A stochastic second-order generalized estimating equations approach for estimating intraclass correlation coefficient in the presence of informative missing data

TL;DR

This paper introduces a stochastic second-order GEE approach with inverse-probability weighting and doubly robust methods for estimating intraclass correlation in cluster trials with missing data, improving computational efficiency and robustness.

Contribution

It extends GEE2 to handle missing data using stochastic algorithms, second-order weighting, and robust estimation, addressing computational challenges and model misspecification.

Findings

Developed a stochastic GEE2 method with inverse-probability weighting.

Achieved faster convergence and reduced reliance on initial parameters.

Enhanced robustness against model misspecification in missing data scenarios.

Abstract

Design and analysis of cluster randomized trials must take into account correlation among outcomes from the same clusters. When applying standard generalized estimating equations (GEE), the first-order (e.g. treatment) effects can be estimated consistently even with a misspecified correlation structure. In settings for which the correlation is of interest, one could estimate this quantity via second-order generalized estimating equations (GEE2). We build upon GEE2 in the setting of missing data, for which we incorporate a "second-order" inverse-probability weighting (IPW) scheme and "second-order" doubly robust (DR) estimating equations that guard against partial model misspecification. We highlight the need to model correlation among missing indicators in such settings. In addition, the computational difficulties in solving these second-order equations have motivated our development of more computationally efficient algorithms for solving GEE2, which alleviates reliance on parameter starting values and provides substantially faster and higher convergence rates than the more widely used deterministic root-solving methods.