Stochastic Curtailment Methods for Single-Arm Clinical Trials with a Time-to-Event Endpoint using Weibull Distribution

Abstract

This dissertation is an outcome of three research projects which attempt to fill some existing gaps in the statistical literature related to the design and analysis of single-arm clinical trials with time-to-event endpoints following a Weibull distribution. In the first project, we proposed a parametric maximum likelihood estimate based method for designing single-arm clinical trials with a time-to-event endpoint that follows a Weibull distribution with known shape parameter. The proposed method is quite flexible in the sense that it permits investigators to incorporate various design features, such as expected loss to follow-up rate, different accrual patterns, and administrative censoring. In the same context, three stochasticcurtailment methods (conditional power, predictive power, Bayesian predictive probability) are presented which can be employed to obtain early evidence of efficacy or futility of an experimental treatment. Finally, we have also discussed the implementation of group sequential designs using the repeated significance approach. The second project primarily focuses on the calculation of the Bayesian predictive probability when a reasonably accurate estimate of the shape parameter of the Weibull distribution for the underlying survival times is not available from historical studies. To suffice our purpose, two approaches based on the posterior mode and the entire posterior distribution of the shape parameter are presented. In addition to calculating the Bayesian predictive probability, we also explored the utility of the internal pilot study approach for reestimating the study sample size based on data accumulated at an interim stage. In the third project, an R package is developed for designing single-arm clinical trials with a time-to-event endpoint following the Weibull distribution, and to implement stochastic curtailment methods discussed in the first two projects. The package will be made available to the scientific community on the Comprehensive R Archive Network (CRAN).