Sequential monitoring with conditional randomization tests

TL;DR

This paper introduces a computational approach for implementing sequential monitoring in clinical trials using conditional randomization tests, extending traditional population model methods to a randomization-based framework.

Contribution

It develops a new technique for approximate conditional tests under restricted randomization procedures and applies it to Efron's biased coin design.

Findings

Provides a method to compute joint distribution of sequential tests

Derives conditional probabilities and covariances for biased coin design

Enables randomization-based sequential monitoring in clinical trials

Abstract

Sequential monitoring in clinical trials is often employed to allow for early stopping and other interim decisions, while maintaining the type I error rate. However, sequential monitoring is typically described only in the context of a population model. We describe a computational method to implement sequential monitoring in a randomization-based context. In particular, we discuss a new technique for the computation of approximate conditional tests following restricted randomization procedures and then apply this technique to approximate the joint distribution of sequentially computed conditional randomization tests. We also describe the computation of a randomization-based analog of the information fraction. We apply these techniques to a restricted randomization procedure, Efron's [Biometrika 58 (1971) 403--417] biased coin design. These techniques require derivation of certain conditional probabilities and conditional covariances of the randomization procedure. We employ combinatoric techniques to derive these for the biased coin design.