Sample size calculation for randomized selection trials with a time‐to‐event endpoint and a margin of practical equivalence

Abstract

Selection trials are used to compare potentially active experimental treatments without a control arm. While sample size calculation methods exist for binary endpoints, no such methods are available for time-to-event endpoints, even though these are ubiquitous in clinical trials. Recent selection trials have begun using progression-free survival as their primary endpoint, but have dichotomized it at a specific time point for sample size calculation and analysis. This changes the clinical question and may reduce power to detect a difference between the arms. In this article, we develop the theory for sample size calculation in selection trials where the time-to-event endpoint is assumed to follow an exponential or Weilbull distribution. We provide a free web application for sample size calculation, as well as an R package, that researchers can use in the design of their studies.

Sample size determination for time-to-event endpoints in randomized selection trials with generalized exponential distribution

“…The current emphasis lies in estimating the median event time for each treatment arm, while accounting for non-informative random right censoring. The likelihood function pertinent to this scenario can be formulated as follows: Using profile likelihood, the MLE of θ [29] (and supplementary text of [17] ) is calculated as follows: and after obtaining , the estimate of can be obtained easily [27] . According to the invariance principle, the MLE of the median becomes .…”

“…Dehbi and Hackshaw [16] computed sample sizes for both two- and three-arm randomized selection trials using precise binomial probabilities, with a predefined margin of practical equivalence (MPE). Later, Dehbi et al [17] developed the theory for SS calculation in selection trials. Billings et al [18] gave an alternative approach for the calculation of SS.…”

“…This study involves a selection trial [17] with time-to-event endpoints and the main objective of this research is to determine SS assuming generalized exponential distribution and further compare it with Weibull distribution based calculation. This study is useful to determine how well the drug works in subjects at a given dose to assess efficacy [22] , [23] , [24] , [25] .…”

Controlled amplification in oncology dose-finding trials

“…The sample size that is required for the randomised comparison, and the principles by which the final selection may be made between adjacent dose levels, can be derived from the principles of selection designs [ 5 , 4 ].…”

“…Importantly, if the objective is to recommend one dose level for further study (i.e. identifying the RP2D), the sample size of the randomised expansion part can be calculated as if it was a selection trial using a margin of practical equivalence [ 22 , 5 , 4 ], as described in Section 3.3 .…”