Coverage Planning for Comparable Rare-Variant Callability

Why Comparable Callability Is a Design Requirement

A rare variant that is not detected cannot contribute to a gene-level association analysis. If a target region is less well covered in cases than in controls, some true case variants may be recorded as missing or missed, while comparable control variants are detected. The reverse imbalance can make controls appear to carry more variants. Either way, a difference in observed variant counts may partly reflect sequencing opportunity rather than biology.

Coverage planning therefore asks more than whether the study has a high average depth. It asks whether the same relevant bases, in the same kinds of samples, have similar chances of yielding a usable call. That requires planning the target regions, sequencing depth, and allocation of reads across case status before analyzing association.

Depth as a Planning Approximation

A simple planning model treats the read depth \(D\) at a target position as a Poisson random variable with mean \(\lambda\), so \(D\sim\operatorname{Poisson}(\lambda)\). This assumes a fixed average depth and approximately independent read sampling across positions. Real depth can be more variable, so the model is a useful calculation, not a guarantee that every site follows a Poisson distribution.

For an initial coverage screen, suppose a position is considered to have adequate depth when it has at least \(m\) reads. The probability of reaching that threshold is \(q(\lambda;m)=P(D\ge m)\). It can be calculated from the Poisson probabilities:

This probability is a depth-based opportunity measure, not the full probability of detecting a genotype. For example, a heterozygous variant may have few alternate reads even when total depth is adequate. A more detailed model for a heterozygous site with alternate-read fraction \(\theta\), where a call requires at least \(a\) alternate reads, is \(c(\lambda,\theta,a)=\sum_{d=0}^{\infty}P(D=d)P\{\operatorname{Binomial}(d,\theta)\ge a\}\). Here the binomial model describes alternate reads conditional on total depth. In practice, empirical validation or a pipeline-specific model may be needed to account for mapping and calling behavior.

Plan the Target and Allocation Together

A target region defines where the study intends to detect variants. If cases and controls are sequenced against different intervals, or if a region is systematically poorly covered in one group, equal nominal sequencing depth elsewhere cannot make their variant opportunities comparable. The target definition should therefore be set in advance, and coverage should be assessed over the same bases and variant classes in both groups.

Allocation decisions should consider the distribution of coverage, not only its mean. Two groups can have the same average depth while one has many well-covered bases and a smaller number of nearly unsequenced bases, whereas the other has more uniform coverage. For rare-variant analyses, those gaps can matter if they occur at positions where variants are present. Useful planning summaries include the fraction of target bases above a prespecified depth threshold, the distribution of per-sample callable fractions, and the callability of relevant variant classes.

A practical design sequence is:

Balancing sequencing batches across case status, as well as ancestry and other design factors, helps prevent coverage differences from being entangled with group membership. However, balanced batch labels do not guarantee balanced callability: actual depth and usable-call rates still need to be checked.

How Callability Differences Affect Gene-Level Comparisons

The same reasoning extends from one variant to a gene-level count. Let \(T_j\) indicate whether a person truly carries variant \(j\), with prevalence \(\pi_j=P(T_j=1)\). Let \(Y_j\) indicate whether that variant is detected. If the probability of detecting it when present is \(c_j\), and false-positive calls are ignored for this derivation, then \(Y_j=1\) requires both a true carrier and a successful detection.

If true prevalence is the same in cases and controls, but callability differs by group, the difference in observed variant prevalence for this site is:

For a gene-level burden defined as the sum of detected carrier indicators across variants, expected burden is the sum of their expected values. This follows from linearity of expectation; the variant indicators do not need to be independent:

When variant prevalences are equal across groups, group differences in the \(c_{j,g}\) terms can still produce differences in the expected observed burden. If false-positive calls are possible, let \(f\) be the probability of a call in a noncarrier. The observed call probability becomes \(\pi c+(1-\pi)f\); unequal false-positive rates can also distort comparisons. This is why comparable sensitivity and specificity, not merely a shared nominal depth, matter.

Design Checks and a Common Pitfall

Comparable opportunity is best evaluated at several levels: across the study's target bases, across individual samples, and across the variant classes relevant to the analysis. A group-level average can hide a small set of poorly covered samples or a low-callability segment within a gene. Review both summaries and their distributions, and examine whether differences track case status, sequencing allocation, ancestry, or processing batch.

Common mistake: “The mean depth is 20-fold in both groups, so every target variant is equally likely to be detected.” This conclusion does not follow. Mean depth says nothing by itself about how unevenly reads are distributed across bases or samples, and equal total depth does not ensure equal alternate-read sensitivity or filtering behavior. The correction is to compare the same target and usable-call criteria, then evaluate site- and sample-level callability by group. A no-call should not automatically be coded as a reference genotype.

Coverage planning matters because a gene-level test compares observed calls, not the unobserved variants that would have been seen under perfect measurement. Designing for comparable callability reduces one avoidable source of differential measurement. It does not establish that an observed association is causal, and it does not replace the other design and inference checks needed for rare-variant studies.