Measuring the Contribution of Each Omics Block

Why Measure a Block’s Contribution?

A full multi-omics model can predict well without every modality contributing useful information. Conversely, a block may make a useful addition to a baseline even when the full model’s overall performance is only moderate. To answer what a particular block contributes, compare predictions from clearly specified models that differ in block availability—not just the full model’s score in isolation.

The key word is incremental. A block-ablation contrast asks how predictive performance changes when one block is removed from an integrated model. A block-addition contrast asks how performance changes when one block is added to a specified set of other blocks. These are related comparisons, but they need not have the same value: redundancy and interactions make a block’s contribution conditional on the comparison being made.

A loss is a quantity whose lower values represent better predictions. Examples include mean squared error for a quantitative outcome and log loss or Brier score for a binary outcome. If the chosen metric is a score for which higher values are better, such as area under the receiver operating characteristic curve, define the contrast in the opposite direction: score with the block minus score without it. State the metric, contrast direction, and units each time. A difference in mean squared error has squared-outcome units; a difference in log loss is in the units of that loss.

Comparisons That Make the Contrast Meaningful

A contrast is interpretable only when its two sides differ in the intended way. Use the same outcome definition, target population, held-out observations, data splits, and performance metric. Fit and evaluate preprocessing separately within the training data for each model: for example, normalization, feature filtering, and imputation must not use information from held-out observations. If the intended comparison is between predictive workflows, tune each workflow using training data only and apply comparable tuning budgets. Otherwise, a block can appear helpful because its model received more tuning effort or because held-out information leaked into its pipeline.

For an ablation comparison, refit the workflow without the block. Setting its measurements to zero after fitting the full model is generally not equivalent: the fitted model may rely on those measurements, and zero may not represent a plausible input. The reduced workflow should receive the same training and validation design, with preprocessing and tuning redone as required for that workflow. This contrast measures the effect of making the block available to the specified modeling procedure, not the effect of deleting a few coefficients from a fixed fitted model.

The comparison should also be specific about what is held fixed. If the goal is to compare block availability under a common model class, keep that class and its flexibility comparable. If the goal is to compare deployable end-to-end procedures, differences in preprocessing or model choice may be part of the procedures being compared. Either can be a legitimate target, but the result should not be described as an isolated biological property of a modality.

Why Addition and Ablation Can Differ

An ablation contrast evaluates a block conditional on all the other blocks already being present. An addition contrast evaluates it conditional on the particular baseline \(B\). Change \(B\), and the contrast can change. For example, two blocks carrying largely redundant signals may each improve a model when added alone, while neither improves it much after the other is included. A block that contains a useful cross-block interaction may make little difference alone but improve prediction when added to the block with which it interacts.

This conditional interpretation follows directly from the contrast definitions. For a loss metric, the addition contrast compares \(\widehat R(M_B)\) with \(\widehat R(M_{B\cup\{j\}})\). If another set \(C\) is used instead, the relevant comparison is \(\widehat R(M_C)\) with \(\widehat R(M_{C\cup\{j\}})\). There is no general algebraic reason for these differences to be equal. In particular, block contributions do not generally add up to the full model’s improvement over a no-block baseline.

Calculation and Interpretation on Held-Out Data

For an individual-level loss \(\ell\), calculate each model’s mean loss on the same \(n_{\mathrm{test}}\) held-out observations. For a block-addition comparison, let \(\ell_i(M_B)\) and \(\ell_i(M_{B\cup\{j\}})\) be the losses for held-out observation \(i\). Then $$ \widehat\Delta_j^{(+\mid B)} =\frac{1}{n_{\mathrm{test}}}\sum_{i=1}^{n_{\mathrm{test}}} \left\{\ell_i(M_B)-\ell_i(M_{B\cup\{j\}})\right\}. $$ The equation is just the difference of two sample mean losses, written as the mean of the paired loss differences. Pairing matters because both predictions concern the same observations; comparing performance numbers from unrelated test sets adds avoidable variation and can confound the block contrast with differences in case mix.

If the fitted models are fixed independently of the test set and test observations represent the target population, the average paired difference estimates the corresponding difference in expected predictive loss for that population. This justification depends on a suitable held-out evaluation design. With a small test set, a positive contrast can be noisy; with dependent observations, an ordinary observation-level average may not represent the uncertainty appropriately. Report the evaluation design and the size of the contrast, not just its sign.

Diagnostics, Alternatives, and Limitations

Before interpreting a contrast, check that it is not an artifact of a faulty comparison. Useful diagnostics include:

• Verify matched evaluation. Confirm that each compared model was assessed on the same held-out individuals and outcome definition. Check that any resampling or split assignment is consistent across models.
• Audit the pipeline. Confirm that filtering, scaling, imputation, feature selection, and tuning were performed without access to held-out outcomes or measurements. Repeat preprocessing and fitting for each ablated or augmented workflow.
• Inspect the distribution of differences. A favorable average can be driven by a few observations or one split. Examine paired loss differences or split-specific contrasts, while respecting dependence in the validation design.
• Check the comparator and direction. State exactly which blocks form the baseline, and verify that a positive number means improvement under the metric’s convention.
• Look for instability. If modest changes in splits, tuning choices, or preprocessing reverse the contrast, treat the estimated contribution as uncertain rather than as a stable ranking of modalities.

Block ablation and addition are not the only ways to describe importance. Single-block model performance asks how well a block predicts by itself; it does not measure what it adds to other blocks. Permutation importance disrupts a block’s values in a fitted model and measures a resulting change in performance, but correlation between blocks can make the disruption unrealistic or redistribute apparent importance. Coefficient-based summaries describe a particular fitted parameterization and can be difficult to compare across differently scaled or correlated features. Shapley-style allocations average contributions over subsets, but require many subset comparisons and depend on the chosen allocation convention. These approaches answer different questions; none turns predictive importance into a causal effect or a measure of biological mechanism.

The principal limitation is conditionality. A block’s measured contribution depends on the other blocks available, the model class, preprocessing, tuning, metric, and target population. Strong redundancy can make an informative block look dispensable in an ablation of the full model; that does not establish that the block contains no predictive information. Conversely, a positive held-out contrast supports incremental predictive value for the evaluated workflow and population, not a claim that the modality is universally useful or that its measurements cause the outcome.