Bayesian Modeling Averaging Approach to Model a Binary Outcome for a Dose Ranging Trial Bob Noble GlaxoSmithKline Director of Statistics and Programming Statistics Leader of Virtual Proof of Concept Unit

Post-operative nausea and vomiting (PONV) often occurs following local, regional, or general anesthesia and is the most frequently reported patient complaint following anesthesia. PONV is often of greater concern to patients than is the avoidance of post- operative pain. In addition to anxiety and discomfort, PONV can lead to complications such as fluid and electrolyte imbalances, surgical wound dehiscence, aspiration of vomitus, and/or severe pulmonary morbidity that can lead to delayed discharge from the recovery area or unscheduled hospital admission. British Journal Of Anaesthesia (2015) 114 (3): Kranke P, Thompson J, Dalby P, Novikova E, Johnson B, Russ S, Noble R, Brigandi R. Comparison of vestipitant with ondansetron for the treatment of breakthrough postoperative nausea and vomiting after failed prophylaxis with ondansetron.

The primary efficacy endpoint is number of subjects achieving Complete Response after receiving study drug to treat breakthrough PONV. Complete Response is defined as no emesis and no further rescue medication through 24 hours or discharge from the hospital/clinic, whichever is sooner. Doses of vestipitant (IP) 6mg, 12mg, 18mg, 24mg, 36mg. Positive control 4mg ondansetron

A concern of the team in characterizing the dose response over a wide range was that high doses of vestipitant may cause nausea and vomiting. Solution: A non-monotonic dose response model. Information available for the efficacy of ondansetron lead the team to a Beta(20,20) prior for the positive control arm. The Bayes estimate using a Beta(20,20) prior will have smaller MSE than the MLE for all n ≤ 20 on the interval 0.35 < p < 0.65.

Piecewise logistic regression model

k=20 Illustration

Likelihood of data Priors Model Version 1

Model Version 2 (BMA framework)

Posterior Probability of Model “i” Posterior distribution of parameter p|dose

Posterior Distribution of Logistic Regression Parameters The posterior distribution of the response rate at a given dose for a given model is just the sampled posterior values from the posterior of the regression parameters plugged into the model. The BMA estimate is the weighted (by the posterior probability of each model) average of the individual model estimates.

Posterior Distributions by Dose

Study stopped early for futility (i.e. probability of success at full enrollment was too low).

Actual nApparent n Control1959 6mg mg mg mg mg Total Resulted in a project savings of more than $7MM and 9-12 months