Estimate multi-locus prevalence and frequency via naive methods

Author

Nick Hathaway

Tool Information

The prevalence of a multi-locus genotype is defined as the proportion of samples in which it is detected. In contrast, genotype frequency, while less straightforward to define, represents the probability that a new malaria infection carries this specific genotype. Prevalence and frequency are not equivalent because individuals can harbour multiple strains of malaria simultaneously. As a result, the sum of prevalence values across all genotypes may exceed 1, whereas genotype frequencies must always sum to exactly 1.

Calculating genotype prevalence and frequency is more complex than it first appears, and depends on the number of heterozygous loci:

  • If there are zero heterozygous loci then we know exactly which genotype is present. The genotype is fully phased.
  • If there is a single heterozygous locus then we know which two phased genotypes must be present in the sample. From the relative read counts at this heterozygous locus we can obtain a rough estimate of the within-sample proportions of each genotype.
  • If there are two or more heterozygous loci then we cannot unambiguously state which genotypes are present. Doing so would require running more advanced methods that attempt to phase genotypes.

We can use these rules to obtain all known phased genotypes from the raw data. For example, imagine we have the following two samples, defined in variant string format:

crt:1_2:A_A/C
crt:1_2_3:A/C_A_A/C

The first sample we can unambiguously phase into the following two genotypes:

crt:1_2:A_A
crt:1_2:A_C

The second sample cannot be unambiguously phased due to the two heterozygous loci.

Now imagine we are comparing both of these phased genotypes back against the original two samples. We would obtain the following matches:

crt:1_2:A_A --> present unambiguously in sample1 and sample2
crt:1_2:A_C --> present unambiguously in sample1 only

Notice that for sample2, even though we were not able to extract its component genotypes, we were still able to identify unambiguous matches against this sample. This is because we were not looking over all three positions, we were only looking at two positions in which there was only one heterozygous locus.

This script performs these operations over an entire dataset. Briefly, it takes the following steps:

  1. Convert input data into variant string format
  2. Extract all unambiguous phased genotypes from the data
  3. Compare all phased genotypes back against the data to estimate prevalence and frequency

Genotype frequency in this case is obtained as the average of the within-sample genotype frequencies (WSGF) over all samples. This has the advantage of being an unbiased estimator of the true population-level genotype frequency (PLGF) without requiring a known complexity of infection for each sample.

Script Usage

The multilocus_prevfreq_naive.R script contains all the functions needed to read in the data, calculate prevalence and frequency, and write results to file.

An example of usage, executed from the root of this repo, would be:

Rscript scripts/multilocus_prevfreq_naive/multilocus_prevfreq_naive.R \
    --aa_table data/example_amino_acid_calls.tsv --loci_groups_input \
    data/example_loci_groups.tsv --output_path mlafp.tsv
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