Noise Is Not Error: Detecting Parametric Heterogeneity Between Epidemiologic Time Series - Romero-Severson, Ethan O.; Ribeiro, Ruy M.; Castro, Mario (Frontiers in Microbiology, 2018)
Mathematical models play a multifaceted role in epidemiology: interpretation and consilience of heterogeneous data, unification of conflicting experimental and observational data, and generation of new hypotheses. Traditional methods based on deterministic assumptions, such as ordinary differential equations (ODE), have been successful in those scenarios. However, "noise" is an intrinsic feature of the cellular/molecular/social world caused by several factors such as measurement error, construct validity, and inherent stochasticity due to small population sizes. Panel data from patients (in the case of infections) or locations (in the case of epidemics) can vary due to intrinsic differences or accidental fluctuations. The use of traditional fitting methods for ODEs applied to noisy problems implies that deviation from some trend can only be due to measurement error or parametric heterogeneity leading to unstable predictions and potentially misguided policies or research programs. In this paper, we quantify the ability of ODEs under different underlying 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 prescriptive approach for determining the limitations and risks of traditional fitting methodologies. Finally, we discuss the implications of our results on the recent 2014-2015 Ebola epidemic in Africa.