This methylation study, explained to a statistician

Experimental units, estimands, contrasts, pairing, count models, technical replication, and multiplicity

The statistical problem

This is an exploratory, cross-sectional, three-group study with paired tissue and plasma specimens, high-dimensional methylation counts, a lower-dimensional serum sIgA outcome, and laboratory technical replication nested within 18 participants.

Alignment and methylation calling are treated as given. The analysis begins with genomic coordinates, methylated counts \(M\), informative coverage \(N\), specimen and replicate identifiers, assay QC, and participant covariates.

Design and hierarchy

The planned groups are high-risk UC (\(n=8\)), CRC (\(n=5\)), and healthy comparators (\(n=5\)). Plasma and colonic tissue are paired within participant. Three technical replicates characterize laboratory variability.

flowchart TD
  G[Clinical group] --> P[Participant: independent unit]
  P --> A[Plasma assay]
  P --> B[Tissue assay]
  P --> C[sIgA assay]
  A --> AR[Three technical replicates]
  B --> BR[Three technical replicates]
  C --> CR[Three technical replicates]
  AR --> AF[CpG and region summaries]
  BR --> BF[CpG and region summaries]
  CR --> CF[One QC-controlled concentration]

Reads are binomial sampling units conditional on a biological specimen; CpGs are repeated genomic features; technical replicates are nested measurements; participants are the biological replicates. Any analysis that treats reads, CpGs, or technical replicates as independent patients is pseudoreplication.

Primary estimands should be explicit

For each tissue type and CpG or region, sensible estimands include:

• mean methylation difference: UC minus healthy;
• mean methylation difference: CRC minus healthy;
• mean methylation difference: CRC minus UC;
• tissue–plasma difference within participant; and
• difference in tissue–plasma concordance across clinical groups.

For sIgA, the natural estimands are group differences in an appropriately transformed concentration and associations with pre-specified methylation summaries after adjustment for group and inflammation.

An ordered “healthy → UC → CRC” contrast may be explored, but it does not estimate progression: the groups are different people observed once, not repeated stages in the same individuals.

Why methylation is a count problem

At CpG \(g\) for sample \(i\):

\[M_{gi}\mid N_{gi},p_{gi}\sim\operatorname{Binomial}(N_{gi},p_{gi}),\]

with biological heterogeneity motivating a beta-binomial extension. Coverage \(N_{gi}\) varies substantially, especially in plasma. A site observed as \(1/2\) and one observed as \(50/100\) both have beta value 0.5 but radically different precision.

For raw EM-seq counts, a count-aware model such as DSS is therefore a defensible primary approach. A transformed continuous model can be a sensitivity analysis when its weights and mean–variance assumptions are explicit. The limma-versus-DSS post develops this distinction with executable real-data R code.

Contrasts and multiplicity

A minimal group parameterization can use healthy as reference:

\[g\{p_{gi}\}=\alpha_g+\beta_{g,UC}I(UC_i)+\beta_{g,CRC}I(CRC_i)+\boldsymbol\gamma_g^T\mathbf z_i,\]

where \(\mathbf z_i\) contains only defensible, pre-specified nuisance variables. With 18 participants, every adjustment consumes scarce information; batch must be prevented from becoming aliased with clinical group by design wherever possible.

The three key contrasts are:

Contrast	Interpretation
\(\beta_{g,UC}\)	UC versus healthy
\(\beta_{g,CRC}\)	CRC versus healthy
\(\beta_{g,CRC}-\beta_{g,UC}\)	CRC versus UC

Report methylation differences with confidence intervals or compatible uncertainty measures, coverage, and FDR. Region calling should require coherent neighboring CpGs and pre-specified thresholds. Nominal \(p<0.05\) across millions of CpGs is not evidence control.

How to handle the three technical replicates

Replicates serve QC and precision estimation. A pre-specified workflow should:

1. retain replicate-level provenance and QC metrics;
2. identify failures using assay-specific rules without looking at group outcomes;
3. quantify concordance and batch/library effects;
4. combine valid sequencing replicates at the count level when scientifically appropriate, so coverage is preserved; and
5. reduce ELISA replicates to a dilution-corrected participant estimate with replicate CV and quantification-limit flags.

If replicate-specific variability is itself important, use an explicit hierarchical model. Do not enter three replicate rows into an ordinary group test and claim 54 degrees of biological replication.

Pairing tissue and plasma

Tissue and plasma are different measurement regimes, not interchangeable repeated assays. A joint model should allow specimen-specific mean, variance, coverage, and mixture effects while using participant pairing.

At a reduced set of regions, one interpretable model is:

\[y_{is}=\alpha+\beta_1 Group_i+\beta_2 Specimen_s+\beta_3(Group_i\times Specimen_s)+b_i+\varepsilon_{is},\]

where \(b_i\) captures participant pairing. The interaction asks whether group differences transfer from tissue to plasma. For raw CpG counts, the analogous structure needs a suitable count likelihood or a carefully constructed region-level response.

Plasma-only effects may reflect systemic or hematopoietic composition; tissue-only effects may be locally strong but too diluted in blood. Neither disagreement pattern is automatically a technical failure.

Integrating sIgA without manufacturing significance

sIgA is one immune-axis variable, not another omics matrix. Useful analyses include:

• robust descriptive group comparisons with raw participant points;
• regression of sIgA on a small number of pre-specified DMR/pathway scores;
• partial association adjusted for group, inflammation, and assay batch; and
• incremental-model comparisons with honest cross-validation if prediction is explored.

Testing sIgA against every CpG recreates the multiplicity problem with little power. Dimension reduction should be biologically or externally specified, or performed within a fully nested validation procedure.

Missingness, sensitivity, and reporting

Coverage-dependent missingness is structural, not generic tabular NA. Report callable loci by specimen and group; pre-specify minimum coverage and sample-presence rules; examine whether filtering changes the estimand. Sensitivity analyses should address technical-replicate combination, coverage thresholds, region definitions, influential participants, and plausible confounding.

The most informative deliverable is a compact results object containing effect, interval, FDR, coverage, replicate QC, genomic annotation, tissue–plasma agreement, and sIgA association—not a binary “significant” column.

ImportantThe statistical takeaway

The study is strongest as effect estimation and candidate-feature discovery under a transparent hierarchy. Its inferential bottleneck is 18 biological units, not the number of reads, CpGs, or technical replicates.

See the study design → · Inspect the three processed data streams → · Read the ML companion → · Review the statistical analysis overview →