Uncertainty and Missingness in Functional Annotation Tracks

Why Missingness Changes a Locus Interpretation

A functional annotation track can show a signal, show no signal, or provide no usable observation at all. These outcomes are not interchangeable. A regulatory assay may not have been run in the relevant cell type; a variant may fall outside the assay’s measured regions; or reads may map ambiguously. In each case, the track may be uninformative about that variant, even if a data table displays a blank or a zero.

This matters when interpreting a fine-mapped locus. A variant with a high posterior probability of being causal can lack an annotation simply because the relevant assay was unavailable. Treating that absence as evidence against function can shift attention toward variants that happened to be measured. The goal is to describe what was observed, how much of the locus’s posterior mass was observable, and how uncertain the observations are.

The posterior probabilities \(\pi_j\) describe uncertainty about which variant is causal; they do not establish what the causal variant does. Annotation availability and measurement uncertainty are separate from that fine-mapping uncertainty. Keeping these sources distinct makes it possible to say, for example, that a candidate variant has substantial causal probability but lacks relevant assay coverage.

Measuring Posterior-Weighted Coverage

A simple count of annotated variants can be misleading because variants in a credible set can have very different posterior probabilities. A more informative coverage summary weights each variant by its posterior probability. For track \(a\), define posterior-weighted coverage as:

If \(C_a=0.80\), then 80% of the locus’s posterior probability is assigned to variants with usable observations in track \(a\). The remaining 20% is posterior mass for which this track does not provide a usable observation. This is a coverage statement, not a probability that the annotation is correct or that the locus is functional.

A positive-signal summary among covered variants can also be calculated:

This quantity describes the posterior-weighted fraction of covered mass with a measured signal. It is conditional on availability in the track. It should not be reported as if it summarized the entire credible set unless coverage is complete or the qualification is made explicit.

When Is a Negative Result Evidence?

A measured negative can count against a functional effect, but its strength depends on whether the assay could detect that effect under the conditions used. A negative result in an irrelevant cell type may say little about a mechanism operating in another cell type. Likewise, a poorly powered assay or one with low sensitivity can miss real effects. A missing track, by contrast, provides no measured negative result to interpret.

A basic way to quantify a negative result is to use the assay’s sensitivity and specificity. Sensitivity is \(P(\text{positive result}\mid\text{functional effect})\); specificity is \(P(\text{negative result}\mid\text{no functional effect})\). These quantities must apply to the relevant assay, cell context, and definition of a functional effect. If the prior probability of an effect is \(P(F)\), Bayes’ rule gives:

A negative result is more informative when it is unlikely under a real effect—that is, when sensitivity is high. A negative from an insensitive assay may barely change the prior assessment. This calculation does not make assay performance known: sensitivity and specificity need credible estimates, and a single estimate may not transfer across cell types or variant classes.

Missingness Can Be Selective

An observed-only summary describes covered posterior mass. It does not automatically estimate what would have been seen if the entire credible set had been measured. This distinction is important because coverage may depend on variant location, assay design, cell type, or other properties that also relate to functional evidence.

The relationship can be stated directly. Let \(\theta_j\) be a quantity of interest for variant \(j\), such as its probability of having a specified functional effect. The full posterior-weighted locus summary is \(\theta=\sum_j\pi_j\theta_j\). For \(C_a>0\), define the covered and uncovered posterior-weighted means as \(\theta_{\mathrm{obs}}\) and \(\theta_{\mathrm{miss}}\), respectively. Then:

This identity follows by splitting the sum for \(\theta\) into variants with \(R_{ja}=1\) and \(R_{ja}=0\), then dividing each part by its posterior mass. It shows why \(\theta_{\mathrm{obs}}\) equals the full-locus summary only when coverage is complete, or when the covered and uncovered groups have the same mean for the quantity of interest. That equality cannot be assumed merely because the available observations are numerous.

Cell Availability, Mapping Quality, and Annotation Confidence

Coverage should be defined in the biological context relevant to the interpretation. If an assay is available only in a different cell type, that may be coverage of a track but not coverage of the relevant biological question. State which cell type or tissue the track represents. Where several cell types are plausible, report coverage separately by cell type rather than treating measurements from them as interchangeable.

Mapping quality introduces uncertainty about whether a signal has been assigned to the correct genomic location or variant. A low-quality mapping should not silently become a confident positive or negative. One option is to set a prespecified quality threshold and classify observations below it as unusable, reporting the resulting coverage. Another is to model mapping uncertainty explicitly, provided the model and its assumptions are stated. These approaches answer different questions and should not be mixed without explanation.

An annotation confidence score also needs careful interpretation. Unless it has been calibrated, a score of 0.8 is not necessarily an 80% probability that the annotation is correct. If a score is calibrated for a defined target and context, it can be treated as an estimated probability for that target. Otherwise, report it as a score, describe its scale, and consider sensitivity to reasonable thresholds rather than converting it to a probability by assertion.

A Practical Reporting Sequence

A transparent locus-level summary makes the observation process visible before drawing a biological conclusion. The following sequence is useful when interpreting any functional track.

Common Mistake: Treating Every Blank as a Negative

A common but incorrect argument is: “This variant has no annotation, so the assay shows it is not functional.” That conclusion does not follow if the relevant track was unavailable, the variant was outside the assay’s coverage, or mapping quality was inadequate. In those cases, there is no usable negative measurement. The correction is to label the observation as missing or unusable, quantify its posterior mass, and reserve negative evidence for a measured result whose assay context and detection ability are relevant.

The same caution applies to a genuine measured negative: it is evidence about the assay’s target under its conditions, not proof that the variant has no function in every context. A careful interpretation separates causal-variant uncertainty, track availability, measurement error, and the biological scope of the assay.