Outcome Prediction in Mathematical Models of Immune Response to Infection.
Clinicians need to predict patient outcomes with high accuracy as early as possible after disease inception. In this manuscript, we show that patient-to-patient variability sets a fundamental limit on outcome prediction accuracy for a general class of mathematical models for the immune response to infection. However, accuracy can be increased at the expense of delayed prognosis. We investigate several systems of ordinary differential equations (ODEs) that model the host immune response to a pathogen load. Advantages of systems of ODEs for investigating the immune response to infection include the ability to collect data on large numbers of 'virtual patients', each with a given set of model parameters, and obtain many time points during the course of the infection. We implement patient-to-patient variability v in the ODE models by randomly selecting the model parameters from distributions with coefficients of variation v that are centered on physiological values. We use logistic regression with one-versus-all classification to predict the discrete steady-state outcomes of the system. We find that the prediction algorithm achieves near 100% accuracy for v = 0, and the accuracy decreases with increasing v for all ODE models studied. The fact that multiple steady-state outcomes can be obtained for a given initial condition, i.e. the basins of attraction overlap in the space of initial conditions, limits the prediction accuracy for v > 0. Increasing the elapsed time of the variables used to train and test the classifier, increases the prediction accuracy, while adding explicit external noise to the ODE models decreases the prediction accuracy. Our results quantify the competition between early prognosis and high prediction accuracy that is frequently encountered by clinicians.
Department of Physics, Yale University, New Haven, Connecticut, United States of America.
Manuel
M
Mai
Department of Mathematics, Colorado State University, Fort Collins, Colorado, United States of America; Department of Mechanical Engineering and Material Science, Yale University, New Haven, Connecticut, United States of America.
Kun
K
Wang
Kavli Institute for Theoretical Physics, Kohn Hall, University of California Santa Barbara, Santa Barbara, California, United States of America.
Greg
G
Huber
Department of Mathematics, Colorado State University, Fort Collins, Colorado, United States of America; Department of Computer Science, Colorado State University, Fort Collins, Colorado, United States of America.
Michael
M
Kirby
Department of Mechanical Engineering and Material Science, Yale University, New Haven, Connecticut, United States of America; Benjamin Levich Institute and Physics Department, The City College of New York, New York, New York, United States of America.
Mark D
MD
Shattuck
Department of Physics, Yale University, New Haven, Connecticut, United States of America; Department of Mechanical Engineering and Material Science, Yale University, New Haven, Connecticut, United States of America; Department of Applied Physics, Yale University, New Haven, Connecticut, United States of America; Graduate Program in Computational Biology and Bioinformatics, Yale University, New Haven, Connecticut, United States of America.
Corey S
CS
O'Hern
D000465:Algorithms; D001424:Bacterial Infections / Q000276:immunology*; D006801:Humans; D008954:Models, Biological; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D017063:Outcome Assessment, Health Care / Q000379:methods*; D011379:Prognosis; D049490:Systems Biology / Q000379:methods*; D014777:Virus Diseases / Q000276:immunology*