Sample size considerations for single-arm clinical trials with time-to-event endpoint using the gamma distribution

Background

Time-to-event (TTE) endpoints are evaluated as the primary endpoint in single-arm clinical trials; however, limited options are available in statistical software for sample size calculation. In single-arm trials with TTE endpoints, the non-parametric log-rank test is commonly used. Parametric options for single-arm design assume survival times follow exponential distribution or Weibull distribution.

Methods

The exponential- or Weibull-distributed survival time assumption does not always reflect hazard pattern of real-life diseases. We therefore propose gamma distribution as an alternative parametric option for designing single-arm studies with TTE endpoints. We outline a sample size calculation approach using gamma distribution with a known shape parameter and explain how to extract the gamma shape estimate from previously published resources. In addition, we conduct simulations to assess the accuracy of the extracted gamma shape parameter and to explore the impact on sample size calculation when survival time distribution is misspecified.

Results

Our simulations show that if a previously published study (sample sizes $\ge$ 60 and censoring proportions $\le$ 20 %) reported median and inter-quartile range of survival time, we can obtain a reasonably accurate gamma shape estimate, and use it to design new studies. When true survival time is Weibull-distributed, sample size calculation could be underestimated or overestimated depending on the hazard shape.

Conclusions

We show how to use gamma distribution in designing a single-arm trial, thereby offering more options beyond the exponential and Weibull. We provide a simulation-based assessment to ensure an accurate estimation of the gamma shape and recommend caution to avoid misspecification of the underlying distribution.