Minimum sample size requirements and its associated precision for biased-coin up and down dose-finding trials using centered isotonic regression estimating upper quantiles (ED95 or ED90): a risk-based approach

Abstract Background : Biased coin up-and-down (BCD) using Centered Isotonic Regression (CIR) is the most widely used method to target the ED95 or ED90 in dose-finding studies conducted in anesthesiology. We study the minimum sample sizes associated with a low risk of not finding an estimate of ED95 or ED90 and test if they are aligned with the most recent sample size recommendations for BCD trials: 60 or 100 observations for ED95 or ED90, respectively. We also report the precision of the CIR estimates associated with the sample sizes found. Method : Simulations are performed on four dose-response curves made of 25, 20, and 15 possible doses equally spaced in volume. The BCD will start at each dose (from dose 1 up to doses 25, 20, or 15), reflecting situations where investigators start the trial close or far from the ED95 or ED90. Finally, the number of Monte Carlo simulations varies between 1,000 and 5,000 in increments of 1,000 in order to estimate the sample size associated with a risk less than 1 over 1,000 up to 5,000 to conduct a BCD trial without obtaining an inconclusive trial. Results : The smallest sample sizes were obtained when: 1) the DRCs are steeper; 2) the dose-finding trial starts at least 2 doses under the true ED95 or ED90; 3) DRCs are composed of fewer doses. Our results suggest the need to recruit the following sample sizes when starting a dose-finding trial under the ED of interest: 1) ED95: for steeper 25-, 20- and 15-dose DRCs, the BCD trials should recruit 150, 125 and 100 patients, respectively and for gradual 25-, 20- and 15-dose DRCs, the BCD trials should enroll 300, 250 and 200 patients, respectively; 2) ED90: for steeper 25-, 20- and 15-dose DRCs, the BCD trials should recruit 100, 80 or 60 patients, respectively and for gradual 25-, 20- and 15-dose DRCs, the BCD trials should enroll 250, 200 and 150 patients, respectively. A positive relationship between sample size and precision of the CIR estimate is found. Finally, the same DRC (e.g., DRC-2) may be precise for ED90 but imprecise for ED95 and the precision of the same DRC varies with the number of doses composing the DRC. Conclusion : Our work indicates that the sample size is highly dependent on the DRC, and requires more observations than previously recommended in the majority of the studied scenarios. The precision of the DRCs varies with the number of doses composing the DRC, and the same DRC may be precise for ED90 but imprecise for ED95. Our work suggests that the BCD with CIR is not the method of choice for estimating the upper quantiles of DRCs when considering the risk probability of leading to an inconclusive trial. Therefore, clinicians should consider alternative mathematical models to the BCD with CIR estimate when conducting dose-finding trials targeting ED95 or ED90.