Overview of the statistical analysis. (A) For each amplicon i, we model the expected fraction of reads harboring the HbS allele in the total cfDNA isolated from the mother as a mixture of fetal (ψ_i) and maternal (ϕ_i) components in proportions determined by the fetal fraction w. The control shares the same expected fraction of mutated reads ϕ_i with the mother, which helps increase the precision of the estimates. (B) For each case, we estimate the expected fetal (ψ₁,ψ₂,ψ₃) and maternal (ϕ₁,(ϕ₂,(ϕ₃) fractions of mutated reads per amplicon. (C) We also estimate the overall distribution (given the data) of each triplet of expected maternal and fetal fractions presented in panel B. For a carrier mother (AS), the distribution of the maternal fractions is close to 50%, while for a fetus with the disease (SS), the corresponding distribution is shifted to the right of the maternal distribution. The stronger this shift E[P], the more likely it is that the fetus has the disease. (D) Overview of model training. We identified an optimal E[P] threshold equal to 0.62. The variance of the various performance metrics was estimated using the bootstrap. (E) Overview of applying the calibrated model on both the training and test cohorts. (F-H) Overview of model performance with decreasing fetal fraction. A false negative arises at a fetal fraction of 0.5%, while false positives arise at fetal fractions <4%. Four samples (in green) with E[P] scores close to the threshold are also characterized by small fetal fractions (≤0.9%). Statistical analysis was conducted in R¹⁰  and Stan.^11,12  Details are given in supplemental Methods. TNR, true negative result; TPR, true positive result.