Informative event rate in study determination, study design, and interim analysis monitoring with non-proportional...

A cancer trial with an immunotherapy or antibody drug conjugate often has a certain delay/crossing time before the drug to take effect. In this paper, we propose to call the events that occur during and after the delay/crossing time as non-informative events and informative events, respectively. We propose to call the rate of number of informative events divided by total number of events as informative event rate ($\gamma$), though this rate has been used in the literature. We show three innovative usages of $\gamma$ under non-proportional hazards (NPH) setting: (1) based on $\gamma$, the minimum average hazard ratio ($\mathrm{aH}{R}_{\min }$) can be calculated analytically and used to determine whether trials are worth being conducted for a test drug to get a meaningful average hazard ratio (aHR) at the planning stage; (2) based on a series of $\gamma$, aHR and power can be calculated and a proper design can be selected for a trial with a targeted aHR at the design stage; (3) based on $\gamma$, a better interim analysis timing to ensure a certain probability for early efficacy/futility stopping can be determined during the course of a study. aHR and the probability for early efficacy/futility stopping under different enrollment scenarios in a simulation were verified by calculation. We propose the concepts of the informative event rate ($\gamma$), $\mathrm{aH}{R}_{\min }$, and a targeted aHR and use them in study determination, study design, and interim analysis monitoring under an NPH setting with a delay/crossing time.