Random Norming Aids Analysis of Non-linear Regression Models with Sequential Informative Dose Selection

TL;DR

This paper introduces three alternative random information measures to improve the asymptotic normalization of MLE in nonlinear regression models with sequential dose selection, especially in small sample scenarios.

Contribution

It proposes new random information measures that better normalize the MLE in adaptive dose-finding designs with dependencies between stages.

Findings

Observed information performs best with small samples.

Random information measures improve asymptotic normalization.

Simulation results support the effectiveness of proposed measures.

Abstract

A two-stage adaptive optimal design is an attractive option for increasing the efficiency of clinical trials. In these designs, based on interim data, the locally optimal dose is chosen for further exploration, which induces dependencies between data from the two stages. When the maximum likelihood estimator (MLE) is used under nonlinear regression models with independent normal errors in a pilot study where the first stage sample size is fixed, and the second stage sample size is large, the Fisher information fails to normalize the estimator adequately asymptotically, because of dependencies. In this situation, we present three alternative random information measures and show that they provide better normalization of the MLE asymptotically. The performance of random information measures is investigated in simulation studies, and the results suggest that the observed information performs best when the sample size is small.