Batch Adjustment Without Test-Set Contamination

Why Batch Adjustment Must Match Deployment

Omics measurements can differ across assay runs, laboratories, instruments, or processing dates. These systematic differences are called batch effects. Adjustment can make measurements more comparable, but in prediction work the source of each adjustment estimate matters: if held-out measurements help determine the transformation applied to those same measurements, the test set is no longer independent of preprocessing.

A fair evaluation should reproduce the information available when the model is used. If a future patient’s specimen will be processed alone, a correction that relies on the other future test specimens cannot be assumed available. If deployment really does process a defined cohort together and permits the use of its unlabeled measurements, joint estimation may match that workflow. The distinction is not simply whether test outcomes were used: test features can also influence a fitted transformation.

A Model for an Additive Batch Effect

For feature \(j\) in sample \(i\), consider the model

Here \(Y_{ij}\) is the measured feature value, \(X_i\) contains measured biological covariates whose effects should be retained, \(b_i\) is the sample’s batch, \(\alpha_j\) is a baseline, \(\beta_j\) describes covariate effects, and \(\gamma_{b_i j}\) is the additive batch effect for that feature. A reference batch is assigned \(\gamma_{b j}=0\). A corrected measurement is \(Y_{ij}-\hat{\gamma}_{b_i j}\); the covariate contribution is retained rather than subtracted.

This model gives a useful starting point, not a guarantee that correction is safe. It assumes that the batch effect is additive for the feature, that the fitted batch and biological effects represent the deployment data, and that the design provides enough information to distinguish them. Errors should be centered around zero conditional on the modeled covariates and batch; dependence between samples or other unmodeled structure can also make simple uncertainty calculations unreliable. In particular, if biological groups and batches do not overlap, their effects may not be separately identifiable.

In prediction, fit the model separately inside each training fold. The fit must not use held-out measurements to estimate feature means, batch offsets, scales, or other correction parameters. Batch labels for held-out samples may be used to select an already estimated offset only if those labels would be known at prediction time. If a held-out sample belongs to a batch absent from training, a training-only fit cannot estimate that batch’s offset without an additional source of information, such as calibration samples or a prespecified reference procedure.

Why Joint Estimation Changes the Evaluation

When the same batch appears in both training and test data, a tempting approach is to estimate its offset from all samples in that batch. Even without outcomes, this allows the held-out feature values to influence the correction. The model and its predictions are therefore conditioned on information from the test set. This may be appropriate for a transductive deployment protocol, but it does not estimate the performance of a procedure that receives one new sample and uses training-only parameters.

The dependence can be seen directly. If a batch offset is calculated as the difference between a batch mean and a reference-batch mean, adding held-out observations to the batch mean changes the estimated offset whenever their average differs from the training average. Subtracting that changed offset then changes the held-out values themselves. This is a form of test-set contamination even though the labels were not used.

Identifiability and Diagnostics

A correction should not be interpreted as separating technical and biological variation unless the study design supports that separation. With batch and biological group observed together, a fitted model can adjust for both only when the design matrix contains enough independent variation to estimate their effects. Replication across batches and overlap of biological groups across batches provide that information. If every control is in one batch and every case in another, the observed difference can be explained by a biological effect, a batch effect, or a combination; the measurements alone cannot distinguish those explanations.

Useful diagnostics therefore concern both the data and the intended use:

• Tabulate batch by biological group. Empty or nearly empty combinations flag confounding or weak overlap.
• Check whether the batch labels and any reference or calibration samples needed for correction will be available for future predictions.
• Compare feature distributions and residuals across batches after adjustment, while remembering that visual similarity does not prove biological information was preserved.
• Inspect whether training and deployment batches are represented comparably. A new laboratory, assay version, or processing protocol may violate the assumption that training-derived offsets transfer.
• Record exactly which samples contributed to every estimated parameter. If held-out features contributed, the evaluation is not a training-only evaluation.

Failure signs include large changes in offsets when a few samples are added, offsets that track biological group differences, and held-out batches for which no valid correction parameter exists. Re-estimating from the test data to make distributions look similar is not a remedy for these problems; it changes the evaluation and can conceal a deployment mismatch.

Choosing a Strategy for the Intended Use

The appropriate alternative depends on what information prediction will actually receive. Training-only correction is the default for an inductive evaluation: it applies fixed, training-estimated parameters to new samples. It is straightforward when future samples belong to known batches represented in training. It cannot, by itself, estimate an effect for a genuinely new batch.

Reference-based correction uses prespecified reference material or calibration samples to estimate how a new run differs from a common scale. This can support correction of new batches if the reference procedure is available at deployment and behaves consistently. The reference measurements are not a license to use held-out evaluation samples to fit their own correction; the evaluation must reproduce the planned reference protocol.

Joint train-test correction can be defensible when deployment will receive a cohort of unlabeled samples together and will use their combined feature distributions before making predictions. The evaluation must then mimic that batch-level workflow, including cohort size and composition. Performance from this setting does not directly answer how the model performs on a single future sample corrected using training data alone. Never use held-out outcomes to estimate corrections, and do not describe a transductive evaluation as training-only.

Other modeling choices include retaining batch as a predictor when its labels will be known and stable at deployment, or using a prespecified external calibration. These approaches have their own assumptions: a batch indicator cannot solve an unseen-batch problem unless the model has a supported way to handle it. Feature-wise methods that also estimate scale or shrinkage parameters require the same discipline about which samples contribute to those estimates. The name of the adjustment method does not determine whether leakage occurs; the fitting data and deployment protocol do.