Bayesian Analysis of Clinical Trials with a Delayed Treatment Effect

Music City Center 

In the analysis of clinical trials with a survival endpoint, it is important to account for the possibility of a delay in the separation of the survival curves, known as a delayed treatment effect (DTE). DTEs are commonly observed in immuno-oncology trials, and failing to account for the possibility of a DTE in the design and analysis of a trial can lead to a substantial loss of power. We introduce a Bayesian method for assessing the efficacy of a treatment in the presence of a DTE. In our method, the baseline hazard is modeled using a cubic spline, which has the advantage over a piecewise constant model of capturing any smooth shape. To account for the treatment effect delay, we specify a non-constant hazard ratio, estimating the delay instead of prespecifying it. We study the properties of the methodology and demonstrate superior power of our method over the Cox proportional hazards model in the case of a nonzero delay. The proposed methodology is applied to the analysis of an immuno-oncology trial for first-line treatment of extensive-stage small-cell lung cancer.

Clinical trial design

Delayed treatment effect

Bayesian design

Cubic spline

Immuno-oncology trial 

Section on Bayesian Statistical Science