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The positivity assumption is crucial when drawing causal inferences from observational studies, but it is often overlooked in practice. A violation of positivity occurs when the sample contains a subgroup of individuals with an extreme relative frequency of experiencing one of the levels of exposure. To correctly estimate the causal effect, we must identify such individuals. For this purpose, we suggest a regression tree-based algorithm.

The effective reproduction number $ R $ was widely accepted as a key indicator during the early stages of the COVID-19 pandemic. In the UK, the $ R $ value published on the UK Government Dashboard has been generated as a combined value from an ensemble of epidemiological models via a collaborative initiative between academia and government. In this paper, we outline this collaborative modelling approach and illustrate how, by using an established combination method, a combined $ R $ estimate can be generated from an ensemble of epidemiological models. We analyse the $ R $ values calculated for the period between April 2021 and December 2021, to show that this $ R $ is robust to different model weighting methods and ensemble sizes and that using heterogeneous data sources for validation increases its robustness and reduces the biases and limitations associated with a single source of data. We discuss how $ R $ can be generated from different data sources and show that it is a good summary indicator of the current dynamics in an epidemic. [ABSTRACT FROM AUTHOR]