Abstract
Objectives
We discuss challenges using computational modeling approaches for personalized prediction in clinical practice to predict treatment response for rare diseases treated by novel therapies using clinical oncology as an example context. Several challenges are discussed, including data scarcity, data sparsity, and difficulties in establishing interdisciplinary teams. Machine learning (ML), mechanistic modeling (MM), and hybrid modeling (HM) are discussed in the context of these challenges.
Materials and Methods
We present an HM approach, combining ML and MM techniques for improved personalized model estimation in the context of chimeric antigen receptor T-cell therapy for aggressive lymphoma.
Results
The HM approach improved the root mean squared error by compared to using MM alone (MM: and HM: , where the units are in cells), computed from 13 patients included in this study.
Discussion
By exploiting the complementary strengths of ML and MM approaches, the developed HM method addresses common limitations such as data scarcity and sparsity in medical settings, especially common for rare diseases.
Conclusion
The HM techniques are likely required to overcome data scarcity and sparsity issues in broad medical settings. Developing these techniques requires dedicated interdisciplinary teams.
Keywords: machine learning, personalized modeling, mechanistic modeling, hybrid modeling, cancer treatment outcome prediction
Introduction
The success of cancer treatment depends critically on our ability to predict which treatment choice will be successful. Incorrect therapy selection leads to treatment failure and unnecessary treatment-associated toxicities. However, in the case of novel treatments for a relatively rare disease, accurate treatment-response prediction is challenging because of data scarcity and sparsity.1,2 Here, we define data scarcity as a limited number of observations or subjects available for analysis. Similarly, we define data sparsity as rare, missing, or incomplete data within single or repeated observations resulting from measurements collected at insufficient frequency. Data scarcity and sparsity problems often require new computational methods and approaches, raising an additional obstacle: the challenges of interdisciplinary collaborations.3 The required insights to develop methods for accurate and useful predictions are only possible when interdisciplinary team members understand each other’s perspectives, needs, and languages. A common informatics goal is to develop methods that are robust and generalize to other diseases with similar data limitations. For example, efficient use of computational methods for different cancer types could have broad implications, such as biomarker and risk factor identification, understanding the underlying dynamics of treatment-immune system-tumor microenvironment, and predicting the treatment option with the highest likelihood of success.4–7 In this Perspective, we discuss recent advances that can potentially support improving patient outcomes through new methods for accurate prediction of treatment responses for novel treatments of relatively rare cancers. We also discuss fundamental roadblocks that are limiting the use of these approaches in clinical oncology. Finally, we offer some potential solutions. We illustrate these concepts with an example of computational modeling in cancer immunotherapy.
Background on computational predictive modeling
Because of data limitations and system complexity, progress in personalized treatment outcome prediction for oncology patients may require multiple computational modeling approaches that combine models that encode knowledge of biological systems via mechanistic modeling (MM) and model-free machine learning (ML). Figure 1 gives a conceptual overview of such a predictive modeling process. Predictive modeling requires two high-level choices: selecting a class of models and an inference method. Two broad classes of models include (i) mechanistic models8,9 that use existing knowledge of the biological system estimated using data assimilation (DA),10,11 a framework that is often known for creating a digital twin12 because the model is constructed to mimic the mechanics of the observed system and is continuously compared and updated with data as they arrive, and (ii) parameterized families (eg, linear, Gaussian) or families of non-parametric functions (eg, neural networks, transformers) estimated with ML methods.13 Inference methods are wide-ranging, including Kalman filtering14,15 optimization, variational techniques,16 stochastic methods such as Markov chain Monte Carlo,17 and are sometimes tied to the model class being estimated.
Figure 1.
Summary of mathematical modeling techniques. Depending on the task, inputs could cover a wide range of variables: patient-specific, disease-specific, and drug-specific variables. Then, based on the data-related constraints and the purposes, the most appropriate modeling approach is selected. This choice also directs the choice of a suitable inference scheme. As a result of the computational framework created by all the components mentioned so far, one or a few of the wide range of outputs could be achieved.
Predictive methodology choice is determined by the context and constraints of the clinical problem. MM and ML methods have distinct strengths and limitations. MM can perform well with small or sparse datasets and is typically estimated separately for each individual.18,19 It leverages known relationships between variables, can infer unmeasured quantities, but requires an existing model or sufficient system knowledge to develop one. ML, by contrast, generally requires large datasets and operates at the population level, applying generalized patterns to individual predictions. While ML can capture complex patterns in high-dimensional data, it lacks built-in knowledge of the underlying system and may struggle in data-sparse settings. To overcome the limitations of each, recent work has focused on developing hybrid MM–ML frameworks that integrate their complementary strengths.20–28
Key challenges of using computational predictive modeling in oncology
In the context of clinical cancer research, both ML and MM approaches have been used for a variety of applications. ML models have been used in oncology for risk assessment,29–34 lesion detection and characterization,35–37 therapy response prediction,38–43 in the design of new drugs, biologics, and cellular immunotherapies.44 MM have been used to describe the time-dependent dynamics of CAR T-cells and tumor cells,45–48 revealing pharmacokinetic/dynamic impacts on adverse events or even the dynamics of cytokines.49 These cases are excellent examples of conceptualizing the challenges discussed in the introduction that have limited the development and implementation of personalized prediction models in clinical oncology, including data sparsity, scarcity, and lack of interdisciplinary collaboration.
Data sparsity and its limitations in predicting cancer treatment outcomes
In the clinic, histologic and radiographic assessments are used, and panel-based sequencing data are increasingly common. However, these clinical data are often incomplete or missing due to technical limitations of testing (eg, limited biopsy specimen, poor quality sample for sequencing), lack of patient follow-up, limited health care system resources, lack of insurance coverage, and the proprietary nature of some drug-specific data. However, a larger problem is the availability of biologically meaningful information to clinicians. Cancers are biologically complex, heterogeneous, and dynamic diseases that evolve genetically over time and interact with the patient’s endogenous tissues, immune microenvironment, microbiome, exogenous environment, and prior treatments.50 Given this biological complexity, routinely collected data for cancer patients capture only a small fraction of the biologically relevant information that could potentially be used for prediction and personalized treatment planning. Although panel-based genomic sequencing of tumors has become common, the significance of the results is often not known or actionable.51,52 It is likely that incorporating more comprehensive and granular data such as whole genome sequencing, transcriptional profiling, tumor microenvironment characteristics, and immunophenotyping of the tumor and endogenous immune system would allow improved prediction.53–58 Finally, because clinical assessments are commonly performed at relatively infrequent intervals (eg, cross-sectional imaging every 3-6 months), the number of observations per patient is limited.
Addressing data scarcity in computational predictive modeling of cancer treatment outcomes
Publicly available data repositories (eg, UK Biobank, All of Us Biobank) are potential sources of granular data for thousands of subjects but often lack key context-specific variables. The sensitive nature of personal medical data has posed a significant challenge to accumulating the large data sets frequently needed for ML analysis. In addition, the relative rarity of many cancer subtypes limits data set sizes. Sophisticated deep learning methods, with millions of parameters, require massive data sets. Even shallow nonlinear ML methods require large data sets unless they are severely regularized.13,59
Diverse approaches are being considered to address these data limitations. First, newer statistical methods are being developed to address data missingness. These include advanced statistical and deep learning-based imputation methods.60,61 MM is well-suited to overcome data scarcity and sparsity issues by exploiting a mathematical representation of the underlying biological system rather than learning by identifying patterns in data alone. While mechanistic models are not completely insensitive to sparse data, they can often accommodate missing data more efficiently than ML models. Combining ML and MM approaches toward the development of predictive models is a novel way to potentially overcome data sparsity limitations. Being relatively new, such hybrid modeling (HM) approaches have started to be applied in different medical settings and are shown to improve prediction accuracy in several cases, such as prediction of metastatic relapse of breast cancer,23 intensive care unit (ICU) mortality prediction,62 risk assessment for stroke,63 and forecasting blood glucose values of type 1 diabetes patients,64 type 2 diabetes and ICU patients.65,66
Another strategy to overcome data scarcity is federated learning.67–69 This is a decentralized, collaborative ML technique in which algorithms are trained on local data sets, with the resulting models subsequently aggregated to generate an updated central model.70,71 There are a few examples of federated learning in oncology,71–73 but application challenges remain. Federated learning provides the ability to use different local data sources by facilitating data privacy, a common concern in medical settings. Although the models are trained locally, a centralized model is updated based on information from local model training, incorporating a large amount of additional data from a wide range of local sources, boosting accuracy without directly accessing the local sensitive data. Finally, although synthetic data sets have been proposed as one solution to data scarcity in biomedical research, the fidelity of such data and a regulatory framework for their use is currently lacking. All these techniques address the data sparsity challenges from different perspectives. Combining these methods could support vast potential improvements in prediction accuracy. For example, using synthetic data generated from real-world data can support the development of accurate hybrid models. The prediction accuracy can be further improved if these hybrid models are employed within federated learning algorithms, being updated once new local data become available, and improving the central model.
Overcoming challenges in cross-disciplinary collaboration for personalized oncology
Interdisciplinary collaboration is challenging and is a critical barrier to advancing personalized oncology. Fundamental differences exist between how a clinical decision-making problem (eg, the likelihood of success of a therapy) is approached by a clinician versus a computational method. A clinician’s approach accounts for many factors that may not be quantifiable (eg, the likelihood of patient compliance) or present as measured data and, therefore, is challenging to incorporate into a modeling framework. In contrast, computational tools can be helpful in extracting intricate patterns from complex data, patterns likely to be overlooked or incomprehensible to clinicians.74
Development of clinically useful computational models requires understanding (i) the day-to-day realities of patient care and the practical considerations of implementing novel clinical tools, (ii) the technical and computational knowledge to develop robust, accurate, and validated tools, and (iii) translation via the design of decision-aid tools that can inject the computational model-based predictions into the clinical decision-making process. This requires the unification of deep clinical, health care process, computational, and human-computer interaction insights. The clinical world is beginning to recognize the critical importance of such collaborative team efforts in advancing these methods in routine clinical practice.75,76
Methods
An illustrative example from large B-cell lymphoma
To illustrate the limitations induced by data scarcity, sparsity, and of using only MM or ML and the potential utility of personalized HM in oncology, we consider the case of relapsed and refractory large B-cell lymphoma (LBCL).77 The development of chimeric antigen receptor (CAR) T-cell therapy has led to a paradigm shift in the treatment of patients with relapsed LBCL. However, despite the significant improvement in outcomes seen with this therapy compared to historical treatment options,78,79 only 40% of patients derive long-term benefits. Early and accurate prediction of treatment outcomes after CAR T-cell therapy infusion would help clinicians strategize the next steps for better health outcomes, especially if the treatment is predicted to fail. Therefore, we aimed to estimate the personalized CAR T-cell and cancer cell dynamics for LBCL patients within fifteen days after the CAR T-cell infusion based on routine clinical data, a challenging problem with data sparsity and scarcity. An accurate estimation of these dynamics could elevate our physiological understanding of the underlying system and could be used for treatment outcome prediction. Here, we merely focus on investigating the usability of MM with extremely sparse routine clinical data and the illustration of one possible approach for HM.
Typical large B-cell lymphoma data
Our data set consisted of routine clinical data from 13 patients, whose clinical data are shown in Table 1. LBCL data with CAR T-cell data are relatively rare, and while our data are representative of such data sets, the limited population size represents a common severe limitation. This study was reviewed and approved by the Colorado Multiple Institutional Review Board (protocol number: 21-4232). We used total metabolic tumor volume (TMTV) to estimate the number of lymphoma cells present before and after CAR T-cell infusion.80 The TMTV measurements are sparse, totaling one to three measurements for each patient, only one of which can be used to create the personalized predictive model. Furthermore, the pre-infusion TMTV measurement, which served as an approximation to tumor volume at the time of CAR T-cell infusion, ranged from 0 to 1942.5 cm3 across patients and was collected up to three months prior to CAR T-cell infusion. One patient had no detectable TMTV on the PET scan. For modeling purposes, we assigned this patient a TMTV of 0.1 cm3, the smallest volume reliably detectable by a PET imaging. The number of infused CAR T-cells was known, and the expansion of CAR T-cells was characterized using the absolute lymphocyte count (ALC) measured over the first fifteen days following CAR T-cell infusion.81 The mean and standard deviation of the number of ALC measurements were , with a range across all patients, highlighting the sparsity of the data. Moreover, although the sample size will grow, the complexity and exploratory nature of using CAR T-cell therapy is likely to remain small until it becomes a more common cancer therapy, as is the case for all new promising treatments.
Table 1.
Summary statistics for all 13 patients, with individual results shown for patients 3, 4, 7, and 13, who were randomly selected and are representative of the cohort’s range of outcomes.a,b
| Variable | Patient 3 | Patient 4 | Patient 7 | Patient 13 | Summary for all 13 patients |
|---|---|---|---|---|---|
| Age at CAR T-cell infusion | 75 | 75 | 65 | 53 | mean: 62.2, stdev: 11.8, median: 65, iqr: 16.3, min: 36, max: 75 |
| Sex | F | F | M | M | Female: 4, Male: 9 |
| Race | White | White | White | American Indian | American Indian: 1, Asian: 1, White: 11 |
| Lymphoma subtype | LBCL | LBCL | LBCL | LBCL | LBCL: 8, HGBL: 5 |
| Ki67(%) | 55 | 85 | 85 | 55 | mean: 77.7, stdev: 17.8, median: 85, iqr: 27.5, min: 40, max: 95 |
| Pre-CAR T infusion TMTV ()c | 196.4 | 1942.5 | 450.9 | 1.6 | mean: 273.9, stdev: 527.3, median: 74.6, iqr: 323.0, min: 0, max: 1942.5 |
| Number of ALC measurements used in modelingd | 10 | 12 | 10 | 11 | mean: 8.8, stdev: 1.8, median: 9, iqr: 2, min: 5, max: 11 |
| Best response to CAR T-cell therapy | CR | PD | PD | CR | Complete remission: 7, Progressive disease: 6 |
| Time from CAR T-cell infusion to the last follow-up (months) | 37.0 | 2.3 | 31.1 | 12.7 | mean: 19.8, stdev: 12.7, median: 18.0, iqr: 23.2, min: 2.3, max: 39.3 |
| Progression at last follow-up | No | Yes | Yes | No | Yes: 7, No: 6 |
| Deceased at last follow up | No | Yes | Yes | No | Yes: 7, No: 6 |
These four patients are included to provide concrete examples of variability in response and to illustrate the specific gains achieved through personalization, complementing the overall summary statistics.
ALC: absolute lymphocyte count; CAR: chimeric antigen receptor; CR: complete remission; DLBCL: diffuse large B-cell lymphoma; HGBL: high-grade B-cell lymphoma; PD: progressive disease; TMTV: total metabolic tumor volume.
Used in the model-based predictive algorithm.
The number of ALC measurements is not directly used in the modeling, but the ALC measurements were used. The rest of the variables are included to provide context and baseline information about the patient cohort of this study.
Hybrid modeling approach
We used the following mechanistic model82 representing the dynamics and interaction of CAR T-cells and cancer cells.
where and are the cancer cell and CAR T-cell counts at day , respectively, is the cancer cell net growth rate (1/day), is the carrying capacity (cell), is the CAR T-cell killing rate (1/(day*cell)), is the net rate of proliferation and exhaustion of CAR T-cells when stimulated by cancer cells (1/(day*cell)) and is the CAR T-cell death rate (1/day).
Model estimation requires estimating unknown model parameters using individual patient data. In this setting, data include only one TMTV measurement and ALC measurements to be used for model fitting. Even for MM, model estimation is difficult when data are this sparse because the response to therapy is entirely missing in these data. Additionally, CAR T-cell data are noisy as we use surrogate measurements (ALC). Instead of exact predictive accuracy, we are focusing on solving the problem of limiting the model parameter space such that accurate solutions can potentially be found. This is an important problem because solving for optimal parameters in nonlinear optimization requires defining a feasible region or the set of parameters to search over. If the feasible region is too large, estimating optimal parameters often fails, a particularly acute problem with sparse data. To address this problem and achieve accurate, personalized prediction, we must guide optimization algorithms using ML toward effective solutions.
As a baseline, we estimated the model for each patient by using only their data over 15 days after CAR T-cell infusion. This window was selected because ALC measurements are considered reliable surrogates for CAR T-cell expansion only during this early phase, due to the transient effects of lymphodepletion.81,83 Beyond this period, the relationship between ALC and CAR T-cell levels becomes less predictable. Although our long-term goal is to forecast tumor burden and treatment outcomes over extended time horizons, this study focuses on the early phase to demonstrate the feasibility of personalized, hybrid modeling approaches. We followed the standard optimization approach: estimating parameters by minimizing the least squares error with constrained optimization, where we defined the feasible region in the standard way (no ML). Without limiting the feasible region, sparse data and the complexity of the underlying system resulted in poor parameter estimation reflected by the model output (blue curve) and data (red circles) in the left-hand panels of Figure 2. We probed the impact of guiding the optimization algorithm using a combination of clinical and computational insight to mitigate this issue by searching parameters over a narrower feasible region, which must be identified for each patient before personalized model estimation. In these plots, the blue crosses represent pointwise simulations, model outputs evaluated only at the time points where data were available, while the blue curve represents the continuous simulation over the full time window. Pointwise and continuous values are identical at data time points; we include both for clarity in comparing observed data and model fit. We then generalized the method for computing a personalized feasible region identification using ML, hybridizing MM with ML. We took the following steps for this HM approach:
Figure 2.
We show data and model output for four patients estimated using the original (panels A, C, E, and G) and personalized (panels B, D, F, and H) feasible regions for two patients. In each plot, the red circles show data, the blue crosses show model output at the time of data points, and the blue curve shows the continuous model output. The term continuous simulation refers to evaluating the model across a fine time grid, independent of when the actual data were collected, whereas pointwise simulation refers to model outputs evaluated only at the time points corresponding to the observed data. As such, pointwise simulation values are identical to the continuous simulation values at those specific time points. We included the pointwise simulation to facilitate visual comparison between the model output and the observed data. Model parameters were estimated by minimizing the least squares distance between the pointwise simulation and the observed data. The visual overlap between pointwise and continuous simulation at the data points is complete by design; their difference lies primarily in presentation and purpose: the continuous curve helps visualize the model’s dynamic behavior over time, while the pointwise markers aid in directly comparing model predictions to available measurements. The plots show that using personalized feasible regions significantly improved model fit for all patients.
Based on clinical and computational insights, we constructed the search space for each parameter by combining literature-reported values, simulation results, and expert clinical input. For instance, the tumor growth rate (1/day) varies widely across cancer types depending on aggressiveness, with literature suggesting a range from 0.001 to 0.5 as broadly representative.80 We found the range [0.01,0.1] to be appropriate for our cohort of 13 patients, balancing biological realism with sufficient flexibility for patient-specific variation. This approach was applied to other parameters to ensure that the model remained physiologically and clinically grounded. Notably, simulations revealed substantial variability in the parameter (CAR T-cell killing rate) across patients. To obtain reasonable model fits, we found that the model required patient-specific feasible range for , while keeping the feasible ranges for all other parameters fixed. However, the selection of the feasible region that results in the best model fit requires automation to be practical in real-world clinical settings.
We estimated the model using each of these feasible regions separately for each patient.
For each patient, we automated the model selection by choosing the model resulting in the smallest mean squared error (MSE) between CAR T-cell count data and model output. We call the feasible region resulting in the optimal model the personalized feasible region. The automated selection of the optimal model at this step is the ML piece of this hybrid methodology.
What is gained by taking an interdisciplinary, MM-ML hybridized approach
To demonstrate the gains of the HM approach, we will present in-depth results from four randomly selected patients (Patients 3, 4, 7, and 13), who are also representative of the overall group of 13. To pull apart the HM gains, we use the root mean squared error (RMSE) computed using CAR T-cell count data (obtained from ALC measurements) and model outputs estimated using the original and personalized feasible regions, and the percentage improvement in RMSE when the HM approach is used compared to using the MM alone. These computational results for all 13 are shown in Table 2. In Table 2, we observe that the personalized feasible regions obtained automatically by hybridizing MM with ML reduce the estimation error for all patients except one. Notably, we did not conduct any ML (alone) estimation with these data because the data sets were too small and led to model estimates that were severely overfit, unreliable, or inestimable, depending on the method chosen. The HM approach demonstrates more accurate performance compared to MM and ML used alone. As an aside, patient 8 has a larger error compared to all the other patients. A likely source of this error is that this patient was delivered a smaller (one order of magnitude smaller) dose of CAR T-cells than all the other patients. Surely, there are other sources of estimation error, and more work is required to develop methods for discovering and understanding the impact of this difference on the model estimation error. Figure 2 shows the model outputs obtained by the original and personalized feasible regions for the four patients selected to show the model’s ability to represent varying system dynamics. We observe similar changes in the estimation results for all patients. The plots on the left-hand panels of Figure 2 show that using the original feasible region with sparse data results in estimates not reflecting the true dynamics. However, the true dynamics can be obtained by constraining the optimization algorithm in a patient-specific way, as shown on the right-hand panels. Figure 2 also shows that the model can represent varying system dynamics depending on the estimated parameters, eg, slower response to therapy (panel B), a rapid response resulting in eradication of cancer cells (panel D), initial response followed by resistance (panel F), and delayed response to therapy (panel H). This example demonstrates the substantial prediction accuracy gains that could be achieved when hybridizing MM with ML in the context of sparse data. Using more sophisticated ML techniques with the investigation of additional feasible regions once larger data sets are available could enhance the model fits shown in Figure 2. It is important to note that here, our goal was to present how HM can improve model fits and potentially prediction accuracy. Complete internal and external model validation requires a less limited data set with a larger population, which is a limitation of the current study that will be addressed in future studies.
Table 2.
We show the root mean squared error (RMSE) for each patient with model output computed by the original and personalized feasible regions and the percentage improvement in the RMSE when the hybrid modeling is used.a
| Patient | RMSE with original feasible region | RMSE with personalized feasible region | % improvement in RMSE |
|---|---|---|---|
| 1 | 64.80 | ||
| 2 | 69.42 | ||
| 3 | 74.14 | ||
| 4 | 78.35 | ||
| 5 | 36.22 | ||
| 6 | 55.08 | ||
| 7 | 90.42 | ||
| 8 | 26.69 | ||
| 9 | 67.94 | ||
| 10 | 70.69 | ||
| 11 | 80.81 | ||
| 12 | 40.12 | ||
| 13 | 42.35 |
The unit for the RMSE is CAR T-cell count.
Discussion
Limitations
A key limitation of this work is the small cohort size (13 patients), which constrains the generalizability of the specific findings and parameter estimates. The feasible regions identified were tailored to this limited group and may not directly apply to larger or more diverse patient populations. However, the methodological pipeline was designed with scalability in mind. The automated selection process is capable of adaptively identifying patient-specific feasible regions and optimal parameter fits, which supports broader application to larger cohorts in future studies. Expanding the approach to more diverse datasets will be important for validating its robustness and clinical utility.
Another limitation is that it does not account for the variability in timing between the last available TMTV measurement and the CAR T-cell infusion. We used the most recent pre-infusion TMTV value as a surrogate for tumor burden at the time of therapy, regardless of the actual time gap. This simplification may affect the accuracy of model fits, particularly for patients with rapidly proliferating disease, where tumor burden can change meaningfully even within short time frames. Incorporating this timing difference into the modeling, such as by forward-simulating tumor growth using proliferation markers like Ki67, could enhance the accuracy of tumor burden estimation and improve the clinical relevance of the approach in decision support settings. We view this as an important direction for future refinement.
Challenges of integrating hybrid modeling into clinical decision support systems
HM has the potential to enhance clinical decision-making by integrating various data sources and leveraging the complementary strengths of ML and MM methods. However, the integration of these models into clinical workflows requires addressing several key considerations. First, prior to incorporation into electronic health record (EHR) systems for clinical decision support (CDS), these models must undergo rigorous validation to ensure reliability and accuracy. Equally important is the way model outputs are presented to clinicians, ensuring the information is clear, actionable, and relevant to support informed decision-making. This requires careful consideration throughout the entire process—from model development to the implementation of a CDS tool—through collaboration with experts in human-computer interaction (HCI). Furthermore, the end users of these CDS tools need to be trained to interpret model-based recommendations and provide feedback for continuous system refinement, similar to what is done when new laboratory measurements become available. The successful deployment of reliable and actionable model-based CDS tools will require collaboration among interdisciplinary teams, including experts in healthcare, data science, HCI, and regulatory compliance, to address these various challenges effectively.
Data privacy and computational feasibility in clinical practice implementation
The hybrid modeling example we present here is computationally efficient, using minimal resources and individual patient data for personalized predictions. The latter feature ensures privacy by keeping protected health information (PHI) within the secure EHR system. This approach’s low computational demands allow for easy integration into existing workflows without significant changes or additional resources. It addresses two critical challenges in leveraging EHR data for computational modeling: it enables seamless incorporation into the EHR system and maintains data privacy by preventing PHI from leaving the secure environment, ensuring compliance with privacy regulations. Overall, it offers a practical solution for integrating advanced models into healthcare without compromising data security.
Enhancing data integration, scalability, and Real-World implementation with hybrid modeling
Hybrid modeling approaches can enhance data integration, scalability, and real-world implementation. For example, the methodological pipeline we develop here facilitates the incorporation of diverse data sources—clinical, genomic, and treatment-related—enabling accurate, personalized predictions. Moreover, its computational efficiency allows scalability to larger populations and diverse medical contexts, making it suitable for broader clinical applications without increasing complexity. Additionally, this example approach preserves data privacy by keeping sensitive information within secure EHR systems, and its simplicity ensures seamless integration into existing clinical workflows, addressing common implementation challenges.
Positioning within the broader informatics landscape
The methodological pipeline we present here is an example of how hybridizing MM and ML extends the framework of predictive modeling in oncology to handle data sparsity and improve prediction accuracy. This approach complements existing informatics methods by addressing key challenges in personalized treatment, including data privacy and computational tractability. Additionally, our hybrid modeling approach aligns with trends in other domains where similar issues of sparse data and the need for personalized predictions exist. For example, hybrid modeling has shown promise in healthcare domains such as ICU mortality prediction62 and risk assessment in stroke patients.63 By situating our methodology within these established frameworks, we demonstrate its potential to enhance predictive modeling efforts not only in oncology but also in other healthcare settings where data limitations are a significant challenge. This positions our approach as both a novel and complementary advancement in the field of medical informatics.
Generalizability to other medical settings
Although the hybrid modeling example we present here was developed for personalized prediction of CAR T-cell therapy outcomes in LBCL patients, the methodological pipeline is generalizable to other medical contexts. Broadly, the goal is to use clinical insight and ML to reduce the model estimation space—the feasible region—such that model estimation is possible with minimal data, a common challenge across many medical settings.28,84,85 Our pathway to address this goal is an interdisciplinary pipeline with three steps. The first step surfaces, discovers, and uses clinical insight and thought processes to identify the potential feasible regions, effectively creating the outlines of an algorithm. The second step is to mathematize this clinical reasoning process into an ML form that can be automated to select the most appropriate, narrowest feasible region for each patient. The third step is the development of the hybridized ML-MM algorithm to forecast treatment outcomes. While different diseases require different physiological models, this framework provides a systematic method to identify personalized feasible regions for optimal parameter estimation and model fitting across diverse clinical settings.
Conclusion
The development and use of computational modeling for clinical decision support in precision oncology demands overcoming both computational and social challenges, particularly in building and using interdisciplinary teams. In our example, data scarcity and sparsity rendered the use of ML and MM approaches alone unstable and inaccurate. An interdisciplinary team was necessary to hybridize MM with ML, guided by clinical insights, to develop an algorithm to achieve accurate and personalized model fits. Understanding the specific needs of clinical and computational fields required extensive discussions and a thorough literature review by all team members. Our conclusion is that building effective interdisciplinary teams requires dedication from team members to understand field-specific needs for the development of useful clinical decision support tools that can improve cancer treatment outcomes. Moreover, a deep understanding of the clinical context is crucial to selecting or developing the right computational approaches, addressing field-specific limitations, and enabling the use of computational modes in precision oncology and other medical fields.
Acknowledgments
The authors acknowledge discussions with Matthew Levine, PhD, about the conceptualization of the HM framework.
Contributor Information
Melike Sirlanci, Department of Biomedical Informatics, University of Colorado Anschutz Medical Campus, Aurora, CO 80045, United States; Department of Applied Mathematics, University of Colorado Boulder, Boulder, CO 80309, United States.
David Albers, Department of Biomedical Informatics, University of Colorado Anschutz Medical Campus, Aurora, CO 80045, United States; Department of Biomedical Informatics, Columbia University, New York, NY 10032, United States; Department of Bioengineering, University of Colorado Denver, Aurora, CO 80045, United States; Department of Biostatistics & Informatics, Colorado School of Public Health, Aurora, CO 80045, United States.
Jennifer Kwak, Department of Radiology, University of Colorado Anschutz Medical Campus, Aurora, CO 80045, United States.
Clayton Smith, Division of Hematology, Department of Medicine, University of Colorado Anschutz Medical Campus, Aurora, CO 80045, United States; CU Innovations, University of Colorado Anschutz Medical Campus, Aurora, CO 80045, United States; OncoVerity, Inc., Aurora, CO 80045, United States.
Tellen D Bennett, Department of Biomedical Informatics, University of Colorado Anschutz Medical Campus, Aurora, CO 80045, United States; Department of Pediatrics (Critical Care Medicine), University of Colorado Anschutz Medical Campus, Aurora, CO 80045, United States.
Steven M Bair, Division of Hematology, Department of Medicine, University of Colorado Anschutz Medical Campus, Aurora, CO 80045, United States.
Author contributions
Melike Sirlanci (Conceptualization, Methodology, Software, Visualization, Writing—original draft, Writing—review & editing), David Albers (Conceptualization, Methodology, Supervision, Writing—review & editing), Jennifer Kwak (Data curation), Clayton Smith (Supervision, Writing—review & editing), Tellen D Bennett (Supervision, Writing—review & editing), and Steven M. Bair (Conceptualization, Methodology, Visualization, Writing—original draft, Writing—review & editing)
Funding
This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.
Conflicts of interest
None declared.
Data availability
The data underlying this article were provided by the University of Colorado Health Cancer Center under license/by permission. Data will be shared on request to the corresponding author with the permission of the University of Colorado Health Cancer Center.
References
- 1. Mitani AA, Haneuse S. Small data challenges of studying rare diseases. JAMA Netw Open. 2020;3:e201965. [DOI] [PubMed] [Google Scholar]
- 2. Mandreoli F, Ferrari D, Guidetti V, Motta F, Missier P. Real-world data mining meets clinical practice: research challenges and perspective. Front Big Data. 2022;5:1021621. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 3. Bao R, Hutson A, Madabhushi A, et al. Ten challenges and opportunities in computational immuno-oncology. J Immunother Cancer. 2024;12:e009721. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 4. Butner JD, Dogra P, Chung C, et al. Mathematical modeling of cancer immunotherapy for personalized clinical translation. Nat Comput Sci. 2022;2:785-796. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 5. Mongeon B, Hébert-Doutreloux J, Surendran A, et al. Spatial computational modelling illuminates the role of the tumour microenvironment for treating glioblastoma with immunotherapies. NPJ Syst Biol Appl. 2024;10:91. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 6. Mortazavi SMA, Firoozabadi B. Towards a framework for predicting immunotherapy outcome: a hybrid multiscale mathematical model of immune response to vascular tumor growth. Biomech Model Mechanobiol. 2024;23:2243-2264. [DOI] [PubMed] [Google Scholar]
- 7. Tao W, Sun Q, Xu B, Wang R. Towards the prediction of responses to cancer immunotherapy: a multi-omics review. Life. 2025;15:283. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 8. Keener JP, Sneyd J. Mathematical Physiology 1: Cellular Physiology. Springer; 2009. 10.1007/978-0-387-75847-3 [DOI] [Google Scholar]
- 9. Keener J, Sneyd J, eds. Mathematical Physiology: II: Systems Physiology. Springer New York; 2009. 10.1007/978-0-387-79388-7 [DOI] [Google Scholar]
- 10. Albers DJ, Levine ME, Stuart A, et al. Mechanistic machine learning: how data assimilation leverages physiologic knowledge using Bayesian inference to forecast the future, infer the present, and phenotype. J Am Med Inform Assoc. 2018;25:1392-1401. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 11. Stuart A, Zygalakis K. Data Assimilation: A Mathematical Introduction. Oak Ridge National Lab. (ORNL; ); 2015. [Google Scholar]
- 12. Asch M. Mathematics in Industry, A Toolbox for Digital Twins: From Model-Based to Data-Driven, Toolbox for Digital Twins: From Model-Based to Data-Driven. SIAM-Society for Industrial and Applied Mathematics; 2022. 10.1137/1.9781611976977 [DOI]
- 13. Hastie T, Friedman J, Tibshirani R. The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Vol. 2. Springer; 2001. 10.1007/978-0-387-21606-5 [DOI]
- 14. Kalman RE. A new approach to linear filtering and prediction problems. J Basic Eng-T ASME. 1960;82:35-45. [Google Scholar]
- 15. Asch M, Bocquet M, Nodet M. Data Assimilation: Methods, Algorithms, and Applications. SIAM-Society for Industrial and Applied Mathematics; 2016. [Google Scholar]
- 16. Strang G. Linear Algebra and Learning from Data. Wellesley Cambridge Press; 2019. [Google Scholar]
- 17. Brooks S, Gelman A, Jones G, Meng XL. eds. Handbook of Markov Chain Monte Carlo. CRC Press; 2011. [Google Scholar]
- 18. Baker RE, Peña J-M, Jayamohan J, Jérusalem A. Mechanistic models versus machine learning, a fight worth fighting for the biological community? Biol Lett. 2018;14:20170660. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 19. Gherman IM, Abdallah ZS, Pang W, et al. Bridging the gap between mechanistic biological models and machine learning surrogates. PLoS Comput Biol. 2023;19:e1010988. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 20. Yazdani A, Lu L, Raissi M, Karniadakis GE. Systems biology informed deep learning for inferring parameters and hidden dynamics. PLoS Comput Biol. 2020;16:e1007575. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 21. Miller AC, Foti NJ, Fox EB. Breiman’s two cultures: you don’t have to choose sides. Observational Stud. 2021;7:161-169. [Google Scholar]
- 22. Miller AC, Foti NJ, Fox E. Learning insulin-glucose dynamics in the wild. In: Machine learning for healthcare conference. PMLR; 2020 Sep 18:172–197.
- 23. Nicolò C, Périer C, Prague M, et al. Machine learning and mechanistic modeling for prediction of metastatic relapse in early-stage breast cancer. JCO Clin Cancer Inform. 2020;4:259-274. [DOI] [PubMed] [Google Scholar]
- 24. Alber M, Buganza Tepole A, Cannon WR, et al. Integrating machine learning and multiscale modeling—perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences. NPJ Digit Med. 2019;2:115. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 25. Axenie C, Kurz D. Chimera: Combining mechanistic models and machine learning for personalized chemotherapy and surgery sequencing in breast cancer. In: International Symposium on Mathematical and Computational Oncology. Springer International Publishing; 2020 Oct 8:13–24.
- 26. Hussain ZM, Krishnan RG, Sontag D. Neural pharmacodynamic state space modeling. In: International Conference on Machine Learning. PMLR; 2021 Jul 1:4500–4510. [Google Scholar]
- 27. Levine M, Stuart A. A framework for machine learning of model error in dynamical systems. Comm Amer Math So. 2022;2:283–344. [Google Scholar]
- 28. Wang Y, Stroh JN, Hripcsak G, et al. A methodology of phenotyping ICU patients from EHR data: high-fidelity, personalized, and interpretable phenotypes estimation. J Biomed Inform. 2023;148:104547. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 29. Tseng Y-J, Wang H-Y, Lin T-W, et al. Development of a machine learning model for survival risk stratification of patients with advanced oral cancer. JAMA Netw Open. 2020;3:e2011768. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 30. Boehm KM, Aherne EA, Ellenson L, et al. ; MSK MIND Consortium. Multimodal data integration using machine learning improves risk stratification of high-grade serous ovarian cancer. Nat. Cancer. 2022;3:723-733. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 31. Höhn J, Krieghoff-Henning E, Wies C, et al. Colorectal cancer risk stratification on histological slides based on survival curves predicted by deep learning. NPJ Precis Oncol. 2023;7:98. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 32. Langberg GSRE, Nygård JF, Gogineni VC, et al. Towards a data-driven system for personalized cervical cancer risk stratification. Sci Rep. 2022;12:12083. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 33. Benzekry S, Sentis C, Coze C, Tessonnier L, André N. Development and validation of a prediction model of overall survival in high-risk neuroblastoma using mechanistic modeling of metastasis. JCO Clin Cancer Inform. 2021;5:81-90. [DOI] [PubMed] [Google Scholar]
- 34. L’Hostis A, et al. Knowledge-based mechanistic modeling accurately predicts disease progression with gefitinib in EGFR-mutant lung adenocarcinoma. NPJ Syst Biol Appl. 2023;9:37. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 35. L’Imperio V, Wulczyn E, Plass M, et al. Pathologist validation of a machine learning–derived feature for colon cancer risk stratification. JAMA Netw Open. 2023;6:e2254891. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 36. Rana SP, Dey M, Tiberi G, et al. Machine learning approaches for automated lesion detection in microwave breast imaging clinical data. Sci Rep. 2019;9:10510. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 37. Yala A, Lehman C, Schuster T, Portnoi T, Barzilay R. A deep learning mammography-based model for improved breast cancer risk prediction. Radiology. 2019;292:60-66. [DOI] [PubMed] [Google Scholar]
- 38. Shipp MA, Ross KN, Tamayo P, et al. Diffuse large B-cell lymphoma outcome prediction by gene-expression profiling and supervised machine learning. Nat Med. 2002;8:68-74. [DOI] [PubMed] [Google Scholar]
- 39. Nardini C. Machine learning in oncology: a review. Ecancermedicalscience. 2020;14:1065. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 40. Xu Y, Hosny A, Zeleznik R, et al. Deep learning predicts lung cancer treatment response from serial medical imaging. Clin Cancer Res. 2019;25:3266-3275. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 41. Laleh NG, et al. Classical mathematical models for prediction of response to chemotherapy and immunotherapy. PLoS Comput. Biol. 2022;18:e1009822. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 42. Adam G, et al. Machine learning approaches to drug response prediction: challenges and recent progress. NPJ Precis Oncol. 2020;4:19. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 43. Michor F, Beal K. Improving cancer treatment via mathematical modeling: surmounting the challenges is worth the effort. Cell. 2015;163:1059-1063. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 44. Dannenfelser R, Allen GM, VanderSluis B, et al. Discriminatory power of combinatorial antigen recognition in cancer T cell therapies. Cell Syst. 2020;11:215-228.e5. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 45. Brummer AB, Xella A, Woodall R, et al. Data driven model discovery and interpretation for CAR T-cell killing using sparse identification and latent variables. Front Immunol. 2023;14:1115536. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 46. Owens K, Bozic I. Modeling CAR T-cell therapy with patient preconditioning. Bull Math Biol. 2021;83:42. [DOI] [PubMed] [Google Scholar]
- 47. Salem AM, Mugundu GM, Singh AP. Development of a multiscale mechanistic modeling framework integrating differential cellular kinetics of CAR T‐cell subsets and immunophenotypes in cancer patients. CPT Pharmacomet Syst Pharmacol. 2023;12:1285-1304. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 48. Cess CG, Finley SD. Data-driven analysis of a mechanistic model of CAR T cell signaling predicts effects of cell-to-cell heterogeneity. J Theor Biol. 2020;489:110125. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 49. Yiu HH, Graham AL, Stengel RF. Dynamics of a cytokine storm. PLoS One. 2012;7:e45027. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 50. Pilié PG, LoRusso PM, Yap TA. Precision medicine: progress, pitfalls, and promises. Mol Cancer Ther. 2017;16:2641-2644. [DOI] [PubMed] [Google Scholar]
- 51. Tourneau CL, et al. Molecularly targeted therapy based on tumour molecular profiling versus conventional therapy for advanced cancer (SHIVA): a multicentre, open-label, proof-of-concept, randomised, controlled phase 2 trial. Lancet Oncol. 2015;16:1324-1334. [DOI] [PubMed] [Google Scholar]
- 52. Salas-Vega S, Iliopoulos O, Mossialos E. Assessment of overall survival, quality of life, and safety benefits associated with new cancer medicines. JAMA Oncol. 2017;3:382–390. [DOI] [PubMed] [Google Scholar]
- 53. Boroughs AC, Larson RC, Marjanovic ND, et al. A distinct transcriptional program in human CAR T cells bearing the 4-1BB signaling domain revealed by scRNA-Seq. Mol Ther. 2020;28:2577-2592. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 54. Sheih A, Voillet V, Hanafi L-A, et al. Clonal kinetics and single-cell transcriptional profiling of CAR-T cells in patients undergoing CD19 CAR-T immunotherapy. Nat Commun. 2020;11:219. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 55. Ramakrishna S, Shah NN. Using single-cell analysis to predict CAR T cell outcomes. Nat Med. 2020;26:1813-1814. [DOI] [PubMed] [Google Scholar]
- 56. Boulch M, Cazaux M, Loe-Mie Y, et al. A cross-talk between CAR T cell subsets and the tumor microenvironment is essential for sustained cytotoxic activity. Sci Immunol. 2021;6:eabd4344. [DOI] [PubMed] [Google Scholar]
- 57. Chen P-H, Lipschitz M, Weirather JL, et al. Activation of CAR and non-CAR T cells within the tumor microenvironment following CAR T-cell therapy. JCI Insight. 2020;5:e134612. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 58. Parikh RB, Obermeyer Z, Navathe AS. Regulation of predictive analytics in medicine. Science. 2019;363:810-812. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 59. Mitchell EG, Tabak EG, Levine ME, Mamykina L, Albers DJ. Enabling personalized decision support with patient-generated data and attributable components. J Biomed Inform. 2021;113:103639. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 60. Luo Y. Evaluating the state of the art in missing data imputation for clinical data. Brief. Bioinform. 2021;23:bbab489. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 61. Liu M, Li S, Yuan H, et al. Handling missing values in healthcare data: a systematic review of deep learning-based imputation techniques. Artif Intell Med. 2023;142:102587. [DOI] [PubMed] [Google Scholar]
- 62. Samadi ME, Guzman-Maldonado J, Nikulina K, et al. A hybrid modeling framework for generalizable and interpretable predictions of ICU mortality across multiple hospitals. Sci Rep. 2024;14:5725. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 63. Herrgårdh T, Madai VI, Kelleher JD, et al. Hybrid modelling for stroke care: review and suggestions of new approaches for risk assessment and simulation of scenarios. Neuroimage Clin. 2021;31:102694. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 64. Miller AC, Foti NJ, Fox E. Learning insulin–glucose dynamics in the wild. Proc Mach Learn Res. 2020;126:1-25. [Google Scholar]
- 65. Levine ME. Machine Learning and Data Assimilation for Blending Incomplete Models and Noisy Data. California Institute of Technology; 2023. [Google Scholar]
- 66. Albers DJ, Hripcsak G, Mamykina L, Sirlanci M, Tabak EG. A new approach to data assimilation initialization problems with sparse data using multiple cost functions. arXiv, arXiv:2411.01786, 2024, preprint: not peer reviewed.
- 67. Khanna A, Schaffer V, Gürsoy G, Gerstein M. Privacy-preserving model training for disease prediction using federated learning with differential privacy. Annu Int Conf IEEE Eng Med Biol Soc. 2022;2022:1358-1361. [DOI] [PubMed] [Google Scholar]
- 68. Elhussein A, Gürsoy G. Privacy-preserving patient clustering for personalized federated learning. Proc Mach Learn Res. 2023;219:150-166. [PMC free article] [PubMed] [Google Scholar]
- 69. Elhussein A, et al. A generalizable physiological model for detection of Delayed Cerebral Ischemia using Federated Learning. 2023 IEEE Int Conf Bioinform Biomed. (BIBM). 2023;00:1886-1889. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 70. Chowdhury A, Kassem H, Padoy N, Umeton R, Karargyris A. Brainlesion: Glioma, Multiple Sclerosis, Stroke and Traumatic Brain Injuries, 7th International Workshop, BrainLes 2021, Held in Conjunction with MICCAI 2021, Virtual Event, September 27, 2021, Revised Selected Papers, Part I. Lect. Notes Comput. Sci. 2022; 3–24. 10.1007/978-3-031-08999-2_1 [DOI]
- 71. Pati S, Baid U, Edwards B, et al. Federated learning enables big data for rare cancer boundary detection. Nat Commun. 2022;13:7346. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 72. Terrail JOd, et al. Federated learning for predicting histological response to neoadjuvant chemotherapy in triple-negative breast cancer. Nat Med. 2023;29:135-146. [DOI] [PubMed] [Google Scholar]
- 73. Rajendran S, Obeid JS, Binol H, et al. Cloud-based federated learning implementation across medical centers. JCO Clin Cancer Inform. 2021;5:1. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 74. Feller DJ, Burgermaster M, Levine ME, et al. A visual analytics approach for pattern-recognition in patient-generated data. J Am Med Inform Assoc. 2018;25:1366-1374. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 75. Srilanci M, Albers D, Hripcsak G. Data assimilation for personalized treatment strategies: glycemic management in the intensive care unit as an illustrative case. SIAM News. 2021. https://sinews.siam.org/Details-Page/data-assimilation-for-personalized-treatment-strategies
- 76. Albers D, Behn CD, Hripcsak G. Data assimilation in medicine. SIAM News. 2020. https://sinews.siam.org/Details-Page/data-assimilation-in-medicine
- 77. SEER. SEER Cancer Stat Facts—DLBCL. 2023. https://seer.cancer.gov/statfacts/html/dlbcl.html
- 78. Crump M, Neelapu SS, Farooq U, et al. Outcomes in refractory diffuse large B-cell lymphoma: results from the international SCHOLAR-1 study. Blood. 2017;130:1800-1808. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 79. Sermer D, Batlevi C, Palomba ML, et al. Outcomes in patients with DLBCL treated with commercial CAR T cells compared with alternate therapies. Blood Adv. 2020;4:4669-4678. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 80. Roesch K, Hasenclever D, Scholz M. Modelling lymphoma therapy and outcome. Bull Math Biol. 2014;76:401-430. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 81. Faude S, Wei J, Muralidharan K, et al. Absolute lymphocyte count proliferation kinetics after CAR T-cell infusion impact response and relapse. Blood Adv. 2021;5:2128-2136. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 82. Sahoo P, Yang X, Abler D, et al. Mathematical deconvolution of CAR T-cell proliferation and exhaustion from real-time killing assay data. J R Soc Interface. 2020;17:20190734. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 83. Saldarriaga MM, et al. Absolute lymphocyte count after BCMA CAR-T therapy is a predictor of response and outcomes in relapsed multiple myeloma. Blood Adv. 2024;8:3859-3869. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 84. Albers D, Sirlanci M, Levine M, et al. Interpretable physiological forecasting in the ICU using constrained data assimilation and electronic health record data. J Biomed Inform. 2023;145:104477. [DOI] [PubMed] [Google Scholar]
- 85. Albers DJ, Blancquart P-A, Levine ME, Seylabi EE, Stuart A. Ensemble Kalman methods with constraints. Inverse Probl. 2019;35:095007. [DOI] [PMC free article] [PubMed] [Google Scholar]
Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Data Availability Statement
The data underlying this article were provided by the University of Colorado Health Cancer Center under license/by permission. Data will be shared on request to the corresponding author with the permission of the University of Colorado Health Cancer Center.


