Well, not really math, but MATH, for mutant-allele tumor heterogeneity. So not math per se, but a measurement. Allow me to explain.

The measurement known as MATH was created by researchers at Massachusetts General Hospital as a way to quantify the degree of heterogeneity of a particular tumor. What is tumor heterogeneity? The thinking goes like this: Multiple genetic mutations are thought to be responsible for the transformation of normal cells into cancerous cells. As cancerous cells continue to evolve, so to speak, the malignant cells become increasingly different, both from their ancestor and from each other. As a rough analogy, it’s like identical twins having their own families. The first cousins are more different from each other than are their parents, and they are more different from each other than from their parents. With second cousins, the differences are even more dramatic. Now picture all those siblings and cousins as cells inside a tumor, and that is (very roughly) the concept of tumor heterogeneity.

And here is the important thing about tumor heterogeneity, at least where treatment is concerned. In general, the more heterogeneous the tumor, the harder it is to treat, or so the thinking goes.

Edmund Mroz and colleagues, who created the MATH measurement, wanted to test out that thinking. Is a high degree of intratumor genetic heterogeneity connected to worse outcomes? Mroz et al conducted a study of patients with head and neck squamous cell carcinoma to see if they could use their MATH measurement to gauge how well patients would do after treatment.

The study, just published in *Cancer*, indicates that yes, the MATH score of a patient’s tumor is significantly associated with both tumor progression and adverse treatment outcomes.

Here’s a little more about how these researchers arrived at their conclusion. First, Mroz and colleagues obtained clinical, pathological, and outcome data for 74 patients with head and neck cancer. These patients had also had next-generation sequencing data obtained. All patients agreed to provide tumor tissue for the study.

The researchers calculated a MATH value for each tumor sample. How that is done is complicated and I don’t think my paraphrasing could do it justice, so I’ll quote from the report, for the actual math-inclined:

“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 [SD]) to the center (median) of its distribution:

MATH = 100 * MAD/median”

Basically, each tumor got measured for genetic heterogeneity, and that heterogeneity was reflected in a numerical score. In this study, the scores ranged from 19 to 55, with a mean of 34, an SD of 10, and a median of 32.

So with those numbers, you can immediately begin to wonder: did patients with a score in the high range fare worse than patients with a score in the low range?

Yes, sadly, they did. “…higher MATH was found to be strongly associated with shorter overall survival,” the study reports. And also: “Each additional unit of MATH was associated with a 4.7% increased hazard of death.”

Interestingly, higher MATH scores were also associated with factors already known to put patients at higher risk for worse outcomes, for example being negative for human papillomavirus, having a *TP53* mutation, or having perineural invasion.

The researchers conclude that their work provides evidence for the connection between high genetic heterogeneity and shorter survival.

However, MATH scores were not associated with the N stage of a cancer (in terms of TNM classification, using for staging cancer by measuring the size of a tumor, the number of tumors, and whether or not the cancer has metastasized), or with TNM stage in general. Thus MATH could be used in the clinic as its own prognostic score, the authors note.

There is more to understand about this work. For example, the authors state that the mutation rate of tumors was not associated with MATH or with outcome. So mutations alone are not enough to increase heterogeneity. What other factor could be promoting the progression and survival of genetically distinct cancer cell progeny? Also, will patients increasingly obtain next-generation sequencing of their tumors as part of treatment? If so, how can that information be used to help them?

The *MATH and Tumors* by *Work In Progress*, unless otherwise expressly stated, is licensed under a Creative Commons Attribution 3.0 Unported License.