@article{banks_meade_schacht_catenacci_thompson_abate-daga_enderling_2020, title={Parameter estimation using aggregate data}, volume={100}, ISSN={["0893-9659"]}, DOI={10.1016/j.aml.2019.105999}, abstractNote={In biomedical/physiological/ecological experiments, it is common for measurements in time series data to be collected from multiple subjects. Often it is the case that a subject cannot be measured or identified at multiple time points (often referred to as aggregate population data). Due to a lack of alternative methods, this form of data is typically treated as if it is collected from a single individual. As we show by examples, this assumption leads to an overconfidence in model parameter (means, variances) values and model based predictions. We discuss these issues in the context of a mathematical model to determine T-cell behavior with cancer chimeric antigen receptor (CAR) therapies where during the collection of data cancerous mice are sacrificed at each measurement time.}, journal={APPLIED MATHEMATICS LETTERS}, author={Banks, H. . T. and Meade, Annabel E. and Schacht, Celia and Catenacci, Jared and Thompson, W. Clayton and Abate-Daga, Daniel and Enderling, Heiko}, year={2020}, month={Feb} }
 @article{banks_thompson_2018, title={RANDOM DELAY DIFFERENTIAL EQUATIONS AND INVERSE PROBLEMS FOR AGGREGATE DATA PROBLEMS}, volume={6}, ISSN={["2308-9822"]}, DOI={10.32523/2306-6172-2018-6-4-4-16}, abstractNote={We consider nonparametric estimation of probability measures for parameters in delay differential equation (DDE) problems where only aggregate (population level) data are available. We summarize an existing computational method for the estimation problem which has been developed over the past several decades [11, 17, 21, 26, 28]. Theoretical results are presented which establish the existence and consistency of very general (ordinary, generalized and other) least squares estimates and estimators for the measure estimation problem with specific application to random DDEs.}, number={4}, journal={EURASIAN JOURNAL OF MATHEMATICAL AND COMPUTER APPLICATIONS}, author={Banks, H. T. and Thompson, W. C.}, year={2018}, pages={4–16} }
 @article{banks_kapraun_thompson_peligero_argilaguet_meyerhans_2013, title={A novel statistical analysis and interpretation of flow cytometry data}, volume={7}, ISSN={["1751-3766"]}, DOI={10.1080/17513758.2013.812753}, abstractNote={A recently developed class of models incorporating the cyton model of population generation structure into a conservation-based model of intracellular label dynamics is reviewed. Statistical aspects of the data collection process are quantified and incorporated into a parameter estimation scheme. This scheme is then applied to experimental data for PHA-stimulated CD4+T and CD8+T cells collected from two healthy donors. This novel mathematical and statistical framework is shown to form the basis for accurate, meaningful analysis of cellular behaviour for a population of cells labelled with the dye carboxyfluorescein succinimidyl ester and stimulated to divide.}, number={1}, journal={JOURNAL OF BIOLOGICAL DYNAMICS}, author={Banks, H. T. and Kapraun, D. F. and Thompson, W. Clayton and Peligero, Cristina and Argilaguet, Jordi and Meyerhans, Andreas}, year={2013}, month={Dec}, pages={96–132} }
 @article{banks_choi_huffman_nardini_poag_thompson_2013, title={Quantifying CFSE label decay in flow cytometry data}, volume={26}, ISSN={["0893-9659"]}, DOI={10.1016/j.aml.2012.12.010}, abstractNote={We developed a series of models for the label decay in cell proliferation assays when the intracellular dye carboxyfluorescein succinimidyl ester (CFSE) is used as a staining agent. Data collected from two healthy patients were used to validate the models and to compare the models with the Akiake Information Criteria. The distinguishing features of multiple decay rates in the data are readily characterized and explained via time dependent decay models such as the logistic and Gompertz models.}, number={5}, journal={APPLIED MATHEMATICS LETTERS}, author={Banks, H. T. and Choi, A. and Huffman, T. and Nardini, J. and Poag, L. and Thompson, W. C.}, year={2013}, month={May}, pages={571–577} }
 @article{banks_kenz_thompson_2012, title={A review of selected techniques in inverse problem nonparametric probability distribution estimation}, volume={20}, number={4}, journal={Journal of Inverse and Ill-Posed Problems}, author={Banks, H. T. and Kenz, Z. R. and Thompson, W. C.}, year={2012}, pages={429–460} }
 @article{banks_sutton_thompson_bocharov_doumic_schenkel_argilaguet_giest_peligero_meyerhans_2011, title={A new model for the estimation of cell proliferation dynamics using CFSE data}, volume={373}, ISSN={["1872-7905"]}, DOI={10.1016/j.jim.2011.08.014}, abstractNote={CFSE analysis of a proliferating cell population is a popular tool for the study of cell division and divisionlinked changes in cell behavior. Recently Banks et al. (2011), Luzyanina et al. (2009), Luzyanina et al. (2007), a partial differential equation (PDE) model to describe lymphocyte dynamics in a CFSE proliferation assay was proposed. We present a significant revision of this model which improves the physiological understanding of several parameters. Namely, the parameter used previously as a heuristic explanation for the dilution of CFSE dye by cell division is replaced with a more physical component, cellular autofluorescence. The rate at which label decays is also quantified using a Gompertz decay process. We then demonstrate a revised method of fitting the model to the commonly used histogram representation of the data. It is shown that these improvements result in a model with a strong physiological basis which is fully capable of replicating the behavior observed in the data.}, number={1-2}, journal={JOURNAL OF IMMUNOLOGICAL METHODS}, author={Banks, H. T. and Sutton, Karyn L. and Thompson, W. Clayton and Bocharov, Gennady and Doumic, Marie and Schenkel, Tim and Argilaguet, Jordi and Giest, Sandra and Peligero, Cristina and Meyerhans, Andreas}, year={2011}, month={Oct}, pages={143–160} }
 @article{banks_sutton_thompson_bocharov_roose_schenkel_meyerhans_2011, title={Estimation of Cell Proliferation Dynamics Using CFSE Data}, volume={73}, ISSN={["1522-9602"]}, DOI={10.1007/s11538-010-9524-5}, abstractNote={Advances in fluorescent labeling of cells as measured by flow cytometry have allowed for quantitative studies of proliferating populations of cells. The investigations (Luzyanina et al. in J. Math. Biol. 54:57–89, 2007; J. Math. Biol., 2009; Theor. Biol. Med. Model. 4:1–26, 2007) contain a mathematical model with fluorescence intensity as a structure variable to describe the evolution in time of proliferating cells labeled by carboxyfluorescein succinimidyl ester (CFSE). Here, this model and several extensions/modifications are discussed. Suggestions for improvements are presented and analyzed with respect to statistical significance for better agreement between model solutions and experimental data. These investigations suggest that the new decay/label loss and time dependent effective proliferation and death rates do indeed provide improved fits of the model to data. Statistical models for the observed variability/noise in the data are discussed with implications for uncertainty quantification. The resulting new cell dynamics model should prove useful in proliferation assay tracking and modeling, with numerous applications in the biomedical sciences.}, number={1}, journal={BULLETIN OF MATHEMATICAL BIOLOGY}, author={Banks, H. T. and Sutton, Karyn L. and Thompson, W. Clayton and Bocharov, Gennady and Roose, Dirk and Schenkel, Tim and Meyerhans, Andreas}, year={2011}, month={Jan}, pages={116–150} }
 @article{banks_charles_jauffret_sutton_thompson_2010, title={Label structured cell proliferation models}, volume={23}, ISSN={["0893-9659"]}, DOI={10.1016/j.aml.2010.07.009}, abstractNote={We present a general class of cell population models that can be used to track the proliferation of cells which have been labeled with a fluorescent dye. The mathematical models employ fluorescence intensity as a structure variable to describe the evolution in time of the population density of proliferating cells. While cell division is a major component of changes in cellular fluorescence intensity, models developed here also address overall label degradation.}, number={12}, journal={APPLIED MATHEMATICS LETTERS}, author={Banks, H. T. and Charles, Frederique and Jauffret, Marie Doumic and Sutton, Karyn L. and Thompson, W. Clayton}, year={2010}, month={Dec}, pages={1412–1415} }