Happens-Before not Being Preserved in Statistical Analysis: Why the Reproduction Rate of a Pandemic Seems to React to An Intervention before the Intervention

Abstract

In this short note, we show that a happens-before relationship may be destroyed when applying various standard methods to adjust data for a duration. An application is the calculation of the time of infection from the time of symptom onset by adjusting with the incubation time period.We first show that the simple adjustment with an expectation of the duration destroys a happens-before relationship.While being a relatively simple artefact, the assumption that a happens-before relationship would hold may easily lead to misinterpretation. An example is the calculation of the reproduction rate as a function of the symptom-onset date, e.g., as it was in done in analysis of the COVID19 pandemic. We illustrate the effect by a simple example and a simple pandemic model using a stochastic incubation time.We then investigate the same situation using a more sophisticated method, the inverse convolution - also known as back-projection. We show that in practical cases, a back-projection also destroys the happens-before relationship. In particular, the degree to which a temporal pattern is altered depends on the accuracy of the estimate of the variance of the incubation time distribution. This is important since the variance is possibly the most uncertain parameter.Disclaimer: The views expressed in this work are the personal views of the authors and do not necessarily reflect the views or policies of current or previous employers.Declaration of Interest: The author confirms that there are no known conflicts of interest associated with this publication. There has been no significant financial support for this work that could have influenced its outcome.