Statistical Decision Making in Early Phase Clinical Trials

The main objective of dose finding trials is to find an optimal dose amongst a candidate set for further research. The trial design in oncology proceeds in stages with a decision as to how to treat the next group of patients made after every stage until a final sample size is reached or the trial stopped early.

The thesis applies a Bayesian decision theoretic approach to the problem focusing on the specification of a novel utility function and the role of correlation in the probability model. Utility independence axioms are used to give a simplified bivariate form to the utility function based on more easily assessed univariate utility functions. Utility functions for both efficacy and toxicity depend upon a reference point with different attitudes to risk depending upon whether above or below the point. A risk averse attitude (concave) is specified for perceived gains and risk prone (convex) for losses. A set of questions are posed for the utility function to be accurately elicited. A novel stopping rule derived from the utility function is also tested.

An inspection of copula theory and a simulation study demonstrate the difficulty in estimating correlation and recommend using a more parsimonious independent model. A simulation study demonstrates that the utility function has merit in further evaluation in this setting. The simulation results show that the decision criteria are more sensitive in detecting the optimal dose when candidate doses are around minimum efficacy and maximum toxicity thresholds.

The specification of the utility function is flexible to accommodate clinical beliefs allowing us to think about acceptable levels of patient risk. The work applies a broad framework to give insight to existing methods and potential to adapt to different endpoints and trial features.