Overcorrection Assessment

A per-cell diversity score computed from local neighborhoods that quantifies the effective number of distinct batches or cell types present. The integration LISI (iLISI) measures batch mixing—higher values indicate better mixing—while the cell-type LISI (cLISI) measures biological signal preservation—values close to 1 indicate pure, well-separated clusters.

• Overcorrection signature: High iLISI coupled with high cLISI, meaning batches are well-mixed but cell types are also blended together
• Optimal outcome: High iLISI (batches mixed) with low cLISI (cell types distinct)
• Implementation: Available in the lisi R package, computed from a k-nearest neighbor graph with a tunable perplexity parameter

A cluster cohesion metric adapted for batch correction evaluation by computing silhouette scores on both batch labels and cell-type labels. The batch ASW measures how well-separated batches remain—values near 0 indicate perfect mixing—while the cell-type ASW measures biological cluster compactness.

• Batch ASW: Ranges from -1 to 1; a score of 0 indicates complete batch mixing, while 1 indicates complete batch separation
• Cell-type ASW: Should remain high (close to 1) after correction; a drop indicates overcorrection
• Aggregate metric: Often reported as 1 - |batch_ASW| to create a 0-to-1 scale where 1 represents ideal mixing

A statistical hypothesis test that evaluates batch mixing quality by comparing the local batch label distribution in a k-nearest neighbor graph to the global batch distribution using a chi-squared test. A well-mixed dataset should have local batch proportions that mirror the overall experimental design.

• Rejection rate: The fraction of neighborhoods where the null hypothesis of good mixing is rejected; a rate near 0 indicates successful correction
• Overcorrection detection: A very low rejection rate combined with blurred biological clusters suggests overcorrection
• Sensitivity: Highly sensitive to local batch effects that global metrics may miss, making it a stringent quality control tool

A post-correction diagnostic that quantifies how much true biological signal remains after batch adjustment by measuring the variance explained by known biological covariates such as cell type, disease state, or treatment condition.

• Principal variance component analysis (PVCA): Partitions total variance into biological and technical components before and after correction
• Overcorrection indicator: A significant drop in the variance explained by biological covariates after correction
• Differential expression concordance: Comparing the overlap of differentially expressed genes before and after correction; high concordance with ground-truth marker genes indicates preservation of biology

An information-theoretic metric that calculates the Shannon entropy of batch labels within each cell's local neighborhood. High entropy indicates that multiple batches are represented in a balanced manner, while low entropy reveals persistent batch clustering.

• Normalized entropy: Scaled to [0,1] where 1 represents perfect mixing with equal representation from all batches
• Regional entropy maps: Visualizing entropy across a UMAP or t-SNE embedding reveals spatial patterns of incomplete mixing
• Overcorrection context: Must be interpreted alongside biological cluster purity metrics; high entropy alone does not guarantee successful correction if cell types are also blended

A kernel-based distribution distance used as both a loss function during deep learning-based batch correction and as a post-hoc evaluation metric. MMD measures the distance between probability distributions of different batches in a latent space.

• Pre-correction MMD: Quantifies the initial batch effect magnitude; larger values indicate stronger batch effects
• Post-correction MMD: Should approach zero, indicating aligned distributions; a value that is too low may signal overcorrection
• Kernel selection: The choice of kernel (e.g., Gaussian RBF) and bandwidth parameter critically affects sensitivity to different scales of distributional mismatch