Statistical Phasing Methods

Why Statistical Phasing Is Needed

An unphased genotype records which alleles an individual carries at each variant, but not which alleles lie together on each chromosome. The earlier material on haplotypes and phase ambiguity established that these different chromosome arrangements can produce the same genotype. Statistical phasing uses patterns in other data—such as haplotype frequencies in a population or inheritance within a family—to assign probabilities to the possible arrangements.

The result is an inference, not a direct observation of the chromosomes. A method may assign high probability to one phase, or leave several phases plausible. That distinction matters: treating an uncertain arrangement as known can affect downstream analyses that use haplotypes.

Population-Based Evidence

A population-based method compares the possible haplotype pairs compatible with an individual’s genotype. Its central idea is that some pairs may be more common in an appropriate reference population than others. To use that idea, the analyst needs haplotype frequencies estimated from individuals whose haplotypes are known or have themselves been inferred. The reference data should be relevant to the individuals being phased; substantial differences in ancestry or data quality can make its frequencies misleading.

For a simple two-locus calculation, suppose the four possible haplotypes are AB, Ab, aB, and ab, with frequencies \(f(AB)\), \(f(Ab)\), \(f(aB)\), and \(f(ab)\). Assume that the two haplotypes forming a person’s diplotype are sampled at random from this population, that genotypes are called accurately, and that the reference frequencies are treated as known. A person heterozygous at both loci, with genotype Aa and Bb, can have diplotype AB/ab or Ab/aB. Under random pairing, the probability of an unordered diplotype with two different haplotypes is twice the product of their frequencies: either haplotype could have been drawn first.

This result follows by conditioning on the observed genotype. Since the compatible diplotypes are mutually exclusive and exhaust the possibilities for the person under consideration, \(P(C)=\sum_j P(C\mid D_j)P(D_j)\). For each compatible diplotype, an accurate genotype call gives \(P(C\mid D_j)=1\); for an incompatible diplotype it gives zero. Substitution into the definition of conditional probability yields the displayed formula. If genotyping error is modeled, the conditional probabilities need not be one or zero, and they must be included in the calculation.

In practice, population-based methods extend this logic across many variants. They use recurring haplotype patterns in the reference data to assess which chromosome sequences plausibly account for each person’s genotype. Some procedures estimate haplotype frequencies and phases together, updating one in light of the other; their output may therefore depend on initialization, sample composition, and convergence. The underlying evidence remains population sharing, not direct observation of the chromosomes.

Family-Informed Evidence

Family data add inheritance constraints. Under Mendelian transmission, a child receives one chromosome from each parent at an autosomal region. If parental haplotypes are known, and the child’s genotype identifies which parental alleles were transmitted, the family can resolve phase even when population frequencies alone would leave alternatives. This reasoning assumes the relationships and genotype calls are correct. It may also require an assumption about recombination across the interval: when recombination is possible, the probability of a transmitted haplotype depends on the interval and the inheritance model.

Family evidence can be informative without resolving every phase. For example, a parent’s unphased genotype may leave two possible haplotype pairs, while the genotypes of that parent’s children rule out one arrangement. Conversely, if both parental arrangements remain compatible with all observed transmissions, pedigree data do not identify a unique phase. More family members do not automatically mean more information; their genotypes must distinguish between the alternatives.

Combining Evidence and Comparing Approaches

Population and family evidence answer related but distinct questions. Population frequencies provide relative support for compatible diplotypes based on how common their haplotypes are in the reference data. Family data provide support based on whether a proposed set of phases can generate the observed parental and offspring genotypes through inheritance. When both are available, a coherent probability model can use both: each candidate configuration receives support from its population probability and from the probability of the observed family data under that configuration.

For clarity, let \(D_1\) and \(D_2\) be possible phases, and let \(F\) denote family observations. If population probabilities are \(P(D_i\mid C)\), a family update takes the form $$ P(D_i\mid C,F)= \frac{P(F\mid D_i,C)P(D_i\mid C)} {\sum_j P(F\mid D_j,C)P(D_j\mid C)}. $$ This expression requires the family likelihoods \(P(F\mid D_i,C)\) to come from an explicit inheritance and error model. They must not be replaced by informal claims that one phase “fits better.” In particular, if the family evidence is deterministic under the assumptions and compatible with only one phase, the other phase has probability zero in that model; if both remain compatible, their relative support depends on the transmission probabilities.

A direct molecular approach, such as sequencing reads that span multiple variants, can provide physical evidence that alleles occur together on the same DNA molecule. That differs from statistical inference based on population patterns or inheritance, although real analyses may combine such evidence. Direct evidence also has limits, including read errors and insufficient coverage across the region. Statistical phasing is useful when direct chromosome-level observations are unavailable or incomplete, but its uncertainty should be retained rather than hidden.

Assumptions, Diagnostics, and Limitations

The calculated probabilities are only as reliable as their model and data. Population-based inference generally depends on representative reference frequencies, appropriately handled ancestry structure, sufficiently accurate genotypes, and a model that captures the relevant haplotype patterns. Family-informed inference depends on accurate relationships and calls, valid inheritance assumptions, and appropriate treatment of recombination and genotyping error. These are not automatic properties of a dataset; they need to be checked in context.

Useful diagnostics include examining whether inferred haplotypes are supported by reference observations, whether posterior probabilities are concentrated or diffuse, and whether family data produce Mendelian inconsistencies. A high proportion of low-confidence phase assignments signals that the data do not identify phase well, even if a software procedure returns one preferred arrangement. Unexpectedly many incompatible transmissions can indicate a sample mix-up, incorrect relationship, call error, or an inadequate model. These checks flag concerns; they do not by themselves identify the cause.

Common failure modes include using a reference panel with mismatched ancestry, overlooking allele-coding or strand problems, and treating a chosen phase as certain simply because it is the most probable. Rare haplotypes are especially difficult to estimate reliably from limited reference data. Population structure can also make a single set of frequencies a poor description of the people being analyzed. Family information may help, but sparse pedigrees or uninformative parental genotypes can leave substantial ambiguity.

No method can recover phase that is not identified by the available data and assumptions. Population evidence can favor a common arrangement without proving it; family evidence can constrain inheritance without distinguishing all alternatives. Good practice is to record the evidence source, model assumptions, and uncertainty, and to avoid interpreting a probabilistic phase as a directly observed chromosome.