Trajectory Analysis in Health Care
This innovative volume introduces Trajectory Analysis, a new systems-based approach to measuring nonlinear dynamics in continuous change, to public health and epidemiology. It synthesizes influential strands of statistical and probability science (includi
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Trajectory Analysis in Health Care
Trajectory Analysis in Health Care
David W. Hollar
Trajectory Analysis in Health Care
David W. Hollar Health Administration Pfeiffer University Morrisville, North Carolina, USA
ISBN 978-3-319-59625-9 ISBN 978-3-319-59626-6 DOI 10.1007/978-3-319-59626-6
(eBook)
Library of Congress Control Number: 2017944366 © Springer International Publishing AG 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
For our daughter, Brooke Hollar, future clinician, courageous follower of Christ, and leader by example.
Preface
The objective of this book is to introduce health researchers, epidemiologists, health policy makers, and clinicians to Trajectory Analysis, a term that I use to refer to the nonlinear analysis of processes. This science was developed by a number of scientists, most notably the French mathematician Henri Poincare and the Russian mathematician Aleksandr Lyapunov during the late 1800s. During the twentieth century, the science gained traction in the physical sciences with the development of quantum mechanics and mathematical descriptions of fluid mechanics, further applied during the latter part of the century to Chaos Theory and the analysis of defects in nanoparticles and crystals. Trajectory Analysis relies heavily on the measurement of continuous change, which is measured using differential equations, although phase transitions across critical transition points are generally non-integrable. I have kept the mathematics to a minimum, but several central equations and rough derivations are provided to demonstrate importance and applicability to health research. Health research and epidemiolog
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