Single-arm Phase II cancer survival trial designs

Abstract

The current practice for designing single-arm phase II trials with time-to-event endpoints is limited to using either a maximum likelihood estimate test under the exponential model or a naive approach based on dichotomizing the event time at a landmark time point. A trial designed under the exponential model may not be reliable, and the naive approach is inefficient. The modified one-sample log-rank test statistic proposed in this paper fills the void. In general, the proposed test can be used to design single-arm phase II survival trials under any parametric survival distribution. Simulation results showed that it preserves type I error well and provides adequate power for phase II cancer trial designs with time-to-event endpoints.

A two‐stage drop‐the‐losers design for time‐to‐event outcome using a historical control arm

“…30 However, this statistical test showed conservativeness in small samples. 21,30 Wu et al 31 proposed a modified one-sample log-rank test defined as:…”

Single-Arm Phase II Survival Trial Design Under the Proportional Hazards Model

“…However, the OSLRT is conservative, as shown by Kwak and Jung (2014); Sun et al (2010); and Wu (2015). Recently, Wu (2015) proposed a MOSLRT that preserves the type I error well and provides adequate power for study design. To introduce the MOSLRT, assume that during the accrual phase of the trial, n subjects are enrolled in the study.…”

“…For the purpose of comparison, the sample size formula for the MOSLRT under the fixed alternative H 1 (Wu, 2015) is also given as follows: $$n=\frac{{\left(\overline{\sigma }{z}_{1-\alpha }+\sigma z_{1-\beta }\right)}^2}{{\omega }^2},$$ where ω = v 1 − v 0 , ${\overline{\sigma }}^2=\left(v_1+v_0\right)/2$, and ${\sigma }^2=v_1-v_1^2+2v_{00}-v_0^2-2v_{01}+2v_0{v}_1$, with v 0 , v 1 , v 00 , and v 01 being given by the following equations: $$v_0=true{\int }_0^{\infty }G\left(t\right)S_1\left(t\right)d{\mathrm{normal\Lambda }}_0\left(t\right),$$ $$v_1=true{\int }_0^{\infty }G\left(t\right)S_1\left(t\right)d{\mathrm{normal\Lambda }}_1\left(t\right),$$ $$v_{00}=true{\int }_0^{\infty }G\left(t\right)S_1\left(t\right){\mathrm{normal\Lambda }}_0\left(t\right)d{\mathrm{normal\Lambda }}_0\left(t\right),$$ $$v_{01}=true{\int }_0^{\infty }G\left(t\right)S_1\left(t\right){\mathrm{normal\Lambda }}_0\left(t\right)d{\mathrm{normal\Lambda }}_1\left(t\right).$$…”

“…However, simulation results showed that Kwak and Jung’s design is conservative and underpowered. To correct the power and conservativeness of the OSLRT, Wu (2015) proposed a modified one-sample log-rank test (MOSLRT) for single-arm phase II survival trial designs. The MOSLRT preserves the type I error well and provides adequate power for trial design for a class of common parametric survival distributions.…”

Reference curve sampling variability in one–sample log–rank tests

“…This sampling variability of the reference curve however, is ignored in the original one–sample log–rank statistic. One–sample log–rank tests rather assume that the reference survival curve is a priori known and deterministic (see [ 2 – 7 , 9 ]). This ignores that the reference curve resulted from an estimation process, complicates interpretation of the test results and implies an inflation in type I error rate.…”