Refphase algorithm

Refphase takes as input a copy number segmentation for each of N tumour samples from the same patient which it processes in four discrete steps or modules (Fig 1 and Methods).

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Fig 1. Overview of Refphase algorithm.

a) Refphase creates a minimum consistent segmentation across the single-sample segmentations input for each tumour. b) In each segment in which at least one sample had allelic imbalance in the tumour input, an optimal reference sample for phasing is determined. c) The phasing of each reference sample is derived from its BAF. d) Phasing is then applied to the BAFs in all other samples which are not the reference. e) Allele-specific copy numbers are re-estimated for each sample utilising the reference phasing, and the most parsimonious phasing solution along each chromosome is then chosen in horizontal phasing optimization. f) In each segment, event categories relative to the input ploidy of the corresponding sample are defined using LogR values. g) Tumour-level events are called and intra-tumour heterogeneity metrics calculated.

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First, a minimum consistent segmentation is created from the union of all segment start and end positions of the input copy number segmentations of each tumour sample (Fig 1A and Methods). Breakpoints separated by a distance smaller than a user-defined maximum gap size (default = 100kbp) are subsequently merged, unless these breakpoints belong to the same sample-of-origin. This exception is invoked to preserve focal gains and losses present in the original samples. This minimum consistent segmentation step yields a final set of m bins.

Next, using this set of m bins, multi-sample reference phasing is performed (Fig 1B and 1E). Heterozygous SNPs are either defined by the user or identified from the BAF values of the normal sample (Methods). For each bin m_i, the sample with the highest degree of allelic imbalance is then identified, which will act as a reference n_ref for m_i (Fig 1B and Methods). This reference sample n_ref is then used to assign alleles of all heterozygous SNPs within m_i to the “A” or “B” haplotype based on their BAFs being greater than or less than a threshold of 0.5 (Fig 1C). This haplotype assignment in turn is then applied to all other tumour samples for the same bin m_i (Fig 1D) and each tumour sample is assessed for the presence of any additional previously undetected allelic imbalance using an effect size threshold based on Cohen’s d (Methods). Haplotype-specific integer copy number states are then re-estimated for all reference phased segments (Fig 1E and Methods).

Reference phasing as described above accurately phases the haplotypes of all samples for each bin relative to one another, but independently of other bins. To phase bins along the genome “horizontally”, we next estimate this horizontal phasing by using an evolutionary criterion. Briefly, the assignment of heterozygous SNPs to “A” and “B” haplotypes for all bins within a single chromosome is chosen to minimise the number of copy number breakpoints across all tumour samples [37] (Figs 1E and S1 and Methods). The relative phasing between samples from the previous step therefore remains unchanged.

The third module then uses the re-estimated copy number and updated allelic imbalance states to determine whether a segment from a tumour sample may be categorised as an SCNA relative to the ploidy of that specific tumour sample, in keeping with both previous genomics studies [8,9,38] and clinical practice [39]. This relative-to-ploidy classification enables the comparison of the same area of the genome in bin m_i between samples with differing ploidies and classifies segments as either an amplification, gain, neutral, or loss relative to sample ploidy (Fig 1F and Methods). Loss of heterozygosity (LOH), copy-neutral loss of heterozygosity (CNLOH) and homozygous deletion events are also classified (Methods).

The fourth and final module integrates the multi-sample reference phasing and relative-to-ploidy classification to produce a tumour-level estimate of SCNA event clonality across all samples and to infer the presence of MSAI (Fig 1G). All events are then summarised as clonal (present in all tumour samples without MSAI) or subclonal (present in only a subset of tumour samples, or in all samples but with MSAI detected) (Methods).

Refphase identifies mirrored subclonal allelic imbalance and parallel evolution

We first demonstrated the functionality of Refphase by analysing WES data from three spatially separated primary tumour samples and a matched normal from a non-small cell lung cancer patient CRUK0034 from the TRACERx 100 cohort [8]. All three tumour samples were pre-segmented with ASCAT [22] and subjected to reference phasing. Dividing the genome into 178 bins, Refphase identified either clonal or subclonal allelic imbalance in 88.6% of the genome, with the remaining 11.4% of the genome allelically balanced. Fig 2 shows parts of the Refphase output for this tumour. A more complete output example is available in S2 Fig. For this example and the remainder of the text, we refer to unphased copy number states in major/minor configuration as e.g. 4/1 and to phased copy number states as e.g. 1|4, in line with genotype notation conventions.

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Fig 2. Detection of mirrored subclonal allelic imbalance and parallel evolution.

a) LogR and BAF tracks in chromosomes 1 to 6 from tumour CRUK0034. LogR tracks show LogR values in light grey points. The black line shows the median LogR within a minimum consistent segment. BAF tracks show phased BAF as either orange “A” haplotype points or blue “B” haplotype points. Unphased BAF values are shown as light grey points. b) SCNA summary tracks showing (top) gains relative to ploidy. The full height grey bar indicates that a gain is identified in every sample from tumour CRUK0034. A light yellow background indicates the presence of a subclonal gain, and the height of the stacked darker yellow bar indicates the proportion of samples in which a subclonal gain is present. (middle) Track indicates the presence of MSAI between at least two samples, shown by purple fill. (bottom) Track indicates the presence of parallel gains, shown by red fill. c) MSAI detected from tumour CRUK0034 affecting chromosome 4. d) Parallel evolution of chromosome arm 5p gain from tumour CRUK0034. e) Schematic of the copy number states related to MSAI and parallel evolution.

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While some SCNAs (e.g. gain on 1q) are clonal and present in all samples from the tumour, Refphase also identifies substantial inter-sample heterogeneity (Figs 2A, 2B, and S2). For example, 3p demonstrates allelic imbalance only in R2, where even after reference phasing, no allelic imbalance was detectable in the other samples, as can be seen from the well mixed BAF values for both haplotypes (orange and blue) on 3p in R1 and R3. Refphase identifies subclonal SCNA events including subclonal gain of 5q affecting R1 and R3, and a subclonal gain of 6p affecting R2.

Reference phasing also permitted the identification of both MSAI and parallel evolution in this tumour. One additional copy of chromosome 4 relative to diploid (Fig 2C) (copy number state 2/1) is present in all tumour samples. Reference phasing revealed that this additional copy was derived from the “A” haplotype (orange) in samples R1 and R3, and from the “B” haplotype (blue) in sample R2, an example of MSAI [8]. A second instance of MSAI on chromosome 5p co-occurs with relative-to-ploidy gains in all three samples with copy number states of 4|2 in R1 and R3 but of 2|3 in R2 (Fig 2D). A schematic outlining the distinction between the classifications applied to the MSAI affecting chromosome 4 and the parallel gains affecting 5p can be seen in Fig 2E. In addition to the detection of MSAI on chromosome 4 and parallel evolution of 5p gain, Refphase also identified an additional instance of MSAI affecting 1p (Fig 2B).

Since MSAI and parallel events are not detectable from the analysis of single tumour samples nor from unphased data, Refphase’s ability to identify haplotype-specific copy number states and its event classifications provide a refined view of the evolution of this tumour.

Refphase quantifies SCNA heterogeneity in complex multi-sample cases

The increasing availability of DNA sequencing data from multiple tumour samples from the same patient has begun to address complex questions regarding SCNA intra-tumour heterogeneity and changes in SCNAs during metastatic dissemination. However, there are no standardised frameworks in which such questions may be addressed and compared between studies. Refphase not only supports the quantification of SCNA clonality across all samples from the same patient but also allows standardised analysis and comparisons of user-defined subgroups of samples within a single patient’s disease. In addition, Refphase produces correctly formatted input for the state-of-the-art SCNA phylogenetic reconstruction algorithm MEDICC2 [36], as well as the option to output its own naive haplotype-specific clustering of minimum consistent segments.

Patient CRUK0063, previously analysed in work by Abbosh et al. in 2017 [40], was examined through the PEACE post-mortem study 24 hours after death. WES data from five post-mortem tumour samples (paravertebral and lung metastases) and five primary tumour samples were pre-segmented using ASCAT and subjected to reference phasing using Refphase. We investigated differences in SCNA profiles between primary and metastatic samples (Fig 3). MEDICC2 [36] was run on the Refphase output and grouped the metastasis samples together in one clade and the primary samples in a separate clade (Fig 3A). Refphase identified SCNA events present in both primary and metastatic samples (Fig 3B), present in primary samples only (Fig 3C), and present in metastatic samples only (Fig 3D).

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Fig 3. Analysis of CRUK0063 multi-sample and multi-time point NSCLC case.

a) MEDICC2 phylogeny. Multi-sample reference phased allele-specific copy number output from Refphase can be passed directly to MEDICC2 to produce a phylogenetic reconstruction. b) SCNA summary tracks for all samples—primary and metastases—from patient CRUK0063. c) BAF profiles and SCNA summary tracks for the primary samples from CRUK0063 are indicated by a red border. d) SCNA summary tracks and BAF profiles from five post-mortem metastatic samples with a blue border. Sample BAF tracks are ordered by their position in the MEDICC2 phylogenetic reconstruction. Green boxes, arrowheads and associated Roman numerals highlight selected examples of MSAI on chromosomes 2p, 6q, 4p and 10q, described in the main text. WGD indicates whole genome doubling events inferred by MEDICC2.

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Examining all CRUK0063 samples together revealed clonal SCNAs (SCNAs here encompassing relative-to-ploidy gains and losses, and LOH events) affecting 25% of the genome, subclonal SCNAs affecting 69% of the genome, MSAI affecting 26% of the genome and parallel evolution evident in 8% of the genome. Refphase also provided the opportunity to analyse the five primary and five metastatic samples separately, while using the phasing derived from all samples. Differences between the two groups emerged and enabled us to distinguish between SCNAs that are clonal and subclonal in the primary samples (primary-clonal/primary-subclonal) and those that are clonal and subclonal in the metastatic samples (metastasis-clonal/metastasis-subclonal). Metastasis-clonal SCNAs were far more prevalent than primary-clonal SCNAs, both in terms of proportion of the genome affected (55% vs. 36%), and of proportion of segments with any SCNA event (relative-to-ploidy gain or loss, or LOH) for which a clonal SCNA was identified, quantified within the respective group of samples (55% vs. 33%). Metastasis-clonal allelic imbalance and LOH were particularly prevalent, affecting 72% and 34% of the genome respectively, while primary-clonal allelic imbalance and LOH affected only 39% and 27% of the genome. The majority of LOH was found to be shared between primary and metastatic samples.

In line with the high levels of metastasis-clonal SCNAs in CRUK0063, the metastatic samples were also characterised by a relative absence of both MSAI and parallel evolution compared to the primary samples (proportion of genome: MSAI, 0.3% vs. 13%; parallel events, encompassing parallel gains, parallel losses and parallel LOH events, 0% vs. 5%). Examples of specific events observed when analysing the primary samples alone are visible in Fig 3 and include parallel gain of 2p (i), and multiple parallel LOH events including on 4p (ii) and 10q (iii). Specifically, primary tumour sample R3 had a different major haplotype to other primary samples at these loci. The divergence of sample R3 from other primary samples is reflected in it branching earlier than the remaining four primary samples in the accompanying MEDICC2 phylogeny. In the Abbosh et al. study [40], mutational phylogenetic analysis suggested that all metastatic samples arose from a single ancestral subclone; similar results are observed using the MEDICC2 phylogenies with all metastatic samples belonging to a single clade. There is also MSAI affecting 13% of the genome and an instance of parallel evolution of LOH affecting 6q between the primary and metastatic samples that are not identified within either the primary samples or metastatic samples alone (Fig 3C and 3D (iv)). Collectively, these MSAI and parallel evolution results suggest that the metastatic samples demonstrate less inter-sample heterogeneity than the primary samples in CRUK0063 and the presence of MSAI and parallel evolution between the primary samples and metastatic samples suggests continued copy number evolution. One area of the genome subject to parallel gain in CRUK0063 is a region of chromosome arm 2p (i), encompassing 2p16, that overlaps the second most commonly amplified locus in lung squamous cell carcinoma revealed by TCGA through GISTIC2 analysis [41,42]. This locus contains the transcription factor BCL11A, a known oncogene in triple-negative breast cancer [43] and B-cell lymphoma [44], that has been described as integral to the pathology of lung squamous carcinoma through its interaction with SOX2 to control the expression of epigenetic regulators [45].

In summary, Refphase revealed novel insights into the evolution of this tumour. The heterogeneity of the primary samples and continued and parallel evolutionary events would have remained hidden without reference phasing and the results from Refphase.

Refphase reveals previously undetected events in low purity samples

To quantify the extent to which Refphase reveals previously undetected SCNAs, we applied Refphase to multi-sample cohorts from two highly-cited studies: (1) a multi-sample investigation of primary colorectal adenocarcinoma and adenoma [46] (15 tumours, 140 samples), and (2) a matched primary sample and metastatic sample cohort of various primary cancer types and their brain metastases [47] (84 tumours, 196 samples) (Fig 4). These datasets demonstrate a range of copy number landscapes, purity levels, and data types (SNP array and WES) found in both research and clinical studies.

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Fig 4. Low cancer cell fraction SCNA detection and cohort-level analysis for the Sottoriva et al. [46] and Brastianos et al. [47] cohorts.

a) Barplots showing the proportion of the genome affected by MSAI in each tumour sample in the pan-cancer cohort grouped by tumour type. b) Barplots showing the proportion of the genome with allelic imbalance that was identified using multi-sample reference phasing and that was previously undetected using ASCAT. Each tumour sample in the pan-cancer cohort is arranged by tumour type. Light blue bars represent the proportion of the genome in each sample affected by previously undetected allelic imbalance that did not result in an alteration in the previously estimated integer allele-specific copy number. Dark blue bars represent instances in which newly detected allelic imbalance that resulted in new integer copy number state being estimated. c) Barplots representing the estimated cancer cell fraction of each sample in the pan-cancer cohort grouped by cancer type. d) Unphased BAF and integer copy number states across the genome from two samples analysed using ASCAT. e) Phased BAF and haplotype-specific copy number states across the genome from two samples analysed using Refphase. f) Line plot showing the proportion of simulated copy-neutral loss of heterozygosity events identified at differing non-cancer proportions of a sample using ASCAT (red) or Refphase (blue).

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As already described, Refphase’s multi-sample phasing permits the detection of MSAI not otherwise discernible with single-sample data or unphased copy number profiles. Examining our cohort utilising the multi-sample reference phasing of all samples of each tumour, we detected MSAI in 65% of tumours (64/99), affecting up to 34% of the genome (IQR across all tumours [0%,3%]; Fig 4A and Methods). In addition to revealing MSAI, multi-sample phasing can be used to identify previously undetected allelic imbalance. This newly identified allelic imbalance is often not MSAI but simply allelic imbalance with the same major haplotype as the other samples from the same tumour previously identified as demonstrating allelic imbalance. Refphase detected new allelic imbalance not previously detected by ASCAT in 77% of tumour samples (256/334). The greatest degree of new allelic imbalance identified was in sample MET019 in which 66% of the genome was identified to be allelically imbalanced by Refphase which had not been identified as such by ASCAT (Fig 4B).

Whilst we identified a significant increase in total allelic imbalance with increasing sample purity (Fig 4C; LME ANOVA p = 0.03, adjusted for patient and cohort—the latter defined by tumour type and profiling platform—as random effects, S3A Fig), we observed a significant negative association between sample purity and newly identified allelic imbalance (Fig 4B and 4C; LME coefficient = -0.28 (2.s.f), LME ANOVA p<0.0001, adjusted, S1 and S3C Fig). This result is consistent with Refphase’s ability to rescue low purity samples and is in accordance with previous work demonstrating that SCNA detection using methods designed for single samples is drastically impaired by low tumour purities when sequencing coverage remains unchanged [48]. No statistically significant associations were observed between purity and MSAI detection at sample or tumour-level (sample-level: LME ANOVA p = 0.5, adjusted, S3D Fig; tumour-level: p = 0.07, adjusted for cohort, S3E Fig). Schematic examples of the effect of tumour purity and copy numbers states on BAF and LogR profiles are shown in S4 Fig.

We further explored the relationship between purity and SCNA event detection for the specific case of tumour MET019 from Brastianos et al.[47], a lung adenocarcinoma containing the sample (M3) which demonstrated the highest amount of newly identified allelic imbalance in our cohort when analysed with Refphase (66% of the genome affected). Notably, this M3 sample showed a markedly lower level of inferred tumour purity compared to the tumour’s other samples (M3–21% compared to R1–47%, M1–80%, M2–86%). Using the same phasing that revealed the newly identified allelic imbalance, we re-estimated the copy number states for all samples across the genome and compared Refphase results to the previous ASCAT-derived estimates. We focussed analysis on detection of CNLOH. ASCAT identified CNLOH affecting five chromosomes in M3 compared to Refphase finding CNLOH on 15 chromosomes, with an increase of 24% of the genome affected when quantified using Refphase. The same analysis of the purer M2 sample yielded an increase of just 0.09% of the genome affected by CNLOH using Refphase (Fig 4D and 4E). This result supports the previous observation of a negative association between sample purity and the extent of newly identified allelic imbalance using Refphase.

Finally, to systematically compare ASCAT and Refphase’s ability to resolve allelic imbalance as a function of purity, we simulated BAF values for CNLOH events at varying tumour purities in samples from multi-sample NSCLC tumours [8] (125 events; each simulated at tumour purities from 1% CCF to 30% CCF at 1% CCF intervals; 200x sequencing coverage) (Methods and Fig 4F). CNLOH events were investigated to ensure that there were no changes to overall sample ploidy and that LogR changes did not influence event detection. Using these simulation parameters, ASCAT was able to detect allelic imbalance at all simulated CNLOH events at tumour purities of 15% or greater and Refphase at purities of 4% or greater (Fig 4F).

Taken together, multi-sample reference phasing improves the limits of detecting allelic imbalance and offers potentially exciting avenues for improving the sensitivity of SCNA detection at low cancer cell fractions, especially in non-WGS contexts.

Refphase improves SCNA intra-tumour heterogeneity estimates

Using the same pan-cancer cohort (Fig 5A), we next leveraged Refphase’s relative-to-ploidy SCNA event classification and standardised SCNA intra-tumour heterogeneity quantification (Methods) to explore cancer evolution in a range of cancer types.

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Fig 5. Cohort-level analysis of cancer evolution for the Sottoriva et al. [46] and Brastianos et al. [47] cohorts.

a) Barplot showing the number of samples per tumour and colored by WGD clonality status with clonal WGD (dark orange), subclonal WGD (light orange), and non-WGD (blue). b) Barplot showing proportion of the genome classified as affected by clonal SCNA (grey) and subclonal SCNA (yellow) from the pan-cancer cohort. c) Barplot showing proportion of the genome affected by parallel evolution of SCNAs relative to ploidy or LOH (red) and parallel evolution of 2|1 copy number states (dark blue). d) BAF of heterozygous SNPs across the genome from tumour samples from colorectal adenocarcinoma U. SNPs are coloured orange and blue according to the phased haplotype they are assigned to while SNPs that could not be phased are coloured grey. Regions of the genome demonstrating parallel evolution of a 2|1 and 1|2 copy number states are highlighted with a dark blue outline. e) Schematic demonstrating whole genome doubling and independent subsequent copy number loss events revealed by MSAI.

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We first quantified the total proportion of the genome affected by SCNAs (here encompassing relative-to-ploidy gains and losses, and LOH) and the proportion of clonal, early SCNAs, compared with subclonal, late SCNAs (Methods and Fig 5B). We identified clonal SCNAs in every tumour and found that 96% (95/99) of the tumours examined had clonal and 95% (94/99) harboured subclonal SCNAs affecting at least 1% of the genome. A median of 31% of the genome was subject to clonal SCNAs and 25% to subclonal SCNAs meaning that in over half of tumours (52/99), 25% or more of the genome was subject to subclonal SCNAs. The SCNA heterogeneity observed in these 99 tumours of various cancer types supports recent work suggesting that ongoing chromosomal instability is pervasive in cancer [9,10].

Importantly, detection of MSAI at a genomic segment renders any clonal SCNA at that segment subclonal since different haplotypes represent the major allele in different tumour samples. This means that Refphase can resolve additional SCNA heterogeneity which would not be possible with methods relying on unphased data. Notably however, despite the detection of MSAI in a subset of tumours (Fig 4A), the cohort-level effect of multi-sample reference phasing was to decrease the average level of SCNA heterogeneity compared to estimates from ASCAT runs on independently analysed tumour samples (paired Wilcoxon signed rank tests, p<0.05, S5 Fig). This suggests that segments previously defined as harbouring subclonal SCNAs are now identified to be clonally affected across all tumour samples. This may in part be due to the increased SCNA detection in low tumour purity samples explored in the previous section.

Overall, these analyses highlight how Refphase can provide potentially more accurate overall estimation of SCNA heterogeneity than approaches relying on unphased data.

Refphase offers insight into associations between parallel evolution and WGD in a pan-cancer cohort

Whole genome doubling (WGD) is considered a transformative event in tumour evolution [49], and tumours with WGD events show increased prevalence of MSAI [8,9]. In order to explore this relationship in our pan-cancer cohort, we determined WGD status using MEDICC2 run on Refphase output to classify the tumours in our pan-cancer cohort as clonal WGD, subclonal WGD, or non-WGD (Methods and Fig 5A). In keeping with previous results, a higher proportion of the genome was observed to be affected by MSAI in whole genome doubled tumours (clonal and subclonal) than non-WGD tumours (Kruskal-Wallis p = 2e-04, S6 Fig).

We next probed further into the nature of MSAI in our cohort. Specifically, we quantified the extent of parallel evolution of the same type of SCNA event (e.g. gains, losses, LOH) occurring in different samples within the same tumour but affecting different haplotypes, which represents just a subset of MSAI events. Using relative-to-ploidy and LOH definitions of parallel evolution (Methods), we observed parallel evolution in all tumour types in our cohort with the exception of the benign colorectal adenomas (Fig 5C). However, this tumour type also had the lowest levels of SCNAs overall with on average <1% of the genome affected by either clonal or subclonal SCNAs (Fig 5B; median percentage of genome affected: clonal 0.7%, subclonal 0.7%). Notably however, we observed parallel evolution of gains in the Sottoriva et al. (malignant) colorectal adenocarcinoma dataset, indicating independent evolution of similar SCNAs in spatially separated areas of tumours, adding additional resolution to the original study [46] (S7 Fig).

Intriguingly, we observed some tumours, such as colorectal adenocarcinoma U from Sottoriva et al. [46] (Fig 5D), with greater than 30% of their genomes affected by MSAI but with only a very small subset of this MSAI constituting parallel gains and losses relative to ploidy (2% of the genome, Fig 5C). Upon exploring MSAI in genomic regions matching the overall ploidy of their respective tumour samples (Methods), we observed that MSAI commonly occurred in a copy-neutral context of arm-level and chromosomal triploidy. Tumour U harboured nine chromosome arms affected by this phenomenon and was found to have undergone a clonal and therefore likely relatively early WGD event. This may suggest parallel evolution of losses from a tetraploid to a sub-tetraploid state (Fig 5E). Consistent with this, 2|1 and 1|2 copy number states were simultaneously observed in 22 tumours, of which 21 were determined to have undergone clonal or subclonal WGD using MEDICC2 (Fig 5A and 5C, Methods) [36]. Other groups have observed such parallel losses in in vitro models of WGD [50], inferred their presence from single-sample data [51] or characterised them in single cell sequencing [32], but to our knowledge this is the first time that such independent losses have been observed and linked to WGD using phasing in multi-sample bulk data. The parallel evolution of losses from a tetraploid state offers new insights into the potential selective pressure for triploidy and the ability to further determine the timing of such events in tumour evolution.

Together, these results highlight the importance of leveraging information from multiple samples to quantify SCNA heterogeneity during tumour evolution and demonstrate the technical advances offered by Refphase compared to single-sample copy number callers, including its ability to identify MSAI, its increased sensitivity of CNLOH detection, and its potentially more accurate overall estimation of SCNA heterogeneity.

Benchmarking Refphase

Nomenclature

We report integer allele-specific copy numbers from SCNA estimation tools that do not perform either statistical or multi-sample reference phasing in the major/minor configuration. We use the / symbol to separate the most common allele and least common allele for a copy number segment or bin covering a genomic region. For example, in two samples (S1 and S2) from the same tumour in which we observe the same unphased allele-specific integer copy number state of 2 of one allele and 1 of the other allele at the same genomic region, we report the allele-specific integer major and minor allele copy number estimate of this bin as 2/1 in S1 and 2/1 in S2. We would also report the non-allele specific total copy number in sample S1 as 3 and in sample S2 as 3.

In the context of multi-sample reference phasing as performed by Refphase, we report phased haplotype-specific “A” haplotype and “B” haplotype copy number written in the format haplotype “A” | haplotype “B”. If Refphase identified MSAI between our example S1 and S2, maintaining the total copy number states of 3 in both, with haplotype “B” being present at 1 copy in S1 but at 2 copies in S2, we would report the copy number in S1 as 2|1 and in S2 as 1|2.

Refphase input data requirements

To perform multi-sample reference phasing for a tumour with N samples, an initial single-sample copy number segmentation and initial estimates of tumour purity ρ_j and ploidy ψ_t,j must be obtained as input for Refphase by applying a single-sample SCNA calling algorithm to each tumour sample j∈{1..N} independently.

Single-sample tools typically follow a common approach for the detection of allele-specific SCNAs, as defined in [22]. Briefly, for each tumour sample, sequencing reads are aggregated at heterozygous germline variants in each tumour and paired normal sample over both parental alleles, yielding two readouts: the log ratio L_i of normalised read counts at variant i compared to the matched normal (LogR) and the relative frequency of the minor (B) allele read counts over the total read counts (B-allele frequency, BAF) b_i at variant position i. SCNAs are called by segmenting both BAF and LogR tracks into homogeneous segments and determining fractional or integer copy numbers for each segment, jointly inferring the purity ρ_j of sample j (the fraction of cancer cells over total number of cells) and the average ploidy ψ_t,j of the tumour sample j as free parameters [22]. Copy numbers are determined per allele, but due to unknown phasing of the underlying germline variants, the values are reported as major (larger) and minor (smaller) copy number instead.

Refphase currently directly supports input derived from the popular segmentation algorithms ASCAT [22] and Sequenza [33], but will run on any user-supplied initial segmentation result which includes estimates of: allele-specific copy number segments (genomic positions and major and minor allele copy number states); sample purity and ploidy estimates; log ratios (LogR) and B-allele frequencies (BAFs) of single nucleotide polymorphisms (SNPs); and—for non-ASCAT input—SNP heterozygosity annotations, for each of the N tumour samples (N≥2) and a matched normal from the same patient.

Refphase algorithm overview

Refphase achieves long-range phasing and haplotype-specific estimation of SCNAs through application of the multi-sample reference phasing algorithm. We assume that the input purity estimates for each tumour sample are correct and Refphase utilises these, alongside the LogR and BAF, to characterise SCNA heterogeneity of the genome in m bins of variable sizes. These bins are derived from a minimum consistent segmentation (see below) created from the input copy number segments for each tumour sample.

The four outputs from Refphase are: (1) a phasing of heterozygous SNPs, (2) an updated set of phased fractional and integer copy number states across the genome for each sample, (3) a sample-level summary of SCNA events, and (4) a summary of SCNA clonality and intra-tumour heterogeneity, defined either at tumour level or between and across user-defined subgroups of samples.

For a schematic overview of the Refphase algorithm see Fig 1.

Minimum consistent segmentation

Having internally preprocessed input data to a standard Refphase format, Refphase combines individual single-sample segmentations to generate a minimum consistent segmentation (MCS) for the set of all N samples of a tumour (Fig 1A). To do this, Refphase first defines the combined set of breakpoints as the union of the set of individual breakpoints, keeping track of the samples-of-origin. Of the new set of segments defined by this union of breakpoints, only segments present in all samples are retained in the subsequent analysis. An iterative merging strategy is then employed which merges breakpoints that originated from different samples if their pairwise distances are below a user-defined maximum gap threshold (default = 100kbp). These slight variations in breakpoint position typically result from variability in the estimation of breakpoint positions in individual samples even if the true underlying breakpoint is the same. The restriction to only merge breakpoints that originated from different samples of origin preserves focal amplifications and losses present prior to merging in individual samples and yields a final set of m bins.

Reference sample selection

Once the MCS is established, Refphase employs the multi-sample reference phasing algorithm to achieve long-range phasing of germline variants and assignment of SCNAs to haplotypes (Fig 1B and 1E). Multi-sample reference phasing leverages the fact that the phase of the underlying germline genetic variants is constant between samples from the same patient. In a segment affected by allelic imbalance, variants whose alternative alleles are residing on the chromosome with higher copy number will show a theoretical BAF above the segment mean, whereas those residing on the minor copy number chromosome will show BAF values below the segment mean, effectively providing phasing information about the variants contained in the segment.

To leverage this information, for each MCS segment, Refphase first iterates through all segments and samples and, using input major and minor copy numbers, for those segments determined to have a major copy number not equal to half of the total copy number (sum of major and minor copy number) in at least one sample, Refphase assigns the sample with the highest mirrored mean BAF as the reference sample (Fig 1B), where the mirrored mean BAF is defined as: (1) where b_k is the BAF at variant position k; m is the total number of variants within the segment indexed from 1; where abs() returns the absolute value (≥0) of the expression contained in brackets; and where variant refers to a heterozygous SNP contained within the segment. Specifically, mirrored mean BAF is calculated directly on all heterozygous SNPs for samples containing fewer than a default of 3 heterozygous SNPs or if the variance of the BAF values for the heterozygous SNPs within a segment is less than a default threshold of 1e-05, and a McClust mixture model applied otherwise.

Segments without copy number imbalance in at least one sample in the input are not considered for reference phasing.

Haplotype phasing of reference sample segments

Within each reference sample, Refphase then assigns alternative alleles to haplotypes H_i by comparing the empirical BAF of each variant i against the segment mean (Fig 1C): (2) where b_i is the BAF at variant position i; m is the total number of variants within the segment indexed from 1; and I is an operator assigning each variant position to one of two haplotypes based on the evaluation of the logical expression in square brackets.

In this way, the definition of haplotypes is entirely based on germline SNP data and does not take into account somatic mutation data such that exactly two haplotypes are defined at each genome position for which phasing is undertaken.

Reference phasing across non-reference sample segments

In the next step, Refphase applies this phasing information to the variants in the same segment in all other non-reference samples to determine haplotype-specific BAF values for every other sample (Fig 1D).

Haplotype-specific copy number quantification

After the variants have been assigned to haplotypes, Refphase uses haplotype-level BAF and LogR values for re-estimation of haplotype-specific copy numbers (Fig 1E).

Here, each sample is tested for allelic imbalance using a Wilcoxon rank-sum test between the BAF values of each haplotype (5% family-wise error rate) and the effect size of allelic imbalance is determined using Cohen’s d [70]. If additional allelic imbalance is detected compared to the initial copy number states, or if the option is applied universally by the user, copy numbers are re-estimated using either a default parametric or a non-parametric model for each haplotype separately.

The parametric model is consistent with the ASCAT formulation for copy number quantification and can accurately describe theoretical LogR and BAF values from a sample with given purity, ploidy and sequencing depth. The parametric model estimates the new haplotype-specific copy numbers n_A,i and n_B,i in segment i based on the mean BAF b_i and LogR L_i of that segment as well as sample purity ρ and average tumour ploidy ψ_t obtained from the initial segmentation as follows, as also described in [22]: (3) (4)

A full derivation of these equations can be found in the Supporting Information of the ASCAT publication [22].

The non-parametric model, in contrast, estimates new copy numbers for a region agnostic of how the LogR and BAF values were calculated by training a naive Bayes classifier on other segments. The non-parametric model was included as an alternative approach to facilitate application of Refphase to the output of copy number calling tools with potentially greatly different mathematical formulations of LogR and BAF. To train the non-parametric model, Refphase uses the mean BAF and LogR values of all other segments of the same sample and from the same segment in all other samples as training data to account for the typical BAF/LogR distributions of the current sample as well as those values from homologous segments in other samples. After re-estimation of all copy number segments, the average tumour ploidy ψ_t of each sample is re-calculated as the sum over the total copy numbers of all segments i = 1..m weighted by their genomic width w_i (in bp) relative to the total width of the genome (in bp). (5)

Re-estimated fractional and integer copy numbers are available to the user.

Horizontal phasing

After individual segments have been phased across all samples, there is still no phasing relationship between neighbouring segments ‘horizontally’ along the genome (Figs 1E and S1). We employ a method for phasing along the genome that uses a parsimony assumption, i.e. the data can be explained with the least amount of copy number changes between neighbouring segments. This is equivalent to the least amount of copy-number breakpoints which we formulate as the total Hamming distance between neighbouring segments (6) where we sum over all N samples and S segments and calculate the Hamming distance H between the copy number and its predecessor for both haplotypes A and B. The Hamming distance H(x, y) computes to 1 if x≠y and 0 otherwise. As the reference phasing algorithm only phases segments across samples, we can achieve an optimal horizontal phasing by “flipping” all haplotype assignments for some of the segments. Flipping the haplotypes of segment i amounts to exchanging n^s_A,i and n^s_B,i for all samples s. As there are a total of 2^S possible configurations, the horizontal phasing problem can be formulated as follows: Choose for each segment s in S its orientation (flipped or unflipped) such that the overall Hamming distance between neighbouring segments (Eq. 6) is minimal.

To identify the optimal horizontal phasing a dynamic programming approach can be conceived. However, many of the 2^S possible configurations are redundant w.r.t. the overall Hamming distance because of the following two equalities and . Therefore, we only have to investigate whether or not to flip a segment w.r.t. its direct predecessor. If flipping the haplotype assignment of segment i does not result in a change of distance D_s (i.e. D_s = D_s^flipped), the segment i is compared to its next predecessor (segment i-2). This is repeated until D_s ≠ D_s^flipped or the beginning of the current chromosome is reached.

After the optimal flipping assignments of all segments w.r.t. their direct predecessors are found, we translate those to a final flipping assignment of the segments 1-S by keeping the first segment fixed and iteratively (from second to last segment) perform the following action: If the segment-boundary between segment i and i-1 is set to be flipped, flip all segments [i, i+1, …, S].

As the assignment to haplotype A and B is arbitrary across chromosome boundaries, for plotting purposes, we flip the A and B allele assignment for all samples on a chromosome-by-chromosome level to ensure that on average haplotype A has a higher copy number than haplotype B.

Sample-level SCNA calling

Following reference phasing, Refphase uses the re-estimated sample ploidies, input purities and segment-level LogR data to call SCNA events in each sample (Fig 1F).

We consider an SCNA to be a deviation of any length from the diploid major/minor copy number state of (1,1). SCNAs with an unequal number of copies on both parental alleles (corresponding to a significant deviation of the BAF from its balanced value of 0.5) are termed allelic imbalance.

Specifically, Refphase calls segment amplifications, gains and losses relative to ploidy as well as LOH events and homozygous deletions. Events are called for each segment and sample independently of others by comparing the mean segment LogR distributions to calculated purity-ploidy derived event thresholds (Eqs 7–9).

The >2× ploidy threshold is the same threshold used for clinical decision making in HER2+ breast cancer using fluorescence in situ hybridization samples [39].

Amplifications are called if (7) gains are called if (8) losses are called if (9) with sample purity ρ and sample ploidy ψ_t.

By default, Refphase also provides additional versions of sample-level SCNA event calls aside from comparing mean segment LogR values to the calculated thresholds (Eqs 7–9). In another version, LogR values within a segment are compared to the calculated thresholds (Eqs 7–9) using a one-tailed Student’s t-test, as in [9]. Additionally, a diploid reference can also be used for both mean and t-test approaches rather than purity-ploidy derived event thresholds. All versions of SCNA calls are available to the user in summary Refphase objects after the completion of the core Refphase algorithm, and plotting options are available to visualise the preferred SCNA event output graphically. For Figs 2 and 3 and associated proportion-of-genome metrics, mean segment LogR values were compared to purity-ploidy derived event thresholds.

LOH events are called for segments in which the rounded copy number state of one allele is 0 and the other strictly greater than 0. Homozygous deletion events are called for those segments where both alleles within a sample have rounded copy number state of 0. Copy neutral LOH (CNLOH) is called for segments in which the major rounded integer copy number state equals the rounded tumour sample ploidy.

Patient-level SCNA calling

Finally, a tumour-level event summary is calculated (Fig 1G).

Inter-sample heterogeneity is quantified. The presence or absence of each class of relative-to-ploidy event, loss of heterozygosity (LOH), and homozygous deletions (HDs) in each tumour sample for each minimum consistent segment is noted. This presence or absence classification is then examined in the context of MSAI detection to determine whether each event affects the same allele in all samples.

For a given segment, an SCNA is considered to be clonal if it is present in every sample and affects the same allele in all samples. An SCNA is assigned as subclonal if it is present in at least one sample but simultaneously absent in at least one other sample (inter-sample subclonality). Crucially, in cases in which the same relative-to-ploidy or LOH event type is determined to occur in every sample of a given tumour but in the context of MSAI such that a different allele is deemed to be the major allele in different samples at the same segment, the event is assigned as subclonal and parallel and not as clonal, since the SCNAs in different samples are deemed to be of different origin and affecting different haplotypes. Specifically, a mirroring of alleles must be observed between the specific samples harbouring the event type of interest for the event to be called parallel. For example, in a tumour composed of three samples, should a gain SCNA be called in Samples 1 and 2 only, the major alleles must differ in Samples 1 and 2 for the gain event—already subclonal—to be called parallel, regardless of allelic arrangement in Sample 3.

Having assigned individual SCNAs as clonal or subclonal, the proportion of the genome affected by each specific event type (e.g. clonal relative-to-ploidy gains, parallel LOH, etc.) is calculated. Proportion of genome measures are calculated over the sum of minimum consistent segment widths for a tumour.

Plotting options are available to visualise tumour-level summary metrics and the degree of reassignment of events from clonal to subclonal based on MSAI context.

Refphase user-defined grouping functionality

Refphase also offers the option for a user to define subgroups of samples and calculate group-level (instead of whole-tumour-level) summary metrics and create within- and between-group summary plots. Examples of primary-sample-specific and metastases-sample-specific summary tracks in which clonality and heterogeneity analyses are restricted to the respective subgroups of samples are shown in Fig 3.

Refphase plotting functionality

Figs 2, 3, and S2 showcase selected tracks from Refphase across-genome plots. Refphase provides several optional output plots as standard including across-genome, chromosome-level, user-defined sample subgroup-oriented, and tumour-level event summary plots.

MEDICC2 implementation and whole genome doubling detection

The phylogeny showcased in Fig 3 was generated by applying MEDICC2 (version 0.6b1) [36] to re-estimated integer copy number states derived from reference phasing of the named 10 input samples for CRUK0063 using default parameters.

In order to derive the WGD status for the Brastianos et al. [47] and Sottoriva et al. [46] datasets, MEDICC2 bootstrapping WGD detection was used. In short, we create three sets of 100 bootstrapping datasets for each individual tumour sample (three representing three small segment filter sizes - 500kbp, 750kbp and 1Mbp) by resampling Refphase copy-number output for the sample chromosome-wise (i.e. drawing 22 chromosomes with replacement). MEDICC2 is then run on each bootstrapped dataset, before checking whether MEDICC2 detects a WGD. Specifically, if at least 5% of the bootstrap runs detect a WGD for at least one of the small segment size filters, the sample is labelled as WGD-positive. This low threshold offsets the otherwise conservative WGD detection, as described in Kaufmann et al. 2022 [36]. Subsequently, if all samples for an individual tumour are determined to harbour WGD, the tumour is labelled as having clonal WGD and subclonal WGD if only a subset of samples have WGD detected.

Definitions of newly identified allelic imbalance and CNLOH (Fig 4)

ASCAT [22] allelic imbalance was defined at the sample-level and assigned for segments where ASCAT non-integer copy number was not equal for the two alleles. Refphase allelic imbalance was assigned for segments at sample-level using the previously described methods (Methods—Haplotype-specific copy number quantification). CNLOH was assigned to segments in which the rounded major copy number state equalled the rounded sample ploidy and the rounded minor copy number state equalled 0, using copy number states and ploidies from ASCAT and Refphase accordingly. Newly identified allelic imbalance and CNLOH specifically referred to scenarios in which the respective event had not been identified in ASCAT and was identified using Refphase. For cases in which multiple ASCAT segments overlapped with the Refphase segment being assessed for allelic imbalance or CNLOH, data for the ASCAT segment most overlapping the Refphase segment under investigation was used.

Copy-neutral LOH event simulation (Fig 4)

CNLOH events were simulated in chromosomal segments from NSCLC multi-sample bulk sequencing from the TRACERx100 cohort [8].

First, Refphase was run on the TRACERx100 tumour samples. Then, pairs of samples were selected from tumours where at the same genomic region, defined by a Refphase bin, one sample, referred to as “reference”, demonstrated allelic imbalance allowing a reference phasing to be obtained and the other sample, referred to as “test” demonstrated total copy number equal to the overall sample ploidy with no allelic imbalance. Specifically, for a genomic bin, the reference sample demonstrated sufficiently clear allelic imbalance in its BAF to be likely to produce a highly accurate phasing if the heuristic condition in Eq 10 was satisfied: (10) where ρ is the tumour purity, n_A the copy number state of allele A and n_B the copy number state of allele B.

Additionally, for candidate samples and segments to be chosen, the following conditions must also be satisfied: Genomic bins had to be ≥1/5 of the size of the chromosome on which they were located and contain ≥1/5 of the heterozygous SNPs present on the same chromosome; the ploidy of the test sample had to be between 1.8 and 2.2 or between 3.8 and 4.2 (lower and upper bounds inclusive); and the total rounded copy number in the genomic bin should equal the total rounded ploidy of the test sample.

This candidate segment selection approach produced 125 segments that were then used to simulate CNLOH at the genomic region in the test sample. CNLOH was simulated at various cancer cell fractions (CCFs) of the sequenced sample, ranging from 1% to 30% in steps of 1%. Specifically, BAF values were assigned at each of the heterozygous SNP positions in candidate segments using a binomial distribution (R rbinom function) with simulated probability equal to the mean BAF which would be predicted for each phased allele at the segment based on copy number and simulated purity and with the number of trials equalling a simulated sequencing coverage of 200(x).

These simulated BAF profiles are then used as input to ASCAT allele specific piecewise constant fitting segmentation and Refphase, making use of the phasing derived reference sample, and detection of allelic imbalance reported for each method independently for each of the 125 candidate segments at each simulated CCF value. Detection of allelic imbalance was reported as detection of a CNLOH event.

Initial copy number estimates for data types

Simulations to estimate MSAI selection

To test whether MSAIs were more frequently found than expected by chance, we created a simulation approach (S8 Fig). To this end, we ran MEDICC2 with the “—events” flag which reconstructs the phylogenetic tree and also infers the copy-number events that lead to the observed profiles for every branch of the phylogenetic tree. Events are defined by MEDICC2 as WGDs, chromosomal gains and losses as well as segmental gains and losses. We then created 350 datasets for each of the 99 patients by re-simulating the events such that every branch of the phylogenetic tree maintained the same number and kind of events but the location of the events were randomly chosen. That means that chromosomal events are randomly assigned to chromosomes with equal probability. Similarly, segmental events are uniformly distributed across all possible chromosomes and uniformly along the chromosome while keeping their lengths fixed. This effectively creates a copy-number profile with the exact same copy-number events (number and type) but with permuted event locations. MSAI enrichment was assessed based on the fraction of the total genome which exhibits MSAIs.

Benchmarking