A copula approach to modelling dependency patterns in routine vital sign observation timeliness

Healthcare staff in a hospital ward setting typically monitor patients by taking vital sign observations at regular intervals, usually every 6 - 12 hours for routine observations, but more frequently for critical patients. Patients on similar schedules have been shown to be regularly batched in a practice called ‘ward rounds’, but to what extent healthcare staff manage observations on ‘non-routine’ intervals independently to those scheduled for the subsequent ward round has yet to be established. This study examines the Time-To-Next-Observation (TTNO) for vital sign observations with planned schedules (e.g., 1 hour) as random variables defined by their hazard distribution functions. Joint distribution functions sampled from any pair of TTNO distributions could be used to calculate the probability that any two observations on set schedules will happen collectively. However, it is clear that this model fails to capture underlying dependency structures seen in empirical results. We propose a copula approach to extract and quantify pairwise nonlinear relationships for all standard observation intervals across 20 study wards. This study showed that most wards operate with significant levels of dependency between observation schedules, largely reflecting broad ward characteristics referenced in other works, yet present a deeper level of insight into individual ward operations. Understanding current levels of dependency between regular observation scheduling and routine operations has the potential to become essential knowledge for ward stakeholders when designing staff resource strategies.