Cross-Cohort Integration With Unequal Assay Panels

Why Unequal Assay Panels Require an Explicit Comparison Plan

Disease cohorts are often collected at different times, in different laboratories, or for different scientific aims. One cohort might have RNA sequencing and DNA methylation, while another has RNA sequencing and proteomics. Even when both cohorts address the same disease question, their combined data do not automatically form one comparable multi-omics table. The first task is to decide which measurements represent the same biological feature in a sufficiently comparable way, and which conclusions must remain specific to an assay or cohort.

The aim is not to force every cohort into a single complete matrix. Instead, define the part of the evidence that can be compared, preserve assay-specific results with clear labels, and state the limits of each conclusion. This separation makes cross-cohort evidence more interpretable and reduces the risk of treating absent measurements as biological absence.

Define the Comparison Before Combining Results

Let \(c\) index cohorts, \(i\) index subjects within a cohort, \(p\) index assay platforms, and \(g\) index biological features. For a disease-versus-control analysis, a cohort-specific effect for feature \(g\) might be the adjusted difference in mean log-expression between disease and control subjects. Write that estimate as \(\hat{\beta}_{cg}\), with standard error \(SE_{cg}\). The exact model depends on the study design, but the target must be stated in the same scientific terms across cohorts before estimates are combined.

For example, a log2-expression difference can be comparable across cohorts if the gene identifiers, expression processing, contrast definition, and adjustment strategy are aligned sufficiently to give the estimates the same interpretation. Raw counts from different sequencing runs are not themselves directly comparable merely because both are called expression. Nor does sharing a gene name guarantee comparability if one platform measures a different transcript region or uses a different feature definition.

A practical comparison plan therefore records, for each cohort, the available assay, the feature identifiers and annotation versions, the measurement scale, quality-control exclusions, and the disease contrast. Ambiguous feature mappings should be excluded from the shared set or reported as uncertain, rather than resolved by silently choosing one mapping. The shared set is often the intersection of eligible features after these checks; the broader union can still be retained for cohort-specific reporting.

Worked Examples

Why Inverse-Variance Pooling Has the Form It Does

The weighting in the previous example gives more influence to estimates with smaller variance. A short derivation shows the basis. Suppose independent cohort estimates \(Y_c=\hat{\beta}_{cg}\) are unbiased for one common effect \(\beta_g\), with known variances \(v_c=SE_{cg}^2\). Consider a weighted average \(\tilde{\beta}_g=\sum_c a_cY_c\), where \(\sum_c a_c=1\). It is unbiased because \(E(\tilde{\beta}_g)=\sum_c a_c\beta_g=\beta_g\). Independence gives variance \(\operatorname{Var}(\tilde{\beta}_g)=\sum_c a_c^2v_c\).

To minimize that variance subject to weights summing to one, use a Lagrange multiplier \(\lambda\) for the constraint. Differentiating \(\sum_c a_c^2v_c-\lambda(\sum_ca_c-1)\) with respect to \(a_c\) gives \(2a_cv_c-\lambda=0\), so \(a_c=\lambda/(2v_c)\). The constraint implies \(\lambda/2=1/\sum_c(1/v_c)\), hence \(a_c=(1/v_c)/\sum_j(1/v_j)\). Therefore the minimum-variance unbiased weighted average has the inverse-variance form used above. This derivation depends on the common-effect, independence, and variance assumptions; it does not establish that those assumptions fit every cross-cohort analysis.

Diagnostics, Alternatives, and Limits

Before interpreting a shared-feature result, check whether the feature mapping is stable, whether units and effect directions agree, and whether the contrast and covariate adjustment are sufficiently aligned. Review cohort-specific estimates and their uncertainty rather than relying only on a combined estimate. A sign reversal or markedly different magnitudes can signal that a single summary obscures relevant differences; it warrants investigation and cautious reporting, not automatic deletion of an inconvenient cohort. Also check whether a feature is genuinely unmeasured in a cohort, rather than recorded under a different identifier or filtered during quality control.

Several approaches are useful, but answer different questions:

A common mistake is to code a feature absent from a cohort’s panel as zero and then include it in a cross-cohort average. This confuses not measured with measured and having a zero value; the resulting summary has no valid interpretation as a shared-feature effect. Keep measurement availability explicit. Another mistake is to standardize every cohort’s values and assume that this makes unlike targets equivalent. Standardization changes numerical scale, but it does not repair a mismatched feature definition, assay target, or scientific contrast.

The shared set can also be narrower than the biologically interesting set, and cohort-specific evidence may be less independently validated than shared evidence. Results from an assay available in one cohort can generate hypotheses, but should be labelled as such and accompanied by the cohort, assay, effect scale, and uncertainty. Cross-cohort integration is strongest when it makes clear both what can be compared and what cannot.