Multi-dimensional response–probability–dose curves for bupivacaine and ropivacaine epidural labour analgesia1

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Describing the relationship between magnitude of response, probability of response, dose and time is difficult using traditional two-dimensional dose–response curves. We devised a novel way of presentation in four dimensions. Data from a previous study of epidural bupivacaine and ropivacaine given for labour analgesia were re-analysed. For a range of response magnitudes (5–95% reduction in pain score), estimates of doses associated with probabilities of response 0.05–0.95 were calculated using probit analysis. Three dimensional surface plots were constructed with axes x = magnitude of response, y = probability of response and z = log(dose) at intervals for 30 min. Arithmetic interpolation was used to assemble an animation depicting temporal changes in relationship between variables (fourth dimension). Response–probability–dose curves in three and four dimensions were constructed and presented for both drugs. We believe that this model is more aligned with the logic of clinical dose selection compared with traditional two-dimensional curves.

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