TWI852661B - Method for evaluating consensus base error rate and a system thereof - Google Patents

Abstract

The present invention discloses a method for evaluating consensus base error rate and a system thereof. The method integrates polymerase chain reaction error rate and sequencing error rate for evaluating error rate of each consensus base. Corresponding consensus quality scores can be calculated, which can improve the precision of current molecular labeling sequencing. On the other hand, during mutation detection, the perplexed interpretation by low-frequency mutation can also be eliminated. The addressed advantages will benefit development of precision medicine in the future.

Description

Consensus base error rate evaluation method and system

The present invention relates to a DNA sequencing data analysis technology field, and more particularly to a method for evaluating consensus base error rate.

Detecting low-frequency mutations has great potential for the development of precision medicine and personalized cancer diagnosis. In current technologies, targeted therapy relies on the detection of somatic cell variants, and the use of tumor cells in the blood circulation can be used for non-invasive DNA testing for tumor classification and disease progression monitoring at low cost. However, when the frequency of variants is equal to or even lower than the sequencing error rate or the sequence reading error rate caused by other technical issues, the use of current technologies will encounter considerable challenges.

In response to the above issues, molecular barcodes (MBC) or unique molecular identifiers (UMI) have been widely used and are quite effective in reducing sequencing errors. In UMI sequencing, each DNA template is first labeled with a UMI, and the labeled template is then subjected to polymerase chain reaction (PCR) for molecular amplification. The resulting amplicons are randomly sampled and sequenced. When there is sufficient sampling, a consensus sequence for the sequenced amplicons can eliminate most sequencing errors.

However, during the polymerase chain reaction, it is also possible that false bases are introduced in the early amplification cycles, resulting in a considerable proportion of the final amplicon pool having false bases. If only a small number of amplicon samples are sampled and sequenced, such false bases may dominate the UMI cluster, resulting in the consensus base being not the original base. In addition, in practical applications, the number of amplicon samples is usually not large. For example, 2 to 3 nucleic acid fragments with the same UMI marker are taken as data sources. However, without taking into account PCR errors, using only a small number of sampled UMI sequencing clusters as data sources cannot effectively eliminate consensus base judgment errors caused by sequencing errors. This further highlights the importance of handling PCR and sequencing errors at the same time. Therefore, in analyzing UMI sequencing data, both PCR and sequencing errors must be taken into consideration at the same time.

Several informatics tools have been applied to variant detection in UMI data, such as DeepSNVMiner, smCounter, MAGERI, smCounter2, or UMI-VarCal; however, these tools use empirical methods to handle PCR errors. For example, smCounter uses a joint model of PCR and sequencing error probabilities to estimate variant detection quality, using a hand-waving heuristic approximation to calculate PCR error probabilities and calculating sequencing error probabilities based on sequencing quality. On the other hand, MAGERI only processes UMI sequencing clusters of at least 5 and assumes that all sequencing errors in the consensus sequence have been eliminated; these conventional techniques not only discard most of the sequencing data, but also cannot guarantee the existence of sequencing errors.

To handle possible PCR errors in consensus sequences, MAGERI assumes that the error rate of consensus bases follows a beta distribution and uses a phenomenological model whose parameters are obtained by fitting UMI training data of known DNA templates; smCounter2 uses a similar approach to MAGERI, establishing a second beta distribution model for UMI sequencing clusters with a number of less than 5, but this is still a phenomenological model and cannot accurately describe sequencing errors. Importantly, these phenomenological models cannot be used to estimate the quality of each UMI consensus base; therefore, UMI sequencing data cannot be analyzed by other known variant detection methods, such as Mutect2, because information about the quality of each consensus base is usually required.

In addition, DeepSNVMiner, which is based on a rule-based approach, cannot reveal information about PCR or sequencing errors, resulting in low reliability and validity of variant detection. On the other hand, it is also difficult to apply UMI-VarCal to evaluate the reliability and validity of variant detection, also because UMI-VarCal adopts a rule-based method. The limitations of the above-mentioned known technologies are due to the lack of a solid statistical framework to describe PCR errors and sequencing errors that occur in UMI sequencing.

According to Chinese patent number CN112687339B, the patent name is "A method and device for counting sequence errors in plasma DNA fragment sequencing data". The patent specifically discloses a method and device for counting sequence errors in plasma DNA fragment sequencing data, which includes reading the real UMI in the library construction process and using it as a UMI reference sequence set; counting the reads of all reads cycles in the sequencing data; The method uses the error rate in individual expansion cycles to evaluate data quality, and can provide the correction base and base quality value in the subsequent cluster correction process, providing a priori probability for cluster correction and quality value correction, so as to improve the accuracy of low-frequency mutation detection; Although Lee et al. have revealed a method that integrates PCR amplification error rate and sequencing error rate as a reference for base correction, the definition of the error rate must be completed after the template is sequenced, and sequence interception and comparison between different nucleic acid fragments are performed. When encountering a situation where an observed base group dominated by erroneous bases appears in random sampling, the method has no ability to determine the authenticity of the consensus base, so it is difficult to describe the error rate of the consensus base and give a quality score for each consensus base. In addition, the method is difficult to implement in the absence of UMI sequencing library construction and sequence alignment.

Since low-frequency mutation detection is an important cornerstone of precision medicine and personalized diagnosis, solving the consensus base misjudgment caused by mutation frequency being lower than the sequencing error rate will have a profound impact on the future development of this field. In the existing technology, in order to eliminate sequencing errors, molecular barcoding technology is widely used. It is to attach molecular barcodes with unique sequences to different nucleic acid fragments, and use PCR to amplify DNA fragments with molecular barcodes, randomly sample and sequence, and use the consensus sequence of the same molecular barcode to eliminate sequencing errors.

However, a considerable amount of PCR errors are encountered during nucleic acid sequence amplification, which requires additional processing; although existing computational tools can process molecular barcode data, they usually use empirical rules or phenomenological models to evaluate PCR errors and cannot provide quality scores for individual consensus bases, which increases the uncertainty and inconvenience of mutation detection. The limitations of existing technologies are due to the lack of a statistical model that can describe the errors that occur during PCR amplification and can simultaneously consider sequencing errors.

Therefore, in order to solve the problems encountered by the aforementioned prior art, the present invention specifically discloses a statistical model for quantifying PCR and sequencing errors, which is used to evaluate the quality of molecular barcode consensus bases and assign a quality score to each consensus base as a reference for evaluating the reliability and validity of the consensus base; the aforementioned statistical model is based on the nature of the PCR process and incorporates sequencing quality information as the basis for calculation, which can be used to evaluate the PCR error rate of each data set and calculate a quality score for each consensus base.

Specifically, one object of the present invention is to provide a method for evaluating the consensus base error rate, which comprises: selecting one or more extended bases from an extender pool, wherein the extender pool is extended from an unknown base N; ordering the j-th selected extended base as an observed base s _j , wherein j is an arbitrary positive integer, and forming the observed bases s _j into an observed base set S; calculating a consensus base c(S) from the observed base set S; calculating a consensus base error rate P _c(S) , which is the probability that the consensus base c(S) is not the unknown base N, wherein the consensus base error rate P _c(S) is the sum of the probabilities that the unknown base N is randomly selected from the observed base set S and is identical to a hypothetical base b, but the hypothetical base b is different from the consensus base c(S), wherein the hypothetical base b is selected from the group consisting of adenine (A), thymine (T), guanosine (G) and cytosine (C), and the hypothetical base b is different from the consensus base c(S).

In the method described above, the consensus base error rate P _{c (S)} is calculated by the following formula: ; Wherein, P(S|N=b) is the probability of randomly selecting the observed base set S from the expander pool when the unknown base N is the same as the assumed base b.

As described above, the method for calculating P(S|N=b) includes: defining an error base fraction _FR , which is the ratio of an extended error base to the extended bases in the extender pool, wherein the extended error base is a base different from the assumed base b; and calculating P(S|N=b) according to the following formula: ; Among them, the For each observed base _sj in the observed base set S, the probability that the unknown base N is the same as the assumed base b and the proportion of the incorrectly extended bases in the expander pool is _FR The total product of .

As described above, when the observed base _sj is the same as the assumed base b, the Equivalent to a correct base fraction , when the observed base _sj is different from the assumed base b, the Equal to the error base score , where the correct base fraction The base score of the error The sum of is 1.

The method as described above further comprises: according to a certain sequence correctness rate P _seq1 , a certain sequence error rate P _seq2 and an expanded base ratio Correct the for , which is when the unknown base N is identical to the assumed base b, and the proportion of an extended base b" in the extender pool that is different from the assumed base b is When the observed base _sj is the same as another observed base b', when the extended base b" is different from the assumed base b, the extended base ratio Equal to the expanded base score , after correction Satisfy the following formula: ; wherein, when the other observed base b' is the same as the assumed base b, P _pcr1 represents the probability that the assumed base b is expanded to a base that is the same as the other observed base b', P _pcr2 represents the probability that the assumed base b is expanded to the expanded base b", and the expanded base b" is not the same as the assumed base b; wherein, when the other observed base b' is different from the assumed base b, P _pcr3 represents the probability that the assumed base b is expanded to a base that is the same as the other observed base b', P _pcr4 represents the probability that the assumed base b is expanded to a base that is the same as the assumed base b, P _pcr5 represents the probability that the assumed base b is expanded to the expanded base b", and the expanded base b" is different from the assumed base b and the other observed base b'; wherein the sequencing accuracy rate _Pseq1 represents the probability that the other observed base b' is sequenced correctly, and the sequencing error rate _Pseq2 represents the probability that the expanded base b" is incorrectly sequenced to the other observed base b'.

The method as described above further includes calculating the sequencing accuracy rate P _seq1 and the sequencing error rate P _seq2 using the sequencing quality score _Qi of the other observed base b', wherein the sequencing accuracy rate P _seq1 can be calculated by the following formula: ; The sequencing error rate P _seq2 can be calculated by the following formula: .

As described above, the observed base set S includes d observed bases _sj , the d observed bases _sj include _nb the same as the assumed base b, and ( _dnb ) the extended error bases different from the assumed base b, wherein the d value is the maximum positive integer value of j, and _nb is a positive integer less than or equal to d; when the observed base _sj is different from the assumed base b, the is equal to the error base fraction _FR , calculate the The total product is as follows: .

As described above, the P(S|N=b) is further approximated by the difference in momentum to obtain: ; Among them, the is the (k+dn _b )th moment value of the probability distribution of the extended error base fraction _FR , where k is any non-negative integer less than or equal to n _b ; where The approximate value of is r/2 ^k+d-nb , where r is the probability of a polymerization cascade amplification error occurring at the locus corresponding to the unknown base N in each cycle.

The method as described above further comprises: taking the template sequence, attaching a molecular barcode, and performing a polymerase chain reaction with the template sequence to generate the amplicon pool; randomly sampling and sequencing from the amplicon pool to establish the observed base set S, wherein the molecular barcode comprises a nucleic acid capture sequence (nucleic acid capture sequence) or a unique molecular identifier sequence (UMIs).

Another object of the present invention is to provide a consensus base error rate evaluation system, which includes a polymerase chain reaction quality evaluation module configured to execute the method as described above to calculate a consensus base error rate P _c(S) .

The system as described above further includes a sequence quality assessment module, which is signal-connected to the polymerase chain reaction quality assessment module and configured to read the sequence quality score _Qi of another observed base b' to calculate a sequence accuracy rate _Pseq1 and a sequence error rate _Pseq2 , wherein the sequence accuracy rate _Pseq1 can be calculated by the following formula: ; The sequencing error rate P _seq2 can be calculated by the following formula: and a consensus base error rate P _c(S) correction unit, which is disposed in the polymerase chain reaction quality assessment module and is connected to the sequencing quality assessment module signal to adjust the sequence accuracy rate P _seq1 , the sequencing error rate P _seq2 and an expanded base ratio Correct the for , which is when the unknown base N is identical to the assumed base b, and the proportion of an extended base b" in the extender pool that is different from the assumed base b is When the observed base _sj is the same as another observed base b', when the extended base b" is different from the assumed base b, the extended base ratio Equal to the expanded base score , after correction Satisfy the following formula: ; wherein, when the other observed base b' is the same as the assumed base b, P _pcr1 represents the probability that the assumed base b is expanded to a base that is the same as the other observed base b', P _pcr2 represents the probability that the assumed base b is expanded to the expanded base b", and the expanded base b" is not the same as the assumed base b; wherein, when the other observed base b' is different from the assumed base b, P _pcr3 represents the probability that the assumed base b is expanded to a base that is the same as the other observed base b', P _pcr4 represents the probability that the assumed base b is expanded to a base that is the same as the assumed base b, P _pcr5 represents the probability that the assumed base b is expanded to the expanded base b", and the expanded base b" is different from the assumed base b and the other observed base b'; wherein the sequencing accuracy rate _Pseq1 represents the probability that the other observed base b' is sequenced correctly, and the sequencing error rate _Pseq2 represents the probability that the expanded base b" is incorrectly sequenced to the other observed base b'.

Another object of the present invention is to provide a consensus base error rate evaluation device, which includes a memory and a processor, wherein the memory is used to store a program; the processor is configured to execute the program to implement the consensus base error rate evaluation method as described above.

The technical solution provided by the present invention can calculate a quality score for each consensus base when detecting low-frequency mutations to accurately reflect its error rate; with the quality score of the consensus base, more accurate low-frequency mutation detection can be expected.

The content of the present invention is further described in detail below through specific implementation methods combined with drawings; in the following implementation methods, the detailed description is to make the present invention easier to understand. However, those skilled in the art can easily understand that some of the technical features can be omitted in different situations, or can be replaced by other components, materials, and methods. In some cases, some operations related to the present invention are not shown or described in the specification in order to avoid the core part of the present invention being overwhelmed by too much description, and for those skilled in the art, it is not necessary to describe these related operations in detail, and they can fully understand these related operations according to the description in the specification and based on the common technical knowledge in this field.

Please refer to FIG. 1A , which illustrates the first embodiment of the present invention, which is a method for evaluating the consensus base error rate, comprising: an extended base selection process (S1): selecting one or more extended bases from an extended sub-pool, wherein the extended sub-pool is extended from an unknown base N; an observed base set establishment process (S2): ordering the j-th selected extended base as an observed base s _j , and grouping the observed bases s _j into an observed base set S, wherein j is an arbitrary positive integer; a consensus base c(S) calculation process (S3): calculating a consensus base c(S) from the observed base set S; Consensus base error rate P _c(S) calculation process (S4): Calculate a consensus base error rate P _c(S) , which is the probability that the consensus base c(S) is not the unknown base N, wherein the consensus base error rate P _c(S) is the sum of the probabilities that the unknown base N is randomly selected from the observed base set S to be the same as a hypothetical base b, but the hypothetical base b is not the same as the consensus base c(S), wherein the hypothetical base b is selected from the group consisting of adenine (A), thymine (T), guanosine (G) and cytosine (C), and the hypothetical base b is not the same as the consensus base c(S).

The so-called consensus base c(S) refers to the observed base _sj with the highest frequency in the observed base set S. For example, in the observed base set S with 6 observed bases _sj , the observed bases _sj are A, A, A, T, T and A respectively. Then the consensus base c(S) of the observed base set S is A, and its frequency of occurrence is 2/3, which is greater than the frequency of occurrence of T, which is 1/3. From the above example, it can be seen that in the expanded bases expanded by the unknown base N, the base with non-consensus base c(S)' appears. Without considering the fixed Under the premise of sequence error, the non-consensus base c(S)' is caused by a polymerase amplification reaction error. Therefore, in the first embodiment, the probability that the consensus base c(S) is not the assumed base b is evaluated, that is, the error rate of the consensus base c(S) is calculated as a basis for judging the validity of the consensus base c(S).

In the consensus base error rate P _c(S) calculation process (S4), the consensus base error rate P _c(S) is calculated by the following formula: ; Wherein, P(S|N=b) is the probability of randomly selecting the observed base set S from the expander pool when the unknown base N is the same as the assumed base b.

In the consensus base error rate Pc _(S) calculation process (S4), the calculation method of P(S|N=b) includes defining an error base fraction _FR , which is the ratio of an extended error base to the extended bases in the extended sub-pool, wherein the extended error base is a base different from the assumed base b, and calculating P(S|N=b) according to the following formula: ; Among them, the For each observed base _sj in the observed base set S, the probability that the unknown base N is the same as the assumed base b and the proportion of the incorrectly extended bases in the expander pool is _FR The total product of .

In this embodiment, when the observed base _sj is the same as the assumed base b, the Equivalent to a correct base fraction , when the observed base _sj is different from the assumed base b, the Equal to the error base score , where the correct base fraction The error base score The sum of is 1.

In this embodiment, the observed base set S includes d observed bases _sj , the d observed bases _sj include _nb the same as the assumed base b, and ( _dnb ) the extended error bases different from the assumed base b, wherein the d value is the maximum positive integer value of j, and _nb is a positive integer less than or equal to d; when the observed base _sj is different from the assumed base b, the is equal to the error base fraction _FR , calculate the The total product is as follows: .

In this embodiment, the calculation of P(S|N=b) is further expanded as follows: in, is the fraction of the wrong base in the observed base set S The moment term of the probability distribution of the expansion subpool; since the expansion subpool is obtained by one or more expansion cycles, the calculation of the moment term will become quite intensive when the number of expansion cycles increases; in principle, when only the first expansion error is considered, the moment term The value of can be processed by approximation to reduce the computational intensity, and further, the value of can be approximated by the difference in momentum to obtain: = ; Among them, the represents the (k+dn _b )th moment value of the probability distribution of the extended error base fraction _FR , where k is any non-negative integer less than or equal to n _b , The approximate value of is r/2 ^k+d-nb , where r is the probability of a polymerization cascade amplification error occurring at the locus corresponding to the unknown base N in each cycle.

Please refer to FIG. 1B , which illustrates the second embodiment of the present invention, which is a method for evaluating the consensus base error rate. The method steps and calculation method are the same as those of the first embodiment, but in the second embodiment, not only the probability of an error occurring in the unknown base N during the expansion cycle is calculated, but also the error rate occurring in the sequencing process after the expansion cycle is completed is included.

To further illustrate, in an observed base set S with 6 observed bases _sj , the observed bases _sj are A, A, A, T, T and A respectively, and the consensus base c(S) is A; since the non-consensus base c(S)' appears in the observed base set S, it can be that the expanded bases expanded by the unknown base N have an expanded base different from the assumed base b, such as T, or it can be that the base that is the same as the assumed base b, such as A, appears, but due to a sequencing error, A is sequenced. It may be T, or a base different from the assumed base b and the non-consensus base c(S)', such as C or G, may appear, but it is sequenced as T due to a sequencing error. Taking the above situation into consideration, in the second embodiment, the polymerase amplification reaction error rate and the sequencing error rate are further integrated to calculate the consensus base c(S) error rate as a basis for determining the reliability and validity of the consensus base c(S).

Accordingly, in the second embodiment, the method further comprises: Calculation and correction processing of consensus base error rate Pc _(S) (S4-1): based on a certain sequence correctness rate _Pseq1 , a certain sequence error rate _Pseq2 and an extended base ratio Correct the for , which is when the unknown base N is identical to the assumed base b, and the proportion of an extended base b" in the extender pool that is different from the assumed base b is When the observed base _sj is the same as another observed base b', when the extended base b" is different from the assumed base b, the extended base ratio Equal to the expanded base score , after correction Satisfy the following formula: ; wherein, when the other observed base b' is the same as the assumed base b, P _pcr1 represents the probability that the assumed base b is expanded to a base that is the same as the other observed base b', P _pcr2 represents the probability that the assumed base b is expanded to the expanded base b", and the expanded base b" is not the same as the assumed base b; wherein, when the other observed base b' is different from the assumed base b, P _pcr3 represents the probability that the assumed base b is expanded to a base that is the same as the other observed base b', P _pcr4 represents the probability that the assumed base b is expanded to a base that is the same as the assumed base b, P _pcr5 represents the probability that the assumed base b is expanded to the expanded base b", and the expanded base b" is different from the assumed base b and the other observed base b'; wherein the sequencing accuracy rate _Pseq1 represents the probability that the other observed base b' is sequenced correctly, and the sequencing error rate _Pseq2 represents the probability that the expanded base b" is incorrectly sequenced to the other observed base b'.

In the second embodiment, the method further comprises: a sequence accuracy rate and a sequence error rate calculation process (S4a): the sequence accuracy rate P _seq1 and the sequence error rate P _seq2 are calculated using the sequence quality score _Qi of the other observed base b', wherein the sequence accuracy rate P _seq1 can be calculated by the following formula: ; The sequencing error rate P _seq2 can be calculated by the following formula: .

In various embodiments, please continue to refer to FIG. 1A to 1B , before selecting the amplicon base, the method further includes an amplicon pool establishment process (S1a), which includes: taking a template sequence, attaching a molecular barcode, wherein the template sequence includes a locus corresponding to the unknown base N, and performing a polymerase chain reaction with the template sequence to generate the amplicon pool, wherein the molecular barcode includes: a nucleic acid capture sequence (nucleic acid capture sequence) or a unique molecular identifier sequence (UMIs), but is not limited thereto.

The following further describes the specific derivation of the calculation basis in each embodiment of the present invention. First, it is assumed that after an ideal PCR cycle, individual DNA templates are copied into duplicates of the same sequence. Each nucleotide in the original single-stranded template sequence remains intact. PCR errors generated in subsequent amplification cycles may still cause incorrect bases to be generated at specific positions in the duplicate sequence, thereby generating different bases in subsequent PCR cycles.

Assume that after R cycles, a total of 2 ^R nucleic acid molecules are amplified from a single double-stranded DNA template sequence, which may contain a base that is different from the base at the corresponding position on the template sequence, that is, a false base. The proportion of false bases depends on the PCR error rate (r) and the number of cycles in which errors occur (i). Among the 2 ^R amplicon, only a small number of amplicon can be randomly sampled and sequenced. When the sampled amplicon carries a false base, the occurrence of PCR errors can be observed. Therefore, observing PCR errors can be imagined as a process of sampling amplicon with erroneous bases from ^2R amplicon, and the estimation of PCR error rate depends on the ratio of erroneous bases in these amplicon ( _FR ). In order to estimate the error rate of PCR, a probability distribution of the ratio of erroneous bases _FR must be established.

In the i-th cycle, let _ti and _fi be the number of true bases and erroneous bases, respectively. Formula (I) specifically describes the probability of m and n erroneous bases being derived from the _ti true bases and the _fi erroneous bases in the next cycle (i+1th cycle). In formula (I), r represents the PCR error rate per base per cycle in each cycle. In this embodiment, r represents the probability of PCR error at the locus corresponding to the unknown base N, and the probability distribution of m erroneous bases derived from the _ti true bases follows the binomial distribution. Under the premise that there is no PCR error for any base preference, the probability of the wrong base derived from the _fi wrong base is 1-r, because it does not need a PCR error to derive an wrong base. Alternatively, if a PCR error occurs, but the error expands the original wrong base to any of the other two wrong bases, the probability is , which explains the .

From formula (I), the probability of generating fi ₊₁ erroneous bases in the i+1th cycle can be calculated by considering all possible combinations of erroneous bases, as represented by formula (II), which include the real bases and erroneous bases present in the i-th cycle. In formula (II), the Kronecker delta function ensures that the derived erroneous bases of ( _{fi+1 –fi} ) come from the erroneous and real bases in the i-th cycle. _fi can be 0, 1, 2, ... or even ²ⁱ -1. Since the original true base must maintain its original appearance after all replications, _fi is less than or equal to fi ₊₁ , so the upper limit is set to fi ₊₁ .

Through the above dynamic equation, the probability P( _FR ) of the wrong base ratio _FR can be calculated by calculating P( _fi+1 ). For example, please refer to Figure 1C, which shows the probability distribution of the wrong base ratio _F10 under the condition of PCR error rate of 0.01; as shown in Figure 1C, three small peaks are close to 0.5, 0.25 and 0.125, which correspond to the first PCR error occurring in the 1st, 2nd and 3rd cycles, respectively, resulting in 1/2, 1/4 and 1/8 of the bases being wrong bases. In addition to mathematical calculations, random PCR errors can also be simulated. In this embodiment, mathematical simulations were performed 1 million times, with a PCR error rate of 0.01 and a total of 10 expansion cycles. The simulation results were consistent with the mathematical calculation results.

After obtaining the probability of the wrong base ratio _FR , under the premise that there is no sequencing error, the probability that the consensus base is not the true base can be further calculated; at a specific location, let S _i be the base on the d-th sampled expander, and S={S _i } is the set of all bases. The so-called consensus base c(S) is the base with the highest frequency in the base set S={S _i }. Through formula (III), the probability P(N≠c(S)|S) that the consensus base c(S) is not the unknown base N can be calculated by Bayesian theorem.

Here we assume that there is no prior information about the unknown base N, that is, the probability that the unknown base N is any of the four bases (A, T, C, G) is the same, then P (N=b) is a constant ; therefore, P(N=b) can be omitted in formula (III). P(S|N=b) is the probability of obtaining a base set S by randomly sampling from 2 ^R expanders, and these expanders are expanded from a hypothetical base b. P(S|N=b) depends on the proportion of incorrect bases in these expanders, _FR , and after considering all possible values of the proportion of incorrect bases _FR , P(S|N=b) can be calculated by formula (IV). Under a specific _FR as the premise, the probability that a randomly sampled base is an incorrect base can be simply reduced to _FR , which is shown in formula (V).

When there are multiple expanders in the sample, the above formula involves the calculation of ΣP(F _R )*F _R ^k , ^which refers to the kth moment of the probability distribution of the error base ratio F _R. In principle, these values can be obtained by formula ( _II ). However, when the R value _is quite large, the amount of calculation involving the above ΣP(F _R )*F _R ^k will also be very large. Therefore, an approximation must be made to the calculation of the above ΣP(F _R )*F _R ^k ; for the approximate calculation of these moment values, when the error rate is small, only the first PCR error needs to be considered. For example, in 10 cycles of PCR amplification, a total of 2 ¹⁰ -1=1,023 replication events occur. Assuming the PCR error rate is only 0.001, the average PCR error is only close to 1.

In addition, a PCR error occurring in an early cycle will result in a significantly higher fraction of erroneous bases and will therefore contribute more to the momentum value. When only the first PCR error is taken into account, these momentum values can be calculated using formula (VI). In formula (VI), i is the cycle number at which the first PCR error occurs. When the PCR error rate r is relatively small, for example r < 2 ^-R , the probability that the first PCR error occurs in the i-th cycle is equal to 2 ^i-1 *r, since there are 2 ^i-1 amplifiers before the i-th cycle and for each amplifier, the probability of a PCR error is r.

If there are no further PCR errors, the final erroneous base ratio is 1/2 ⁱ . However, further PCR errors are possible, but their contribution to the moment values belongs to higher powers, such as r ² , r ³ , ...., and the moment values are quite small when r << 1. Please refer to Figure 2, which presents the theoretical values of _{the FR} moment values in different PCR cycles; as shown in Figure 2, the theoretical values of the _FR probability distribution moment values of the first 5 erroneous base ratios at a PCR error rate of 0.001 can be calculated by formula (II). In addition, Figure 2 also presents the approximate moment values based on formula (VI), which are quite consistent with the theoretical values. With these approximate moments, the probability that the consensus base c(S) is not the unknown base N can be calculated more efficiently without incorporating the detailed probability distribution of _FR .

With these moment values, the probability that the consensus base c(S) is not the unknown base N can be calculated by formula (VII) and formula (VIII); in an exemplary calculation, let the observed bases be A and C, and in this observed base set S, the number of A n _A is greater than the number of C n _C ; In formula (VIII), when the PCR error rate r＜＜1, the probability that the unknown base N is G or T, P(S|N=G), P(S|N=T), will be much smaller than the probability that the unknown base N is A or C, P(S|N=A), P(S|N=C), and therefore can be ignored; It should be noted that under the conditions of different types of bases, formulas (VII) and (VIII) must be adjusted according to the number of base types, and the adjustment method will be further explained in the following text.

In addition to PCR errors, sequencing errors may also cause erroneous observed bases s _j ; therefore, in this embodiment, sequencing errors are also included to evaluate the probability that the consensus base c(S) is not the unknown base N; generally speaking, the probability of erroneous sequencing q _i can be calculated by the sequencing quality score Q _i , which is calculated by formula (IX); under the premise that there is no prior information about the erroneous bases generated by these sequencing errors, the probability of observing any erroneous base among these erroneous bases is q _i /3. With this information in mind, PCR errors and sequencing errors can be integrated to assess the quality of the consensus base c(S).

Under the premise of considering both PCR errors and sequencing errors, we must return to formula (IV) to further explain how the probability that the consensus base c(S) is not the unknown base N is specifically calculated; specifically, P(s _i |N= _b∩FR = _FR ) must be rewritten; as described in formula (X), when the unknown base N is the assumed base b, the probability of observing another observed base b', where Fb _{'' ≠ b} represents the proportion of erroneous bases of the type of amplified base b' in the final amplicon pool, and in {} is a combination representing the type of amplified base b'. When the observed another observed base b' is the assumed base b, it can be the probability of the correct PCR amplification ( ) and the probability of correct sequencing ( ), or the probability of a PCR amplification error resulting in an incorrectly extended base b” (PE _{bb '' ≠ b} ) plus the probability of a sequencing error sequencing the extended base b” as a hypothetical base b (SE _b”b ).

When the observed base b' is not the assumed base b, there are three scenarios that lead to this result: (1) a PCR amplification error results in the generation of an incorrect observed base b' (different from the assumed base b) without any sequencing error; (2) the PCR amplification did not go wrong, but the assumed base b was incorrectly sequenced as an observed base b' different from the assumed base b; (3) A PCR amplification error produces an incorrect extended base b", but the extended base b" is neither the assumed base b nor another observed base b', and the extended base b" is subsequently incorrectly sequenced as another observed base b'.

Assuming that PCR errors and sequencing errors are independent events, the probability in the above scenario can be calculated by formula (X), where _FR represents the total proportion of erroneous bases, for example, _FR =Σ _{b” ≠ b} F _{b ”} . By incorporating formula (X) into formula (VII) and formula (VIII), the probability of the consensus base c(S) can be calculated to assign a quality score to the consensus base c(S). The quality score not only specifically considers PCR errors but also integrates sequencing errors. (X)

In the above equations, three different types of incorrectly observed bases are combined. Since these three types of incorrectly observed bases do not appear with equal probability, the equations need to be further modified; for example, assuming that the hypothetical base b is adenine A, the probability of observing two cytosine C in the final expansion pool is greater than one cytosine C and one guanosine G, because the former only requires one PCR error, but the latter requires at least two PCR errors.

Therefore, all four bases (A, T, C, G) need to be taken into account in these equations; specifically, when assuming that base b is adenine A, the probability P( _FR ) originally adopted will be replaced by the probability P({ _FC , _FG , _FT }) for the four bases to correct the above equations; it should be noted that the key to the simplification of this evaluation model is the approximate treatment of the moment; in the case of treating four bases, the multivariate moments of formula (XI) need to be further approximated; again, under the premise that the PCR error rate r is much less than 1, the approximate treatment of these moment values only needs to consider the first few PCR errors.

The evaluation model can be further extended to take into account the double-stranded nature of DNA; for a double-stranded nucleic acid template, a single PCR error results in an incorrect base in the synthesized sequence, and it takes another cycle to produce the result that both strands carry the incorrect base. Therefore, a PCR error in the first cycle only results in Rather than The final amplification pool has an erroneous base. It should be noted that a UMI usually only marks one strand of the DNA template. After integrating the above factors, the multi-term difference values can be approximated. Here, the level of the multi-term difference values is defined by the number of 0s in the powers; the higher the level, the smaller the difference values.

The above description is only used to illustrate the mathematical derivation of the statistical model of the consensus base error rate evaluation method provided by the present invention, and is not intended to limit the specific implementation of the method of the present invention.

The third embodiment of the present invention provides a consensus base error rate evaluation system (1), see FIG3A . The system (1) includes a polymerase chain reaction quality evaluation module (11) configured to execute the method described in the first embodiment to calculate a consensus base error rate P _c(S) .

In various embodiments, please continue to refer to FIG. 3A , the system (1) further comprises a scoring module (14) signal-connected to the polymerase chain reaction quality assessment module (11) and configured to identify the consensus base error rate P _c(S) value and give the consensus base c(S) a quality score Q _c .

In some other embodiments, please continue to refer to Figure 3A, the system (1) further includes a judgment module (15), which is signal-connected to the scoring module (14) and the polymerase chain reaction quality assessment module (11), and is configured to receive the quality score _Qc and compare it with a second quality score _{P'c (S)} to generate a judgment indication, wherein the _{P'c (S)} is output by the polymerase chain reaction quality assessment module (11), when the _{P'c (S)} is greater than the _Qc , the judgment indication is reliable and valid, and when the _{P'c (S)} is less than the Qc, the judgment indication is not reliable and valid.

For example, after obtaining the quality score Q _c , the user can focus on the base group with high quality score, and set the cutoff score Q _x based on the quality score Q _c . In the subsequent batch processing of sequencing data, the cutoff score Q _x can be used to determine the reliability and validity of the consensus base. The cutoff score setting in the above example can be extended to include a consensus sequence composed of more than one consensus base c (S). For another example to illustrate the specific reliability and validity judgment of the consensus sequence, please refer to Table 1. By sequencing an unknown sequence, consensus sequence 1 and consensus sequence 2 are obtained in different batches. Among them, the observation base set is read from the 5' end to the 3' end to obtain the observation base set S _1-1 ={A ₁ C ₁ C ₁ }, observed basis set S _1-2 ={A ₂ G ₂ A ₂ } and observed basis set S _1-3 ={G ₃ A ₃ A ₃ }, the system determines that consensus sequence 1 is 5'-CAA-3' according to each observed basis set; on the other hand, consensus sequence 2 is determined to be 5'-CAG-3' by observed basis set S _2-1 ={A ₁ C ₁ C ₁ }, observed basis set S _2-2 ={A ₂ G ₂ A ₂ } and observed basis set S _2-3 ={G ₃ G ₃ A ₃ }; after calculating the quality score for each consensus base, the system compares the consensus sequence 1 determined by the consensus basis set S The quality score of the consensus base A obtained in _1-3 is judged to be less than the cut-off score Q _x , so the judgment indication is given as not having reliability and validity; while the quality scores of all the consensus bases in the consensus base sets S _2-1 , S _2-2 and S _2-3 are greater than the cut-off score Q _x , so the judgment indication is given as having reliability and validity; here, the user can determine the reliability and validity of the consensus sequence according to the judgment indication given by the system, and make the most appropriate sequence judgment. Table 1 Observation base set Consensus base Quality Score Judgment Instructions Consensus sequence 1 5'-CAA-3' S _1-1 A ₁ C ₁ C ₁ C ＞Q _x Reliable and valid S _1-2 A ₂ G ₂ A ₂ A ＞Q _x Reliable and valid S _1-3 G ₃ A ₃ A ₃ A ＜Q _x No reliability or validity Consensus sequence 2 5'-CAG-3' S _2-1 A ₁ C ₁ C ₁ C ＞Q _x Reliable and valid S _2-2 A ₂ G ₂ A ₂ A ＞Q _x Reliable and valid S _2-3 G ₃ G ₃ A ₃ G ＞Q _x Reliable and valid

The fourth embodiment of the present invention provides a consensus base error rate evaluation system 1, see FIG. 3B , the basic components and operation principle of which are the same as those of the third embodiment, except that the system (1) further includes a sequence quality evaluation module (12) signal-connected to the polymerase chain reaction quality evaluation module (11) and configured to read the sequencing quality score _Qi of another observed base b' to calculate a sequence accuracy rate _Pseq1 and a sequence error rate _Pseq2 , wherein the sequence accuracy rate _Pseq1 can be calculated by the following formula: The sequencing error rate P _seq2 can be calculated by the following formula: and a consensus base error rate P _c(S) correction unit (11a), which is disposed in the polymerase chain reaction quality assessment module (11) and is signal-connected to the sequencing quality assessment module (12) to adjust the base error rate P c(S) according to the sequencing accuracy rate P _seq1 , the sequencing error rate P _seq2 and an expanded base ratio Correct the for , which is when the unknown base N is identical to the assumed base b, and the proportion of an extended base b" in the extender pool that is different from the assumed base b is When the observed base _sj is the same as another observed base b', when the extended base b" is different from the assumed base b, the extended base ratio Equal to the expanded base score , after correction Satisfy the following formula: ; wherein, when the other observed base b' is the same as the assumed base b, P _pcr1 represents the probability that the assumed base b is expanded to a base that is the same as the other observed base b', P _pcr2 represents the probability that the assumed base b is expanded to the expanded base b", and the expanded base b" is not the same as the assumed base b; wherein, when the other observed base b' is different from the assumed base b, P _pcr3 represents the probability that the assumed base b is expanded to a base that is the same as the other observed base b', P _pcr4 represents the probability that the assumed base b is expanded to a base that is the same as the assumed base b, P _pcr5 represents the probability that the assumed base b is expanded to the expanded base b", and the expanded base b" is different from the assumed base b and the other observed base b'; wherein the sequencing accuracy rate _Pseq1 represents the probability that the other observed base b' is sequenced correctly, and the sequencing error rate _Pseq2 represents the probability that the expanded base b" is incorrectly sequenced to the other observed base b'.

The fifth embodiment of the present invention provides a consensus base error rate evaluation device 2, please refer to Figure 4, which includes a memory 21 and a processor 22, wherein the memory 22 is used to store a program P; the processor 22 is signal-connected to the memory 21 and is configured to execute the program P to implement the consensus base error rate evaluation method described in the first embodiment or the second embodiment, or to implement the system described in the third embodiment or the fourth embodiment.

All or part of the functions of the method provided by the present invention can be implemented by hardware mounting or by software program; when all or part of the functions of the method are implemented by software program, the program can be stored in a storage device, which can be a read-only memory, random access memory, a disk, an optical disk, a hard disk, etc., and the program is executed by a processor to implement the above functions. For example, the program is stored in the memory of the sequencing device. When the program in the memory is executed by the processor, all or part of the above functions can be realized. In addition, the program can also be stored in a storage device such as a server, another computer, a disk, an optical disk, a flash memory or a portable hard disk, and transferred to the memory of the sequencing device by downloading, transmitting, copying, etc., or the system of the sequencing device can be overwritten or updated with different versions. When the program in the memory is executed by the processor, all or part of the functions in the above method can be realized.

Embodiment 1 ：Based on PCR and sequencing error probability to calculate consensus bases c(S) Quality

In this embodiment, the method provided by the present invention is used to calculate the probability that the consensus base c(S) is not the true base; take an observed base set S={A ₁ C ₂ A ₃ }, and calculate the consensus base c(S) to be A; please refer to the following formula (XII), which presents the probability of observing each base according to formula (X) when the assumed base b and the wrong base composition {F _{b'' ≠ b} } are known. In formula (XII), u _ki and v _ki are defined as the observed base that is the same as and different from the assumed base b, respectively. The indexes k and i indicate the order and the i-th observed base, respectively. Based on formula (XII), the probability of observing a base S given a hypothetical base b can be calculated using formula (XIII).

The above calculation can be expressed as a weighted multiple moment value. The weighting is determined by the following factors, including whether the observed base matches the assumed base b, the order of the moment value, and the sequencing quality of the observed base. Since the corresponding F is a simple _FR , it represents the total proportion of 3 different types of erroneous bases, so "3" appears before some of the moment values. With these weights, the probability that the consensus base c(S) is not the assumed base b can be calculated according to formula (XIV). In Example 1, the consensus base error rate calculation based on two bases is realized, and when there are more than three different types of observed bases, the above calculation method can be further modified while following similar logic. …………(XIII)

Embodiment 2 :evaluate PCR Error rate

In Example 2, adenine (A) is used as the assumed base b. When there is an erroneous base, such as C, G or T, the first moment M _x00's in formula (XI) can be replaced (r/3) with the corresponding substitution rate, such as p _AC , p _AG or p _AT ; see formula (XV), m _x00 is defined as the moment without substitution rate and is expressed as p _{bb '} . Similarly, the second moment can be replaced by the product of the corresponding substitution rates (r/3) ² , for example, when the erroneous base is C and G, p _AC *p _AG is used to replace M _xy0's . Here, the quality score of the consensus base c(S) can be calculated by simply replacing the single variable moment in the original calculation formula with the multivariate moment.

When the base b is assumed to be known, the PCR substitution rate can be estimated using the maximum approximation method. In Example 2, the focus is on a locus with a true base of adenine A. Under the premise of no sequencing error, when the corresponding known position on the locus is not adenine A, it means that a PCR error has occurred; in Example 2, the situation where the locus has 2 or 3 incorrect bases is ignored because its frequency is much smaller under the condition of low PCR error rate; given the base observed at the locus, the probability of observing the base can be calculated by formula (XVII), where it is assumed that each locus is independent of each other. In the following formula, _Si is the base observed at locus i, { _Si } represents the observed base set, and { _{pbb ''} } represents the PCR error assessment model provided by the present invention. The probability that all observed bases are adenine A can be calculated by formula (VXIII), and the probability that some of the observed bases are erroneous bases, for example, the erroneous base is cytosine C, can be calculated by formula (XIX).

In Example 2, the substitution rate p _AC is calculated by the maximum likelihood approach, and p _AC gives a log likelihood with a derivative of zero. In formula (XX), n _AA and n _AC are the number of samples with adenine A or adenine A and cytosine C, respectively. According to formula (XX), p _AC is proportional to the number of loci that are converted from adenine A to cytosine C, wherein the denominator involves the error value of the loci without the wrong base, which can specifically reflect the PCR process.

Embodiment 3 : Evaluate background error rate

After calculating the error probability of the consensus base c(S) obtained based on the UMI-labeled nucleic acid fragment cluster, a cutoff score can be set by the probability to further focus on the consensus base c(S) with a high quality score, wherein the consensus base c(S) with a high quality score can be estimated to have only a relatively low proportion of PCR and/or sequencing errors. Therefore, it can be reasonably known that the only erroneous bases are derived from background errors, such as random mutations generated during the DNA fragmentation process; the UMI sequencing method is applied to the known DNA template sequence, and the consensus base error rate obtained in Example 1 is used as the basis to estimate the background error rate occurring in the UMI sequencing.

Embodiment 4

In Example 4, 100 random sequences of 100 base pairs in length were used as reference sequences for "normal cells", and mutation detection was performed on ¹⁰⁷ loci in 1000 normal cells. Then, the UMI molecular barcode was attached to the reference sequence, and the double-stranded sequence labeled by the UMI was subsequently amplified by PCR for 20 cycles, with an amplification error rate r of 0.001.

For each UMI, 3 or 5 extenders are randomly sampled for sequencing; the extenders sequenced for each UMI are grouped into a consensus sequence, and the quality of each consensus base is calculated using the aforementioned evaluation method; in Example 4, the evaluation method is used to identify erroneous consensus bases and simultaneously calculate the frequency of individual quality scores; then, the observed frequency is compared with the expected frequency.

See Figure 5A, which shows the consensus quality of a 3-base UMI consensus sequence. The degree of fit between the observed frequency and the expected frequency is shown in FIG. 5A , which shows a high fit. Referring to FIG. 5B , the observed frequency and the expected frequency of the consensus quality score of the UMI consensus sequence of 5 bases also show a high fit, except that some quality scores show a large fluctuation. This may be due to the low error rate and insufficient loci with such quality scores and/or only a few or even no erroneous consensus bases. The model fitting of Example 4 is sufficient to illustrate that the evaluation method provided by the present invention can provide the true error probability of the consensus base as a basis for calculating the consensus base and even the consensus sequence quality score.

The present invention specifically provides a method for evaluating the consensus base error rate, establishes a consensus base error probability evaluation model under the premise of simultaneously incorporating PCR errors and sequencing errors, and accurately evaluates the consensus base error rate generated by molecular tag (UMI) sequencing.

Secondly, through the method provided by the present invention, an accurate quality score can be given to each consensus base on the consensus sequence, thereby eliminating the impact of low-frequency mutations on sequencing accuracy, effectively improving sequencing accuracy, and having considerable potential for improving future precision medicine.

Thirdly, through the method provided by the present invention, after completing the evaluation of the error probability of the consensus base, the background error rate occurring in each molecular tag sequencing can be further estimated, which can be used as a reference for improving the program design, reagent quality, primer planning, etc. of molecular tag sequencing, which will be helpful for improving the quality of nucleic acid sequencing in the future.

The above contents are further explanations of the contents of the present invention in combination with specific implementations, and it cannot be determined that the specific implementation of the present invention is limited to the contents of these descriptions and exemplary embodiments; for those with ordinary knowledge in the technical field to which the present invention belongs, simple modifications or substitutions can be made without departing from the concept of the present invention.

1: Consensus base error rate evaluation system 11: Polymerase chain reaction quality evaluation module 11a: Consensus base error rate P _c(S) correction unit 12: Sequencing quality evaluation module 14: Scoring module 15: Judgment module 2: Consensus base error rate evaluation device 21: Processor 22: Storage S1: Amplifier pool selection process S1a: Amplification base establishment process S2: Observation base set establishment process S3: Consensus base c(S) calculation process S4: Consensus base error rate P _c(S) calculation process S4a: Sequencing accuracy and sequencing error rate calculation process S4-1: Consensus base error rate P _c(S) calculation and correction process

FIG. 1A is a step flow chart for illustrating the method provided by the first embodiment; FIG. 1B is a step flow chart for illustrating the method provided by the second embodiment; FIG. 1C is a probability distribution diagram for illustrating the probability distribution of the error base ratio _F10 after ten amplification cycles under the condition that the PCR error rate is 0.01; FIG. 2 is a probability distribution diagram for illustrating the fit between the theoretical value and the approximate value of the error rate in different amplification cycles; FIG. 3A is a block diagram for illustrating the consensus base error rate evaluation system provided by the third embodiment; FIG. 3B is a block diagram for illustrating the consensus base error rate evaluation system provided by the fourth embodiment; FIG. 4 is a block diagram illustrating a consensus base error rate evaluation apparatus provided in the fifth embodiment; and FIGS. 5A to 5B are probability distribution diagrams illustrating the fit between the observed frequency and the expected frequency of consensus base quality in the fourth embodiment.

S1: Expanded sub-pool selection process

S1a: Extended base building process

S2: Observe the base set establishment process

S3: Consensus base c(S) calculation processing

S4: Consensus base error rate P _c(S) calculation process

Claims (8)

A method for evaluating a consensus base error rate comprises: selecting one or more extended bases from an extender pool, wherein the extender pool is extended from an unknown base N; ordering the jth selected extended base as an observed base s _j , and grouping the observed bases s _j into an observed base set S, wherein j is an arbitrary positive integer; calculating a consensus base c(S) from the observed base set S; calculating a consensus base error rate P _c(S) , which is the probability that the consensus base c(S) is not the unknown base N, wherein the consensus base error rate P _c(S) is the sum of the probabilities that the unknown base N randomly selected from the observed base set S is the same as a hypothetical base b, but the hypothetical base b is not the same as the consensus base c(S), which is obtained by the following formula:

Wherein, the P(S|N=b) is the probability of randomly selecting the observed base set S from the expander pool when the unknown base N is the same as the assumed base b, and the calculation method thereof includes: defining an error base fraction _FR , which is the ratio of an extended error base to the extended bases in the expander pool, wherein the extended error base is a base different from the assumed base b; and calculating the P(S|N=b) according to the following formula:

wherein P ( S | N = b ∩ FR = FR ) is the total product of the probability P ( s j | N = b ∩ _FR = _FR ) for each observed base s _j in the observed base set S when the _unknown base N is the same as the assumed base b and the proportion of the _erroneous expanded base in the expander pool is _FR ; wherein the assumed base b is selected from the group consisting of adenine (A), thymine ( _T ), guanosine (G) and cytosine (C), and the assumed base b is different from the consensus base c(S). A method as described in claim 1, wherein, when the observed base _sj is the same as the assumed base b, the P ( sj | _N = b ∩ FR = _FR ) is equal to a correct base score FR _' , and when the observed base _sj is different from the assumed base _b , the P ( sj | _N = b ∩ FR _{= FR} ) is equal to the incorrect base score FR, wherein the sum of the correct base score FR' and _the incorrect base _{score FR} is 1 . The method as described in claim 2 further comprises: correcting P ( s _j | N = b ∩ FR = _FR ) to P ( s _j = b' | N = b ∩ { F _{b " ≠ b } = { F b " ≠ b }} ) _{according to a certain} sequence correctness rate P seq1 , a certain sequence error rate P _seq2 and an extended base ratio F _{b" ≠ b} , which is when the unknown base N is the same as the assumed base b , and the ratio of an extended base b" in the extender pool that is different from the assumed base b is F _{b" ≠ b} , the observed base s The probability that _j is the same as another observed base b', wherein, when the extended base b" is different from the assumed base b, the extended base ratio F _{b" ≠ b} is equal to the extended base fraction FR , _and the _modified P ( sj = b' | N = b ∩{ F _{b " ≠ b} }={ F _{b" ≠ b} }) satisfies the following formula:

Wherein, when the other observed base b' is the same as the assumed base b, P _pcr1 represents the probability that the assumed base b is expanded to a base that is the same as the other observed base b', P _pcr2 represents the probability that the assumed base b is expanded to the expanded base b", and the expanded base b" is not the same as the assumed base b; wherein, when the other observed base b' is different from the assumed base b, P _pcr3 represents the probability that the assumed base b is expanded to a base that is the same as the other observed base b', P _pcr4 represents the probability that the assumed base b is expanded to a base that is the same as the assumed base b, P _pcr5 represents the probability that the assumed base b is expanded to the expanded base b", and the expanded base b" is different from the assumed base b and the other observed base b'; wherein the sequencing accuracy rate _Pseq1 represents the probability that the other observed base b' is sequenced correctly, and the sequencing error rate _Pseq2 represents the probability that the expanded base b" is incorrectly sequenced to the other observed base b'. The method as claimed in claim 3 further comprises calculating the sequencing accuracy rate P _seq1 and the sequencing error rate P _seq2 using the sequencing quality score _Qi of the other observed base b', wherein the sequencing accuracy rate P _seq1 can be calculated by the following formula:

The sequencing error rate P _seq2 can be calculated by the following formula:

A method as described in any one of claims 1 to 4, wherein the observed base set S includes d observed bases s _j , the d observed bases s _j include n _b the same as the assumed base b, and (dn _b ) the extended error bases different from the assumed base b, wherein the d value is the maximum positive integer value of j, and the n _b is a positive integer less than or equal to d; when the observed base s _j is different from the assumed base b, the P ( s _j | N = b ∩ FR = _FR ) is equal to the error base fraction FR , and _the total product of the P ( s _j | N = b ∩ FR ₌ FR ₎ is calculated as shown in the following _formula :

The method of claim 5, wherein P(S|N=b) is further approximated by the difference in momentum to obtain:

Among them, the

is the (k+dn _b )th moment value of the probability distribution of the extended error base fraction _FR , where k is any non-negative integer less than or equal to n _b ; where

The approximate value of is r/2 ^k+d-nb , where r is the probability of a polymerization cascade amplification error occurring at the locus corresponding to the unknown base N in each cycle. A consensus base error rate evaluation system includes a polymerase cascade reaction quality evaluation module configured to execute the method described in any one of claims 1 to 4 to calculate a consensus base error rate P _c(S) . The evaluation system as claimed in claim 7 further comprises a sequence quality evaluation module, signal-connected to the polymerase chain reaction quality evaluation module, configured to read the sequence quality score _Qi of another observed base b' to calculate a sequence accuracy rate _Pseq1 and a sequence error rate _Pseq2 , wherein the sequence accuracy rate _Pseq1 can be calculated by the following formula:

The sequencing error rate P _seq2 can be calculated by the following formula:

and a consensus base error rate P _c(S) correction unit, which is configured in the polymerase chain reaction quality assessment module and is signal-connected to the sequencing quality assessment module to correct the P ( s j | N = b ∩ FR = FR ) to P ( s _j = b _' | _N = b ∩ { F _{b " ≠ b }={ F b " ≠ b} } ) according _to the sequencing accuracy rate P seq1 , the sequencing error rate P _seq2 and an extended base ratio F _{b " ≠ b ,} which is when the unknown base N is the same as the assumed base b , and the ratio of an extended base b" in the amplicon pool that is different from the assumed base b is F _{b" ≠ b} , the probability that the observed base _sj is the same as another observed base b', wherein, when the extended base b" is different from the assumed base b, the extended base ratio Fb _{" ≠ b} is equal to the extended _{base fraction FR} , and the modified P ( sj ₌ b' | N = b ∩{ Fb _{" ≠ b} }={ Fb _{" ≠ b} }) satisfies the following formula:

Wherein, when the other observed base b' is the same as the assumed base b, P _pcr1 represents the probability that the assumed base b is expanded to a base that is the same as the other observed base b', P _pcr2 represents the probability that the assumed base b is expanded to the expanded base b", and the expanded base b" is not the same as the assumed base b; wherein, when the other observed base b' is different from the assumed base b, P _pcr3 represents the probability that the assumed base b is expanded to a base that is the same as the other observed base b', P _pcr4 represents the probability that the assumed base b is expanded to a base that is the same as the assumed base b, P _pcr5 represents the probability that the assumed base b is expanded to the expanded base b", and the expanded base b" is different from the assumed base b and the other observed base b'; wherein the sequencing accuracy rate _Pseq1 represents the probability that the other observed base b' is sequenced correctly, and the sequencing error rate _Pseq2 represents the probability that the expanded base b" is incorrectly sequenced to the other observed base b'.

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