Statistical analysis
It was reported that anesthesia researches using the up-and-down methodology typically need 20-40 patients per group [9,16,17]. We have also considered a dropout rate of 10%. Therefore, the estimated sample size will be 30 patients per group, and a total of 90 patients will be randomized.
Data were expressed as mean (standard deviation, SD) for continuous variables, median (Min, Max) for continuous variables with skewed distribution, or number (n) for categorical variables. First, all data are tested for normality by shapiro.test. For data that does not conform to the normal distribution, we use the Kruskal-Wallis rank sum test to check the differences between groups; for the data whose variance conforms to the normal distribution, we use the Bartlett test of homogeneity of variances to test whether the variances are homogeneous. Subsequently, we used ANOVA’s Tukey method or Kramer Nemenyi test to test the differences between groups, as appropriate. The modified Dixon’s up-and-down method was used for determining the ED50 of propofol with different doses of esketamine. We use Dixon method to test either the minimum or maximum value is an outlier. Using log-logistic dose-response model test was used to test the differences of EC50 between groups. We defineP value < 0.05 as a significant difference between groups.