Bioinformatics and multi-omics

Each omics layer measures a different physical quantity with a different instrument, and the differences do not cancel when the tables are joined. A transcript count is a small integer drawn from a sampling process; a protein abundance is a ratio of ion intensities on a log scale; a methylation value is a bounded fraction; a metabolite peak is an intensity that may not correspond to any identified molecule. Integration is hard not because the software is immature but because these are incommensurable measurements of a system whose layers are coupled by mechanisms that operate on different timescales.

Noise structure differs by layer

Count data from sequencing is overdispersed relative to Poisson: biological variability adds a variance term that grows with the square of the mean, which is why count models rather than normal models underlie differential expression. Mass-spectrometry intensities are roughly log-normal but bounded below by a detection limit. Array-based methylation is bounded on both sides and heteroscedastic near the boundaries. A method that transforms everything onto a common scale and applies one variance assumption throws away exactly the information that made each measurement trustworthy.

Missingness is not random

The layers also disagree about what a blank cell means. In single-cell RNA sequencing a zero usually reflects sampling depth rather than absence of the transcript. In mass spectrometry a missing value is often left-censored — the peptide was there and below the limit of detection — and the probability of missingness therefore depends on the abundance you are trying to estimate. Imputing such values with a layer-blind method (column means, nearest neighbours) inserts a systematic bias that then propagates into every downstream correlation.

Batch effects confounded with biology

The most common failure in published integrations is structural rather than statistical. If cases were processed in one run and controls in another, no correction can separate batch from condition, because the two are the same variable. Corrections that appear to work in these designs generally work by removing real biological signal along with technical variation. The defence is design — randomising sample order across runs, distributing conditions across plates and lanes, including bridging replicates — not a better algorithm afterwards. Where the design was fixed before the analyst arrived, the honest report says the effect is not identifiable.

The arithmetic of power

Multi-omics multiplies features, not samples. A study with fifty subjects and a hundred thousand measured features tests far more hypotheses than it has independent observations, so with familywise or false-discovery correction it can only detect effects that are very large. Cross-layer correlations found in such data are frequently unreplicable, and the number of possible pairwise associations between two layers grows as the product of their feature counts. A useful discipline is to state, before analysis, what effect size the design could detect, and to treat integration outputs as hypothesis-generating unless an independent cohort has confirmed them.

None of this makes integration futile. It does mean that the value usually comes from constraining one layer with another — using chromatin accessibility to prioritise which expression differences are plausibly regulatory, for instance — rather than from expecting a joint model to reveal what no single layer could.