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# Bayesian inference of parental allele inheritance in fetus for noninvasive prenatal diagnosis

Ghislain Durif, Cathy Liautard-Haag, Marie-Claire Vincent

► To cite this version:

Ghislain Durif, Cathy Liautard-Haag, Marie-Claire Vincent. Bayesian inference of parental allele inheritance in fetus for noninvasive prenatal diagnosis. StatLearn 2023, Apr 2023, Montpellier, France. , https://statlearn.sciencesconf.org/459803. hal-04059861

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Submitted on 5 Apr 2023

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Distributed under a Creative Commons Attribution 4.0 International License
# Bayesian inference of parental allele inheritance in fetus for noninvasive prenatal diagnosis

Ghislain Durif ¹,²

Cathy Liautard-Haag ³

Marie-Claire Vincent ³,⁴

¹IMAG, Université de Montpellier, CNRS UMR 5149, Montpellier, France

²LBMC, ENS de Lyon, CNRS UMR 5239, Inserm U1293, Université Claude Bernard Lyon 1, Lyon, France

³Laboratoire de Génétique Moléculaire, Institut Universitaire de Recherche Clinique, Université de Montpellier, CHU Montpellier, Montpellier, France

⁴PhyMedExp, Université de Montpellier, CNRS UMR 9214, INSERM U1046, Montpellier, France

## More info

<figure><img src="image_3.png" /></figure>

## The problem (c.f. figure 1)

Noninvasive prenatal diagnosis (NIPD) [2] used to detect **pathogenic** genetic variation potentially **transmitted to the fetus** by a parent at risk without a hazardous invasive prenatal diagnosis (PND), i.e. risk of miscarriage

NIPD successfully applied for single-gene disorders [3] but still **challenging for triplet-repeat expansion diseases**, a.k.a. trinucleotide repeat disorder (e.g., myotonic dystrophy type 1, Huntington's disease, fragile X syndrome)

Fetal genotyping using circulating cell-free fetal DNA (cff-DNA) from maternal blood may **not** be able to **detect complex genetic patterns** in the fetal DNA that could have been inherited from a parent at risk

## The proposed method (c.f. figure 1)

Directly infer which **haplotypes** among the **pair** of parental **homologous chromosomes** have been **inherited** by the fetus

→ to determine if the **haplotype region** carrying the **pathogenic variation** was **transmitted to the fetus or not**

## The data (c.f. figure 2)

* parental **phased haplotypes** for the targeted chromosomic region

* maternal plasma cell-free DNA (cf-DNA) **genotype** for the targeted chromosomic region

<figure><img src="image_4.png" /><figcaption>Figure 2. Available data to infer the parental allele origin in the fetus</figcaption></figure>

## The perspectives

* Integrate the **fetal fraction** (=proportion of fetal DNA in sampled maternal plasma DNA) **estimation** [4] in the Bayesian model

* Run a **larger-scale study** with a different phasing protocol

<figure><img src="image_5.png" /><figcaption>Figure 1. Inheritance pattern of the pathogenic genetic variation</figcaption></figure>

## The Bayesian model

**Output:** $O_ℓ = (\text{matX}, \text{patY})$ fetal allele origin among the pair of homologous haplotypes from each parent ($\text{mat} = \text{maternal}$, $\text{pat} = \text{paternal}$ and $X, Y \in \{1, 2\}$) at locus $ℓ$

**Objective:** infer $(O_1, \dots, O_ℓ, \dots, O_L)$ over all locus inside the targeted region

**Tool:** estimate the **full posterior** jointly over all locus

$$P(O_1, \dots, O_ℓ, \dots, O_L | \text{data})$$

**Issue:** impossible because of **combinatorial cost** (no independence between locus)

**Workaround:** use a **Markov chain Monte Carlo (MCMC)** algorithm to estimate the full posterior, specifically a **Gibbs sampler** based on iterative sampling from the conditional marginal posterior

$$P(O_ℓ|\text{data}, O_{ℓ-1}) \sim P(\text{data at locus } ℓ|O_ℓ) \times P(O_ℓ|O_{ℓ-1})$$

* $P(O_ℓ|O_{ℓ-1})$ = **transition probability** (depending on recombination probability and potential phasing error in both parents between locus $ℓ$ and $ℓ-1$)

* $P(\text{data at locus } ℓ|O_ℓ)$ = **conditional likelihood** that can be explicitly derived from fetal genotype model using read counts and fetal fraction estimation (as in the locus-independent fetal genotyping Hoobari model [3])

## The results

**Analysis:** a cohort of 14 families, each including one parent with a pathogenic genetic variation

Non conclusive(2) 9/14

**Comparison** between Bayesian NIPD and invasive PND results (=ground truth)

Accordance 4/14

Error 1/14

(2) because of either poor polymorphism or phasing quality

## References

[1] C. Liautard-Haag et al. en. In: *Scientific Reports* 12.1 (July 2022), p. 11423. ISSN: 2045-2322. DOI: 10.1038/s41598-022-15307-2.

[2] Lisa Hui. eng. In: *Methods in Molecular Biology (Clifton, N.J.)* 1885 (2019), pp. 45-58. ISSN: 1940-6029. DOI: 10.1007/978-1-4939-8889-1_3.

[3] Tom Rabinowitz et al. In: *Genome Research* 29.3 (Mar. 2019), pp. 428-438. ISSN: 1088-9051. DOI: 10.1101/gr.235796.118.

[4] Landon L. Chan and Peiyong Jiang. eng. In: *Clinical Biochemistry* 48.15 (Oct. 2015), pp. 962-975. ISSN: 1873-2933. DOI: 10.1016/j.clinbiochem.2015.04.022.