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Title: Noise Is Not Error: Detecting Parametric Heterogeneity Between Epidemiologic Time Series

Abstract

Mathematical models play a central role in epidemiology. For example, models unify heterogeneous data into a single framework, suggest experimental designs, and generate hypotheses. Traditional methods based on deterministic assumptions, such as ordinary differential equations (ODE), have been successful in those scenarios. However, noise caused by random variations rather than true differences is an intrinsic feature of the cellular/molecular/social world. Time series data from patients (in the case of clinical science) or number of infections (in the case of epidemics) can vary due to both intrinsic differences or incidental fluctuations. The use of traditional fitting methods for ODEs applied to noisy problems implies that deviation from some trend can only be due to error or parametric heterogeneity, that is noise can be wrongly classified as parametric heterogeneity. This leads to unstable predictions and potentially misguided policies or research programs. In this paper, we quantify the ability of ODEs under different hypotheses (fixed or random effects) to capture individual differences in the underlying data. We explore a simple (exactly solvable) example displaying an initial exponential growth by comparing state-of-the-art stochastic fitting and traditional least squares approximations. We also provide a potential approach for determining the limitations and risks of traditional fittingmore » methodologies. Finally, we discuss the implications of our results for the interpretation of data from the 2014-2015 Ebola epidemic in Africa.« less

Authors:
ORCiD logo [1]; ORCiD logo [2];  [3]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. de Lisboa, Lisbon (Portugal)
  3. Univ. Pontificia Comillas, Madrid (Spain); Unic. of Leeds, Leeds (United Kingdom)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA); National Institutes of Health (NIH)
OSTI Identifier:
1557747
Report Number(s):
LA-UR-18-28685; LA-UR-19-30215
Journal ID: ISSN 1664-302X
Grant/Contract Number:  
89233218CNA000001; R01-AI087520; R01-AI104373; FIS2013-47949-C2-2-P; FIS2016-78883-C2-2-P
Resource Type:
Accepted Manuscript
Journal Name:
Frontiers in Microbiology
Additional Journal Information:
Journal Volume: 9; Journal ID: ISSN 1664-302X
Publisher:
Frontiers Research Foundation
Country of Publication:
United States
Language:
English
Subject:
59 BASIC BIOLOGICAL SCIENCES; Biological Science; stochastic; deterministic; epidemiology; panel data; random effects; fixed effects

Citation Formats

Romero-Severson, Ethan, Ribeiro, Ruy Miguel, and Castro Ponce, Mario. Noise Is Not Error: Detecting Parametric Heterogeneity Between Epidemiologic Time Series. United States: N. p., 2018. Web. doi:10.3389/fmicb.2018.01529.
Romero-Severson, Ethan, Ribeiro, Ruy Miguel, & Castro Ponce, Mario. Noise Is Not Error: Detecting Parametric Heterogeneity Between Epidemiologic Time Series. United States. doi:10.3389/fmicb.2018.01529.
Romero-Severson, Ethan, Ribeiro, Ruy Miguel, and Castro Ponce, Mario. Thu . "Noise Is Not Error: Detecting Parametric Heterogeneity Between Epidemiologic Time Series". United States. doi:10.3389/fmicb.2018.01529. https://www.osti.gov/servlets/purl/1557747.
@article{osti_1557747,
title = {Noise Is Not Error: Detecting Parametric Heterogeneity Between Epidemiologic Time Series},
author = {Romero-Severson, Ethan and Ribeiro, Ruy Miguel and Castro Ponce, Mario},
abstractNote = {Mathematical models play a central role in epidemiology. For example, models unify heterogeneous data into a single framework, suggest experimental designs, and generate hypotheses. Traditional methods based on deterministic assumptions, such as ordinary differential equations (ODE), have been successful in those scenarios. However, noise caused by random variations rather than true differences is an intrinsic feature of the cellular/molecular/social world. Time series data from patients (in the case of clinical science) or number of infections (in the case of epidemics) can vary due to both intrinsic differences or incidental fluctuations. The use of traditional fitting methods for ODEs applied to noisy problems implies that deviation from some trend can only be due to error or parametric heterogeneity, that is noise can be wrongly classified as parametric heterogeneity. This leads to unstable predictions and potentially misguided policies or research programs. In this paper, we quantify the ability of ODEs under different hypotheses (fixed or random effects) to capture individual differences in the underlying data. We explore a simple (exactly solvable) example displaying an initial exponential growth by comparing state-of-the-art stochastic fitting and traditional least squares approximations. We also provide a potential approach for determining the limitations and risks of traditional fitting methodologies. Finally, we discuss the implications of our results for the interpretation of data from the 2014-2015 Ebola epidemic in Africa.},
doi = {10.3389/fmicb.2018.01529},
journal = {Frontiers in Microbiology},
number = ,
volume = 9,
place = {United States},
year = {2018},
month = {7}
}

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