Models for targeted sequencing

1. A method comprising:

generating a plurality of candidate variants of a cell free nucleic acid sample of a subject;

for each position of a plurality of positions of a reference allele:

determining a first depth and a first alternate depth of first sequence reads from the cell free nucleic acid sample, wherein the first sequence reads are obtained from a sample of blood, whole blood, plasma, serum, urine, cerebrospinal fluid, feces, saliva, tears, a tissue biopsy, pleural fluid, pericardial fluid, or peritoneal fluid of the subject, and wherein the first depth represents a total number of the first sequence reads at the position, and wherein the first alternate depth represents a number of the first sequence reads having a mutation at the position based on the reference allele; and

determining a second depth and a second alternate depth of second sequence reads from a genomic nucleic acid sample of the subject, wherein the second sequence reads are obtained from a sample of white blood cells or tumor cells of a tumor biopsy of the subject, and wherein the second depth represents a total number of the second sequence reads at the position, and wherein the second alternate depth represents a number of the second sequence reads having a mutation at the position based on the reference allele;

determining a first likelihood of true alternate frequency of the cell free nucleic acid sample by applying a Bayesian hierarchical model to model the first alternate depths using aa first function parameterized by the first depths and the true alternate frequency of the cell free nucleic acid sample and (ii) a first noise level of mutations with respect to healthy cell free nucleic acid samples, wherein the first noise level describes expected noise rates per position of the first sequence reads;

determining a second likelihood of true alternate frequency of the genomic nucleic acid sample by applying the Bayesian hierarchical model to model the second alternate depths using aa second function parameterized by the second depths and the true alternate frequency of the genomic nucleic acid sample and (ii) a second noise level of mutations with respect to healthy genomic nucleic acid samples, wherein the second noise level describes expected noise rates per position of the second sequence reads;

filtering the plurality of candidate variants at least by a machine learning model using the first likelihood and the second likelihood to determine a probability that the true alternate frequency of the cell free nucleic acid sample is greater than a function of the true alternate frequency of the genomic nucleic acid sample; and

outputting the filtered candidate variants.

2. The method of claim 1 , wherein the first function is a Poisson distribution function parameterized by a product of one of the first depths and the true alternate frequency of the cell free nucleic acid sample, and wherein the second function is another Poisson distribution function parameterized by another product of one of the second depths and the true alternate frequency of the genomic nucleic acid sample.

3. The method of claim 1 , wherein the probability represents a confidence level that mutations from the first sequence reads from the cell free nucleic acid sample are not found in the second sequence reads from the genomic nucleic acid sample of the subject.

4. The method of claim 1 , further comprising:

responsive to determining that the probability is greater than one or more parameters, determining that at least some mutations from the first sequence reads from the cell free nucleic acid sample are not found in the second sequence reads from the genomic nucleic acid sample of the subject.

5. The method of claim 1 , wherein determining the probability further comprises:

determining the probability that the true alternate frequency of the cell free nucleic acid sample is greater than the true alternate frequency of the genomic nucleic acid sample multiplied by one or more parameters.

6. The method of claim 1 , wherein determining the probability comprises:

determining a joint likelihood of the first likelihood and the second likelihood, the first likelihood and the second likelihood being conditionally independent given the first sequence reads and the second sequence reads.

7. The method of claim 1 , wherein determining the probability comprises numerically approximating a joint likelihood of the first likelihood and the second likelihood by:

determining a cumulative sum of one of the first and second likelihoods; and

determining an integral of the other of the first and second likelihoods.

8. The method of claim 1 , wherein determining the probability is further based on a first parameter determined using a third function taking as input an alternate frequency of healthy genomic nucleic acid samples.

9. The method of claim 8 , wherein the third function is defined by criteria to guard against loss of heterozygosity events in sequence reads.

10. The method of claim 9 , wherein the third function is a non-linear function.

11. The method of claim 9 , wherein the criteria indicates a value of 3 for the first parameter and a lower threshold value of ⅓ for the alternate frequency of the healthy genomic nucleic acid samples.

12. The method of claim 1 , wherein determining the probability is further based on a first parameter determined using a third function taking as input (i) one of the second alternate depths of the second sequence reads from the genomic nucleic acid sample, (ii) a reference depth of the genomic nucleic acid sample, and (iii) a model of noise levels of mutations with respect to healthy genomic nucleic acid samples.

13. The method of claim 12 , wherein determining the probability is further based on a second parameter, the first and second parameters determined empirically by cross-validating with sets of cell free nucleic acid samples and genomic nucleic acid samples of a plurality of individuals.

14. The method of claim 13 , wherein the first parameter has a value between 1 and 5, inclusive, and wherein the second parameter has another value between 0.5 and 1.

15. The method of claim 13 , wherein the cross-validating includes applying candidate parameter values derived using samples associated with a plurality of types of diseases to test another sample associated with a different type of disease.

16. The method of claim 1 , further comprising:

determining the first noise level of mutations with respect to the healthy cell free nucleic acid samples using a third function parameterized by first parameters; and

determining the second noise level of mutations with respect to the healthy genomic nucleic acid samples using a fourth function parameterized by second parameters.

17. The method of claim 16 , wherein modeling the first alternate depths includes adding the first noise level to an output of the first function, and wherein modeling the second alternate depths includes adding the second noise level to another output of the second function.

18. The method of claim 16 , wherein the first and second parameters represent parameters of distributions that encode noise levels of mutations with respect to a given position of a sequence read.

19. The method of claim 16 , wherein the third and fourth functions are each a negative binomial function parameterized by a mean rate and dispersion parameter.

20. The method of claim 16 , wherein the third and fourth functions are a same type of function and parameterized by same types of parameters.

21. The method of claim 16 , wherein the first parameters are derived using a first machine learning model trained using a set of cell free nucleic acid samples, and the second parameters are derived using a second machine learning model trained using a set of genomic nucleic acid samples.

22. The method of claim 21 , wherein the set of genomic nucleic acid samples are from white blood cells.

23. The method of claim 21 , wherein the first and second machine learning models are Bayesian Hierarchical models.

24. The method of claim 21 , wherein the first and second machine learning models are a same type of model.

25. The method of claim 1 , further comprising:

collecting or having collected the cell free nucleic acid sample from a blood sample of the subject; and

performing enrichment on the cell free nucleic acid sample to generate the first sequence reads.

26. The method of claim 1 , wherein the first sequence reads are obtained from an isolate of cells from blood including at least CD4+cells of the subject.

27. A computer-product comprising a non-transitory computer readable medium storing a plurality of instructions for controlling a computer system to:

generate a plurality of candidate variants of a cell free nucleic acid sample of a subject;

for each position of a plurality of positions of a reference allele:

determine a first depth and a first alternate depth of first sequence reads from the cell free nucleic acid sample, wherein the first sequence reads are obtained from a sample of blood, whole blood, plasma, serum, urine, cerebrospinal fluid, feces, saliva, tears, a tissue biopsy, pleural fluid, pericardial fluid, or peritoneal fluid of the subject, and wherein the first depth represents a total number of the first sequence reads at the position, and wherein the first alternate depth represents a number of the first sequence reads having a mutation at the position based on the reference allele; and

determine a second depth and a second alternate depth of second sequence reads from a genomic nucleic acid sample of the subject, wherein the second sequence reads are obtained from a sample of white blood cells or tumor cells of a tumor biopsy of the subject, and wherein the second depth represents a total number of the second sequence reads at the position, and wherein the second alternate depth represents a number of the second sequence reads having a mutation at the position based on the reference allele;

determine a first likelihood of true alternate frequency of the cell free nucleic acid sample by applying a Bayesian hierarchical model to model the first alternate depths using aa first function parameterized by the first depths and the true alternate frequency of the cell free nucleic acid sample and (ii) a first noise level of mutations with respect to healthy cell free nucleic acid samples wherein the first noise level describes expected noise rates per position of the first sequence reads;

determine a second likelihood of true alternate frequency of the genomic nucleic acid sample by applying the Bayesian hierarchical model to model the second alternate depths using aa second function parameterized by the second depths and the true alternate frequency of the genomic nucleic acid sample and (ii) a second noise level of mutations with respect to healthy genomic nucleic acid samples, wherein the second noise level describes expected noise rates per position of the second sequence reads;

filter the plurality of candidate variants at least by a machine learning model using the first likelihood and the second likelihood to determine a probability that the true alternate frequency of the cell free nucleic acid sample is greater than a function of the true alternate frequency of the genomic nucleic acid sample; and

output the filtered candidate variants.

28. A system comprising a computer processor and a memory, the memory storing computer program instructions that when executed by the computer processor cause the processor to perform steps comprising:

generating a plurality of candidate variants of a cell free nucleic acid sample of a subject;

for each position of a plurality of positions of a reference allele:

determining a first depth and a first alternate depth of first sequence reads from the cell free nucleic acid sample, wherein the first sequence reads are obtained from a sample of blood, whole blood, plasma, serum, urine, cerebrospinal fluid, feces, saliva, tears, a tissue biopsy, pleural fluid, pericardial fluid, or peritoneal fluid of the subject, and wherein the first depth represents a total number of the first sequence reads at the position, and wherein the first alternate depth represents a number of the first sequence reads having a mutation at the position based on the reference allele; and

determining a second depth and a second alternate depth of second sequence reads from a genomic nucleic acid sample of the subject, wherein the second sequence reads are obtained from a sample of white blood cells or tumor cells of a tumor biopsy of the subject, and wherein the second depth represents a total number of the second sequence reads at the position, and wherein the second alternate depth represents a number of the second sequence reads having a mutation at the position based on the reference allele;

determining a first likelihood of true alternate frequency of the cell free nucleic acid sample by applying a Bayesian hierarchical model to model the first alternate depths using (i) a first function parameterized by the first depths and the true alternate frequency of the cell free nucleic acid sample and (ii) a first noise level of mutations with respect to healthy cell free nucleic acid samples, wherein the first noise level describes expected noise rates per position of the first sequence reads;

determining a second likelihood of true alternate frequency of the genomic nucleic acid sample by applying the Bayesian hierarchical model to model the second alternate depths using aa second function parameterized by the second depths and the true alternate frequency of the genomic nucleic acid sample and (ii) a second noise level of mutations with respect to healthy genomic nucleic acid samples, wherein the second noise level describes expected noise rates per position of the second sequence reads;

filtering the plurality of candidate variants at least by a machine learning model using the first likelihood and the second likelihood to determine a probability that the true alternate frequency of the cell free nucleic acid sample is greater than a function of the true alternate frequency of the genomic nucleic acid sample; and

outputting the filtered candidate variants.