Predicting response to pembrolizumab in metastatic melanoma by a new personalization algorithm

Abstract

Background: At present, immune checkpoint inhibitors, such as pembrolizumab, are widely used in the therapy of advanced non-resectable melanoma, as they induce more durable responses than other available treatments. However, the overall response rate does not exceed 50% and, considering the high costs and low life expectancy of nonresponding patients, there is a need to select potential responders before therapy. Our aim was to develop a new personalization algorithm which could be beneficial in the clinical setting for predicting time to disease progression under pembrolizumab treatment.

Methods: We developed a simple mathematical model for the interactions of an advanced melanoma tumor with both the immune system and the immunotherapy drug, pembrolizumab. We implemented the model in an algorithm which, in conjunction with clinical pretreatment data, enables prediction of the personal patient response to the drug. To develop the algorithm, we retrospectively collected clinical data of 54 patients with advanced melanoma, who had been treated by pembrolizumab, and correlated personal pretreatment measurements to the mathematical model parameters. Using the algorithm together with the longitudinal tumor burden of each patient, we identified the personal mathematical models, and simulated them to predict the patient's time to progression. We validated the prediction capacity of the algorithm by the Leave-One-Out cross-validation methodology.

Results: Among the analyzed clinical parameters, the baseline tumor load, the Breslow tumor thickness, and the status of nodular melanoma were significantly correlated with the activation rate of CD8+ T cells and the net tumor growth rate. Using the measurements of these correlates to personalize the mathematical model, we predicted the time to progression of individual patients (Cohen's κ = 0.489). Comparison of the predicted and the clinical time to progression in patients progressing during the follow-up period showed moderate accuracy (R2 = 0.505).

Conclusions: Our results show for the first time that a relatively simple mathematical mechanistic model, implemented in a personalization algorithm, can be personalized by clinical data, evaluated before immunotherapy onset. The algorithm, currently yielding moderately accurate predictions of individual patients' response to pembrolizumab, can be improved by training on a larger number of patients. Algorithm validation by an independent clinical dataset will enable its use as a tool for treatment personalization.

Trial registration: ClinicalTrials.gov NCT02581228.

Keywords: Advanced melanoma; Effector CD8+ T Lymphocytes; Immune checkpoint blocker; Immunotherapy; Mathematical model; PD-1; Pembrolizumab; Personalized treatment; Prediction algorithm; T cell exhaustion.

Conflict of interest statement

ZA holds 15% shares in Optimata. Other authors declare that they have no competing interests.

Figures

Fig. 1

A schematic representation of the model for the main interactions between the melanoma cancer, the cellular immune system, and the immune checkpoint blocker pembrolizumab. The model is based on the following assumptions: tumor cells stimulate antigen-presenting cells, APCs, depending on the tumor immunogenicity; functional APCs activate effector CD8+ T cells, which may eliminate tumor cells; tumor infiltrating lymphocytes, TILs, become exhausted, independently of the tumor cells elimination; tumor growth is determined by its net growth rate and by the rate of its destruction by Effector TILs; immunotherapy extends the activation of effector TILs, and reduces their exhaustion. Annotated ellipses represent the dynamic variables of the model, while arrows represent the interaction between them (see legends in the box)

Fig. 2

Representative fitting results of patients, whose target lesions completely shrunk under treatment with pembrolizumab (a), shrunk by more than 30% from baseline size (b), increased by over 20%, relative to the nadir measurement (c), was stabilized, as determined when the conditions for disease progression, partial response, and complete response were not met (d). The ranges of the personalization parameters used for the simulation are specified in Table 3. SOD sum of diameters

Fig. 3

Fitting results of the model-simulated tumor size in the patients’ cohort (N = 54), with the clinically observed tumor sizes. a Each point shows the fitted versus the clinically measured sum of diameters (SOD) of a patient, at the time an imaging assessment took place in the clinic. The observed SOD on the reference line equals to the fitted values. The personalization parameter ranges used for the simulation are specified in Table 3, and the values of the other model parameters are summarized in Table 1. Numerical analyses and simulations were performed using the ode15s Runge–Kutta ODE solver of Matlab R2016a (The Mathsworks, UK). From the initial time of the simulation (t = 0) to the time of treatment initiation (t = t1), the model in Tsur et al. [39], was simulated, and from t1 until the end of the simulation period, the model in Eq. (1) was simulated. The effect of pembrolizumab on the immune system and tumor was implemented here by the parameters apem and bpem. b Fitted versus observed SOD on a log scale. Values of 0 were excluded from the dataset for calculation of R-squared

Fig. 4

Histogram of apem values, obtained from fitting of the mathematical model to the clinically observed tumor size. The initial range of apem for the fit is defined in Table 3. a Absolute values of apem. b Transformed values of lnapem

Fig. 5

Patient-specific values of lnapem, as obtained from fitting the mathematical model to the data of each patient in the training set, versus the estimated values of lnapem by a Leave-One-Out cross-validation (COO CV) of the k-NN algorithm. Each point represents the parameter values of one patient and the reference line satisfies equality between the fitted and regression-derived parameter values (see “Methods” section)

Fig. 6

Comparison between the sum of diameters (SOD), derived by the personalization algorithm, and the value measured from imaging assessments, at each clinically measured time point, for all patients, presented on a normal scale (a), and on a log scale (b). The reference line marks equality between the fitted and predicted SOD values. Values of 0 were excluded from the dataset for calculation of R-squared

Fig. 7

Comparison between the predicted time to progression (TTP) and the measured clinical TTP, including only the cases in which disease progression was determined clinically, as well as by the personalization algorithm. Points on the reference line satisfy equality between the observed and computationally derived TTP