Balancing Sequencing Batches Across Case Status

Why Sequencing Allocation Is Part of Study Design

Rare-variant association studies depend on comparing genetic data from cases and controls. But sequencing data are produced through technical processes: samples are placed on plates, processed in batches, and often handled at multiple centers. If cases are concentrated in one batch and controls in another, a technical difference between batches can become entangled with the phenotype comparison. The design problem is therefore not merely how many samples to sequence. It is how to distribute them so that technical groups contain informative representation of the phenotype and recruitment sources.

Balancing does not mean that every batch must have exactly equal numbers of cases and controls. Case-control ratios, plate capacity, center availability, and source-specific sample counts can make that impossible or inappropriate. The essential goal is overlap: wherever feasible, each technical group should include both cases and controls, and the allocation should avoid making batch or center a near-perfect proxy for phenotype or source.

Plan Across the Technical Hierarchy

Technical units may be nested. For example, plates may be processed in batches, and batches may be handled at centers. Balancing only at the broadest level can leave a finer level completely confounded: a center might contain both cases and controls overall, while each individual plate contains only one status. Planning should therefore identify the units at which meaningful technical variation may occur and seek phenotype overlap at those levels, subject to capacity and workflow constraints.

A useful planning table crosses phenotype status with technical unit. For each unit \(j\), record the number of cases \(n_{1j}\), controls \(n_{0j}\), and total participants \(n_j=n_{1j}+n_{0j}\). The within-unit case proportion is \( \hat{p}_j=n_{1j}/n_j \). A design in which every \(\hat{p}_j\) is close to the overall case proportion is generally preferable to one in which some units are nearly all cases and others nearly all controls. The target is not necessarily \(0.5\); it depends on the planned case-control ratio.

Recruitment source should also be included in the planning table when source-specific sampling or processing is relevant. If one source contributes mostly cases and another mostly controls, assigning each source to a different center would make center, source, and phenotype difficult to distinguish. Where feasible, place participants from each source and status across the technical units, while respecting the actual numbers available from each source. This allocation does not eliminate any underlying source-phenotype association; it prevents the sequencing assignment from adding another avoidable alignment.

Worked Allocations

Why Overlap Supports a Separate Phenotype Comparison

The reason to avoid complete batch-phenotype alignment can be shown directly from the additive model above. Suppose there are two batches and every participant in Batch 1 is a case while every participant in Batch 2 is a control. Let \(B_i=1\) for Batch 1 and \(B_i=0\) for Batch 2. Then \(D_i=B_i\) for every participant. The model terms \(\beta D_i\) and the batch contrast are therefore indistinguishable: changing the estimated phenotype effect can be offset by changing the estimated batch effect, without changing fitted values. The data do not identify these two effects separately.

When both statuses occur within batches, phenotype varies even after batch membership is held fixed. A within-batch case-control contrast is then available. For a simple illustration of the information in that contrast, assume independent errors with common variance \(\sigma^2\), a correctly specified additive batch model, and fixed batch membership. The information for the status coefficient after accounting for batch is proportional to

For a given batch size \(n_j\), the factor \(\hat{p}_j(1-\hat{p}_j)\) is largest when the two statuses are equally represented. To verify this, complete the square:

Thus, if the overall design permits it, equal status counts within a unit maximize this component. With an unequal overall case-control ratio, the corresponding practical target is usually to keep batch-specific proportions near the overall proportion, not to force every batch to 50% cases. The derivation relies on the stated model and variance assumptions; it explains a design principle, not a guarantee that any particular analysis is valid.

Common Mistakes and Practical Limits

• Checking only the overall totals. An overall 1:1 case-control ratio can conceal batches that are nearly all cases or nearly all controls. Inspect the status counts within each technical unit.
• Balancing centers but ignoring plates. A center may have a balanced total while its individual plates are status-specific. Check each level at which technical effects may arise.
• Confusing balance with identical source composition. Source-specific counts may make identical composition infeasible. Preserve overlap where possible and document unavoidable empty cells.
• Assuming allocation repairs source-phenotype confounding. Distributing each source across batches can prevent batch from simply reproducing source membership, but it cannot create cases or controls in a source that has none.
• Treating a statistical adjustment as a substitute for design. Including batch terms in an analysis cannot separate batch and phenotype effects when the allocation makes them perfectly aligned. Design overlap is needed for the data to contain the relevant comparison.
• Randomizing without constraints. Unrestricted random placement can produce avoidable imbalances, especially with small samples. Randomize within source-status blocks or use constrained randomization, then verify the realized counts.

A useful allocation record includes the planned and realized counts by status, source, center, plate, and processing batch. When deviations occur, document their reasons before analysis. If capacity or eligibility constraints prevent overlap, state that limitation clearly; no allocation algorithm can manufacture missing combinations.