Statistical Challenges in Single-Cell ATAC-seq

Why Single-Cell ATAC-seq Needs Careful Inference

Single-cell ATAC-seq measures transposition-associated fragments across genomic regions in individual cells. Compared with an assay summarized over a bulk sample, it can reveal cell-to-cell variation and accessibility patterns within cell types. But a cell-by-region matrix is often mostly zero, cells can have very different numbers of usable fragments, and cells from the same donor are not independent biological replicates. Each feature affects differential accessibility testing.

The central inferential question is usually whether accessibility differs between conditions in a target cell population. The treatment or condition is assigned at the donor level in many studies, while thousands of cells may be measured per donor. Counting every cell as an independent replicate can therefore make uncertainty appear much smaller than it is. The analysis must reflect both the sequencing process and the study’s actual replication structure.

Sparsity and Unequal Fragment Depth

A zero count has several possible explanations: the region may be inaccessible in that cell, the region may be accessible but not sampled by any fragment, or technical features such as low library complexity may have limited detection. Thus, zero is an observed count, not direct proof of biological absence. This is particularly important when a region is weakly accessible or when a cell has few fragments overall.

Depth changes the chance of observing at least one fragment. As a simplified illustration, suppose fragments are sampled independently and a region contributes a small fraction \(q\) of a cell’s fragments. With \(L\) sampled fragments, the probability of observing no fragment from that region is approximately \((1-q)^L\), which is close to \(e^{-Lq}\) when \(q\) is small. The approximation shows why the same underlying accessibility can produce zeros more often in a low-depth cell. Real data also have biological and technical variation beyond this simple sampling model.

A common count-model formulation uses \(Y_{ir}\), the fragment count for region \(r\) in cell \(i\), and \(L_i\), that cell’s usable fragment depth. A log-depth offset accounts for the expected increase in counts with library size. For example, a negative-binomial model may specify

Here \(T_i\) indicates condition, \(\phi_r\) describes overdispersion under the chosen negative-binomial parameterization, and the omitted terms may represent covariates or donor effects. The offset treats depth as exposure: it adjusts the expected count for the number of fragments sampled, rather than claiming that depth differences are themselves biological effects. The model still needs a suitable mean-variance form, a design that separates condition from other covariates, and an account of dependence among cells from the same donor.

Cells Are Nested Within Donors

Cells from one donor share genetic background, sample handling, and other donor-specific features. Their measurements can therefore be correlated. If a condition is applied to donors, the independent evidence for a condition effect comes primarily from the number of donors, not from the number of cells alone. When donors contribute cells to both conditions, the analysis should also preserve that pairing.

The consequence of ignoring within-donor correlation can be seen from a simple cluster-sampling calculation. Suppose each of \(D\) donors contributes \(m\) cells, each cell-level measurement has variance \(\sigma^2\), and two different cells from the same donor have correlation \(\rho\). The variance of the overall cell mean is

To obtain this expression, sum the variances of the \(Dm\) observations and their covariances. There are \(Dm\) variance terms, each \(\sigma^2\). Within each donor, there are \(m(m-1)\) ordered pairs of distinct cells, each with covariance \(\rho\sigma^2\); cells from different donors are assumed independent. Dividing the total variance by \((Dm)^2\) gives the formula. The factor \(1+(m-1)\rho\) is the design effect relative to treating all cells as independent.

This calculation assumes equal cluster sizes and a common within-donor correlation; real data can be more complicated. It nevertheless makes the basic issue clear: even modest correlation matters when many cells come from each donor. The formula does not make the cells equivalent to that many independent donors. It quantifies loss of information from clustering under its simplified assumptions.

Cell-Level Models and Pseudobulk

A cell-level strategy models individual cell counts, often with a depth offset and donor represented through fixed effects, random effects, or a suitable correlation structure. It can use cell-level variation and accommodate covariates that vary across cells. Its validity depends on correct modeling of count variation and donor dependence. A model that includes thousands of cells but treats them as independent does not meet that requirement when cells are clustered by donor.

In a pseudobulk strategy, counts are summed across cells within each donor, condition, and cell type. The resulting donor-by-condition-by-region count is analyzed as a sample-level count, with an offset based on the aggregate library depth and a design that accounts for condition and any pairing or covariates. Summing counts avoids treating each cell as a separate replicate. It also means the analysis targets accessibility differences in the aggregated population; variation between cells is not separately modeled.

Neither strategy is automatically correct in every design. Cell-level models may be useful when cell-level covariates or distributions are of direct interest, provided dependence is modeled and there are enough independent donors to estimate the effect. Pseudobulk analyses are often easier to align with donor-level replication and count-based differential testing, but they require sufficient cells and fragments within each aggregate and can conceal cell-to-cell heterogeneity. In either approach, donor-level confounding between condition and batch cannot be repaired by simply adding more cells from the same donors.

Diagnostics, Failure Modes, and Limitations

Before interpreting differential accessibility results, check that the analysis reflects the experimental design. Useful checks include the following:

• Inspect depth and sparsity by donor and condition. Compare fragment-depth distributions, the fraction of zero entries, and cell numbers. A condition with systematically lower depth may have more zeros for sampling reasons.
• Check donor representation. Confirm that the condition effect is not inseparable from donor or batch. For paired designs, verify that the same donors contribute eligible cells to both conditions.
• Examine donor-level results. Look for a reported effect driven almost entirely by one donor. A large number of cells does not make that donor-specific pattern broadly replicated.
• Review model fit and uncertainty. Check whether residual variation or overdispersion is compatible with the fitted count model, and whether standard errors reflect clustering when cells are analyzed individually.
• Assess aggregate adequacy. Pseudobulk groups with very few cells or fragments may be unstable. Excluding groups must be justified and reported; selective removal can change which donors contribute to the comparison.

A common mistake is to reason, “There are 5,000 cells in each condition, so the test has thousands of independent replicates and very high precision.” If cells came from only a few donors, this treats subsamples as independent experimental units and can produce overly small standard errors and misleadingly small \(p\)-values. The correction is to model donor dependence at the cell level or aggregate to donor-level pseudobulks, then base condition inference on the independent donors. More cells can improve measurement of each donor’s profile, but they cannot replace additional donors.

Both strategies have limits. Sparse counts can make region-specific estimates unstable, particularly in low-depth aggregates. Pseudobulk sums can mask mixtures of cell states or opposing responses among cells. Cell-level methods can be sensitive to distributional assumptions and computational choices. In both cases, conclusions apply to the sampled donors, cell-type definition, regions tested, and experimental conditions; they do not by themselves establish a causal mechanism. The earlier material on differential chromatin accessibility provides the broader count-testing context, while the present choices concern how to preserve the single-cell sampling and donor structure.