## Mutant-allele tumor heterogeneity(MATH)

MATH算法最早可追溯到发表于2013年Oral Oncol期刊的MATH, a novel measure of intratumor genetic heterogeneity, is high in poor-outcome classes of head and neck squamous cell carcinoma文章。后来该作者在Cancer上发表了一篇关于头颈部鳞状细胞癌的文章High intratumor genetic heterogeneity is related to worse outcome in patients with head and neck squamous cell carcinoma，并再次说明了MATH的有效性，高MATH的病人与低整体存活率有关等等

，最终导致肿瘤的生长、侵染、预后等指标的差异。最近几年对于肿瘤异质性的研究小结可以粗略的看下【盘点】浅谈肿瘤异质性

The MATH value for each tumor was based on the distribution of mutant-allele fractions among tumor-specific mutated loci, calculated as the percentage ratio of the width (median absolute deviation, MAD, scaled by a constant factor so that the expected MAD of a sample from a normal distribution equals the standard deviation) to the center (median) of its distribution:

the steps to determine the MATH value can be summarized as follows: (1) calculating the mutant-allele fraction (MAF) for each locus as the ratio of mutant reads to total reads; (2) obtaining the absolute differences of each MAF from the median MAF value, multiplying the median of these absolute differences by a factor of 1.4826, thus the median absolute deviation (MAD) was generated; (3) calculating MATH as the percentage ratio of the MAD to the median of the MAFs among the tumor’s mutated genomic loci, presented as MATH = 100 * MAD/median.

Each tumor’s MATH value was calculated from the median absolute deviation (MAD) and the median of its mutant-allele fractions at tumor-specific mutated loci:MATH=100 * MAD/median. Calculation of MAD followed the default in R, with values scaled by a constant factor (1.4826) so that the expected MAD of a sample from a normal distribution equals the standard deviation.

1. 首先通过测序数据计算每个样本的MAF（mutant-allele fractions）值，一般软件结果都会给出这个数据