Detecting changes in task length due to task-switching in the presence of repeated length-biased sampling

Clinical work is characterised by frequent interjection of external prompts causing clinicians to switch from a primary task to deal with an incoming secondary task, a phenomenon associated with negative effects in experimental studies. This is an important yet underexplored aspect of work in safety critical settings in general, since an increase in task length due to task-switching implies reduced efficiency, while decreased length suggests hastening to compensate for the increased workload brought by the unexpected secondary tasks, which is a potential safety issue. In such observational settings, longer tasks are naturally more likely to have one or more task-switching events: a form of length bias. To assess the effect of task-switching on task completion time, it is necessary to estimate counterfactual task lengths had they not experienced any task-switching, while also accounting for length bias. This is a problem that appears simple at first, but has several counterintuitive considerations resulting in a uniquely constrained solution space. We review the only existing method based on an assumption that task-switches occur according to a homogeneous Poisson process. We propose significant extensions to flexibly incorporate heterogeneity that is more representative of task-switching in real-world contexts. The techniques are applied to observations of emergency physicians' workflow in two hospital settings.