Cancer immunotherapy trial design with cure rate and delayed treatment effect

Abstract

Cancer immunotherapy trials have two special features: a delayed treatment effect and a cure rate. Both features violate the proportional hazard model assumption and ignoring either one of the two features in an immunotherapy trial design will result in substantial loss of statistical power. To properly design immunotherapy trials, we proposed a piecewise proportional hazard cure rate model to incorporate both delayed treatment effect and cure rate into the trial design consideration. A sample size formula is derived for a weighted log‐rank test under a fixed alternative hypothesis. The accuracy of sample size calculation using the new formula is assessed and compared with the existing methods via simulation studies. A real immunotherapy trial is used to illustrate the study design along with practical consideration of balance between sample size and follow‐up time.

A unified approach to power and sample size determination for log-rank tests under proportional and nonproportional hazards

“…Thus f1(t)=f0(t) if t<ϒ, and f1(t)=c(ϒ)[θλ0*(t)][S0*(t)]θ if t≥ϒ. Wei and Wu’s 19 power formula is similar to equation (7).…”

“…Many sample size procedures have been developed for the log-rank test in superiority 1–3,6–17,19 and NI trials. 4,5 These methods will be compared on the basis of the way of approximating the mean and variance of the log-rank statistic, and extended to the NI, equivalence and maximum combination tests whenever appropriate in sections 3.1, 3.2 and 3.3.…”

“…Suppose the experimental treatment has no effect before ϒ, and reaches its full effect after ϒ. The following model was proposed by Hasegawa 41 and Wei and Wu 19 …”

“…For oncology trials, it involves determining an appropriate combination of the sample size, patient accrual rate, and trial duration to ensure a sufficient power for detecting a clinically important effect. Since the seminal work of Schoenfeld, 1 many sample size methods have been developed under proportional hazards (PH 1–5 ) and non-proportional hazards (NPH 3,6–19 ). Most works focus on a somewhat different scenario (i.e.…”

On the empirical choice of the time window for restricted mean survival time

“…The purpose of this new simulation was to investigate the finite sample performance of the proposed inferential procedure, when the hazard rate decreases toward the end of follow‐up (Figure 3). This type of survival profile featured by a long nearly flat tail of the Kaplan‐Meier estimator have been observed in many positive immunotherapy trials and attracted attention recently (Liu et al ., 2018; Wei and Wu, 2020). The true survival function was given in Figure 3.…”