Patient Characteristics
A total of 15 patients were enrolled to the ETB protocol between 5/5/2020 and 4/7/2022. As described below, we also used a retrospective cohort to calibrate the model. This cohort consisted of a total of 26 patients with HNSCC and were obtained from the phase II clinical trial of cetuximab and nivolumab8,9. The patient characteristics for the ETB and retrospective patients are summarized in Table 1. The prior line of therapy is defined as the number of treatment regimens that the patient received from the time of recurrent and/or metastatic disease diagnosis. Most patients were heavily treated before enrolling to the trial, but 14 of 15 (93%) patients had good performance status with ECOG PS 0–1.
Development of Therapeutic Strategies based on Mathematical Modeling
The overall ETB workflow is summarized in Fig. 1A. Each individual patient’s history was collected based on the protocol requirement and summarized. Examples of the prior treatment history and data collection along with available treatment options and their estimated outcome are shown in Supplemental Table 1 and Supplemental Table 2. The collected data were graphed to visualize an accurate timeline of disease burden based on the radiographical imaging studies, drug dosing, and all sequences of previous treatments (Fig. 1B). If imaging data informed tumor burden, then the volume dynamics, appearance, and disappearance of each lesion were also included. Aggregating this information into a standardized visual treatment and response chart has proved to be an invaluable tool for ETB discussion.
The available clinical data points were integrated to calibrate mathematical models that explore treatment options using a system of ordinary differential equations (ODEs). The equations have sufficient complexity to capture the key disease dynamics observed in patients and remain simple enough to avoid overfitting (Figure 1C). Data available for each individual patient tend to be sparse in terms of the number of time points, and thus unsuitable for fitting models with numerous parameters10. In our primary model, termed the GDRS model, we focus on four aspects of tumor dynamics: tumor Growth, tumor Death, evolution of drug Resistance, and drug re-Sensitization. The model is an extension of a tumor-growth inhibition model11-14 and consists of n+m differential equations, where n is the number of distinct lesions, and m the number of drugs that are administered. We let Ti be the volume of lesion i=1,…n; and Dj be the dose (as a function of time) of drug j=1,…,m. The efficacy of each drug over time (Ej) is distinct for each drug, and changes to reflect the evolution of resistance or subsequent resensitization. In the following equations, Ti, Dj and Ej are time-dependent:
\({\dot{T}}_{i}=\left(\stackrel{Growth}{\underset{{\gamma }_{i}}{⏞}}-\stackrel{Treatment response}{\underset{\sum _{j}{\delta }_{j}{E}_{j}{D}_{j}}{⏞}}\right) {T}_{i}\) \({\dot{E}}_{j}=\left(\stackrel{Sensitization}{\underset{{s}_{j}\left(1-{E}_{j}\right)\left(1-{D}_{j}\right)}{⏞}}-\stackrel{Evolution of Resistance}{\underset{{r}_{j}{D}_{j}}{⏞}}\right){E}_{j}\) \({D}_{j}={D}_{j}\left(t\right)\)
In this eco-evolutionary model, Ti models the ecological dynamics, Ej the evolutionary dynamics, and Dj the choices of the physician and patient. The model is further described in Supplemental File 1.
Model Calibration Using ETB Patient Specific Data
To apply the model to an ETB patient’s data, we made the following assumptions. First, we assumed that all the lesions within a patient shared the same growth parameter (γi) unless there were significant indications from the data suggesting that a particular lesion should have its own individualized fit. Thus, tumors within a patient only differed in terms of their date of first appearance and initial size. When possible, growth rates were calculated from a pair of consecutive increasing volumetric measurements for a lesion. These pairs of points were picked with the following prioritization scheme: 1) two measurements for the primary lesion prior to initial therapy; 2) two measurements for any metastatic lesion while off therapy; 3) maximal growth rate found within all increasing sequential measured volumetric pairs regardless of therapy status. In cases where multiple pairs of points satisfied the same level from the prioritization scheme, the maximal growth rate was used as the baseline. The growth rate, γ, thus derived is set to be the exponential growth parameter for the patient as a whole, for all lesions. An exception arises if one or more lesions are clearly significantly different in its growth rates, in which case the outlier lesion is given its own growth rate γi.
An additional factor can affect the growth rates, namely the appearance of new lesions relative to the dates of patient scans. When a new lesion is detected, the volume is noted. Following that, the previous scan of that same area is rechecked for any prior evidence of that lesion. This is a relevant check as the threshold for identifying a lesion de novo is larger than identifying it post hoc, when the location is now known from later scans. In either case, imaging has a lower limit of measurable size determined by contrast, voxel size, etc. When tracing a new lesion back through previous scans, eventually a scan is reached where there is no evidence of that lesion. For the model, we set its initial size in accordance with the minimal detection size of the instrument. Thus, this may be an over-estimate and consequently may underestimate the tumor’s growth rate when calculated from the next scan, where the lesion was identified and measured. In some cases, this underestimate may still be higher than the growth rates measured from other lesions, in which case the new lesion may receive its own higher growth rate for fitting purposes. This approach of tracking individual lesions backwards in time is a novel aspect of the ETB, allowing for the extraction of additional data regarding the lesion dynamics that would otherwise not be available.
To fully fit the drug-induced death and resistance parameters, at least two volumetric measurements while on the same therapy are needed. In this case, the starting tumor size (calculated from the pre-treatment scan), the growth rate, and the two on-treatment time points are sufficient to fit the ‘U-shaped’ ecological dynamics of the tumors. The model then reflects initial drug efficacy (drug-induced death rate, δ) followed by increasing drug resistance. In cases where there is only one on-treatment measurement, drug-induced death rate and rate of increasing drug resistance, r, cannot both be estimated. In such cases, we specify a functional form that generates pairs of parameters that fit the single on-treatment data point (Supplemental File 1). This function defines a set of parameter pairs all of which fit the patient data points. In principle, this set is wide-ranging, although biologically realistic bounds can be placed on δ and r, particularly using historical data from independent cohorts. The predictions arising from the possible pairs of δ and r can vary greatly. Thus, constraining the set of plausible pairs is of high value for predicting the future course of the patient’s disease.
Model Calibration Using Historical Data
A key aspect of the ETB process is the use of retrospective cohort data to constrain the predictions generated for the specific ETB patient. As such, we evaluated a retrospective cohort of patients with recurrent and/or metastatic HNSCC (Tables 1 and 2). For these 26 retrospective patients, we applied the ETB analysis approach to their available historical data. Imaging scans were retrieved and remeasured to both generate volumetric measures of each lesion and look for non-target lesions that may not have been considered during typical RECIST follow-up analysis at the time of their care. These data were then modeled using the above procedures to find parameter ranges for each patient that matched their data. Specifically, ranges of growth rates for lesions (γ), their response to any applied therapies (δ), and their rate of becoming resistant to such therapies (r) were determined. These ranges give a starting point for predicting the outcomes of the ETB patient, putting expected bounds on their growth rate and response to treatments, wherever the ETB patient’s data itself does not offer a fit. In our exemplar patient that we describe below, we used the retrospective cohort of patients receiving combination cetuximab and nivolumab to predict the widest range of response to these agents expected in the ETB patient. The patient’s own lesion dynamics then further refines the predictions within that retrospective range of possibilities.
Evaluation Of Primary Endpoint Of The Pilot Study
In 15 patients enrolled to date, 11 patients (73%) met the primary endpoint (Table 3). In cases where the end point was not met, the reasons are: 1) the patient was deceased before the date of the first ETB presentation, 2) insufficient historical data/analysis at the time of ETB to predict response to additional therapy options, 3) the patient was taken off the study at physician's discretion before the ETB presentation, and 4) the patient did not have measurable lesions delaying the presentation at ETB. In the 11 cases with recommendations, subsequent systematic chart reviews were conducted to determine if the treating physician altered the patient’s treatment plan based on the evolutionary therapies recommended by the ETB. The physician and patient followed the recommendation of the model in all 11 cases. All patients were longitudinally followed on the protocol for continued chart review to evaluate, after sufficient follow up, whether the patient had an improved outcome compared to the a priori prognosis for similar patients under standard of care.
The ETB has developed a framework to evaluate novel therapeutic strategies for individual patients, including tools for temporal visualization of the treatment and responses throughout the patient’s cancer journey, and application of the GDRS model to volumetric and other biomarker data. These tools are critical in facilitating treatment decisions for each individual patient in an efficient and consistent manner. Due to the often-sparse nature of clinical data, and need to constantly refine treatment decisions, we developed the following decision support workflow for fitting, prediction, and analysis using the ETB framework (Fig. 2A).
Evaluation Of Hnscc Based On The ETB Recommendation
To determine the initial feasibility of the ETB based approach, we focused on the evaluation of HNSCC because of the immediate availability of the retrospective cohort through a recently completed clinical trial. Parallel efforts for each enrolled patient in other disease sites to develop a similar model is ongoing and will be reported separately. For HNSCC, we enrolled a 66-year-old man with an initial diagnosis of HNSCC (subject ID: ETB-003) with base of tongue primary site and cervical lymph node metastasis based on imaging studies. The patient pursued non-standard of care alternative therapy and had local disease progression (Supplemental Table 1). The repeat biopsy of cervical lymph node at the time of disease progression was p16-positive squamous cell carcinoma. The patient started palliative chemotherapy with cisplatin, 5-fluorouracil, and cetuximab. Unfortunately, the regimen was discontinued because of toxicity after one cycle. Pembrolizumab was started, and chemotherapy was added due to disease progression on the pembrolizumab monotherapy. Again, the treatment was discontinued due to toxicities. The patient completed the concurrent carboplatin, paclitaxel, and radiation for durable locoregional control. The patient developed disease progression locally and distantly with lung metastasis and was treated with cetuximab and nivolumab.
For this patient with metastatic relapse, we analyzed the potential outcomes that might arise with the application of first-strike second-strike therapy, also known as extinction therapy (Fig. 2B and Fig. 2C). Upon relapse, the patient was put on the combination of cetuximab and nivolumab (the first strike), which we label F1 here. The goal of our analysis was to determine when the patient might fail this combination and therefore intervene at the appropriate time with a second strike. In this case, there were two chemotherapy options available as second strikes: carboplatin plus paclitaxel (S1) and cisplatin plus 5-fluorouracil (S2). Ideally, the first strike will be applied until efficacy wanes and the nadir of tumor burden is near, at which point the switch to the second strike would occur. In our analysis of this patient, we used retrospective cohort data, the patient’s previous imaging data, and the temporal follow-up data to determine 1) when the nadir of F1 may occur, and 2) which of the second strikes to switch to.
Initial Analysis And Model Fits
Figure 2B shows the initial analysis of the patient that was produced after enrollment. The dynamics of their lesions pre-ETB are shown to the left of the solid vertical line, which represents the time at which the patient was first analyzed by the ETB. Some of the early historical data was not available since the patient was treated at another institution prior to being seen at Moffitt Cancer Center. Volumetric measurements for all available scans were performed retrospectively for each detectable lesion and are shown as dots on the plot. The horizontal time axis is scaled relative to the first available scan.
The patient was administered several different therapies to address the primary disease: combination regimens of chemotherapies, targeted therapy, immunotherapy, and radiotherapy, with the latter causing regression of the primary disease around day 760. A follow-up scan on day 878 showed no evidence of disease; however, on day 1026 there was evidence of lung and lymph node metastases. These were measured volumetrically. Knowing their positions in the lungs, the previous scan with no evidence of disease (NED) at day 878 was reexamined to see if very small lesions were indeed detectable, but they remained NED. Therefore, we consider that these lesions are smaller than the detection threshold of the instrument, and they are marked with ‘x’ markers on Fig. 2B. Shortly before enrolling on the ETB, the patient began their first-strike therapy (F1) for the metastatic disease.
In accordance with the methods, we fit the model to the available data. The growth rate ranges were primarily fit from the metastatic disease dynamics, since there were two measurements prior to starting therapy F1, and an additional upper limit from the NED scan on day 878. Using these ranges of growth rate, we fit efficacy and resistance parameters for the dynamics of the primary disease (of which a representative fit for the largest primary lesion is shown in Fig. 2B in dark blue). A confounding factor is that the drugs were primarily given in combination, and furthermore the imaging data is sparse compared to the multiple changes of agents. However, some constraints on the drug behaviors can be gained from these fits.
We also leveraged our retrospective data for the first-strike therapy from patients having received the same F1 combination of cetuximab and nivolumab, from the clinical trial described above. By fitting to the dynamics of the patients in that cohort, we determined ranges of efficacy for F1 (Table 2). Application of this range to the current patient (using the intrinsic range of growth rates and resistance rates found from their own lesion dynamics) produced the predictive cone shown in light blue (the widest cone). Naturally, since some retrospective patients progressed rapidly and others had significant responses, the cone encompasses a wide range of possible responses for the current patient. Taking the average retrospective behavior and applying it to the current patient produces the darker shaded region.
At this stage of the analysis and patient decision-making process, we are primarily interested in knowing when the efficacy of F1 will be significantly diminished, and therefore the nadir of tumor volume will be approached. This will be the time to switch to a second strike. The time-to-nadir (TTN) for the retrospective cohort parameter ranges applied broadly to this patient ranges from 0 months (i.e., the efficacy of F1 is low enough that the lesions are already growing through it) to 7.3 months. To refine the patient-specific prediction of the nadir, we leverage model fits derived from the earlier lesion dynamics, and restrict the fits generated by the retrospective cohort parameter ranges to those that match the current patient’s fits. After this constraint, the model predicts that the current patient is likely to do significantly better than the average response of the retrospective cohort. The likely TTN range is now between 4.2 months and 6.9 months. Since the next scan is anticipated to be within two months of starting the therapy, the model strongly suggests that switching therapies should wait until follow-up imaging is obtained.
First Follow-up Analysis
Upon imaging and performing volumetric measurements of the lesions, we reanalyze the patient dynamics. Figure 2C shows the results after the first follow-up scan for the patient at day 1119. The largest lesion has declined significantly under the first strike, F1. This decline was in line with the “Patient fit” prediction cone of Fig. 2B, suggesting that the growth rates and treatment dynamics determined from earlier timepoints remained consistent for this lesion over time. The updated prediction cone for F1 is narrower after follow-up analysis using the additional data point. The TTN now ranges from 1.5 to 3.5 months (from the time of follow-up, not the start of F1). The model again suggests that the first strike is most likely to remain efficacious until the next imaging cycle, with only a small fraction of simulations suggesting that the nadir will be reached prior to that time.
At the same time, we examine what the effect of switching to a second strike would be at this time, since we do not want to wait until the nadir is reached to switch. In the insets of Fig. 2C, we show the predicted range of effect for switching from the F1 to either second-strike S1 (inset A) or S2 (inset B). In both cases, the range of efficacy for the strike is determined by both retrospective cohort responses and the current patient’s response, since they were previously administered these agents during primary tumor treatment. S1 was administered at the end of the primary disease treatment, and therefore the estimates are better than for S2, which was only administered in combination with other agents, and therefore has confounding factors in the primary fits. However, in both cases, the model suggests that compared to staying with the first strike, the second strikes appear to bring no advantage at this time. Therefore, since the model predicts that there is likely some efficacy remaining in F1 and that both S1 and S2 currently provide little comparative advantage, the decision is to continue the therapy until the next imaging time point.
Second Follow-up Analysis
For any patient in follow-up, the ETB process repeats with each new scan. Volumetric measures for the next follow-up scan were attained and the updated analysis is shown in Fig. 2D. The tumor has continued to shrink, albeit at a slower rate than during the initial phase. Reanalyzing the data with the model leads to updated predictions for the TTN, which now ranges from 0 to 1.7 months (from the reanalysis time point). This suggests that the efficacy of F1 is approaching its end. The insets in the figure show the predicted efficacy of the two second-strike options, and as opposed to Fig. 2C, both now are likely to have a better effect on tumor burden than continuing with F1.
Decision Support In The ETB
The ETB is a non-interventional trial, and therefore the decisions of when to switch therapies and what to switch to remain in the hands of the oncologist and the patient. Here, the model analysis and predictions used in the ETB workflow aim to give insight into the temporal dynamics of the patient’s specific disease, which can aid in making the above decisions. In the exemplar case above, the model initially suggested continuing the first strike, and similarly continuing after the first follow-up imaging point, after which the model began to suggest that a second-strike option should be applied soon. For this patient, an additional treatment option, radiotherapy, arose at the time, and was chosen as a second strike. The insight gained regarding the efficacy and expected nadir of the first strike was valuable in making the subsequent treatment decisions for the patient.