covariates to the full model.