Erratum to: Bayesian optimal interval designs for phase I clinical trials (Journal of the Royal Statistical Society: Series C (Applied Statistics), (2015), 64, 3, (507-523), 10.1111/rssc.12089)

Bayesian optimal interval designs for phase I clinical trials We discovered that in Liu and Yuan (2015) the dose de-escalation rule was incorrectly stated as to de-escalate the dose if ‘ (Formula presented.) ’, which should be ‘ (Formula presented.) ’. Accordingly, the decision rule to stay at the current dose should be revised from ‘ (Formula presented.) ’ to ‘ (Formula presented.) ’. This error does not affect the application of the BOIN design as it is virtually impossible that (Formula presented.) in practice. We examined the target DLT rate ϕ ∈ {0.1000, 0.1001, 0.1002,…, 0.4000} with (Formula presented.) (i.e. up to treating 30 patients per dose), we do not find any case that (Formula presented.). In addition, de-escalation if ‘ (Formula presented.) ’ is slightly more conservative than de-escalation if ‘ (Formula presented.) ’. Therefore, even if the equal sign could be taken, no any safety concerns arise for the trials using the ‘original’ rule. Liu and Yuan (2015) provided a point solution (equations (2) and (3) in Supplementary Materials) that minimizes the overall decision error under the local optimal design. Due to the discrete nature of DLT data, the complete solution is an interval. In the supplementary materials, we provide the revised derivation that offers the complete interval solution. This expanded solution does not affect the validity of the result in Liu and Yuan (2015) as the point solution is located within the interval solution and indeed minimizes the overall decision error. Compared to the complete interval solution, the point solution is simpler and greatly facilitates the application of the design. Lastly, the proof Theorem 1 in Liu and Yuan (2015) utilized the closed-form solution of (Formula presented.) and (Formula presented.) (equations (2) and (3) in Supplementary Materials), which may not be available when an informative prior is used, see the supplementary materials. We clarify that Theorem 1 holds when the non-informative prior (i.e. (Formula presented.)) is used. It is not clear whether Theorem 1 continues to hold when an informative prior is used.