Marginal quantile regression for dependent data with a working odds-ratio matrix

Dependent data arise frequently in applied research and several approaches to adjusting for the dependence among observations have been proposed in quantile regression. Cluster bootstrap is generally inefficient and computationally demanding, especially when the number of clusters is large. When the primary interest is on marginal quantiles, estimating equations have been proposed that estimate a working correlation matrix from the regression residuals' sign. However, the Pearson's correlation coefficient is an inadequate measure of dependence between binary variables because its range depends on their marginal probabilities. Instead, we propose to model the working correlation matrix through odds ratios. Different working structures can be easily estimated by suitable logistic regression models. These structures can be parametrized to depend on covariates and clusters. Simulations show that the proposed estimator has similar behavior to that of generalized estimating equations applied to regression for the mean. We study marginal quantiles of cognitive behavior with data from a randomized trial for treatment of obsessive compulsive disorder.