Integrative Clustering for Autoimmune Disease Endotypes

From Multilayer Profiles to Candidate Endotypes

Autoimmune disease labels can encompass patients with different molecular patterns and clinical courses. Transcriptomic measurements may reflect immune-cell activation, proteins may capture circulating inflammatory signals, and clinical measurements may summarize disease activity or organ involvement. Integrative clustering asks whether patients can be grouped using these measurements together, without using a preassigned diagnosis as the grouping target.

A cluster is a group formed by a specified algorithm and a specified representation of the data. An endotype is a proposed disease subgroup characterized by a biological pattern that may help explain disease heterogeneity. A cluster can suggest a candidate endotype, but the algorithm does not establish a biological mechanism, a clinical diagnosis, or a treatment recommendation. Those claims require additional evidence.

The clustering unit must be clear: here it is the patient. Measurements from different blocks should refer to the same patient and a scientifically comparable time point. If repeated measurements during treatment are used, a patient’s measurements cannot be treated as independent patients; the design must first define which time point or patient-level summary enters this clustering analysis. This tutorial concerns patient-level grouping, not modeling within-patient change.

A Block-Weighted Distance

For a transparent construction, suppose each block contains continuous features that have been transformed as appropriate and standardized feature by feature. Write \(z_{ij}^{(m)}\) for patient \(i\)'s standardized value on feature \(j\) in block \(m\), and let \(p_m\) be the number of features in that block. For patients \(i\) and \(i'\), define the average squared distance within block \(m\) as the mean squared difference across its features. Combine block distances using nonnegative weights \(w_m\) that sum to 1:

This definition gives each block an explicit role. With equal weights, a block contributes its average squared feature difference, rather than a sum that automatically grows with the number of features. Equal weights do not guarantee equal biological influence: correlated features, differing measurement reliability, and the features chosen within each block still matter. The weights should therefore be selected for a stated scientific reason and reported.

For complete continuous data, one possible clustering rule is weighted \(K\)-means: choose \(K\) groups and minimize the total weighted squared distance from each patient to the centroid of the assigned group. A centroid is the vector of feature means within a group. The optimization objective is:

where \(C_k\) is the set of patients assigned to cluster \(k\), \(z_i^{(m)}\) is patient \(i\)'s vector for block \(m\), and \(\bar{z}_{C_k}^{(m)}\) is the block-specific centroid. This objective is appropriate only if the features and distances represent meaningful patient similarity. \(K\)-means also favors roughly compact groups in this distance representation; it is not a general model for every possible cluster shape.

Worked Examples

Why Scaling and Block Size Matter

Standardizing features and balancing blocks address different issues. Feature standardization prevents a variable measured on a numerically large scale from dominating simply because of its units. Block normalization prevents a block with many measured features from contributing a large sum solely because it contains more terms. Neither step repairs poor measurement, inappropriate transformations, or redundant features.

Interpreting Profiles and Checking the Analysis

To interpret groups, report their sizes and summarize the features that distinguish them, using the original measurement scales where possible. A useful profile distinguishes what was used to create the clusters from what was examined afterward. When the same features are used both to form and describe clusters, separation on those features is expected by construction and should not be presented as independent evidence.

A practical analysis should check whether the data representation supports the intended biological interpretation. For example, examine feature distributions and outliers before distance calculations; confirm that transformations suit skewed measurements; and inspect whether assay platform, collection site, or missingness patterns align with the resulting groups. If a cluster is largely defined by a technical batch or by missing-data patterns, its apparent biological profile may be misleading. Relevant earlier material includes the standard topics of cohort and platform confounding and subjects with incomplete omics profiles.

These checks are diagnostic, not proof that a cluster is real. The forthcoming material on subgroup instability and replication addresses questions of robustness and external confirmation; a profile table alone cannot answer them.

Integrative clustering is one option among several. Single-block clustering is easier to interpret but can miss cross-layer patterns. Early integration combines features before clustering and can be sensitive to feature counts and scaling. The block-weighted distance used here makes each block’s contribution explicit. Latent-factor approaches instead represent shared variation through a smaller set of learned components, which can simplify high-dimensional profiles but may make the resulting clusters harder to explain in the original measurements. Clinical-label-based grouping answers a different question: it groups patients by an existing clinical category rather than discovering groups from the measured profiles.

No method can make an arbitrary partition into a biological endotype. Interpretations are limited by sample size, feature selection, assay quality, treatment and disease timing, and whether the study population represents the intended clinical setting. A clinically useful classification also needs evidence that it improves understanding or decisions beyond the measurements and labels already available.

A Practical Reporting Sequence