@article{shao_canner_everett_bekele-maxwell_kuerbis_stephenson_menda_morgenstern_banks_2023, title={A Comparison of Mathematical and Statistical Modeling with Longitudinal Data: An Application to Ecological Momentary Assessment of Behavior Change in Individuals with Alcohol Use Disorder}, volume={85}, ISSN={["1522-9602"]}, DOI={10.1007/s11538-022-01097-1}, abstractNote={Ecological momentary assessment (EMA) has been broadly used to collect real-time longitudinal data in behavioral research. Several analytic methods have been applied to EMA data to understand the changes of motivation, behavior, and emotions on a daily or within-day basis. One challenge when utilizing those methods on intensive datasets in the behavioral field is to understand when and why the methods are appropriate to investigate particular research questions. In this manuscript, we compared two widely used methods (generalized estimating equations and generalized linear mixed models) in behavioral research with three other less frequently used methods (Markov models, generalized linear mixed-effects Markov models, and differential equations) in behavioral research but widely used in other fields. The purpose of this manuscript is to illustrate the application of five distinct analytic methods to one dataset of intensive longitudinal data on drinking behavior, highlighting the utility of each method.}, number={1}, journal={BULLETIN OF MATHEMATICAL BIOLOGY}, author={Shao, Sijing and Canner, Judith E. E. and Everett, Rebecca A. and Bekele-Maxwell, Kidist and Kuerbis, Alexis and Stephenson, Lyric and Menda, Jennifer and Morgenstern, Jon and Banks, H. T.}, year={2023}, month={Jan} }
 @misc{everett_flores_henscheid_lagergren_larripa_li_nardini_nguyen_pitman_rutter_2020, title={A tutorial review of mathematical techniques for quantifying tumor heterogeneity}, volume={17}, ISSN={["1551-0018"]}, DOI={10.3934/mbe.2020207}, abstractNote={Intra-tumor and inter-patient heterogeneity are two challenges in developing mathematical models for precision medicine diagnostics. Here we review several techniques that can be used to aid the mathematical modeller in inferring and quantifying both sources of heterogeneity from patient data. These techniques include virtual populations, nonlinear mixed effects modeling, non-parametric estimation, Bayesian techniques, and machine learning. We create simulated virtual populations in this study and then apply the four remaining methods to these datasets to highlight the strengths and weak-nesses of each technique. We provide all code used in this review at https://github.com/jtnardin/Tumor-Heterogeneity/ so that this study may serve as a tutorial for the mathematical modelling community. This review article was a product of a Tumor Heterogeneity Working Group as part of the 2018-2019 Program on Statistical, Mathematical, and Computational Methods for Precision Medicine which took place at the Statistical and Applied Mathematical Sciences Institute.}, number={4}, journal={MATHEMATICAL BIOSCIENCES AND ENGINEERING}, author={Everett, Rebecca and Flores, Kevin B. and Henscheid, Nick and Lagergren, John and Larripa, Kamila and Li, Ding and Nardini, John T. and Nguyen, Phuong T. T. and Pitman, E. Bruce and Rutter, Erica M.}, year={2020}, pages={3660–3709} }
 @article{murad_tran_banks_everett_rosenberg_2019, title={IMMUNOSUPPRESSANT TREATMENT DYNAMICS IN RENAL TRANSPLANT RECIPIENTS: AN ITERATIVE MODELING APPROACH}, volume={24}, ISSN={["1553-524X"]}, DOI={10.3934/dcdsb.2018274}, abstractNote={Finding the optimal balance between over-suppression and under-suppression of the immune response is difficult to achieve in renal transplant patients, all of whom require lifelong immunosuppression. Our ultimate goal is to apply control theory to adaptively predict the optimal amount of immunosuppression; however, we first need to formulate a biologically realistic model. The process of quantitively modeling biological processes is iterative and often leads to new insights with every iteration. We illustrate this iterative process of modeling for renal transplant recipients infected by BK virus. We analyze and improve on the current mathematical model by modifying it to be more biologically realistic and amenable for designing an adaptive treatment strategy.}, number={6}, journal={DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B}, author={Murad, Neha and Tran, H. T. and Banks, H. T. and Everett, R. A. and Rosenberg, Eric S.}, year={2019}, month={Jun}, pages={2781–2797} }
 @misc{rieger_allen_bystricky_chen_colopy_cui_gonzalez_liu_white_everett_et al._2018, title={Improving the generation and selection of virtual populations in quantitative systems pharmacology models}, volume={139}, ISSN={["0079-6107"]}, DOI={10.1016/j.pbiomolbio.2018.06.002}, abstractNote={Quantitative systems pharmacology (QSP) models aim to describe mechanistically the pathophysiology of disease and predict the effects of therapies on that disease. For most drug development applications, it is important to predict not only the mean response to an intervention but also the distribution of responses, due to inter-patient variability. Given the necessary complexity of QSP models, and the sparsity of relevant human data, the parameters of QSP models are often not well determined. One approach to overcome these limitations is to develop alternative virtual patients (VPs) and virtual populations (Vpops), which allow for the exploration of parametric uncertainty and reproduce inter-patient variability in response to perturbation. Here we evaluated approaches to improve the efficiency of generating Vpops. We aimed to generate Vpops without sacrificing diversity of the VPs' pathophysiologies and phenotypes. To do this, we built upon a previously published approach (Allen et al., 2016) by (a) incorporating alternative optimization algorithms (genetic algorithm and Metropolis-Hastings) or alternatively (b) augmenting the optimized objective function. Each method improved the baseline algorithm by requiring significantly fewer plausible patients (precursors to VPs) to create a reasonable Vpop.}, journal={PROGRESS IN BIOPHYSICS & MOLECULAR BIOLOGY}, author={Rieger, Theodore R. and Allen, Richard J. and Bystricky, Lukas and Chen, Yuzhou and Colopy, Glen Wright and Cui, Yifan and Gonzalez, Angelica and Liu, Yifei and White, R. D. and Everett, R. A. and et al.}, year={2018}, month={Nov}, pages={15–22} }
 @article{banks_everett_murad_white_banks_cass_rosenheim_2018, title={OPTIMAL DESIGN FOR DYNAMICAL MODELING OF PEST POPULATIONS}, volume={15}, ISSN={["1551-0018"]}, DOI={10.3934/mbe.2018044}, abstractNote={We apply SE-optimal design methodology to investigate optimal data collection procedures as a first step in investigating information content in ecoinformatics data sets. To illustrate ideas we use a simple phenomenological citrus red mite population model for pest dynamics. First the optimal sampling distributions for a varying number of data points are determined. We then analyze these optimal distributions by comparing the standard errors of parameter estimates corresponding to each distribution. This allows us to investigate how many data are required to have confidence in model parameter estimates in order to employ dynamical modeling to infer population dynamics. Our results suggest that a field researcher should collect at least 12 data points at the optimal times. Data collected according to this procedure along with dynamical modeling will allow us to estimate population dynamics from presence/absence-based data sets through the development of a scaling relationship. These Likert-type data sets are commonly collected by agricultural pest management consultants and are increasingly being used in ecoinformatics studies. By applying mathematical modeling with the relationship scale from the new data, we can then explore important integrated pest management questions using past and future presence/absence data sets.}, number={4}, journal={MATHEMATICAL BIOSCIENCES AND ENGINEERING}, author={Banks, H. T. and Everett, R. A. and Murad, Neha and White, R. D. and Banks, J. E. and Cass, Bodil N. and Rosenheim, Jay A.}, year={2018}, month={Aug}, pages={993–1010} }
 @article{banks_bekele-maxwell_everett_stephenson_shao_morgenstern_2017, title={Dynamic Modeling of Problem Drinkers Undergoing Behavioral Treatment}, volume={79}, ISSN={["1522-9602"]}, DOI={10.1007/s11538-017-0282-5}, abstractNote={We use dynamical systems modeling to help understand how selected intra-personal factors interact to form mechanisms of behavior change in problem drinkers. Our modeling effort illustrates the iterative process of modeling using an individual's clinical data. Due to the lack of previous work in modeling behavior change in individual patients, we build our preliminary model relying on our understandings of the psychological relationships among the variables. This model is refined and the psychological understanding is then enhanced through the iterative modeling process. Our results suggest that this is a promising direction in research in alcohol use disorders as well as other behavioral sciences.}, number={6}, journal={BULLETIN OF MATHEMATICAL BIOLOGY}, author={Banks, H. T. and Bekele-Maxwell, Kidist and Everett, R. A. and Stephenson, Lyric and Shao, Sijing and Morgenstern, Jon}, year={2017}, month={Jun}, pages={1254–1273} }
 @article{banks_everett_hu_murad_tran_2017, place={Banks, R.A}, title={Mathematical and statistical model misspecifications in modelling immune response in renal transplant recipients}, volume={26}, ISSN={1741-5977 1741-5985}, url={http://dx.doi.org/10.1080/17415977.2017.1312363}, DOI={10.1080/17415977.2017.1312363}, abstractNote={We examine uncertainty in clinical data from a kidney transplant recipient infected with BK virus and investigate mathematical model and statistical model misspecifications in the context of least squares methodology. A difference-based method is directly applied to data to determine the correct statistical model that represents the uncertainty in data. We then carry out an inverse problem with the corresponding iterative weighted least squares technique and use the resulting modified residual plots to detect mathematical model discrepancy. This process is implemented using both clinical and simulated data. Our results demonstrate mathematical model misspecification when both simpler and more complex models are assumed compared to data dynamics.}, number={2}, journal={Inverse Problems in Science and Engineering}, publisher={Informa UK Limited}, author={Banks, H. T. and Everett, R. A. and Hu, Shuhua and Murad, Neha and Tran, H. T.}, year={2017}, month={Apr}, pages={203–222} }
 @article{banks_banks_everett_stark_2016, title={AN ADAPTIVE FEEDBACK METHODOLOGY FOR DETERMINING INFORMATION CONTENT IN STABLE POPULATION STUDIES}, volume={13}, ISSN={["1551-0018"]}, DOI={10.3934/mbe.2016013}, abstractNote={We develop statistical and mathematical based methodologies for determining (as the experiment progresses) the amount of information required to complete the estimation of stable population parameters with pre-specified levels of confidence. We do this in the context of life table models and data for growth/death for three species of Daphniids as investigated by J. Stark and J. Banks [17]. The ideas developed here also have wide application in the health and social sciences where experimental data are often expensive as well as difficult to obtain.}, number={4}, journal={MATHEMATICAL BIOSCIENCES AND ENGINEERING}, author={Banks, H. T. and Banks, John E. and Everett, R. A. and Stark, John D.}, year={2016}, month={Aug}, pages={653–671} }
 @article{everett_nagy_kuang_2016, title={Dynamics of a Data Based Ovarian Cancer Growth and Treatment Model with Time Delay}, volume={28}, ISSN={1040-7294 1572-9222}, url={http://dx.doi.org/10.1007/S10884-015-9498-Y}, DOI={10.1007/S10884-015-9498-Y}, number={3-4}, journal={Journal of Dynamics and Differential Equations}, publisher={Springer Science and Business Media LLC}, author={Everett, R. A. and Nagy, J. D. and Kuang, Y.}, year={2016}, month={Sep}, pages={1393–1414} }