Modelling treatment-response rates

Abstract

The time course of tumour responses to immunotherapies can be mathematically predicted on the basis of tumour-growth rates, the rates of immune activation and of tumour–immune-cell interactions, and the efficacy of immune-mediated tumour killing.

A longside radiotherapy, surgery and chemotherapy¹, cancer immunotherapy has become a major contributor to the armamentarium for the treatment of cancer. Yet only a subset of the patients who receive immunotherapies benefit from them^2,3. And even for patients who respond to these therapies, changes to the tumour are not observable for some time. This makes it difficult to quickly distinguish patients who will respond to the therapy from those who will not. Identifying biomarkers that distinguish potential responders from non-responders is therefore an unmet clinical need. Such biomarkers would ensure that non-responders are identified early, so that they may be offered other treatment options. Also, given the costs and potential toxicities of immunotherapy, patients need to be stratified according to their potential to respond to the therapy before it is administered to them, so that non-responders are not exposed to the side-effects of the costly drugs for no therapeutic benefit. Moreover, although the expression status of particular molecular biomarkers by immunohistochemistry is clinically used to inform decisions on immunotherapy treatments, non-invasive biomarkers would be useful when immunohistochemistry fails or when biopsied tissue is not available. Non-invasive biomarkers could also allow for longitudinal assessments that inform clinical-decision support.

Following the start of immunotherapy, the RECIST (version 1.1) criteria⁴ are often used to quantify tumour-volume changes with respect to a baseline. Yet considering both tumour volume and how it changes over time would allow assessments of the speed of tumour growth or shrinkage, and thus of tumour aggressiveness. Mathematical models are being developed to meet these needs⁵. They use clinically measurable inputs, and leverage known tumour behaviour and physical laws to generate interpretable treatment responses. Yet current modelling efforts are limited by the way input data are acquired and by cost-effectiveness. Reporting in Nature Biomedical Engineering, Zhihui Wang, Vittorio Cristini and colleagues now describe a mathematical model for the assessment of patient responses to immunotherapies early during treatment that only requires the dimensions of the tumour as obtained from computed tomography or magnetic resonance imaging⁶. At its essence, the model adds a time dimension to the RECIST criteria, and could thus be used to update and refine predictions when new imaging data become available.

Wang and co-authors report the performance of the model for four cancer types: lung cancer, melanoma, renal cell carcinoma and urothelial cell carcinoma. Their results suggest that two parameters in the model — a parameter englobing the antitumour immune status and tumour-cell killing rates, and another related to the tumour-growth rate at first tumour restaging (normalized by tumour burden at the start of the treatment) — may serve as biomarkers of immunotherapy responses regardless of the specific cancer and immunotherapy drug (Fig. 1). These two ‘universal’ parameters were validated across multiple independent cohorts. In particular, across patients with different types of cancer and receiving different checkpoint-blockade immunotherapies, the authors show that the predictions from the model correlated with post-hoc tumour behaviour, and that the projected long-term tumour burden correlated with the final measured tumour volume. Model-predicted and measured tumour-growth rates after treatment also correlated well. Furthermore, the authors validated model-derived quantitative measures of the sensitivity of a particular cancer type to a specific drug (unsurprisingly, the strength of the immune response was different for each drug–cancer-type combination). The model could thus aid physicians in decision-making, in particular for the selection of optimal drug choices on the basis of the specific cancer and immune health status of the patient. The authors’ analysis also suggests that a change in the kinetics of tumour growth before and after treatment may help identify patients who have stable disease according to the RECIST criteria yet who may benefit from discontinuing treatment or from a change in treatment protocol.

Fig. 1 |. A general mathematical model can discriminate patients who respond to immunotherapies from those who do not.

Distributions of two parameters of the model — the strength of the immune response (Λ×μ; Λ represents the coupling of immune-cell activity to tumour-cell death, and μ is the rate of cancer cells killed by immune cells), and a normalized growth rate at first tumour restaging (α_imaging; determined via computed-tomography data) — for all patients in three different clinical trials (left, a basket cohort of 93 patients treated with ipilimumab, NCT02239900; middle, a cohort of 35 patients with non-small-cell lung cancer treated with pembrolizumab, NCT02444741; and right, a cohort of 21 patients with melanoma metastatic to the brain treated with ipilimumab, nivolumab or a combination of both). Red line, mean values; error bars indicate standard deviation. P values were determined by a two-tailed Wilcoxon rank-sum test. Figure reproduced with permission from ref. ⁶, Springer Nature Ltd.

The mathematical formulation of the model is general enough for it to work across many cancer types and drugs; still, in view of the large number of immunotherapeutic drugs that are currently undergoing clinical trials, the model warrants further validation in larger patient cohorts and for a broader set of tumour types and drug combinations. Naturally, a single model that can be used independently of the cancer–drug combination is much more clinically valuable. This contrasts with data-driven predictive modelling studies using machine-learning techniques, which may, however, have higher predictive power for specific clinical scenarios⁷. Recent previous work by the authors established that clinical outcomes in patients with advanced cancer treated with checkpoint-inhibitor immunotherapy could be mathematically predicted on the basis of computed-tomography data⁸. Similarly, by using data from computed tomography or magnetic resonance imaging, which are readily available as part of the standard of care, the now more extensively validated model could be used at the time of first restaging of the cancer, and complementary to other biomarkers so as to enhance accuracy.

Wang and co-authors’ work exemplifies the potential of mathematical models to provide more information than that obtained from radiographic metrics at fixed time points. Because the model incorporates the dynamics of the entire tumour burden, it can, in principle, distinguish quantitatively between lesions that respond differently to a given treatment. This would aid decisions of whether to treat non-responding lesions with surgery, radiotherapy⁹ or other local therapies, thereby increasing the chances of patient survival¹⁰. And comparisons of predictions with models leveraging machine-learning techniques could help to provide consensus predictions.

The benefits of predicting early whether a patient will respond to a therapy cannot be underestimated. A large number of treatment options exist for many types of cancer, and matching patients quickly to the most beneficial therapy is paramount. Also, sustained tumour growth (and with it the constant evolution of clonogenic cells) increases the chances of resistance-causing mutations emerging, and thus lowers the probability that the tumour responds to other therapeutic drugs and approaches. Moreover, substantial healthcare disparities in high-income countries are driven by high costs that limit access to treatment, and patients in most low- and middle-income countries cannot currently even contemplate immunotherapy as a treatment option. Hence, prediction models that can help stratify the patients who are likely to benefit the most from high-cost treatments may help reduce healthcare-system costs and widen the efficient use of cutting-edge treatments.