Title: Sequential Quantile Estimation Using Continuous Outcomes with Applications in Dose Finding
Description: We consider dose finding studies where a binary outcome is obtained by dichotomizing a continuous measurement. While the majority of existing dose finding designs work with dichotomized data, two procedures that operate on continuous measurements have been proposed. One is based on stochastic approximation and the other on least square recursion. In both cases, estimating the variance of the continuous measurement is an integral part of the design. In their originally proposed forms, variance estimation is based on data from the most current cohort only. This raises the question of whether performance of the two designs can be improved by incorporating better variance estimators. To this end, we propose estimators that pool data across cohorts. Asymptotic properties of both designs with the proposed estimators are derived. Operating characteristics are also investigated via simulations in the context of a real Phase I trial. Results show that performance of least square recursion based procedure can be substantially improved through pooling data in variance estimation while performance of stochastic approximation based procedure is only marginally improved.

The second problem considered in this dissertation deals with the limitation shared by both designs that complete follow-up of all current patients is required before new patients can be enrolled. This may result in impractically long trial duration. We consider situations where besides the final measurement that the outcome of the study is defined on, each patient has an additional intermediate continuous measurement. By extending least square recursion through incorporating intermediate measurements, continual patient accrual is allowed. Simulation results show that under reasonable patient accrual rate, the proposed procedure is comparable to the original in terms of accuracy while shortening the trial duration considerably.