Comparing the Four Methods on CLL

Four methods, one cohort, four kinds of math. MOFA fits a Bayesian factor model, SNF runs spectral clustering on a fused patient network, DIABLO fits a supervised sparse regression, and MCIA computes a non-parametric ordination. They share no assumptions. Run on the same 200 CLL patients, they reach the same conclusion.

They all find IGHV

The single most useful result in this section is that every method puts IGHV mutation status on its leading axis, without being told to, except DIABLO which was.

Method	Leading component	Association with IGHV
MOFA	Factor 1	Wilcoxon p = 5e-28
SNF	Cluster split, K = 2	Fisher p = 4e-40
MCIA	Axis 1	Wilcoxon p = 3e-29
DIABLO	Components 1 and 2	8% cross-validated error

Three of the four are unsupervised. They were handed the four data layers with no labels and, from the joint structure alone, recovered the split that a hematologist would draw. When methods with unrelated assumptions converge like this, the signal is real rather than an artifact of any one model. That is the whole argument for running more than one method: agreement is evidence.

They agree on the mechanism too

The convergence goes deeper than the split itself. Two methods, by different routes, name the same layer as the one carrying it. SNF measures which layer’s own clustering most agrees with the fused result and finds methylation far ahead at NMI 0.54. DIABLO measures which block discriminates best and finds methylation first at AUC 0.996. Two independent questions, one answer: in CLL the IGHV distinction is written most clearly in the epigenome. DIABLO adds a second corroboration by selecting, from the mutations layer, exactly the known CLL drivers (TP53, NOTCH1, ATM, SF3B1, del11q22.3, del13q14, del17p13).

Where they differ

Convergence on the answer does not make the methods interchangeable. They return different objects and answer different questions.

	MOFA	SNF	DIABLO	MCIA
Supervised	no	no	yes	no
Returns	factors + weights	patient clusters	feature panel	ordination + loadings
Missing data	native	impute	impute	impute
Feature-level output	yes	no	yes	yes
Runtime	minutes	seconds	minutes with CV	seconds

If you want the axes of variation and per-feature weights, MOFA. If you want discrete subtypes, SNF. If you have a label and want a short signature, DIABLO. If you want a fast check that the layers share structure at all, MCIA. The method chooser walks through the decision in full.

The one honest disagreement

The methods do not agree on everything, and the disagreement is instructive. SNF’s clusters recover IGHV at p = 4e-40, yet the same clustering scores a silhouette of 0.004, which reads as no separation at all. The internal geometry of the fused network is smooth, so a compactness index sees nothing while the biology is unambiguous. The lesson generalizes past SNF: validate an integration result against known biology, not against a cluster-quality number. On this cohort the biology is the ground truth, and every method finds it.