Study duration for three-arm non-inferiority survival trials designed for accrual by cohorts

Study planning is particularly complex for survival trials because it usually involves an accrual period and a continued observation period after accrual closure. The three-arm clinical trial design, which includes a test treatment, an active reference, and a placebo control, is the gold standard design for the assessment of non-inferiority. The existing statistical methods of calculating minimal sample size for non-inferiority trials with three-arm design and survival-type endpoints cannot take into consideration the accrual rate of patients to the trial, the length of accrual period, the length of continued observation period after accrual closure, and unbalanced allocation of the total sample size. The purpose of this paper is to develop a statistical method, which allows for all these sources of variability for planning non-inferiority trials with the gold standard design for censored, exponentially distributed time-to-event data. The proposed method is based on the assumption of exponentially distributed failure times and a non-inferiority test formulated in terms of the retention of effect hypotheses. It can be used to calculate the duration of accrual required to assure a desired power for non-inferiority trials with active and placebo control. We illustrate the use of the method by considering a randomized, active- and placebo-controlled trial in depression associated with Parkinson's disease. We then explore the validity of the proposed method by simulation studies. An R-language program for the implementation of the proposed algorithm is provided as supplementary material.