k-nearest Neighbor Batch Effect Test (kBET)

The core metric of kBET is the acceptance rate, derived from a chi-squared test. For a random subset of cells, the algorithm identifies their k-nearest neighbors and compares the observed local batch label distribution to the expected global distribution. A well-mixed dataset yields an acceptance rate near 1.0, while a score near 0.0 indicates strong local batch clustering. This provides a single, interpretable scalar value for integration quality.

Unlike global metrics that only compare overall distributions, kBET operates on a local graph topology. It constructs a k-nearest neighbor (kNN) graph and tests for batch label homogeneity within each cell's immediate neighborhood. This makes it exceptionally sensitive to local batch effects—pockets of cells from the same batch that remain clustered together—which global distribution comparisons like PCA visualization might miss.

kBET is grounded in formal statistical testing. The null hypothesis states that the batch labels within any local neighborhood are drawn from the same multinomial distribution as the global batch proportions. A rejection of this null hypothesis for a high proportion of neighborhoods indicates incomplete mixing. This framework allows users to set a significance level (alpha) to control the stringency of the mixing assessment.

To manage the computational complexity of testing every cell in large datasets, kBET employs a random sampling strategy. It iteratively selects a fraction of cells, computes their kNN graph, and performs the chi-squared test. The final acceptance rate is the average over these iterations. This approach provides a robust estimate of overall mixing while maintaining scalability for modern single-cell datasets containing millions of cells.

The choice of k (the number of neighbors) is a critical parameter that tunes the scale of the mixing assessment. A small k tests for very fine-grained, local mixing, while a larger k evaluates mixing over broader cellular neighborhoods. The kBET framework recommends testing a range of k values to understand the multi-scale mixing properties of an integrated dataset, ensuring that correction is not just superficial.

kBET is a standard evaluation tool in single-cell RNA sequencing workflows. It is implemented in the kBET R package and is frequently used to benchmark integration methods like Harmony, Seurat, and scVI. A high kBET acceptance rate, combined with a high cell-type Average Silhouette Width (ASW), provides strong evidence that a batch correction method has successfully removed technical variation while preserving biological signal.