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Design and analysis of cluster randomized trials must take into accountcorrelation among outcomes from the same clusters. When applying standardgeneralized estimating equations (GEE), the first-order (e.g. treatment)effects can be estimated consistently even with a misspecified correlationstructure. In settings for which the correlation is of interest, one couldestimate this quantity via second-order generalized estimating equations(GEE2). We build upon GEE2 in the setting of missing data, for which weincorporate a "second-order" inverse-probability weighting (IPW) scheme and"second-order" doubly robust (DR) estimating equations that guard againstpartial model misspecification. We highlight the need to model correlationamong missing indicators in such settings. In addition, the computationaldifficulties in solving these second-order equations have motivated ourdevelopment of more computationally efficient algorithms for solving GEE2,which alleviates reliance on parameter starting values and providessubstantially faster and higher convergence rates than the more widely useddeterministic root-solving methods.

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