Reply to ten Kate et al

We thank Prof ten Kate et al¹ for the useful observations, which will allow us to clarify some aspects of the HI method.^{2, 3}

With regard to the inclusion of mutations with relative frequency below 1% in the formula, we may notice how these negligibly affect the final result, with a gene frequency increasing from 1.90 to 1.95%. This corresponds to an even smaller increase in the prevalence of the disease (from 3.65 × 10⁻⁴ to 3.8 × 10⁻⁴, if we assume P=q² to simplify).

With reference to the exclusion of heterozygous patients from the formula, this is a conservative choice that we made under the basic assumption of strict recessive inheritance in the model, as including them would mean to (erroneously) assume that they are all compound heterozygotes. We also underline that, in this specific study, every sample was first investigated for the six most common reported mutations in Sardinia, and then, if no mutation was found, by single-strand conformation polymorphisms and Sanger sequencing of all exons and of the flanking intronic regions in the ATP7B gene. This makes it highly unlikely that a mutation already found in the Sardinian population was undetected.

Finally, we agree that in a non-random mating population q→P (instead of P=q², as per Hardy–Weinberg equilibrium). However, the current Sardinian population is characterized by high endogamy more than by high frequency of consanguineous matings. Under this scenario, also known as ‘random inbreeding’,⁴ the chance that an individual will mate with a genetically related one will be higher, and will finally lead to P≈q², as already discussed in a recent letter published in this Journal.⁵

Nonetheless, we acknowledge that this is an unavoidable approximation and we always mentioned the gene frequency (q) of a recessive disorder instead of the Prevalence (P) as the main output of the HI method, inferring P only when required for a comparison with other epidemiological methods.^{2, 3}

In summary, we agree with ten Kate et al¹ that all of these details only slightly affect the final result but we disagree that they will jointly create a big discrepancy between our q estimate and the real one, as also demonstrated by the factual equivalence between our q and the one estimated by Zappu et al⁶ through a classical and reliable neonatal molecular screening. What is more important, the main purpose of the HI method is not to make a precise inference of the prevalence of a given recessive disorder in a population (as variables like the inbreeding coefficient can still be a source of error), but to produce ‘a ranking order of the prevalence of autosomal recessive disorders, thus establishing priorities for genetic testing at the population level’.^{2, 3}

Our wish is that the HI method becomes of common use by public health institutions, especially in those country characterized by highly endogamous/consanguineous populations, and that it can be improved by making use of precise estimates of the inbreeding coefficient based on the analysis of genomic patterns of homozygosity.⁷