Does Timing Matter? Exploring the Effects of Measurement Error on Models
by Brock D. Sherlock; Marko A.A. Boon; Maria Vlasiou; Adelle C.F. Coster
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Measurement error is inevitable in experimental data collection. Mathematical biologists typically account for dependent variable errors, while independent variable errors are less commonly considered. This work investigates how independent-variable measurement error affects parameter inference in biological systems and reviews statistical methods to address it. We find that parameter inference is often robust to measurement errors, even without explicitly accounting for them. However, some systems are susceptible to these errors, leading to biased parameter estimates. We evaluate correction methods, focusing on their assumptions and data requirements, to guide researchers in selecting appropriate approaches for their specific contexts.
Image Description: Illustration of the effects of measurement error in the independent variable. An oscillating model, the amplitude is estimated from synthetic data. The experimental protocol prescribes independent variable values for data collection. These designated times align with the peaks and troughs of the oscillation. However, the independent variable is subject to error and the true values at which measurements are taken are distributed about the prescribed values. When the true independent variable values are recorded (top) naïve parameter estimation can recover the amplitude that generated the data. However, when only the protocol prescribed values are recorded, as opposed to the true independent variable value at measurement, (bottom) naive parameter estimation leads to a biased estimate.
