Mathematical model of the risk of drug error during anaesthesia: the influence of drug choices, injection routes, operation duration and fatigue

The incidence of an anaesthetic drug error can be directly observed in large trials. In an alternative approach, we developed a probabilistic mathematical model in which the anaesthetist is modelled as a 'fallible entity' who makes repeated drug administration choices during an operation. This fallibility was factored in the model as an initial 'intrinsic error rate'. The choices faced included: dose; timing of administration; and the routes available for injection (e.g. venous, arterial, epidural, etc.). Additionally, we modelled the effect of fatigue as a factor that magnifies the cumulative error rate. For an initial intrinsic error rate of 1 in 1000 (which from first principles we consider a reasonable estimate), our model predicted a cumulative probability of error over a ~12 h operation of ~10%; that is, 1 in 10 operations this long results in some drug error. This is similar to the rate reported by large observational trials. Serious errors constitute a small fraction of all errors; our model predicts a Poisson distribution for the uncommon serious errors, also consistent with independent observations. Even modest assumptions for the development of fatigue had a dramatic and adverse impact on the cumulative error rate. The practice implications of our modelling include: exercising caution or avoiding starting work if under par; added vigilance in unfamiliar environments; keeping anaesthetic recipes simple; and recognising that operation durations > 5-6 h constitute a time of exaggerated risk. These implications are testable predictions in observational trials. If validated, our model could serve as a potential research tool to investigate the impact of safety interventions on the rate of intrinsic error using simulation.