📄 systems biology

The trade-off between parsimony and model complexity for understanding biomedical mechanisms from mathematical models

This paper demonstrates through ovarian cancer modeling that while statistical metrics like AIC and BIC help balance goodness-of-fit with parsimony, selecting the most biologically insightful model requires a deliberate trade-off between statistical simplicity and the inclusion of essential physiological mechanisms to avoid unidentifiability and overfitting.

Original authors: Lamirande, P., Brunetti, M., Easlick, T., Beigmohammadi, F., Craig, M.

Published 2026-09-01

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Lamirande, P., Brunetti, M., Easlick, T., Beigmohammadi, F., Craig, M.

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

In the complex landscape of cancer research, scientists often face a difficult choice: build a simple map that is easy to read but misses important terrain, or construct a detailed, intricate map that captures every hill and valley but becomes so complicated it is hard to use. This tension lies at the heart of mathematical modeling, a field where researchers use equations to simulate how diseases grow and how treatments might stop them. The goal is not merely to draw a line that fits past data points, but to understand the hidden biological machinery driving those points. When studying ovarian cancer, a disease that is often diagnosed late and becomes resistant to standard chemotherapy, understanding these mechanisms is a matter of life and death. Researchers must decide how much biological detail to include in their models. Too little detail, and the model cannot explain why a treatment works for one patient but fails for another. Too much detail, and the model becomes a tangled web of guesses that cannot be trusted. The challenge is finding the sweet spot where the model is simple enough to be reliable, yet complex enough to reveal the true secrets of the disease.

A team of researchers at the Université de Montréal and CHU Sainte-Justine Azrieli Research Centre set out to navigate this challenge using two distinct mouse models of high-grade serous ovarian cancer. One model, known as MP, represents tumors that are proficient in a specific DNA repair mechanism, while the other, MPB1, represents tumors that lack this repair ability. These two types of tumors respond very differently to treatment, particularly to a common chemotherapy drug called cisplatin and a newer type of therapy known as immune checkpoint blockade, which helps the body's own immune system fight cancer. The researchers built a hierarchy of mathematical models, starting with the simplest possible description of tumor growth and gradually adding layers of biological complexity. They began with a basic model that simply described how a tumor expands until it hits a size limit. They then added a layer to describe how the chemotherapy drug moves through the body and kills cells. Finally, they constructed the most complex version, which included the interactions between the tumor, the immune system, and the drugs, tracking how natural killer cells and T cells move in and out of the tumor environment.

The researchers found that the simplest model, while good at predicting the overall size of the tumor over time, failed to explain the biological reasons behind the differences between the two mouse types. When they looked at the numbers generated by this simple model, the results were confusing; the model suggested that the drug changed the tumor's growth rate in one mouse and its maximum size in the other, but it could not clearly distinguish between these two effects. However, when they switched to the more complex model that included the drug's specific mechanics, a clear picture emerged. The complex model revealed that the MPB1 tumors were roughly eight times more sensitive to the killing power of cisplatin than the MP tumors. This specific insight, which the simple model obscured, showed that the difference in treatment success was not just a matter of growth speed, but a fundamental difference in how the drug attacked the cancer cells.

The story became even more revealing when the researchers added the immune system to the equation. In the simplest view, the immune system is just another factor that slows down tumor growth. But by modeling the specific interactions between immune cells and the tumor, the researchers discovered that the two mouse types suppress their immune defenses in very different ways. The MP tumors were found to be much more effective at disabling the immune cells that try to attack them, essentially blunting the body's natural defense. In contrast, the MPB1 tumors were less successful at this suppression. When the researchers simulated the use of immune checkpoint blockade therapy, the complex model predicted that this treatment would work much better on the MPB1 tumors. It did so by specifically reducing the rate at which the tumor disabled the immune cells, a mechanism that the simple model could not detect. The model showed that for the MPB1 tumors, the therapy successfully reawakened the immune system, leading to a significant drop in the tumor's ability to hide from attack.

Perhaps the most striking finding came when the researchers combined the chemotherapy and the immune therapy in their simulations. The complex model predicted that the superior response seen in the MPB1 mice was due to a powerful one-two punch: the tumor was not only more sensitive to the direct killing power of the drug, but the drug also triggered a strong recruitment of immune cells to the tumor site. In the MP mice, this immune recruitment was virtually non-existent. The model suggested that the MPB1 tumors benefited from both the drug killing cells directly and the drug helping the immune system find and destroy the rest. This dual mechanism explained why the combination therapy was so effective in one group but not the other. The researchers noted that while the simplest model often provided a better statistical fit to the raw data, it offered no insight into these underlying causes. The more complex models, despite being harder to build and requiring more data to support them, provided the biological clarity needed to understand why the treatments worked.

The study concludes that relying solely on statistical measures to choose the "best" model can be misleading if the goal is to understand biology. A model that fits the data perfectly might still be biologically wrong if it ignores key mechanisms. The researchers demonstrated that by carefully balancing simplicity with the necessary biological detail, they could uncover specific reasons for treatment success or failure. They found that the HR-deficient MPB1 tumors, which mimic a specific type of human ovarian cancer, respond better because they are inherently more vulnerable to the drug and are less able to shut down the immune system. This understanding, derived from a model that explicitly tracked immune cells and drug effects, offers a clearer roadmap for future research than a simple curve-fitting exercise ever could. The work underscores that in the quest to understand cancer, sometimes the most useful map is the one that shows the most detail, provided it is built on a foundation of reliable data.

Technical Summary: The Trade-off Between Parsimony and Model Complexity in Biomedical Mechanisms

Problem Statement
Mechanistic mathematical models are essential for elucidating biological mechanisms, such as tumor growth and treatment response, yet they face a fundamental tension between biological realism and model tractability. While statistical metrics like the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) are standard tools for selecting the most parsimonious model by balancing goodness-of-fit against complexity, an over-reliance on these metrics can lead to the selection of models that lack sufficient biological insight. Conversely, overly complex models risk overfitting and parameter unidentifiability. This study addresses the challenge of determining the appropriate level of model complexity to capture specific biological mechanisms—specifically in the context of ovarian cancer treatment—without sacrificing the ability to generate testable biological hypotheses.

Methodology
The authors developed a hierarchical framework of mathematical models with increasing biological complexity to describe ovarian cancer growth and response to cisplatin and immune checkpoint blockade (ICB) in two mouse models: MP (homologous recombination [HR]-deficient) and MPB1 (HR-proficient). The modeling hierarchy proceeded as follows:

Simple Growth Models: Standard tumor growth equations (Exponential, Logistic, Gompertz) were fitted to untreated tumor volume data to establish baseline dynamics.
Pharmacokinetic/Pharmacodynamic (PK/PD) Integration: A cisplatin PK/PD model was integrated to explicitly describe drug exposure and its delayed cytotoxic effects on tumor cells, moving beyond simple treatment-specific parameter adjustments.
Tumor-Immune Interactions: The models were extended to include immune dynamics, specifically the interactions between tumor cells, Natural Killer (NK) cells, and CD8+ T cells. This incorporated terms for immune cell recruitment, tumor-mediated inactivation, and immune-mediated killing.
Full Mechanistic Integration: The final model combined the PK/PD framework with the tumor-immune dynamics, adding terms for cisplatin-induced immune recruitment and ICB-mediated reduction in T-cell inactivation.

Parameter estimation was performed using longitudinal tumor volume and flow cytometry data from Pattenholz et al. To manage complexity, many parameters were fixed based on prior literature (e.g., de Pillis et al., Mongeon and Craig), while key biological parameters were estimated from the data. Practical identifiability was assessed using univariate profile likelihood curves, and model selection was evaluated using corrected AIC (AICc) and BIC.

Key Results

Growth Dynamics: Both MP and MPB1 tumors exhibited saturating growth. While statistical criteria (AICc/BIC) favored the Logistic model for MP and Gompertz for MPB1, a common Logistic model was selected to facilitate cross-model comparison.
Cisplatin Sensitivity: Simple logistic models with treatment-specific parameters showed compensatory effects between growth rate and carrying capacity, making biological interpretation difficult. In contrast, the PK/PD-integrated model revealed that MPB1 tumors have an approximately 8-fold higher cisplatin-induced killing rate ( $k_2$ ) compared to MP tumors, quantifying intrinsic sensitivity differences that simpler models obscured.
Immune Dynamics: The tumor-immune extended model successfully recapitulated observed immune cell counts. It estimated that MP tumors exerted significantly stronger tumor-mediated immune suppression (higher inactivation rates $p$ and $q$ ) compared to MPB1 tumors.
Treatment Mechanisms:
- ICB: The mechanistic model revealed that ICB treatment significantly reduced the tumor-mediated inactivation of CD8+ T cells in MPB1 tumors (approx. 5-fold reduction) but had negligible effect in MP tumors. This provided a mechanistic explanation for differential treatment efficacy that simple growth models could not offer, despite the simpler models having better statistical fit scores.
- Combination Therapy: The full integrated model predicted that the superior response of MPB1 tumors to cisplatin is driven by both enhanced intrinsic cytotoxicity and a favorable, cisplatin-induced recruitment of CD8+ T cells. In MP tumors, cisplatin-induced immune recruitment was not practically identifiable, suggesting a lack of this mechanism.
Model Selection vs. Biological Insight: Across all treatment scenarios, statistical criteria (AICc/BIC) consistently favored the simpler logistic growth models over the more complex mechanistic models. However, the authors demonstrate that the complex models provided critical biological insights—such as specific immune recruitment rates and inactivation mechanisms—that were inaccessible to the parsimonious models.

Significance and Claims
The paper argues that while statistical model selection criteria are valuable for descriptive accuracy, they are insufficient when the primary goal is biological understanding and hypothesis generation. The authors claim that:

Context-Dependent Complexity: The "best" model depends on the specific biological question. For describing tumor volume trajectories, simple models may suffice; for understanding why a treatment works (e.g., distinguishing between direct cytotoxicity and immune recruitment), increased complexity is necessary.
Limitations of Parsimony: Relying solely on parsimony can lead to erroneous biological conclusions (e.g., missing the distinct mechanisms of HR-deficient vs. HR-proficient responses) or the "long-branch attraction" problem where distinct mechanisms are conflated.
Utility of Identifiability Analysis: Practical identifiability analysis is crucial for determining whether added complexity is supported by data. In this study, it helped distinguish between MP tumors (where immune recruitment parameters were unidentifiable) and MPB1 tumors (where they were identifiable).
Framework for Mechanistic Insight: The study demonstrates that a hierarchy of models allows researchers to balance tractability with the need to uncover causal links between parameters and observed dynamics, ultimately providing a roadmap for future experimental investigation into differential treatment responses in ovarian cancer.

The authors conclude that model selection should be guided by a balance between statistical performance and the ability of the model to address specific biological questions, rather than relying exclusively on statistical criteria.

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