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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.

Original publication




Journal article



Publication Date





992 - 1000


drug error, mathematical modelling, patient safety, safe surgery, Anesthesia, Anesthetics, Fatigue, Humans, Injections, Medication Errors, Models, Theoretical, Operative Time, Risk