Copula-based pairwise estimator for quantile regression with hierarchical missing data

Quantile regression can be a helpful technique for analysing clustered (such as longitudinal) data. It can characterize the change in response over time without making distributional assumptions and is robust to outliers in the response. A quantile regression model using a copula-based multivariate asymmetric Laplace distribution for addressing correlation due to clustering is introduced. Furthermore, we propose a pairwise estimator for the parameters of the model. Since it is based on pseudo-likelihood, it needs to be modified to avoid bias in presence of missingness. Therefore, we enhance the model with inverse probability weighting. In this way, our proposal is unbiased under the missing at random assumption. Based on simulations, the estimator is efficient and computationally fast. Finally, the methodology is illustrated using a study in ophthalmology.