Why transparent reporting matters
A fine-mapping result is conditional on a defined region, a set of candidate variants, a statistical model, prior assumptions, and linkage disequilibrium (LD) information. A list of variants with large posterior inclusion probabilities (PIPs) is therefore not a complete result. Readers need enough information to understand what those probabilities refer to, how a credible set was formed, and whether reasonable changes in assumptions alter the conclusion.
Transparent reporting does not make a model assumption-free. It makes the assumptions visible and the analysis reproducible. In particular, a posterior probability is a probability under the stated model and priors; it is not a direct measurement of biological causality. The earlier material on prior sensitivity analysis and LD sensitivity analysis provides the relevant framework for reporting how these choices affect results.
Define the analysis before presenting its results
The region must be identifiable without ambiguity. Give the chromosome, start and end coordinates, coordinate convention, and genome assembly, such as GRCh38. State how the region was selected and whether boundaries were expanded or otherwise changed during analysis. Identify the phenotype, the association-study sample or summary-statistics source, and relevant sample characteristics, including ancestry. If multiple ancestries, cohorts, or phenotypes were combined, describe that combination rather than reporting a single undifferentiated result.
Describe the candidate-variant set, not just the region boundary. Report the number of variants considered, the variant identifiers and alleles, and any exclusions or harmonization rules that could change which variants are represented. A variant absent from the analyzed set cannot receive a reported PIP. Where variant identifiers or allele alignment matter, provide a machine-readable table rather than relying only on prose.
State the model at the level needed to interpret its outputs: whether it allows zero, one, or multiple causal variants; how signals or causal configurations are represented; and the assumed relationship between association evidence and LD. Also report the prior specification, including the prior probability or expected number of causal variants, any variant-specific prior weights, and any effect-size prior or other model-specific parameters. If software supplies default values, identify the software and version and give the values actually used. “Default settings” alone is not a sufficient description.
These details matter because the same data can yield different posterior summaries under different models or priors. A report should not imply that one specification is the only possible model. It should make clear which specification generated the results being shown and direct attention to sensitivity results when these are available.
Report probabilities and credible sets precisely
In a model that permits multiple causal variants, marginal PIPs need not sum to one: their sum is the posterior expected number of included variants. By contrast, probabilities used to rank candidates for a particular signal are often normalized across variants conditional on that signal being present. The report must say which quantity it presents. This distinction is especially important when a method also assigns probability to a null or no-signal model. A set constructed from probabilities conditional on a signal should not be described as accounting for uncertainty that the signal exists unless that uncertainty is included in the calculation.
A credible set for a signal is a collection of candidate variants whose cumulative signal-specific posterior probability reaches a stated target, such as 0.95. One common construction ranks variants from largest to smallest signal-specific probability and takes the shortest leading sequence whose cumulative probability reaches the target. Report the target and the construction rule. If the software uses a different rule, describe that rule instead of assuming the common one.
Purity summarizes how strongly the variants in a set are correlated in the LD matrix. A common convention is the minimum pairwise \(r^2\) among distinct variants in the set. State the convention explicitly: some software uses a different summary, such as an absolute correlation or a quantile of pairwise values. A numerical purity value without its definition cannot be compared reliably across analyses. Purity is a property of the set under the specified LD data; it is not a probability that the set contains the causal variant.
How the ranked construction works
Suppose the signal-specific probabilities are \(q_1,\ldots,q_m\), with \(q_j \geq 0\) and \(\sum_{j=1}^{m}q_j=1\). For a target \(c\), sort them in descending order, so \(q_{(1)}\geq q_{(2)}\geq\cdots\geq q_{(m)}\), and choose the smallest \(K\) such that the cumulative sum reaches or exceeds \(c\):
This is a smallest-cardinality set among sets formed from those candidate variants: for any set of \(k\) variants, its total probability cannot exceed the sum of the \(k\) largest probabilities. Consequently, if the leading \(K-1\) probabilities sum to less than \(c\), no set of fewer than \(K\) variants can reach the target. This justification depends on the probabilities being the appropriate normalized probabilities for the signal; it does not make an incorrectly defined or incompletely specified probability suitable for set construction.
Worked Example: Constructing and Reporting a 95% Set
Consider a hypothetical single-signal analysis with five variants and signal-specific probabilities \(0.42, 0.27, 0.18, 0.08,\) and \(0.05\). These values sum to \(1.00\), as expected for probabilities conditional on this signal being present and assigned to one of the five variants.
Construction. The cumulative sums in ranked order are \(0.42\), \(0.42+0.27=0.69\), \(0.69+0.18=0.87\), and \(0.87+0.08=0.95\). Thus the 95% set contains the first four variants. The four-variant set reaches the target exactly, while the three-variant set has only 0.87 cumulative probability.
Suppose the minimum pairwise \(r^2\) among these four variants, calculated from the reported LD matrix, is 0.31. The transparent result is: “The signal-specific 95% credible set contains four variants and has minimum pairwise \(r^2=0.31\), using the stated LD reference and purity convention.” It would be misleading to call this a single-variant resolution or to imply that the four variants have equal support.
Make the LD and sensitivity analysis auditable
LD is not a generic property supplied by the word “reference.” Report the source population or reference panel, sample size if known, ancestry, variant set, and the procedure used to estimate or obtain the LD matrix. Include the genome build and allele harmonization details needed to align LD variants with association data. If LD was estimated in the association sample, say so; if a reference panel was used, identify it and its version or release. Explain how missing or mismatched variants were handled. These items let readers judge whether the LD input plausibly represents the analyzed samples.
Sensitivity results should be concise but concrete. For each alternative prior or LD specification, identify what changed and report the corresponding quantities used to assess the conclusion: for example, PIP changes for leading variants, set membership, set size, or purity. State which choices were held fixed. If a finding changes, describe the change rather than compressing it into “sensitive.” If it does not change, avoid calling that proof of robustness to all possible model errors; the tested alternatives only cover the choices examined.
A compact table can make the main result and alternatives easier to compare. Give each row a clearly identified signal and analysis specification. A reader should be able to distinguish a change in the model from a change in the LD source, and to tell whether PIPs are marginal or signal-specific.
Worked Example: Summarizing Prior Sensitivity
In a hypothetical region, the primary model uses a stated prior that permits up to two causal variants. For one signal, the leading signal-specific probabilities are 0.55, 0.25, 0.12, and 0.08. A 95% set includes all four, since \(0.55+0.25+0.12=0.92\) and adding 0.08 gives 1.00. Under an alternative prior, the corresponding probabilities are 0.48, 0.30, 0.14, and 0.08. The first three now sum to \(0.48+0.30+0.14=0.92\), so the 95% set still contains all four.
A report should not say that the probabilities were unchanged: the leading variant decreased by \(0.55-0.48=0.07\), and the second increased by \(0.30-0.25=0.05\). It can accurately say that the top-ranked variant remained the same and that the four-variant set membership and set size were unchanged under this alternative. It should identify the changed prior and report purity for each specification if the LD matrix or set membership differs. This describes the tested sensitivity without claiming that all prior choices would have the same effect.
Worked Example: Reporting Multiple Signals and Their Probabilities
Suppose a hypothetical two-signal model reports marginal PIPs of 0.62, 0.41, and 0.18 for variants A, B, and C, respectively. These three values sum to \(0.62+0.41+0.18=1.21\). That sum is not an error by itself: under a model allowing multiple causal variants, marginal PIPs across variants do not have to total one.
For signal 1, suppose the signal-specific probabilities for A, B, and C are 0.58, 0.32, and 0.10. For a 95% target, the first two sum to \(0.58+0.32=0.90\), so all three are needed; their total is 1.00. For signal 2, suppose the reported set consists of variants B and D, with signal-specific probabilities 0.72 and 0.28. At a 95% target, both are needed. Variant B appears in both signal-specific sets, so the report should preserve the signal labels rather than presenting one combined list as though the signals were interchangeable.
A clear table would label the 0.62, 0.41, and 0.18 values as marginal PIPs, and separately list the probabilities, threshold, membership, and purity for each signal-specific set. If the model assigns probability to a no-signal possibility, report that uncertainty in the form provided by the method; do not silently treat conditional-on-signal probabilities as unconditional evidence that a signal exists.
Diagnostics, limitations, and common reporting failures
Before release, check that variant identifiers and alleles align across the association data, LD matrix, and PIP output; that the stated genome build is consistent; and that the reported set membership reproduces from the probabilities and threshold. Check that purity is computed on the members of the set, with the stated definition, and that the LD matrix contains the required variant pairs. When these checks fail, a report may contain plausible-looking numbers that describe different variants or different inputs.
A broad set with low minimum pairwise \(r^2\) can be difficult to summarize as one tightly correlated group. Report that result, rather than hiding it behind a threshold label. Conversely, high purity does not establish that the set contains the causal variant: the conclusion remains conditional on the candidate set, model, priors, and LD input. An omitted causal variant or a poorly matched LD reference can undermine interpretation even when the reported calculations are internally consistent.
Common mistakes include reporting PIPs without defining whether they are marginal or signal-specific; calling a PIP a probability that a variant is biologically causal without qualification; reporting a “95% set” without the construction rule; and giving a purity number without defining the LD summary. Another frequent error is reporting only the primary specification while describing results as robust, with no alternatives or comparison quantities. The correction is to state the conditioning and definitions, provide the needed inputs and settings, and report sensitivity evidence in terms that can be checked.
The main alternative to a detailed narrative is a structured table with accompanying machine-readable files. Tables are efficient for comparing signals and specifications, but only if the columns define the quantities and units clearly. A prose-only report can explain modeling choices, while a table or supplementary file is better for long variant lists. Neither format removes the need to state model, prior, threshold, purity, and LD conventions. Even a fully reproducible report remains limited by the assumptions and data available; transparency supports evaluation, not certainty.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions.
- Why can marginal PIPs in a multi-causal model sum to more than one?
- Signal-specific probabilities in ranked order are 0.50, 0.29, 0.13, and 0.08. How many variants are needed for a 95% set?
- A report gives a credible-set purity of 0.40 but does not say how purity is defined. What information is missing?
- Under an alternative prior, the leading PIP changes but the set membership does not. What can be reported, and what would be an overstatement?
Solutions. (1) A marginal PIP is the probability that a variant is included; with multiple causal variants, the sum across variants is the expected number included and can exceed one. (2) The first three sum to \(0.50+0.29+0.13=0.92\); adding the fourth gives 1.00, so four are needed. (3) The report must specify the LD quantity and aggregation, such as minimum pairwise \(r^2\) among distinct members, and identify the LD matrix used. (4) Report the changed probability and unchanged membership under the named alternative. Claiming that the probabilities were unchanged, or that the result is robust to every possible prior, would overstate the evidence.