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Mathematical Model Of Treatment Response ‘Designed For Clinical Translation’

By Deborah Borfitz

March 4, 2021 | Researchers at Houston Methodist and MD Anderson Cancer Center have come up with a mathematical model for estimating the response of cancer patients to immunotherapy and, unlike most existing predictive tools in the clinic, it factors time into the equation. The model is based on the fundamental biology and physics behind the disease and treatment modalities that cannot be measured in patients (e.g., immune cells or drugs that penetrate a tumor) and the inputs are already being routinely measured in patients, says Zhihui Wang, Ph.D., associate professor in the Mathematics in Medicine Program at the Houston Methodist Research Institute.

A specific set of model parameters can serve as “mathematical markers” for predicting the strength of immune response for each drug-cancer type pairing examined. Mathematical markers are a new concept that cannot be simply derived from conventional statistical data mining and machine learning approaches, but instead are drawn from complex differential equations, says Wang, who has been working on chemotherapy outcome prediction models for many years. Genomic and proteomic tools, based on deep learning, may be able to tell physicians what kind of cancer patients have and identify drugs that could have an impact, but they usually do not provide any time information.

Calculations of these mathematical markers are based on CT and MRI images. The new model quantifies patients’ sensitivity to various combinations of immune checkpoint inhibitors and long-term tumor burden and is “designed specifically for clinical translation.”

According to Wang, “Our model can predict at which time point [doctors] need to do another treatment, increase the [immunotherapy] dose, or consider moving the patient to another treatment plan. It can be used to estimate patient response as early as possible after the start of treatment.”

Ultimately, the plan is to add the model to a software package for predicting patient response to immunotherapy as well as other types of cancer treatments such as chemotherapy, continues Wang. The model is currently in research mode and will need to be validated with more patient data before it is in real-world clinical use.


More Studies Planned

In a proof-of-concept study recently published in Nature Biomedical Engineering (DOI: 10.1038/s41551-020-00662-0), the research team demonstrated the model accurately and reliably characterized the strength of a cancer type to a specific immunotherapy treatment. As a first step, they obtained CT and MRI scan data of tumors from before, during, and after immunotherapy in 124 patients treated with checkpoint inhibitor immunotherapy in one of four in-house trials.

These were then analyzed with their model to arrive at specific numeric measures of therapeutic response—the presence and health of the immune presence within the tumor and the resulting kill rate of cancer cells by immunotherapy-activated immune cells—which were combined into a single measure that was highly correlated with long-term tumor burden. At the journal’s request, these results were further validated with data from 177 additional patients treated with one of the most common checkpoint inhibitor immunotherapies (anti-CTLA4 or anti-PD1/PDL1 monotherapies), says Wang.

The idea here is to give doctors a supplemental tool, on top of all the other information already at their disposal, to help guide their decision-making and “optimize their treatment plan,” Wang says. Under the best of circumstances, it can be difficult for treating physicians to determine if an immunotherapy drug will have an impact and, if so, how long it will work—let alone which specific drug or combinations would be most beneficial.

In the best-case scenario, the model will be able to predict treatment efficacy for specific patients over a two- to three-year period, says Wang, who holds no illusions about the difficulty in achieving that mathematical feat. Discussions have been underway with MD Anderson Cancer Center for many months now about collaborating on a clinical trial putting the model in the hands of treating physicians, which could get underway before the end of the year.

In its current state, the model can be used to predict treatment outcomes as well as segment patients into responder and non-responder groups, “but there are still some errors in between,” says Wang. To further improve its prediction accuracy, the researchers are now adding blood samples and histological data as inputs and hope to begin a new model validation study soon.

The outcome prediction model is already being tested in additional cancer drug combinations to see if it can be more broadly applied to other, more advanced treatment regimens, says Wang.

The inclusion of a time scale in the model makes it more precise than prognostics based solely on tumor volume, such as RECIST, he notes. The model may also be able to identify individual patient response sooner since it reveals tumor growth kinetics pre- and post-treatment.


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