Luo, Nikolopoulou and Gevertz (Frontiers in Oncology 2022) showed that when a previously validated five-equation model of murine melanoma treated with an oncolytic adenovirus (Ad/4-1BBL/IL-12) plus dendritic-cell injections is refit to individual mice rather than to the population average, the predicted response to a 6-day treatment protocol depends strongly on the fitting methodology: quasi-Monte Carlo and nonlinear mixed-effects fits agree on only 73.75% of mouse-protocol qualitative predictions, because the T-cell activation and cytotoxicity parameters lack practical identifiability from sparse individual tumor-volume data. The paper proposed targeted additional measurements (a single viral-load or T-cell-count measurement near the end of the data window) as a remedy and noted that classifying protocols as fragile or robust relies on generating and simulating a virtual-population cohort (Barish et al. 2017). The open problem is whether such targeted measurements restore identifiability and cross-methodology consistency of individualized fits, and how far the cautionary conclusion extends beyond the single model, dataset and species in which it was observed.

Background

Mathematical models in oncology translate biological hypotheses into ordinary differential equations (ODEs) whose parameters (growth rates, killing rates, immune-stimulation rates) are estimated by fitting model outputs to experimental data. Personalized (individualized) fitting means estimating a separate parameter set for each individual animal or patient, so that the model can be used to predict that individual's response to candidate treatment protocols, rather than fitting only the average trajectory of a cohort.

The source work is Luo, Nikolopoulou and Gevertz (bioRxiv 2021, published as 'From Fitting the Average to Fitting the Individual: A Cautionary Tale for Mathematical Modelers', Frontiers in Oncology 2022). It analyzes a five-equation ODE model with state variables for uninfected tumor volume, oncolytic-virus-infected tumor volume, free virus volume, tumor-targeting T-cell volume, and injected dendritic-cell (DC) volume. An oncolytic virus (OV) is a virus engineered to selectively infect and lyse cancer cells; in the underlying dataset of Huang et al. (Molecular Therapy 2010) the OV is an adenovirus armed with the transgenes 4-1BBL and IL-12, which stimulate tumor-targeting T cells, and it is combined with injections of dendritic cells, antigen-presenting cells that provoke an adaptive antitumor immune response. The model was built and validated in earlier work (Wares et al. 2015; Gevertz & Wares 2018) against the average tumor-volume trajectory of eight mice.

Two fitting methodologies are compared for individualized fitting: quasi-Monte Carlo (QMC), which independently minimizes a cost function for each mouse's tumor-volume data, and nonlinear mixed effects (NLME) fitting, a hierarchical approach in which each mouse's parameters are drawn from a lognormal population distribution. Practical identifiability — whether a parameter can be uniquely recovered from available noisy data, as opposed to structural identifiability, which is a property of the model equations alone — is assessed with the profile likelihood method (Raue et al. 2009): one parameter is fixed over a range of values while all others are refit, and a flat profile signals that very different parameter values fit the data equally well.

The key findings are: (1) fitting to individual mice, the tumor growth rate rr and infectivity β\beta are practically identifiable, but the T-cell activation parameters χD\chi_D (activation by DCs) and cTc_T (stimulation by the virus-released immunostimulants) are not, and the enhanced-cytotoxicity rate ckillc_{kill} has a flat profile indicating local structural unidentifiability; (2) QMC- and NLME-derived parameter sets agree on the qualitative prediction (tumor eradication, volume below 1 mm³ at day 30, versus failure) for only 73.75% of the 160 mouse-protocol combinations across the 20 possible orderings of three OV doses (V) and three DC doses (D) over six days; for the two worst mice (Mouse 1 and Mouse 4) the two methodologies place the fitted parameters sufficiently close to a bifurcation surface that methodology-induced parameter changes yield opposite long-term outcomes, driven by the unobserved virus and T-cell variables; (3) a thought experiment shows that a single additional measurement of viral load or T-cell count at the end of the 30-day data window would go a long way towards reconciling the discrepant fits, but this prediction cannot be tested retrospectively and awaits new experiments; (4) the population-level benefit of hierarchical fitting is unavailable when fitting a single individual, and the identifiability problems it circumvented therefore resurface; (5) whether a dosing protocol is robust or fragile — whether individuals deviating from the average respond qualitatively like the average — is currently decided by generating a virtual population (a large cohort of plausible parameter sets, as in Barish et al. 2017) and simulating each member; and (6) all conclusions rest on one simple model, one immunotherapy combination and one murine melanoma dataset, so their generalizability is unknown.

Problem Statement

The overarching objective, taken from Luo, Nikolopoulou and Gevertz (2022), is to make individualized (per-mouse or per-patient) predictions of the five-equation oncolytic-virus plus dendritic-cell (OV+DC) immunotherapy model trustworthy when only sparse individual data — a single tumor-volume trajectory per individual over about 30 days — are available. Two linked questions constitute the problem, both in service of that objective:

  1. Identifiability restoration via targeted measurements: do the suggested additional measurements — concretely, a single measurement of free-virus (viral load) or tumor-targeting T-cell volume near the end of the data-collection window, or an identifiability-optimized choice of variable and timing — in practice restore practical identifiability of the parameters that are presently unidentifiable from tumor-volume data alone — the T-cell activation parameters χD\chi_D and cTc_T and the enhanced-cytotoxicity rate ckillc_{kill}, whose flat profile reflects a (local) structural unidentifiability with respect to that tumor-volume-only observable and which the added viral-load or T-cell measurements therefore have the potential to resolve — and reconcile the divergent predictions of different fitting methodologies (e.g., quasi-Monte Carlo versus nonlinear mixed-effects) for the same individual? Because the prediction cannot be tested retrospectively on the existing tumor-volume data, resolving this question requires evidence beyond the current Huang et al. murine melanoma Ad/4-1BBL/IL-12 + DC dataset.

  2. Generalizability: does the methodology-sensitivity of individualized predictions (agreement on qualitative eradication-versus-failure outcomes across fitting methods) persist for other models in this class, other cancer types and treatment modalities, dosing schedules, and human patient data — or was the 73.75% agreement observed on this dataset an artifact of one simple model?

The two questions are linked. The first can be resolved only from evidence beyond the existing tumor-volume dataset — new measurements obtained experimentally, or evaluated prospectively on simulated augmented data — as to whether the specified additional measurements make individualized OV+DC model fits identifiable and methodology-robust. The second concerns how far the cautionary conclusion extends: it applies beyond the Luo et al. setting to the extent that at least one of the enumerated axes — another model in this class, another cancer type or treatment modality, another dosing schedule, or human patient data — is covered, and the remaining axes, including human patient data, remain scientifically open.

References

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