Model-assisted designs for drug combination trials have been proposed as novel designs with simple and superior performance. However, model-assisted designs have the disadvantage that the sample size must be set in advance, and trials cannot be completed until the number of patients treated reaches the pre-set sample size. Model-assisted designs have a stopping rule that can be used to terminate the trial if the number of patients treated exceeds the predetermined number, there is no statistical basis for the predetermined number. Here, I propose two methods for data-dependent early completion of dose-finding trials for drug combination: (1) an early completion method based on dose retainment probability, and (2) an early completion method in which the dose retainment probability is adjusted by a bivariate isotonic regression. Early completion is determined when the dose retainment probability using both trial data and the number of remaining patients is high. Early completion of a virtual trial was demonstrated. The performances of the early completion methods were evaluated by simulation studies with 12 scenarios. The simulation studies showed that the percentage of early completion was an average of approximately 70%, and the number of patients treated was 25% less than the planned sample size. The percentage of correct maximum tolerated dose combination selection for the early completion methods was similar to that of non-early completion methods with an average difference of approximately 3%. The performance of the proposed early completion methods was similar to that of the non-early completion methods. Furthermore, the number of patients for determining early completion before the trial starts was determined and a program code for calculating the dose retainment probability was proposed.
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