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Quant. Biol.    2020, Vol. 8 Issue (2) : 95-108    https://doi.org/10.1007/s40484-020-0203-8
REVIEW
Applications of probability and statistics in cancer genomics
Xiaotu Ma(), Sasi Arunachalam, Yanling Liu
Department of Computational Biology, and Cancer Biology Program, Comprehensive Cancer Center, St Jude Children’s Research Hospital, Memphis, TN 38105, USA
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Abstract

Background: The past decade has witnessed a rapid progress in our understanding of the genetics of cancer and its progression. Probabilistic and statistical modeling played a pivotal role in the discovery of general patterns from cancer genomics datasets and continue to be of central importance for personalized medicine.

Results: In this review we introduce cancer genomics from a probabilistic and statistical perspective. We start from (1) functional classification of genes into oncogenes and tumor suppressor genes, then (2) demonstrate the importance of comprehensive analysis of different mutation types for individual cancer genomes, followed by (3) tumor purity analysis, which in turn leads to (4) the concept of ploidy and clonality, that is next connected to (5) tumor evolution under treatment pressure, which yields insights into cancer drug resistance. We also discuss future challenges including the non-coding genomic regions, integrative analysis of genomics and epigenomics, as well as early cancer detection.

Conclusion: We believe probabilistic and statistical modeling will continue to play important roles for novel discoveries in the field of cancer genomics and personalized medicine.
Keywords cancer genomics      sequence analysis      probability and statistics     
Corresponding Author(s): Xiaotu Ma   
Online First Date: 29 April 2020    Issue Date: 13 July 2020
 Cite this article:   
Xiaotu Ma,Sasi Arunachalam,Yanling Liu. Applications of probability and statistics in cancer genomics[J]. Quant. Biol., 2020, 8(2): 95-108.
 URL:  
https://academic.hep.com.cn/qb/EN/10.1007/s40484-020-0203-8
https://academic.hep.com.cn/qb/EN/Y2020/V8/I2/95
Fig.1  Mutation types.
Fig.2  Cancer driver genes.
Fig.3  Mutation frequency of drivers and power consideration for gene discovery.
Fig.4  Tumor purity and tumor-in-normal contamination. (A) Statistical model. A biopsy sample can have tumor purity ranging from 0% to 100%. An ideal scenario is to have 0% CCF in the normal sample and 100% CCF in the tumor sample. However, in practice the normal sample can have small fraction of cancer cells and the tumor sample may contain normal cells as well. (B) Statistical detection of true somatic mutation can be compromised by tumor-in-normal-contamination. (C) Assessing potential tumor-in-normal contamination by genotyping chimeric reads (where DNA sequence from one locus (black lines) is fused to another locus (blue lines)) in normal sample ascertained from copy number variation or structural variation.
Fig.5  A mathematical model of ploidy, clonality, and tumor purity. (A) Example scenarios of copy gain/loss (differentiating paternal (blue) or maternal (green)). Mutant allele fraction (MAF) of the marker (solid dot) is illustrated for each scenario. (B) Example showing calculation of expected allele fraction (eAF) of somatic mutation (red star) from a tumor with purity p. (C) Example showing calculation of expected allele fraction of germline polymorphism (black dot) from a tumor with purity p. (D) Expected allele fraction of somatic mutation as a function of tumor purity and selected local ploidy. Gain_1 wildtype: the mutation allele has 1 copy while the wildtype has two copies; Gain_1 mutant: the mutant allele has two copies while the wildtype has 1 copy; Loss 1 copy: only 1 mutant copy exists; CN-LOH: only 2 mutant copies exist; Diploid: 1 mutant and 1 wildtype copy.
Fig.6  Inferring mutational timing in melanoma cell line COLO829. In this cell line, it is known that chr1q (from 150M to 249M) has four copies from the same parental origin due to loss of heterozygosity and re-duplication. (A) Mutant allele fraction of somatic mutations in this region formed three clusters consistently supported by four sequencing efforts (GSC, Tgen, Pleasance, and Illumina): Early, Middle, and Late, which are defined by aggregating read counts from all four sequencing efforts (B). (C) Proposed model of mutational timing during tumorigenesis of COLO829. One of the two parental alleles of 1q was lost (for simplicity, assuming paternal allele was lost), and the remaining allele acquired 492 mutations (triangle) before its first duplication. Afterwards, 411 mutations (square) were acquired in one of the two copies of 1q before the second duplication event, following which additional 62 mutations (circle) were acquired in one of the four copies of 1q before diagnosis.
Fig.7  Intra-tumor Heterogeneity. (A) Modeling clonal evolution. The population size of a given subclone is a function of its growth rate and its age. For example, subclone #4 has a small diagnosis fraction due to lower growth rate than subclone #2 and #3. (B) Common clonal evolution patterns in relapsed ALL. Upon diagnosis, intensive treatment will be applied so that the overall tumor burden will reduce. Predominant diagnosis subclone (blue) was eradicated by treatment; while a minor subclone (orange) that also carries the ancestral mutations (green) can survive treatment and seed relapse. New mutations (red), such as NT5C2 and PRPS1, can be acquired and lead to drug resistance.
Fig.8  Detecting low frequency mutations. (A) Potential applications of low frequency mutation detection. (B) Sequencing cost analysis. Data (accessed Nov 1, 2019) from www.genome.gov/sequencingcostsdata. (C) Reported error rate of next generation sequencing technology in past decade. Pubmed ID of corresponding literatures listed.
Fig.9  Integrating cancer genomics with epigenomics data. (A) Mutation status of MYCN and ATRX, two primary driver genes for neuroblastoma, from 136 cases. Dark gray: MYCN or ATRX mutant; black: MYCN and ATRX double-mutant (in which ATRX has mutation T1582fs). MYCN and ATRX mutant samples has a trend of mutual exclusivity, though statistical significance is not reached (P=0.12, two-sided Fisher’s exact test). (B) The MYCN and ATRX double-mutant sample is from a female patient with both alleles of chrX intact in the tumor (blue and green represent the two parental alleles, respectively). Since only the wildtype ATRX allele is expressed, it is hypothesized that the T1582fs mutation happened on the allele with X-inactivation (gray solid dots), and therefore carries no function, so that it is still biologically compatible with MYCN high amplification. As a result, the updated P value of 0.02 has reached statistical significance for the mutual exclusivity.
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