Does Timing Matter? Exploring the Effects of Measurement Error on Models

Measurement error is an unavoidable feature of experimental data collection. It is common in mathematical biology to consider measurement error in the dependent variable. However, less attention has been given to errors in the independent variable. This work is focussed on the effects of independent variable measurement error in the biological sciences and the available statistical methods to account for these errors when performing parameter inference. Through a series of synthetic data studies, the effects of various error models are investigated, with a particular focus given to error in the time a measurement is taken. Across many scenarios, parameter inference proves robust to these errors, even without directly accounting for them. However, we find some systems, such as oscillating systems, are particularly susceptible to these errors and parameter estimates become biased. To aid researchers in the biological sciences, we review some statistical methods to correct for measurement error. We assess the applicability of these methods in a biological context by considering data availability and necessary assumptions for the methods. We find measurement error can have non-trivial and counter-intuitive effects on parameter inference and suggest assessing the available data should be an integral step in the modelling workflow. This allows researchers to identify when the integration of statistical methods to correct for measurement error are warranted.