## Introduction

Human birth defects occur in ~3%–5% of liveborns1. It has been estimated that 15%–25% of birth defects were attributed to recognizable genetic diseases2. There are over 8600 diseases with a known or suspected underlying genetic etiology, most of which have no effective treatments3. To provide management options for pregnancies at risk of life-threatening genetic disorders such as sickle cell anemia, Tay-Sachs disease, and cystic fibrosis, population-based genetic screening has been carried out since the 1970s with proven clinical utility4. In the past decade, non-invasive prenatal screening (NIPS) was developed and implemented worldwide to screen for common fetal chromosomal aneuploidies such as trisomy 21 (T21, also known as Down syndrome)5. Recently, NIPS has expanded to cover chromosomal microdeletion and microduplication syndromes (MMS) such as DiGeorge syndrome6. Studies have also demonstrated that fetal cell-free DNA (cfDNA) is useful for the diagnosis or screening of common monogenic conditions such as achondroplasia and Noonan spectrum disorders7,8. However, a comprehensive NIPS test for concurrent screening of chromosomal and monogenic disorders has yet to be developed and implemented to battle the large catalog of genetic birth defects.

NIPS utilizes a simple draw of maternal blood containing both maternal and fetal circulating cfDNA5. Fetal cfDNA is believed to be derived from the apoptotic cells of the outer layer of placental trophoblast, which then enters maternal circulation9. The fetal cfDNA accounts for only a small proportion of the total cfDNA in maternal plasma which is estimated only ~10% on average during the 2nd trimester and even lower during late 1st trimester when NIPS is offered clinically10. At such a low level, the fetal variants can only be recognized when any detectable difference introduced by the fetal genetic abnormality (signal) exceeds that associated with assay variations (noise). In previous studies, up to ~11,000–20,000 loci were used in NIPS to detect common aneuploidies11,12. Apparently, the single nucleotide polymorphism (SNP)-based NIPS can be improved by increasing the signal-to-noise ratio so that far fewer SNP loci need to be interrogated. Besides the analytical challenge of detecting low-level fetal variants in the maternal and fetal cfDNA admixture, accurate NIPS results are often obscured by multiple gestations, maternal germline copy number variations (CNVs), absence of heterozygosity (AOH), and other analytical challenges13,14,15. In twin pregnancies, the individual cfDNA contributed by each fetus is usually lower than that of a singleton fetus affected with an aneuploidy which exacerbates the NIPS assay sensitivity16. In addition, ultrasound may not accurately identify twin zygosity or vanishing twins which can cause increased health risks for the fetus(es). Maternal CNVs such as non-pathogenic duplications cause a significant number of false-positive fetal trisomies detected by NIPS17. Maternal AOH reduces the number of the interpretable heterozygous loci for the detection of fetal chromosomal copy number abnormalities in NIPS assays depending on genotype information18. These confounders, if not properly recognized, lead to false screening results, which in turn may result in missed diagnoses or unnecessary invasive procedures for diagnostic confirmation.

Currently, there are two prevailing NIPS approaches that involve low-coverage whole genome sequencing (WGS) or targeted sequencing for SNPs to infer fetal chromosome copy number5,11. WGS-based NIPS utilizes chromosome-specific read depth (RD) data to identify fetal chromosomal aberrations based on a Z-score calculation5. SNP-based NIPS detects chromosomal aberrations at selected loci by the quantitation of skewed allelic fraction (AF) caused by CNVs19. These two methods have distinct strengths and limitations for the analyses of fetal cfDNA. For instance, SNP-based NIPS is limited in detecting fetal copy number changes at regions with maternal AOH18,19. The low-coverage WGS method is constrained due to its inability to discriminate maternal and fetal genotypes, which limits its clinical utility for the detection of hydatidiform moles or unrecognized twin or vanishing twin pregnancies13. The combined use of RD and AF for high-coverage NIPS has been proposed from a simulation dataset, but the clinical validity of this approach needs to be substantiated by larger studies20.

Besides the RD and AF data mentioned above, the cfDNA fragmentation pattern can also be informative for the detection of fetal variants in NIPS. The size of fetal cfDNA fragment is usually shorter than the maternal counterpart21,22. The assay sensitivity can be improved by sampling shorter cfDNA fragments from the maternal plasma when a higher percentage of fetal cfDNA molecules are recovered in the NIPS test23,24. Human aneuploidies were reported to be associated with aberrant maternal meiotic recombination presenting with an erratic number of crossovers and unusual chromosome breakpoints25,26,27. Therefore, the discovery of chromosome recombinants would serve as additional evidence for the detection of aneuploidies in NIPS. However, aberrant meiotic crossovers associated with human aneuploidies have not been reported in cfDNA likely due to current assay limitations. Overall, the recognition of fetus-specific cfDNA characteristics including its fragment length or meiotic crossovers can improve the performance of NIPS as additional information is utilized to discriminate the fetal variants from the maternal background.

In this study, we present a new NIPS approach employing non-biased allelic target enrichment followed by next-generation sequencing (NGS) for the comprehensive analyses of fetal chromosomal aneuploidies, MMS, and monogenic disorders. This approach uses deep sequencing to analyze genomic regions associated with three distinct types of genetic disorders with test resolution from single base variant to whole chromosome copy number change. In addition, this method genetically deconvolutes the fetal and maternal cfDNA admixture by querying NGS data associated with maternal/fetal genotype, RD, SNP linkage, and cfDNA fragment lengths. With the concerted analysis of multidimensional genomic cues, this new NIPS assay yielded much improved analytical performance and addressed the limitations of current methods caused by multiple assay confounders. Furthermore, we discovered meiotic errors associated with aberrant chromosome recombinants from the cfDNA studies providing important insights into the origins of human aneuploidies.

## Results

### Coordinative allele-aware target enrichment suppresses allelic hybridization bias

The fetal fraction (FF) is ~10% on average during the 2nd trimester and even lower during late 1st trimester present in maternal plasma10. The variation of SNP AF caused by fetal chromosomal copy number abnormality is subtle and only detectable when it exceeds that caused by assay artifacts. In conventional liquid-phase hybridization for target enrichment, oligonucleotide probes are designed to perfectly match reference sequences (Fig. 1a). When the number of complementary base pairs is increased, the total gain in free Gibbs energy-related duplex formation rises28. Therefore, DNA fragments harboring the reference allele (wild-type allele) have a higher pairing affinity to probes than those with the alternative allele (variant allele; Fig. 1a, b). This small but significant allelic bias disfavoring the alternative allele confounds the NIPS assay for the detection of low-level fetal chromosome CNV. We found that the average AF at the maternal heterozygous loci was always lower than 0.5, indicating that fewer DNA fragments with variant alleles were recovered than those with the wild-type alleles (Fig. 1c, d; Materials and methods). To reduce such allelic biases, probes were designed for SNPs on different chromosomes associated with the most common human aneuploidies or MMS (see Materials and methods), which have a minimal difference of the hybridization equilibrium constants for the reference and alternative alleles (ΔK = KK’ ≈ 0; Fig. 1b). Noteworthily, the sequences of these probes may not be perfectly complementary to either the reference or alternative alleles (Fig. 1b; Materials and methods). This new target enrichment strategy for NGS was named coordinative allele-aware target enrichment sequencing (COATE-seq). We found that the COATE-seq yielded less allelic bias for hybridization-based target enrichment than sequencing performed with conventional probes (CON-seq; Fig. 1c–e). The median of the AF across all maternal heterozygous loci, was significantly elevated and closer to 0.5 when COATE-seq was performed (Fig. 1c, d). In addition, the AF coefficient of variation (CV) of fetal variants was also significantly reduced in COATE-seq (Fig. 1e; Supplementary Fig. S1). To evaluate whether COATE-seq was indeed beneficial for fetal SNP AF quantification, the FF determined by the AF values of all informative SNP loci was compared to that calculated by the Y chromosome-based method. The COATE-seq yielded a higher correlation of coefficient (R2 = 0.97) for the SNP-based method than that of CON-seq (R2 = 0.91; Fig. 1f, g). Consistently, we found that the COATE-seq yielded a smaller bias for the FF estimation when using the fetal heterozygous SNPs at loci where the mother was homozygous for the reference or alternative allele (Supplementary Fig. S2). Overall, the above results demonstrate that COATE-seq produces more accurate quatification for fetal SNP AF than the conventional enrichment method which is critical to improve the signal-to-noise ratio in the NIPS assay for the detection of chromosomal aberrations.

### Multidimensional cfDNA analyses for the detection of fetal chromosome CNV

While COATE-seq improves fetal variant genotyping accuracy, multiple gestations, maternal CNV, and AOH can confound the detection of abnormal fetal variant intermixed in the total maternal plasma cfDNA. Such obstacles can be overcome when the fetal and maternal genetic profiles are separated at large. To this end, we developed algorithms for concurrent analyses of chromosome dosage and genotype by surveying both the RD and AF data as opposed to conventional NIPS tests depending on either RD or AF data only (Fig. 2a–i). Using this joint analysis, dizygotic twin pregnancies and maternal CNV and AOH can be detected prior to fetal variant calling as a quality control step to reduce analytical errors (Fig. 2a). In 419 samples used for analytical validation, there were 17 (4.1%) with maternal CNV with a size of ≥ 200 kb (Fig. 3a–c), 10 (2.4%) with maternal AOH regions with ≥ 75 consecutive homozygous loci (Fig. 3d–f), and 10 (2.4%) with multiple gestations or non-maternity (Fig. 3g, h). After accounting for confounders including ≥ 3 Mb maternal CNV, maternal chromosomal AOH diminishing heterozygous SNP loci, and non-singleton pregnancy, the RD-based analysis identified all aneuploidies but one T18 resulting in a test sensitivity at 97.5% (95% confidence interval (CI), 87.1%–99.6%) and a positive predictive value (PPV) at 84.8% (95% CI, 70.5%–93.2%) (Fig. 2h, i; Supplementary Fig. S3). The AF-based method detected 34 out of 40 aneuploidies producing an 85.0% (95% CI, 70.9%–92.9%) sensitivity and a 91.9% (95% CI, 76.9%–97.9%) PPV (Fig. 2h, i). The combined RD and AF approach detected all aneuploidies with a 100% (95% CI, 91.2%–100%) sensitivity and an 80.0% (95% CI, 65.9%–89.5%) PPV (Fig. 2h, i). These results demonstrated that the combined use of RD and AF data had a higher test sensitivity than either method used alone. Importantly, the AF-based method is useful to calculate FF and recognize multiple gestations and maternal AOH (Figs. 2a, 3d–g). In addition, the AF-based method is highly sensitive for the detection of fetal chromosomal aberrations derived from paternal meiotic errors (Fig. 2c, e, g). Another added advantage of the AF-based method is the ability to detect the parental and meiotic origin of fetal chromosomal aberrations (Fig. 2b–g; Supplementary Fig. S4a–c). On the other hand, RD analysis complements the AF analysis for cases in which the number of informative loci for the detection of CNV is reduced (Supplementary Fig. S4d).

### Characterization of chromosome recombinants and origins of meiotic nondisjunction (NDJ) by fetal cfDNA profiling

It is known that maternal age is an important risk factor for common aneuploidies, e.g., T21, T18, and T1329. These aneuploidies are mostly of maternal origin and associated with aberrant meiotic recombination25,26,27. However, evidence for the interplay between meiotic crossovers and human aneuploidies is scarce likely due to the difficulty of collecting a large number of human eggs or invasively collected prenatal specimens. Given these challenges, the NIPS approach would seem to be an ideal alternative. We then examined whether recombinants associated with aneuploidies could be detected using our COATE-seq method, which had improved analytical performance over conventional approaches (Supplementary Figs. S5, S6; Materials and methods). In 33 sets of samples consisting of matched fetal, maternal DNA, and their admixtures, we identified the chromosome recombinants in mixed DNA and confirmed the recombinants in the fetal genome based on linked SNPs (Fig. 4a–c; Materials and methods). Similarly, the homologous chromosome recombinants can be detected using the same method for the plasma cfDNA samples from pregnant women and their respective amniocytes (Fig. 4d–f; Supplementary Fig. S7). In 73 aneuploidy samples tested in this study, 47 T21 (63.8%) cases had maternal meiosis I (MI) NDJ, with the remaining in maternal meiosis II (MII) NDJ (27.7%), paternal meiosis I (PI) NDJ (2.1%), and paternal meiosis II (PII) NDJ (6.4%), respectively (Fig. 4g; Supplementary Table S1). While MI NDJ (50.0%) was more frequent than other meiotic errors in T13 as seen in T21, MII NDJ (57.1%) was the most frequent one in T18 (Fig. 4g; Supplementary Table S1). Among these samples, 44/73 (60.3%; 25 T21, 9 T18, and 10 T13) with recombinants were detected (Fig. 4h; Supplementary Table S1 and Fig. S8). In the validation set, 34/40 (85.0%) aneuploidies were identified by the AF method when recombination was considered (Fig. 2h), but the detection rate dropped to 67.5% if crossovers were disregarded. Next, we characterized the crossovers associated with the origins of meiotic errors. Altogether, we found that T21 cases with detectable recombinants had more with a single crossover in MI, while in T18 and T13, more cases had two or more crossovers (Supplementary Table S1). The distribution of meiotic errors and crossovers identified in this cohort was consistent with previous reports (Fig. 4h, i)25,26,27. For instance, in T21 due to maternal NDJ with a single crossover, most MI cases had breakpoints near the telomeric region, while breakpoints near the centromeric region were more frequent in MII cases (Supplementary Fig. S9). Again, these results were consistent with previous studies characterizing the occurrence of meiotic recombination in T21 using invasive fetal samples30. Overall, these data demonstrated that our NIPS method was highly accurate in characterizing the origin of meiotic errors and crossovers in common aneuploidies.

### Improved detection of fetal de novo and paternally inherited monogenic variants based on fetal cfDNA fragment characteristics

Unlike fetal chromosomal aberrations involving multiple loci in targeted regions, it requires higher analytical resolution to detect fetal monogenic variants associated with discrete loci. To this end, a new multidimensional algorithm was developed to identify de novo or paternally inherited fetal single gene variants (Fig. 5a, b). The detection of fetal single nucleotide variants (SNVs) can be considered as a process of sampling a population of mixed fetal and maternal DNA molecules. Then the likelihood for an SNV being of fetal origin can be calculated using a beta-binomial distribution based on the number of total DNA molecules detected, FF, and the alternative (alt) allele counts (Materials and methods). We named the filtering step depending on the number of variant allele reads Allele Count Distribution (ACD) filtering (Fig. 5a; Materials and methods). We also found that the fetal cfDNA fragments were ~10 bp on average shorter than the maternal counterpart, while the fragments harboring false positive variants were similar in length to the maternal fragments (Fig. 5c; Supplementary Fig. S10). Fetal-Maternal Insert-size Distribution (FMID) filtering was then established based on the difference of fetal and maternal cfDNA fragment length to discern fetal variants (Fig. 5b). In FMID filtering, a fetal-maternal nearest neighbor insert-size calibration was performed for each NGS read harboring an alt allele at loci where the mother was homozygous for the reference (ref) allele. A binary search was then used to exclude the ref allele read with the closest fragment length to an alt allele read (Fig. 5b). After multiple iterations for all the alt allele reads, the surviving ref allele reads could be regarded maternal. The insert sizes of the remaining reads were then tested under different hypotheses followed by a median comparison to examine whether the alt allele fragments were indeed statistically different or shorter than the ref allele fragments in length (Fig. 5a; Materials and methods). Using the above multidimensional analysis, we examined 28 plasma cfDNA samples and their respective amniocytes collected from pregnant women for 463 genes associated with monogenic disorders. In this test validation set, both common SNPs and rare sequence variants were analyzed (Supplementary Table S2). When the ACD and FMID filters were both applied, the analytical sensitivity and specificity were 99.5% and 99.9%, respectively, improved from the no-filter or ACD filter only method (Fig. 5d, e; Supplementary Table S2). Noteworthily, the ACD and FMID filters were deployed sequentially to filter in variants to avoid over-filtering when variants surviving any of the filtering steps were deemed positive (Fig. 5a; Supplementary Table S3). In summary, by integrating both the allele count and cfDNA fragment length information, we established a new and highly accurate fetal SNV detection method to detect monogenic disorders caused by de novo and paternally inherited sequence variants.

### Evaluation of clinical validity using retrospective pregnant women’s plasma samples

Prenatal/postnatal diagnostic results for all cases were retrieved from clinical records to compare with the cfDNA screening results. In 1129 samples analyzed for the validation study, 77 were positive in which 70 were true positive, including 38 T21, ten T18, six T13, eight MMS, and eight monogenic disorder cases (Fig. 6 and Table 1). A total of 1052 cases were tested negative for the disorders screened for. There were zero false negative and seven false positive cases (Fig. 6). The combined sensitivity and specificity for these disorders were 100% (95% CI, 94.9%–100%) and 99.3% (95% CI, 98.6%–99.7%), respectively (Supplementary Table S6). Overall, the validation study demonstrated that this new NIPS approach yielded highly accurate results for the concurrent screening of different types of human genetic disorders.

## Discussion

Accurate and early prenatal diagnosis is essential for the management of the fetal risks for severe genetic diseases. NIPS, through the analysis of fetal cfDNA present in maternal plasma has thus become a prevalent screening approach for common aneuploidies with improved analytical accuracy over conventional biochemical methods or ultrasound screening32,33. Significant advances have been made for NIPS by NGS technologies in recent years, which expanded its use for more genetic disorders12,20,34,35,36,37,38,39,40. However, the inability to reconcile different genetic cues in a single NIPS assay prevents its expansion for the concurrent screening of different types of genetic disorders and improvements on test performance (Supplementary Table S7).

To develop an expanded and enhanced NIPS test in the present work, we applied a top-down design strategy comprised of novel laboratory technologies, comprehensive genomic algorithms, and diseases-specific interpretation analytics. Importantly, a new hybridization-based target enrichment method, termed COATE-seq, was established through allelic probe sequence manipulation (Fig. 1). COATE-seq suppresses the allelic enrichment biases and sequencing variations inherent to conventional methods, which are detrimental to the detection of low-level fetal variants in maternal plasma (Fig. 1). With much improved signal-to-noise ratio, COATE-seq requires only ~20% of the loci used in previous methods to detect common human aneuploidies11,12. Next, genomic algorithms were developed to analyze multidimensional cfDNA data including RD, AF, fragment lengths, and linked SNPs to uncover maternal/fetal genotype, meiotic error origins, and meiotic recombination (Figs. 25). Overall, the above inventions for important assay reagents, laboratory procedures, and genomic algorithms enabled comprehensive delineation of the fetal genome, which allows the highly accurate detection of fetus-specific variants (Supplementary Table S6).

An important finding resulting from the improved analytical performance of COATE-seq is the discovery of aneuploidy chromosome recombinants in fetal cfDNA (Fig. 4). Common aneuploidies have characteristic parental and meiotic NDJ patterns26,27,41. Previous studies showed that the number of meiotic recombination events and the location of crossovers were associated with aneuploidies caused by different meiotic errors30,42. Using the NIPS method in this work, we found that 22 T21 cases had a single crossover associated with meiotic NDJ in which most MI NDJ cases had breakpoints within the ~10 Mb of the telomere, while most MII NDJ cases had breakpoints within ~6 Mb of the centromere (Supplementary Fig. S9). This finding is consistent with previous reports showing that recombination breakpoints identified in MI or MII NDJ are in proximity to either telomere or centromere, respectively30,42. These results contrast with the location of breakpoints of normal meiotic recombinants which are evenly distributed on both ends of the chromosome30,42. With millions of NIPS tests conducted worldwide every year, our method provides a unique tool to investigate the origins of aneuploidies and meiotic recombination from the population perspective.

It should be noted that many frequent and severe recessive monogenic diseases are caused by complex variants residing in genomic regions with homologous sequences (e.g., SMN1, HBA1/A2, CYP21A2, etc.). Recent developments in NGS or long-read sequencing analytics enabled the detection of carriers of the pathogenic variants in these difficult genes43,44,45. However, such variants are not amenable to NIPS tests largely due to the short fragment length of cfDNA. Haplotype-based NIPS for recessive variants has limited utility as pretest information of parental haplotype cannot be readily obtained in population screening. A significant amount of work on current platforms or new technologies are required to develop a practical NIPS test which has superior performance to current carrier testing for those important recessive disorders mentioned above.

Concurrent NIPS for different types of genetic disorders is of obvious clinical value. Monogenic diseases which do not present with gross structural anomalies during early fetal development (e.g., FGFR3-related skeletal dysplasia) may be missed in the first-trimester ultrasound screening. By coupling monogenic diseases and chromosomal aberrations for NIPS in early gestation, it allows a more inclusive genetic screen complementing current image-based approaches. While expanding the scope of NIPS has sensible benefits, evidence-based studies for such screening are yet to be performed to prove its clinical utility. In future studies, it will be important to address key issues such as disease inclusion criteria for screening, proper testing indications, and reporting or genetic counseling strategies for variants of phenotypic variability or incomplete penetrance. In addition, pregnancy management options and their outcomes need to be evaluated for individuals affected by either positive or negative screening results to weigh the benefits and risks of offering a comprehensive NIPS test.

Overall, we presented here a comprehensive NIPS approach with improvements in assay performance, underlying technical innovations, and new cfDNA analytical algorithms. This new approach overcomes the limitations of current methods, which do not concurrently screen chromosomal and monogenic disorders and are confounded by multiple gestations, and maternal CNV and AOH. This method shows its potential in clinical application, especially enabling a more accurate prenatal screening on a broad spectrum of genetic diseases and providing valuable assistance for risk evaluation and timely management of pregnancy.

## Materials and methods

### Study subjects and ethics protocol

A total of 1182 samples from human subjects were included in the clinical validation study. This study was approved by the institutional review boards of China International Peace Maternity and Child Health Hospital (GKLW2019-52) and Obstetrics and Gynecology Hospital of Fudan University (2020-178). Informed consent was obtained from all study participants. This study collected leftover samples from subjects who underwent amniocentesis or chorionic villus sampling for standard prenatal diagnosis. Maternal plasma was collected before their invasive prenatal diagnosis procedures. The results from karyotyping, microarray-based comparative genomic hybridization, and/or sequencing data were collected for all cases with available pregnancy outcome data for the validation study.

### cfDNA extraction and NGS

The maternal plasma was separated through a two-step centrifugation process. At least 0.8 mL maternal plasma was first separated from the whole blood by centrifugation of the collection tube at 1600× g for 15 min at 4 °C. Then the plasma was centrifuged at 16,000× g for 10 min at 4 °C. cfDNA extraction was performed using Magnetic Serum/Plasma Circulating DNA Maxi Kit (Tiangen, China). For the NGS library construction, the cfDNA was end-repaired using the manufacturer’s protocol (Nanodigbio, China) followed by ligation at 20 °C for 15 min using adapters with unique molecular indexes. The sample barcode was introduced by PCR: 98 °C for 2 min, then nine cycles at 98 °C for 15 s, 60 °C for 30 s, and 72 °C for 30 s followed by a final extension at 72 °C for 2 min. The PCR products were then quantified using QubitTM 1× dsDNA HS Assay Kits (Invitrogen, United States). All the cfDNA extracted from each sample was used for library construction, which must be at least 400 ng after PCR amplification before proceeding to the next step for target enrichment. 12–36 samples were then pooled together for target enrichment at 65 °C or 68 °C for 16 h. Hybridization probes were added to the pooled DNA using the manufacturer’s protocol (Heristar LLC, United States). The recovered DNA was washed and purified using Dynamag-270 magnetic beads (Invitrogen, United States). Another PCR was performed to generate sequencing library: 98 °C for 2 min, then 12 cycles at 98 °C for 15 s, 60 °C for 30 s, and 72 °C for 30 s and a final extension at 72 °C for 2 min. Single-stranded circular DNA libraries were prepared by MGI-Easy Circularization Kit (MGI, China). Circular DNA was produced to generate DNA nanoballs by rolling circle amplification using the manufacturer’s protocol (MGI, China). The concentration of sequencing library was quantified by Qubit using Qubit ssDNA Assay Kits (Invitrogen, United States). The final DNA library was sequenced on MGISEQ-2000 (MGI, China) using 2× 100 paired-end mode.

### COATE probe design

Probes were designed to target SNPs on the entire or critical regions of chromosomes 1, 2, 4, 5, 8, 13, 15, 18, 21, 22, X, and Y to screen for T13, T18, T21, and sex chromosome aneuploidies or 1p36 microdeletion (chr1:800,095-12,734,180), 2q33.1 microdeletion (chr2:196,535,270- 202,435,277), Wolf-Hirschhorn syndrome (chr4:425,435-2,108,509), Cri du Chat syndrome (chr5:10,001-18,399,891), Langer-Giedion syndrome (chr8:116,700,000-126,300,000), Jacobsen syndrome (chr11:114,629,279-135,076,622), Prader-Willi syndrome/Angelman syndrome (chr15:23,334,675-28,323,850), and DiGeorge syndrome (chr22:17,322,843-21,118,912). All chromosome coordinates are GRCh38. The probes must reside in targeted regions where the GC content ranges from 30% to 70%. Additional probes were designed to target the coding sequences of genes including COL1A1, COL2A1, FGFR2, FGFR3, COL1A2, PTPN11, RAF1, RIT1, and SOS1 which are associated with frequent human dominant monogenic disorders. To reduce the probe hybridization bias between the reference and alternative alleles, one of four possible nucleotides (A, C, G, and T) is selected at the locus corresponding to the target SNP (Fig. 1b). Such probes are expected to have the minimum melting temperatures (Tm) difference for their pairing with reference allele Nref and alternative allele NAlt. The Nearest Neighbor model is used to calculate the Tm46.

$$\mathop {{\rm{argmin}}}\limits_N \left\{ {\left| {T_m\left( {N_{\rm{ref}}} \right) - T_m\left( {N_{\rm{alt}}} \right)} \right|} \right\},N \in \left\{ {A,C,G,T} \right\}$$

### The FF calculation

At any biallelic locus, there are two possible euploid maternal-fetal genotype combinations including AA-AB and BB-AB (A: alternative allele, B: reference allele) informative for the FF calculation. At SNP i, let N be the total NGS reads of the A and B alleles, and NAi be the number of A allele reads. At the loci where the mother is homozygous (AA or BB) and the fetus is heterozygous (AB), the locus-specific FF (denoted by FFAAi or FFBBi) can be computed.

$$FF_{AA_i} = 2\left( {1 - \frac{{NA_i}}{N}} \right)$$
$$FF_{BB_i} = \frac{{2NA_i}}{N}$$
$$N = NA_i + NB_i$$

Denote FFAA and FFBB the median of the FFs calculated for all informative SNPs, the sample FF is then calculated.

$$FF = \left( {FF_{AA} + FF_{BB}} \right)/2$$

A RD-based method was used to quantify Y chromosome dosage for FF in pregnancies with male fetus. Specifically, uniquely mapped reads to the Y and X chromosomes were counted followed by a normalization step. Then the ratio of median counts of normalized reads for the Y and X chromosomes was used to estimate the FF.

$$FF = RDchrY/\left( {RDchrY + RDchrX} \right)$$

### The locus-specific loglikelihood of different aneuploid states

The AF of SNP i can be considered as the probability of sampling the A allele (pAi). Let Ni be the total NGS reads of the A and B alleles at the SNP i and NAi be the number of A allele reads. The beta-binomial distribution is used to calculate the likelihood of sampling A allele with parameters based on different ploidy hypotheses. For the beta function, α is set at an empirical value of 3000. The AFs (or pAi) can be computed when fetal genotypes in different ploidy state and FF are accounted for (Supplementary Table S8). Then, the β is calculated.

$$\beta = \alpha /pA_i-\alpha$$

The pAi under different H, was derived from a linear combination of the conditional beta-binomial distributions which were weighted by the multinomial factor πk and $$\mathop {\sum }\limits_k \pi k = 1$$ using a modified method from a previous study47. Finally, with the depth and A allele reads, the likelihood can be computed by the beta-binomial distribution as follows:

$$p\left( {NAi|N,\alpha ,\beta ,FF,H} \right) = \mathop {\sum }\limits_k \pi _k\left( {\begin{array}{*{20}{c}} N \\ {NAi} \end{array}} \right)\frac{{B\left( {NAi + \alpha ,N - NAi + \beta } \right)}}{{B\left( {\alpha ,\beta } \right)}}$$
$$H\,\upepsilon\, \left\{ {D,MI,MII,PI,PII,LM,LP} \right\}$$

where D, MI, MII, PI, PII, LM and LP are disomy, trisomy (maternal meiosis I nondisjunction), trisomy (maternal meiosis II nondisjunction), trisomy (paternal meiosis I nondisjunction), trisomy (paternal meiosis II nondisjunction), monosomy (maternal meiosis nondisjunction) and monosomy (paternal meiosis nondisjunction), respectively. The following formulas are used to calculate πk:

$$\pi _k = \mathop {\sum}\limits_{PAT_i} {p\left( {FET} \right) \ast p\left( {PAT_i} \right)}$$
$$PAT_{ki} \in \left\{ {AA,AB,BB} \right\}$$

where the p(PAT) is the probability of the paternal genotype at the SNP i locus and the p is the population frequency of SNP i and the p(FET) is the probability of a specific fetal genotype in different euploid and aneuploid states when a familial trio is analyzed following the Mendelian inheritance principle (Supplementary Table S9). The p(PAT) is computed using the Hardy-Weinberg equilibrium.

$$p\left( {AA} \right) = p^2$$
$$p\left( {AB} \right) = 2p\left( {1 - p} \right)$$
$$p(BB) = (1 - p)^2$$

After pAi of all SNPs on each target chromosome were calculated, a Hampel filter was used to detect and remove outliers.

### Maximum likelihood of fetal chromosome ploidy

When there is no meiotic recombination, the fetus should always inherit all the SNPs from an entire parental chromosome. Let m be the total number of informative SNPs on the target chromosome. Then the maximum likelihood of fetal chromosome ploidy can be computed by taking the aggregate likelihoods of ploidy state at each informative locus. A particular fetal aneuploidy state could be established in which the respective ∆L value is negative and the lowest among all possible H:

$$\Delta L = \mathop {\sum}\limits_{i = 1}^M {\left( {\log \left( {Lp\left( {D_i} \right)} \right) - \log \left( {p\left( {H_i} \right)} \right)} \right)}$$
$$H\,\upepsilon\, \left\{ {MI,MII,PI,PII,LM,LP} \right\}$$

where the ∆L is sum of the locus-specific loglikelihood difference between a euploidy and an aneuploidy state, denoted by p(Di) and p(HF), respectively.

If there is meiotic recombination associated with aneuploidy, the fetus inherits the SNPs on a recombinant chromosome derived from the paired homologous chromosomes in the chiasma stage. The maximum likelihood of chromosome aneuploidy with one recombination is computed:

$$\Delta L = \min \left( {\mathop {\sum}\limits_1^k {\left( {{\text{log}}\left( {LD_i} \right) - \log \left( {LH1_i} \right)} \right)} + \mathop {\sum}\limits_{k + 1}^M {\left( {\log \left( {LD_i} \right) - \log \left( {LH2_i} \right)} \right)} } \right)$$
$$\{ H1,H2|H1\mathop { \cup }\nolimits H2 \in \left\{ {{{{\mathrm{MI,MII}}}}} \right\}\,{{{\mathrm{or}}}}\,\,H1\mathop { \cup }\nolimits H2 \in \{ {{{\mathrm{PI,PII}}}}\} \}$$

Similarly, the maximum likelihood is computed with two breakpoints a chromosome:

$$\Delta L\left( {H1,H2} \right) = \min \left( \begin{array}{l}\mathop {\sum}\limits_1^{b1} {\left( {\log \left( {LD_i} \right) - \log \left( {LH1_i} \right)} \right)} \\ + \mathop {\sum}\limits_{b1 + 1}^{b2} {\left( {\log \left( {LD_i} \right) - \log \left( {LH2_i} \right)} \right)} \\ + \mathop {\sum}\limits_{b2 + 1}^M {\left( {\log \left( {LD_i} \right) - \log \left( {LH1_i} \right)} \right)} \end{array} \right)$$
$$\left\{ {H1,H2|H1\mathop { \cup }\nolimits H2 \in \left\{ {{{{\mathrm{MI,MII}}}}\;{{{\mathrm{or}}}}\;H1\mathop { \cup }\nolimits H2 \in \left\{ {{{{\mathrm{PI,PII}}}}} \right\}} \right.} \right\}$$

### Chromosome CNV analysis using the RD data

The NGS raw reads were aligned to hg38 followed by unique molecular index (UMI)-based deduplication to suppress PCR amplification artifacts. Unmapped or ambiguously mapped reads were excluded from the coverage-based copy number analysis. For data normalization, the RD medians for each target chromosome (e.g., chr21, chr18, chr13, chr22, etc.) were found. Then, the median of the above chromosome-specific RD medians was used as the normalized sample coverage. SNP-specific RD was scaled proportionally to the normalized sample average for inter-sample comparison. A Hampel filter was used to remove loci with skewed RD which had > 3 standard deviations of the moving average. Principle component analysis (PCA) was used to remove the primary components of the reads which were independent of copy number changes48. This PCA-adjusted RD was then used for Z-score calculation. The entire dataset was divided into two groups. One group of 405 samples was used for method development and the other group of 724 samples was used for validation. The ratio of each target chromosome to the total reads of reference chromosomes within each sample was calculated for comparison. Z-score was calculated based on all samples in the same processing batch:

$$Z_i = \frac{{R_i - \mu _i}}{{\sigma _i}}$$

where Ri, µi, and σi are the ratio, average and variance of the ratio of target region, respectively. After multiple in silico experiments of pair-wise parameters for FF, RD, and the number of informative loci, we determined that the FF-RD product must reach 48 and the total number of informative SNPs must be > 60 to guarantee a test sensitivity ≥ 95%.

### The detection of maternal CNV and dizygotic twins

Maternal CNV is detected based on both the RD and the SNP AF data. The RD of each SNP is normalized by dividing it with the median depth of reference chromosome SNPs. Next, the median and standard deviation of normalized RD of each SNP is calculated, followed by Z-score calculation which is subjected to a smoothing step using a mean-shift algorithm. For each cluster, if the center has a Z-score > 3 or < –3, then a potential maternal CNV is called. This cut-off is set based on the assumption that the FF is usually < 0.5, a level at which the expected Z-score for each SNP is between –2.5 and 2.5, even when the fetus has a chromosome copy number gain or loss. For samples with maternal mosaic CNV, if the mosaic level is < 0.6, it is beyond the detection limit using the Z-score method. To reduce the false positive calls, the SNP AFs in regions with potential maternal CNV are also examined. For samples that have a maternal deletion, the heterozygous SNP AF is > 0.6 or < 0.4. For samples that have a maternal duplication, the heterozygous AF is between 0.4 and 0.6. The maternal CNV call is rejected if there is any conflicting result from the SNP AF data. Dizygotic twin pregnancy is determined by the increased number of fetal SNPs detected and the variation of the AF of fetal SNPs (Fig. 3g).

### The detection of meiotic homologous recombination for aneuploidies

The value of SNP AF is dictated by the specific combination of the maternal and fetal genotypes associated with different ploidy states (Supplementary Fig. S6a). In trisomies caused by maternal meiotic errors, multiple consecutive fetal homozygous SNPs (AAA or BBB) at the loci where the mother is heterozygous are indicative of MII NDJ (Supplementary Fig. S6a). Similarly, when the homologs are transmitted in MI NDJ, no extensive stretch of fetal homozygous SNPs should be present at the loci where the mother is heterozygous (Supplementary Fig. S6a). Therefore, the presence of both MI NDJ and MII NDJ fetal genotypes are suggestive of a recombinant event (Supplementary Fig. S6b, c). In MI NDJ causing fetal trisomy, at the maternal heterozygous loci (AB), the probability of fetus being heterozygous (ABA or ABB) is 1 (Supplementary Fig. S5). Therefore, when fetal homozygosity (genotype AAA or BBB) disrupting the MI NDJ pattern is seen, it can only be explained by an event of meiotic recombination. In MII NDJ, the probability of a fetus being heterozygous (genotype AAB or ABB) at a maternal heterozygous locus is 0.5 (Supplementary Fig. S5). Assuming all loci are transmitted independently and there is no recombination, the probability of 10 consecutive informative SNPs showing only fetal heterozygosity is 2−10 in MII. Therefore, we use a cut-off of 10 continuous fetal heterozygous loci to determine whether there is a MI NDJ.

### Monogenic variant detection

To screen for fetal SNVs in the regions of interest, repeat region filter was applied for all repeat region marked by RepeatMasker and excluded from the benchmark validation set. All fetal SNVs of cfDNA samples and related germline SNPs of amniocyte samples in the qualified region were identified by a modified BWA-GATK based in-house pipeline. For all amniocyte samples, germline SNPs with depth ≥ 100 and AF ≥ 30% were utilized as golden standard for cfDNA fetal SNV calling results. As for cfDNA samples, sites with depth ≥ 200 or AF ≥ 1% were used for the benchmark process.

ACD filter was established to identify paternally inherited or de novo fetal SNVs based on the expected alternative allele counts. The beta-binomial distribution was used to calculate the likelihood of a variant being from a non-fetal origin. When the absolute value of the log cumulative distribution function (CDF) value is between –10 and –0.001, the variant is considered positive. Note that the variants not falling in this range can still be considered positive if they satisfy downstream fragment size-based inclusion filters. Beta-binomial cumulative distribution function:

$$F\left( {x\left| {n,\alpha ,\beta } \right.} \right) = P\left( {X \le x} \right) = \mathop {\sum}\limits_{i = 0}^{\lfloor{x}\rfloor} {\left( {\begin{array}{*{20}{c}} n \\ i \end{array}} \right)\frac{{B\left( {i + \alpha ,n - i + \beta } \right)}}{{B\left( {\alpha ,\beta } \right)}}}$$
$$\alpha = \frac{{d_vmf}}{{2d_{avg}}}$$
$$\beta = \frac{{d_vm\left( {2 - f} \right)}}{{2d_{avg}}}$$

where the x is the alternative allele depth for a certain variant; n is the total sequencing depth for a certain variant; α is the effective alternative allele DNA molecule count for a certain variant and sample before PCR; β is the effective reference allele DNA molecule count for a certain variant and sample before PCR; davg is the sample average effective sequencing depth; dv is the variant effective sequencing depth; m is the empirical value of total effective DNA molecule count before PCR; and f is the FF.