Integration reports are usually judged on one thing: do the batches mix? That is half a metric — perfect mixing is trivially achieved by destroying the signal, and the plots look better as that happens. Here is the other half, measured, on GEO GSE96583 — 8 donors, control vs IFN-β.
For every cell we take its 30 nearest neighbours and ask two questions: what fraction share its donor, and what fraction share its condition. Good integration pushes the first down towards chance (12.5% for 8 donors) and leaves the second alone.
| Same-donor neighbours should fall |
Same-condition neighbours should hold | |
|---|---|---|
| Before integration | 25.2% | 92.2% |
| After Harmony | 20.1% | 92.1% |
| Fully mixed baseline | 12.5% | — |
Two things are true here and both belong in a report. The donor effect was reduced by 20.2% but not eliminated — 20.1% of neighbours still share a donor against a 12.5% floor, which is what real biological variation between people looks like and is not something to force away. And the treatment signal moved by -0.1% — that is the number that matters: the correction did not dissolve the interferon response it was supposed to leave alone.
Had we tuned the integration harder until donors mixed perfectly, the second number would have fallen with it, and the paper would have reported a weakened treatment effect caused entirely by the analysis.