### Department of Biostatistics Seminar/Workshop Series

# Case Study of a Maximally Flexible Bayesian Design in Pancreatic Cancer Therapeutics

## Frank E. Harrell Jr., PhD

Nate Mercaldo, MS

Dept of Biostatistics, Vanderbilt University School of Medicine

David Apelian, MD, PhD, MBA

Timothy C. Rodell, MD

GlobeImmune, Inc.

### *presented by:* Frank E. Harrell, Jr., PhD

### Professor and Chair, Department of Biostatistics

Vanderbilt University School of Medicine

### Wednesday, February 4, 1:30-2:55pm, MRBIII Conference Room 1220

### Intended Audience: Persons interested in applied statistics, statistical theory, epidemiology, health services research, clinical trials methodology, statistical computing, statistical graphics, R users or potential users, Bayesians

This presentation will cover the development of a Bayesian flexible design for a biologic agent in an ongoing Phase II trial in pancreatic cancer. The design allows for infinitely many looks at the data and for possible study extension and conversion to adaptive allocation. Unlike frequentist sample size re-estimation procedures, the Bayesian procedure does not require penalizing the final analysis for having done earlier analyses nor does it require downweighting of data collected before the decision to extend the study. The study is easily extended if results obtained at the originally planned study termination are equivocal. The final analysis uses the same analysis procedure as used at the initial analysis, whereas there is no consensus in the frequentist world for how to analyze an extended study.

Our primary analysis is based on a Bayesian Cox proportional hazards model using a skeptical prior distribution. The endpoint is time to cancer recurrence or death. Evidence for efficacy is taken to be a posterior probability of efficacy >= 0.95 at any analysis time, where "efficacy" means a true hazard ratio < 1.0. The planned rule for extending the study is a probability of efficacy >= 0.7 at the last pre-planned analysis. Results of simulations to study the properties of the design will be presented, and experience in presenting the design to the FDA will be briefly discussed.

The traditional frequentist approach, in order to compute the probability of getting a result as or more impressive than that observed if there is truly no treatment effect (the P-value), requires
contemplating experiments that were never carried out and analyses that were never done. Great simplicity is had when only "forward" probabilities (Bayesian posterior probabilities) are computed, conditioning only on what has been observed up to the time of analysis and not conditioning on unknowable information such as the true population treatment effect.

Presenter Information