2.4. BCD-UDM

The BCD-UDM was performed as follows, and the two groups were studied separately. According to the previous study on the inhibition of emergency coughing in patients with an SLT [6,31], the effect-site concentration of remifentanil received in the first patient of the two groups was set at 2.5 ng/ml. For the subsequent patient, the remifentanil concentration was based on the previous patient's response. If a patient experienced smooth emergence before completion of the study, the concentration of remifentanil set for the next patient was randomized with a biased coin, with 11% (b = 0.11) probability of decreasing by one unit (0.5 ng/ml) and 89% (1-b = 0.89) probability of remaining at the same dose [32], with a concentration change set as an increment or decrement of 0.5 ng/ml; the concentration change was determined as a value greater than the standard deviation (SD) in the previous study [6]. If coughing occurred in the previous patient, the concentration of remifentanil was increased by 0.5 ng/ml.

In a dose-finding study using the BCD-UDM, the distribution of data was unknown and not independent. Simulation studies suggested that the stopping rule of enrolling at least 20–40 participants can provide a stable estimate of the target dose for most realistic cases [32,33]. A larger sample size results in increased statistical accuracy, as is evident from the smaller standard errors [34]. Thus, we chose a sample size of 60 to accommodate a potential dropout rate of 5% for each group. A total of 120 patients were recruited, and additional patients were recruited if the number of positive reactions was insufficient until there were 45 patients with a positive response in any of the two groups.

The EC₉₀ along with the 95% confidence intervals (CIs) was calculated via the BCD-UDM and isotonic regression method along with the pooled-adjacent-violators algorithm approach (PAVA) using R software, version 3.4.4 (R Foundation of Statistical Computing, Vienna, Austria).