Functional Data Models for Dose Finding Studies with Meta Data

Abstract

The primary objective of dose-finding studies is to estimate the optimal dose level based on experimental subjects’ responses, specifically ‘Efficacy’ and ‘Toxicity’. The optimal dose level is identified at the point of maximum probability, where there is significant dose efficacy without toxicity. While some studies have employed Emax, quadratic models, or other non-linear models, these models are not suitable for non-monotonic curves. Crippa Orsini (2016) proposed the utilization of regression splines to flexibly model the dose of interest, but it may not adequately describe reasonable dose-response distributions. This paper introduces functional models for dose-finding studies, marking a novel approach as no one has previously applied functional models in dose-finding studies using meta-analysis data. Our focus is on three outcome probabilities: P (Efficacy), P (Toxicity) and P (Efficacy but No Toxicity), guided by assumptions that these are monotonic and/or unimodal functions. We employ functional data models to estimate these probability distributions and introduce adjusted confidence intervals. Finally, we apply our functional models to analyze data on alcohol consumption and colorectal cancer risk.