Bayesian Phase II optimization for time-to-event data based on historical information.

After exploratory drug development, companies face the decision whether to initiate confirmatory trials based on limited efficacy information. This proof-of-concept decision is typically performed after a Phase II trial studying a novel treatment versus either placebo or an active comparator. The article aims to optimize the design of such a proof-of-concept trial with respect to decision making. We incorporate historical information and develop pre-specified decision criteria accounting for the uncertainty of the observed treatment effect. We optimize these criteria based on sensitivity and specificity, given the historical information. Specifically, time-to-event data are considered in a randomized 2-arm trial with additional prior information on the control treatment. The proof-of-concept criterion uses treatment effect size, rather than significance. Criteria are defined on the posterior distribution of the hazard ratio given the Phase II data and the historical control information. Event times are exponentially modeled within groups, allowing for group-specific conjugate prior-to-posterior calculation. While a non-informative prior is placed on the investigational treatment, the control prior is constructed via the meta-analytic-predictive approach. The design parameters including sample size and allocation ratio are then optimized, maximizing the probability of taking the right decision. The approach is illustrated with an example in lung cancer.

The predictive distribution of the residual variability in the linear-fixed effects model for clinical cross-over trials.

In the linear model for cross-over trials, with fixed subject effects and normal i.i.d. random errors, the residual variability corresponds to the intraindividual variability. While population variances are in general unknown, an estimate can be derived that follows a gamma distribution, where the scale parameter is based on the true unknown variability. This gamma distribution is often used for the sample size calculation for trial planning with the precision approach, where the aim is to achieve in the next trial a predefined precision with a given probability. But then the imprecision in the estimated residual variability or, from a Bayesian perspective, the uncertainty of the unknown variability is not taken into account. Here, we present the predictive distribution for the residual variability, and we investigate a link to the F distribution. The consequence is that in the precision approach more subjects will be necessary than with the conventional calculation. For values of the intraindividual variability that are typical of human pharmacokinetics, that is a gCV of 17-36%, we would need approximately a sixth more subjects.