Robust Sequential Hypothesis Testing with Generalized Estimating Equations for Incomplete Clustered and Longitudinal Data

TL;DR

This paper introduces a robust sequential hypothesis testing method using generalized estimating equations that handles incomplete data and broad hypotheses without relying on restrictive modeling assumptions, improving accuracy and applicability.

Contribution

It develops a model-agnostic sequential testing framework with submatrix-level asymptotic theory and novel efficacy boundary estimation, accommodating incomplete data and multiple imputation.

Findings

Controlled Type I error and maintained power in simulations.

Enhanced efficacy boundary estimation at interim analyses.

Successful application to hepatitis C treatment data.

Abstract

Existing sequential generalized estimating equation methodology for longitudinal and group-correlated data focuses on narrow hypotheses concerning treatment efficacy and often makes modeling assumptions that impede the desirable robustness of the involved test statistics. Drawing upon the well-established theory of incremental information gain for well-posed sequential analyses, we develop an approach that does not rely on modeling assumptions that infringe upon the robustness of the resulting estimators while simultaneously testing a much wider range of hypotheses. Our methodology provides general submatrix-level asymptotic theory for the evaluation of joint covariance matrices of sequential test statistics. Moreover, this framework allows us to construct a novel approach to computing efficacy boundaries, the likes of which can be estimated with greater precision at later interim times. These constructions also accommodate accessible multiple imputation procedures, thereby allowing for our approach to be applied to incomplete datasets. Type I error and power are assessed through a series of comprehensive simulations mirroring the simulations of recent work to facilitate a proper comparison. We conclude by applying our methods to a dataset from a longitudinal study concerning the impact of race on the efficacy a treatment for hepatitis C.